|\^/| Maple 2016 (X86 64 LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. #BEGIN OUTFILE1 # before write maple top matter # before write_ats library and user def block #BEGIN ATS LIBRARY BLOCK # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc # End Function number 2 # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc # End Function number 3 # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc # End Function number 4 # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 5 # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 6 # Begin Function number 7 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := sec_temp mod int_trunc(glob_sec_in_minute); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," 0.0 Seconds"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " 0.0 Seconds") end if; fprintf(fd, "\n") end proc # End Function number 7 # Begin Function number 8 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year)); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour)); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod int_trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" 0.0 Seconds\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" 0.0 Seconds\n") end if end proc # End Function number 8 # Begin Function number 9 > zero_ats_ar := proc(arr_a) > global ATS_MAX_TERMS; > local iii; > iii := 1; > while (iii <= ATS_MAX_TERMS) do # do number 1 > arr_a [iii] := glob__0; > iii := iii + 1; > od;# end do number 1 > end; zero_ats_ar := proc(arr_a) local iii; global ATS_MAX_TERMS; iii := 1; while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1 end do end proc # End Function number 9 # Begin Function number 10 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > global ATS_MAX_TERMS; > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := glob__0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7 > ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); > fi;# end if 7; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; global ATS_MAX_TERMS; ret_ats := glob__0; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]) end if; iii_ats := iii_ats + 1 end do end if; ret_ats end proc # End Function number 10 # Begin Function number 11 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global ATS_MAX_TERMS; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := glob__0; > if (jjj_att < mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7 > ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / c(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global ATS_MAX_TERMS; ret_att := glob__0; if jjj_att < mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/c(mmm_att) end if; ret_att end proc # End Function number 11 # Begin Function number 12 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc # End Function number 12 # Begin Function number 13 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc # End Function number 13 # Begin Function number 14 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc # End Function number 14 # Begin Function number 15 > logitem_good_digits := proc(file,rel_error) > global glob_small_float,glob_prec; > local good_digits; > fprintf(file,""); > fprintf(file,"%d",glob_min_good_digits); > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float, glob_prec; fprintf(file, ""); fprintf(file, "%d", glob_min_good_digits); fprintf(file, "") end proc # End Function number 15 # Begin Function number 16 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc # End Function number 16 # Begin Function number 17 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc # End Function number 17 # Begin Function number 18 > logitem_h_reason := proc(file) > global glob_h_reason; > fprintf(file,""); > if (glob_h_reason = 1) then # if number 6 > fprintf(file,"Max H"); > elif > (glob_h_reason = 2) then # if number 7 > fprintf(file,"Display Interval"); > elif > (glob_h_reason = 3) then # if number 8 > fprintf(file,"Optimal"); > elif > (glob_h_reason = 4) then # if number 9 > fprintf(file,"Pole Accuracy"); > elif > (glob_h_reason = 5) then # if number 10 > fprintf(file,"Min H (Pole)"); > elif > (glob_h_reason = 6) then # if number 11 > fprintf(file,"Pole"); > elif > (glob_h_reason = 7) then # if number 12 > fprintf(file,"Opt Iter"); > else > fprintf(file,"Impossible"); > fi;# end if 12 > fprintf(file,""); > end; logitem_h_reason := proc(file) global glob_h_reason; fprintf(file, ""); if glob_h_reason = 1 then fprintf(file, "Max H") elif glob_h_reason = 2 then fprintf(file, "Display Interval") elif glob_h_reason = 3 then fprintf(file, "Optimal") elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy") elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)") elif glob_h_reason = 6 then fprintf(file, "Pole") elif glob_h_reason = 7 then fprintf(file, "Opt Iter") else fprintf(file, "Impossible") end if; fprintf(file, "") end proc # End Function number 18 # Begin Function number 19 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 19 # Begin Function number 20 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 20 # Begin Function number 21 > chk_data := proc() > global glob_max_iter,ALWAYS, ATS_MAX_TERMS; > local errflag; > errflag := false; > if (glob_max_iter < 2) then # if number 12 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 12; > if (errflag) then # if number 12 > quit; > fi;# end if 12 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, ATS_MAX_TERMS; errflag := false; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc # End Function number 21 # Begin Function number 22 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := c(clock_sec2); > sub1 := c(t_end2-t_start2); > sub2 := c(t2-t_start2); > if (sub1 = glob__0) then # if number 12 > sec_left := glob__0; > else > if (sub2 > glob__0) then # if number 13 > rrr := (sub1/sub2); > sec_left := rrr * c(ms2) - c(ms2); > else > sec_left := glob__0; > fi;# end if 13 > fi;# end if 12; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := c(clock_sec2); sub1 := c(t_end2 - t_start2); sub2 := c(t2 - t_start2); if sub1 = glob__0 then sec_left := glob__0 else if glob__0 < sub2 then rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2) else sec_left := glob__0 end if end if; sec_left end proc # End Function number 22 # Begin Function number 23 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 12 > rrr := (glob__100*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 12; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := glob__100*sub2/sub1 else rrr := 0. end if; rrr end proc # End Function number 23 # Begin Function number 24 > comp_rad_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 12 > ret := float_abs(term1 * glob_h / term2); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM TWO TERM RADIUS ANALYSIS > end; comp_rad_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2) else ret := glob_larger_float end if; ret end proc # End Function number 24 # Begin Function number 25 > comp_ord_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM ORDER ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 12 > ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no)); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM TWO TERM ORDER ANALYSIS > end; comp_ord_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)* c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no)) else ret := glob_larger_float end if; ret end proc # End Function number 25 # Begin Function number 26 > c := proc(in_val) > #To Force Conversion when needed > local ret; > ret := evalf(in_val); > ret; > #End Conversion > end; c := proc(in_val) local ret; ret := evalf(in_val); ret end proc # End Function number 26 # Begin Function number 27 > comp_rad_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret,temp; > temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3); > if (float_abs(temp) > glob__0) then # if number 12 > ret := float_abs((term2*glob_h*term1)/(temp)); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM THREE TERM RADIUS ANALYSIS > end; comp_rad_from_three_terms := proc(term1, term2, term3, last_no) local ret, temp; global glob_h, glob_larger_float; temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2 - term1*term3*c(last_no) + term1*term3); if glob__0 < float_abs(temp) then ret := float_abs(term2*glob_h*term1/temp) else ret := glob_larger_float end if; ret end proc # End Function number 27 # Begin Function number 28 > comp_ord_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM ORDER ANALYSIS > local ret; > ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3)); > ret; > #TOP THREE TERM ORDER ANALYSIS > end; comp_ord_from_three_terms := proc(term1, term2, term3, last_no) local ret; ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3 - glob__4*term2*term2*c(last_no) + glob__4*term2*term2 + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no)) /(term2*term2*c(last_no) - glob__2*term2*term2 - term1*term3*c(last_no) + term1*term3)); ret end proc # End Function number 28 # Begin Function number 29 > comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > #TOP SIX TERM RADIUS ANALYSIS > global glob_h,glob_larger_float,glob_six_term_ord_save; > local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs; > if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12 > rm0 := term6/term5; > rm1 := term5/term4; > rm2 := term4/term3; > rm3 := term3/term2; > rm4 := term2/term1; > nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2; > nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3; > dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; > dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; > ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; > ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; > if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13 > rad_c := glob_larger_float; > ord_no := glob_larger_float; > else > if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2; > if (float_abs(rcs) <> glob__0) then # if number 15 > if (rcs > glob__0) then # if number 16 > rad_c := sqrt(rcs) * float_abs(glob_h); > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 16 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 15 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 14 > fi;# end if 13 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 12; > glob_six_term_ord_save := ord_no; > rad_c; > #BOTTOM SIX TERM RADIUS ANALYSIS > end; comp_rad_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no, ds1, rcs; global glob_h, glob_larger_float, glob_six_term_ord_save; if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and term2 <> glob__0 and term1 <> glob__0 then rm0 := term6/term5; rm1 := term5/term4; rm2 := term4/term3; rm3 := term3/term2; rm4 := term2/term1; nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1 + c(last_no - 3)*rm2; nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2 + c(last_no - 4)*rm3; dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; if float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0 then rad_c := glob_larger_float; ord_no := glob_larger_float else if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2; if float_abs(rcs) <> glob__0 then if glob__0 < rcs then rad_c := sqrt(rcs)*float_abs(glob_h) else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if; glob_six_term_ord_save := ord_no; rad_c end proc # End Function number 29 # Begin Function number 30 > comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > global glob_six_term_ord_save; > #TOP SIX TERM ORDER ANALYSIS > #TOP SAVED FROM SIX TERM RADIUS ANALYSIS > glob_six_term_ord_save; > #BOTTOM SIX TERM ORDER ANALYSIS > end; comp_ord_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) global glob_six_term_ord_save; glob_six_term_ord_save end proc # End Function number 30 # Begin Function number 31 > factorial_2 := proc(nnn) > ret := nnn!; > ret;; > end; Warning, `ret` is implicitly declared local to procedure `factorial_2` factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc # End Function number 31 # Begin Function number 32 > factorial_1 := proc(nnn) > global ATS_MAX_TERMS,array_fact_1; > local ret; > if (nnn <= ATS_MAX_TERMS) then # if number 12 > if (array_fact_1[nnn] = 0) then # if number 13 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 13; > else > ret := factorial_2(nnn); > fi;# end if 12; > ret; > end; factorial_1 := proc(nnn) local ret; global ATS_MAX_TERMS, array_fact_1; if nnn <= ATS_MAX_TERMS then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc # End Function number 32 # Begin Function number 33 > factorial_3 := proc(mmm,nnn) > global ATS_MAX_TERMS,array_fact_2; > local ret; > if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12 > if (array_fact_2[mmm,nnn] = 0) then # if number 13 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 13; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 12; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global ATS_MAX_TERMS, array_fact_2; if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc # End Function number 33 # Begin Function number 34 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 34 # Begin Function number 35 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 35 # Begin Function number 36 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 36 # Begin Function number 37 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 37 # Begin Function number 38 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 38 # Begin Function number 39 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 39 # Begin Function number 40 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer))); > omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,""); > omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,""); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS))); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(glob__10, c(-glob_desired_digits_correct))* c(float_abs(c(estimated_answer))); omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""); omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "") ; omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := c(float_abs(desired_abs_gbl_error)/( sqrt(c(estimated_steps))*c(ATS_MAX_TERMS))); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc # End Function number 40 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(c(0.0)); > end; exact_soln_y := proc(x) return c(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_2D0, > array_const_3D0, #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_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local min_size; > min_size := glob_estimated_size_answer; > if (float_abs(array_y[1]) < min_size) then # if number 3 > min_size := float_abs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < glob__1) then # if number 3 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, 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_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; min_size := glob_estimated_size_answer; if float_abs(array_y[1]) < min_size then min_size := float_abs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #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_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := glob__small; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, 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_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; max_estimated_step_error := glob__small; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := float_abs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #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_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3 > est_tmp := c(glob_prec) * c(float_abs(array_y[1])); > fi;# end if 3; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3 > array_max_est_error[1] := c(est_tmp); > fi;# end if 3 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, 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_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; est_tmp := c(float_abs(array_y[no_terms - 3])) + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #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_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, 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_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #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_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > 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)*24*ATS_MAX_TERMS/float_abs(numeric_val)); > if (evalf(est_rel_err) > glob_prec) then # if number 6 > glob_est_digits := -int_trunc(log10(est_rel_err)) + 3; > else > glob_est_digits := Digits; > fi;# end if 6; > else > relerr := glob__m1 ; > glob_est_digits := -16; > fi;# end if 5; > array_est_digits[1] := glob_est_digits; > if (glob_iter = 1) then # if number 5 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 5; > array_est_rel_error[1] := est_rel_err; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," "); > omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," "); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 4; > #BOTTOM DISPLAY ALOT > fi;# end if 3; > end; display_alot := proc(iter) local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, 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_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, 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)*24*ATS_MAX_TERMS/float_abs(numeric_val)) ; if glob_prec < evalf(est_rel_err) then glob_est_digits := -int_trunc(log10(est_rel_err)) + 3 else glob_est_digits := Digits end if else relerr := glob__m1; glob_est_digits := -16 end if; array_est_digits[1] := glob_est_digits; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; array_est_rel_error[1] := est_rel_err; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Desired digits ", 32, glob_desired_digits_correct, 4, " "); omniout_int(INFO, "Estimated correct digits ", 32, glob_est_digits, 4, " "); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc # End Function number 8 # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #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_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := (clock_sec1) - (glob_orig_start_sec); > glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); > left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); > expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); > opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr((total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr((glob_clock_sec)); > if (c(percent_done) < glob__100) then # if number 3 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr((expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr((glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr((glob_total_exp_sec)); > fi;# end if 3; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr((left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, 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_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(glob_clock_sec); if c(percent_done) < glob__100 then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(expect_sec); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(glob_optimal_expect_sec); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(glob_total_exp_sec) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(left_sec); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc # End Function number 9 # Begin Function number 10 > check_for_pole := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #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_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; > #TOP CHECK FOR POLE > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,1] := glob_larger_float; > array_ord_test_poles[1,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 3 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 3; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 4 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_rad_test_poles[1,1]) then # if number 6 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,1] := rad_c; > array_ord_test_poles[1,1] := tmp_ord; > fi;# end if 6; > fi;# end if 5; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 5 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 5; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 6 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 7 > found_sing := 0; > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_rad_test_poles[1,2]) then # if number 8 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 9 > glob_min_pole_est := rad_c; > fi;# end if 9; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 8; > fi;# end if 7; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 7 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 7; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 8 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 9 > found_sing := 0; > fi;# end if 9; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 9 > if (rad_c < array_rad_test_poles[1,3]) then # if number 10 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 11 > glob_min_pole_est := rad_c; > fi;# end if 11; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test1 > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 10; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 9; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 9 > display_poles(); > fi;# end if 9 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad, last_no; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, 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_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 1] := glob_larger_float; array_ord_test_poles[1, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 1] then array_rad_test_poles[1, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 1] := rad_c; array_ord_test_poles[1, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 2] then array_rad_test_poles[1, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 3] then array_rad_test_poles[1, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 3] := tmp_ord end if end if; if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc # End Function number 10 # Begin Function number 11 > atomall := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #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_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > 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_2D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_3D0[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp3[1] := sqrt(array_tmp2[1]); > array_tmp4_a1[1] := sin(array_tmp3[1]); > array_tmp4_a2[1] := cos(array_tmp3[1]); > array_tmp4[1] := (array_tmp4_a1[1] / array_tmp4_a2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[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_tmp5[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_2D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/glob__2; > #emit pre tan $eq_no = 1 > array_tmp4_a1[2] := att(1,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[2] := neg(att(1,array_tmp4_a1,array_tmp3,1)); > array_tmp4[2] := (array_tmp4_a1[2] - ats(2,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := 0; > array_tmp3[3] := neg(ats(3,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre tan $eq_no = 1 > array_tmp4_a1[3] := att(2,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[3] := neg(att(2,array_tmp4_a1,array_tmp3,1)); > array_tmp4[3] := (array_tmp4_a1[3] - ats(3,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := 0; > array_tmp3[4] := neg(ats(4,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre tan $eq_no = 1 > array_tmp4_a1[4] := att(3,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[4] := neg(att(3,array_tmp4_a1,array_tmp3,1)); > array_tmp4[4] := (array_tmp4_a1[4] - ats(4,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := 0; > array_tmp3[5] := neg(ats(5,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre tan $eq_no = 1 > array_tmp4_a1[5] := att(4,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[5] := neg(att(4,array_tmp4_a1,array_tmp3,1)); > array_tmp4[5] := (array_tmp4_a1[5] - ats(5,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp4[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_tmp5[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 sqrt LINEAR $eq_no = 1 > array_tmp3[kkk] := 0; > array_tmp3[kkk] := neg(ats(kkk,array_tmp3,array_tmp3,2)) /array_tmp3[1] / glob__2; > array_tmp4_a1[kkk] := att(kkk-1 ,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[kkk] := neg(att(kkk-1,array_tmp4_a1,array_tmp3,1)); > array_tmp4[kkk] := (array_tmp4_a1[kkk] - ats(kkk ,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[kkk] := array_tmp4[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_tmp5[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y[kkk + order_d] := c(temporary); > array_y_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, 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_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, 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_2D0[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_3D0[1]; array_tmp3[1] := sqrt(array_tmp2[1]); array_tmp4_a1[1] := sin(array_tmp3[1]); array_tmp4_a2[1] := cos(array_tmp3[1]); array_tmp4[1] := array_tmp4_a1[1]/array_tmp4_a2[1]; array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp5[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_2D0[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*glob__2); array_tmp4_a1[2] := att(1, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[2] := neg(att(1, array_tmp4_a1, array_tmp3, 1)); array_tmp4[2] := ( array_tmp4_a1[2] - ats(2, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp5[2] := array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y[3] := temporary; array_y_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp3[3] := 0; array_tmp3[3] := neg(ats(3, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4_a1[3] := att(2, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[3] := neg(att(2, array_tmp4_a1, array_tmp3, 1)); array_tmp4[3] := ( array_tmp4_a1[3] - ats(3, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp5[3] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y[4] := temporary; array_y_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp3[4] := 0; array_tmp3[4] := neg(ats(4, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4_a1[4] := att(3, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[4] := neg(att(3, array_tmp4_a1, array_tmp3, 1)); array_tmp4[4] := ( array_tmp4_a1[4] - ats(4, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp5[4] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y[5] := temporary; array_y_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp3[5] := 0; array_tmp3[5] := neg(ats(5, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4_a1[5] := att(4, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[5] := neg(att(4, array_tmp4_a1, array_tmp3, 1)); array_tmp4[5] := ( array_tmp4_a1[5] - ats(5, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp5[5] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y[6] := temporary; array_y_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y_higher[2, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp3[kkk] := 0; array_tmp3[kkk] := neg(ats(kkk, array_tmp3, array_tmp3, 2))/( array_tmp3[1]*glob__2); array_tmp4_a1[kkk] := att(kkk - 1, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[kkk] := neg(att(kkk - 1, array_tmp4_a1, array_tmp3, 1)); array_tmp4[kkk] := ( array_tmp4_a1[kkk] - ats(kkk, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp5[kkk] := array_tmp4[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_tmp5[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y[kkk + order_d] := c(temporary); array_y_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1 do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := c(temporary)*c(adj2)/c(glob_h) else temporary := c(temporary) end if; array_y_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #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_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 40; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=40; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(40),[]); > array_norms:= Array(0..(40),[]); > array_fact_1:= Array(0..(40),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(40),[]); > array_x:= Array(0..(40),[]); > array_tmp0:= Array(0..(40),[]); > array_tmp1:= Array(0..(40),[]); > array_tmp2:= Array(0..(40),[]); > array_tmp3:= Array(0..(40),[]); > array_tmp4_g:= Array(0..(40),[]); > array_tmp4_a1:= Array(0..(40),[]); > array_tmp4_a2:= Array(0..(40),[]); > array_tmp4:= Array(0..(40),[]); > array_tmp5:= Array(0..(40),[]); > array_m1:= Array(0..(40),[]); > array_y_higher := Array(0..(2) ,(0..40+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..40+ 1),[]); > array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(40) ,(0..40+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 40) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp4_g[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp4_a1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp4_a2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp5[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=40) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_y); > zero_ats_ar(array_x); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4_g); > zero_ats_ar(array_tmp4_a1); > zero_ats_ar(array_tmp4_a2); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_tmp5); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_2D0); > array_const_2D0[1] := c(2.0); > zero_ats_ar(array_const_3D0); > array_const_3D0[1] := c(3.0); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_h := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 1000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > array_y_set_initial[1,31] := false; > array_y_set_initial[1,32] := false; > array_y_set_initial[1,33] := false; > array_y_set_initial[1,34] := false; > array_y_set_initial[1,35] := false; > array_y_set_initial[1,36] := false; > array_y_set_initial[1,37] := false; > array_y_set_initial[1,38] := false; > array_y_set_initial[1,39] := false; > array_y_set_initial[1,40] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 40; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/tan_sqrt_linpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=40;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := c(0.1);"); > omniout_str(ALWAYS,"x_end := c(5.0) ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_min_h := c(0.001);"); > 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(0.5);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=8;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"glob_max_iter:=100000;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);"); > omniout_str(ALWAYS,"glob_look_poles:=false;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(c(0.0));"); > 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_min_h := c(0.001); > 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(0.5); > 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 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 10 > logstart(html_log_file); > logitem_str(html_log_file,"2016-08-26T17:06:11-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"tan_sqrt_lin") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ; ") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_h_reason(html_log_file) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_float(html_log_file,glob_desired_digits_correct) > ; > if (array_est_digits[1] <> -16) then # if number 11 > logitem_integer(html_log_file,array_est_digits[1]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_min_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > logitem_integer(html_log_file,ATS_MAX_TERMS) > ; > if (glob_type_given_pole = 0) then # if number 11 > logitem_str(html_log_file,"Not Given") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 4) then # if number 12 > logitem_str(html_log_file,"No Solution") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 5) then # if number 13 > logitem_str(html_log_file,"Some Pole") > ; > logitem_str(html_log_file,"????") > ; > elif > (glob_type_given_pole = 3) then # if number 14 > logitem_str(html_log_file,"No Pole") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 1) then # if number 15 > logitem_str(html_log_file,"Real Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > elif > (glob_type_given_pole = 2) then # if number 16 > logitem_str(html_log_file,"Complex Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > fi;# end if 16; > if (glob_least_ratio_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_ratio_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_3_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_3_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_6_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_6_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,(glob_clock_sec)) > ; > if (c(glob_percent_done) < glob__100) then # if number 16 > logitem_time(html_log_file,(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 16; > log_revs(html_log_file," 308.maple.seems.ok ") > ; > logitem_str(html_log_file,"tan_sqrt_lin diffeq.mxt") > ; > logitem_str(html_log_file,"tan_sqrt_lin maple results") > ; > logitem_str(html_log_file,"PROBLEM - Singularity not accurate") > ; > logend(html_log_file) > ; > ; > fi;# end if 15; > if (glob_html_log) then # if number 15 > fclose(html_log_file); > fi;# end if 15 > ; > ;; > fi;# end if 14 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, found_h, repeat_it; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, 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_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 40; Digits := 32; max_terms := 40; glob_html_log := true; array_y_init := Array(0 .. 40, []); array_norms := Array(0 .. 40, []); array_fact_1 := Array(0 .. 40, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 40, []); array_x := Array(0 .. 40, []); array_tmp0 := Array(0 .. 40, []); array_tmp1 := Array(0 .. 40, []); array_tmp2 := Array(0 .. 40, []); array_tmp3 := Array(0 .. 40, []); array_tmp4_g := Array(0 .. 40, []); array_tmp4_a1 := Array(0 .. 40, []); array_tmp4_a2 := Array(0 .. 40, []); array_tmp4 := Array(0 .. 40, []); array_tmp5 := Array(0 .. 40, []); array_m1 := Array(0 .. 40, []); array_y_higher := Array(0 .. 2, 0 .. 41, []); array_y_higher_work := Array(0 .. 2, 0 .. 41, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []); array_y_set_initial := Array(0 .. 2, 0 .. 41, []); array_given_rad_poles := Array(0 .. 2, 0 .. 4, []); array_given_ord_poles := Array(0 .. 2, 0 .. 4, []); array_rad_test_poles := Array(0 .. 2, 0 .. 5, []); array_ord_test_poles := Array(0 .. 2, 0 .. 5, []); array_fact_2 := Array(0 .. 40, 0 .. 41, []); term := 1; while term <= 40 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 40 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 40 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp4_g[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp4_a1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp4_a2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 40 do term := 1; while term <= 40 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_y); zero_ats_ar(array_x); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4_g); zero_ats_ar(array_tmp4_a1); zero_ats_ar(array_tmp4_a2); zero_ats_ar(array_tmp4); zero_ats_ar(array_tmp5); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_2D0); array_const_2D0[1] := c(2.0); zero_ats_ar(array_const_3D0); array_const_3D0[1] := c(3.0); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_h := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 1000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; array_y_set_initial[1, 31] := false; array_y_set_initial[1, 32] := false; array_y_set_initial[1, 33] := false; array_y_set_initial[1, 34] := false; array_y_set_initial[1, 35] := false; array_y_set_initial[1, 36] := false; array_y_set_initial[1, 37] := false; array_y_set_initial[1, 38] := false; array_y_set_initial[1, 39] := false; array_y_set_initial[1, 40] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 40; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/tan_sqrt_linpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = tan ( sqrt ( 2.0 \ * x + 3.0 ) ) ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=40;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := c(0.1);"); omniout_str(ALWAYS, "x_end := c(5.0) ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_min_h := c(0.001);"); 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(0.5);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=8;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "glob_max_iter:=100000;"); omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);"); omniout_str(ALWAYS, "glob_look_poles:=false;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(c(0.0));"); 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_min_h := c(0.001); 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(0.5); 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 ) = tan ( sqrt ( 2.\ 0 * x + 3.0 ) ) ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2016-08-26T17:06:11-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "tan_sqrt_lin"); logitem_str(html_log_file, "diff ( y , x , 1 ) = ta\ n ( sqrt ( 2.0 * x + 3.0 ) ) ; "); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_h_reason(html_log_file); logitem_integer(html_log_file, Digits); logitem_float(html_log_file, glob_desired_digits_correct); if array_est_digits[1] <> -16 then logitem_integer(html_log_file, array_est_digits[1]) else logitem_str(html_log_file, "Unknown") end if; if glob_min_good_digits <> -16 then logitem_integer(html_log_file, glob_min_good_digits) else logitem_str(html_log_file, "Unknown") end if; if glob_good_digits <> -16 then logitem_integer(html_log_file, glob_good_digits) else logitem_str(html_log_file, "Unknown") end if; logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); logitem_integer(html_log_file, ATS_MAX_TERMS); if glob_type_given_pole = 0 then logitem_str(html_log_file, "Not Given"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 4 then logitem_str(html_log_file, "No Solution"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 5 then logitem_str(html_log_file, "Some Pole"); logitem_str(html_log_file, "????") elif glob_type_given_pole = 3 then logitem_str(html_log_file, "No Pole"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 1 then logitem_str(html_log_file, "Real Sing"); logitem_float(html_log_file, glob_least_given_sing) elif glob_type_given_pole = 2 then logitem_str(html_log_file, "Complex Sing"); logitem_float(html_log_file, glob_least_given_sing) end if; if glob_least_ratio_sing < glob_large_float then logitem_float(html_log_file, glob_least_ratio_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_3_sing < glob_large_float then logitem_float(html_log_file, glob_least_3_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_6_sing < glob_large_float then logitem_float(html_log_file, glob_least_6_sing) else logitem_str(html_log_file, "NONE") end if; logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, glob_clock_sec); if c(glob_percent_done) < glob__100 then logitem_time(html_log_file, glob_total_exp_sec); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 308.maple.seems.ok "); logitem_str(html_log_file, "tan_sqrt_lin diffeq.mxt"); logitem_str(html_log_file, "tan_sqrt_lin maple results"); logitem_str(html_log_file, "PROBLEM - Singularity not accurate") ; 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/tan_sqrt_linpostode.ode################# diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=40; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := c(0.1); x_end := c(5.0) ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_min_h := c(0.001); 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(0.5); 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(0.0)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop memory used=4.1MB, alloc=40.3MB, time=0.09 x[1] = 0.1 y[1] (closed_form) = 0 y[1] (numeric) = 0 absolute error = 0 relative error = -1 % Desired digits = 8 Estimated correct digits = -16 Correct digits = -16 h = 0.001 memory used=18.5MB, alloc=40.3MB, time=0.26 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 0 y[1] (numeric) = -0.044601613960418243968668110698576 absolute error = 0.044601613960418243968668110698576 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 0 y[1] (numeric) = -0.088066884075519907980802638190262 absolute error = 0.088066884075519907980802638190262 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 memory used=62.8MB, alloc=52.3MB, time=0.77 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 0 y[1] (numeric) = -0.13045284233220728109182318862601 absolute error = 0.13045284233220728109182318862601 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 0 y[1] (numeric) = -0.1718122558682538203483354896552 absolute error = 0.1718122558682538203483354896552 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 memory used=107.1MB, alloc=52.3MB, time=1.26 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 0 y[1] (numeric) = -0.21219404226654027677010426618427 absolute error = 0.21219404226654027677010426618427 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (closed_form) = 0 y[1] (numeric) = -0.25164363549036244560739423708931 absolute error = 0.25164363549036244560739423708931 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 memory used=151.4MB, alloc=52.3MB, time=1.77 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (closed_form) = 0 y[1] (numeric) = -0.29020330933658473378989857472295 absolute error = 0.29020330933658473378989857472295 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (closed_form) = 0 y[1] (numeric) = -0.32791246419096267736377193497656 absolute error = 0.32791246419096267736377193497656 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 memory used=195.7MB, alloc=52.3MB, time=2.26 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (closed_form) = 0 y[1] (numeric) = -0.36480788197145358510992738182062 absolute error = 0.36480788197145358510992738182062 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (closed_form) = 0 y[1] (numeric) = -0.40092395340288090553292973425444 absolute error = 0.40092395340288090553292973425444 relative error = -1 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -16 h = 0.001 memory used=239.9MB, alloc=52.3MB, time=2.75 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (closed_form) = 0 y[1] (numeric) = -0.4362928811500711360799567266717 absolute error = 0.4362928811500711360799567266717 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (closed_form) = 0 y[1] (numeric) = -0.47094486182290834659326127575715 absolute error = 0.47094486182290834659326127575715 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=284.2MB, alloc=52.3MB, time=3.24 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (closed_form) = 0 y[1] (numeric) = -0.50490824943683429630961666167456 absolute error = 0.50490824943683429630961666167456 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=328.6MB, alloc=52.3MB, time=3.73 x[1] = 0.24 y[1] (closed_form) = 0 y[1] (numeric) = -0.53820970255110409348478697127365 absolute error = 0.53820970255110409348478697127365 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (closed_form) = 0 y[1] (numeric) = -0.57087431700247977711210747563124 absolute error = 0.57087431700247977711210747563124 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=372.9MB, alloc=52.3MB, time=4.23 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (closed_form) = 0 y[1] (numeric) = -0.60292574589422435654613996228287 absolute error = 0.60292574589422435654613996228287 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (closed_form) = 0 y[1] (numeric) = -0.63438630828130766960442391062786 absolute error = 0.63438630828130766960442391062786 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=417.3MB, alloc=52.3MB, time=4.72 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (closed_form) = 0 y[1] (numeric) = -0.66527708780618238183074780616251 absolute error = 0.66527708780618238183074780616251 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (closed_form) = 0 y[1] (numeric) = -0.69561802238003815862697045318553 absolute error = 0.69561802238003815862697045318553 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=461.8MB, alloc=52.3MB, time=5.21 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (closed_form) = 0 y[1] (numeric) = -0.7254279858677436651474137013587 absolute error = 0.7254279858677436651474137013587 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (closed_form) = 0 y[1] (numeric) = -0.75472486261715122189802432691986 absolute error = 0.75472486261715122189802432691986 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=506.1MB, alloc=52.3MB, time=5.70 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (closed_form) = 0 y[1] (numeric) = -0.78352561557209731698466338487678 absolute error = 0.78352561557209731698466338487678 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (closed_form) = 0 y[1] (numeric) = -0.81184634862081631015774629824741 absolute error = 0.81184634862081631015774629824741 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=550.5MB, alloc=52.3MB, time=6.20 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (closed_form) = 0 y[1] (numeric) = -0.83970236375553792600365107566092 absolute error = 0.83970236375553792600365107566092 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (closed_form) = 0 y[1] (numeric) = -0.8671082135530416918022340233542 absolute error = 0.8671082135530416918022340233542 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=594.6MB, alloc=52.3MB, time=6.69 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (closed_form) = 0 y[1] (numeric) = -0.89407774942845060385893432451037 absolute error = 0.89407774942845060385893432451037 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (closed_form) = 0 y[1] (numeric) = -0.92062416606434804935435499637115 absolute error = 0.92062416606434804935435499637115 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=638.6MB, alloc=52.3MB, time=7.18 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (closed_form) = 0 y[1] (numeric) = -0.9467600423733719031329955639706 absolute error = 0.9467600423733719031329955639706 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (closed_form) = 0 y[1] (numeric) = -0.9724973793139107477043541082161 absolute error = 0.9724973793139107477043541082161 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=682.8MB, alloc=52.3MB, time=7.67 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (closed_form) = 0 y[1] (numeric) = -0.99784763484466355356923147775142 absolute error = 0.99784763484466355356923147775142 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (closed_form) = 0 y[1] (numeric) = -1.0228217562739998397795689187221 absolute error = 1.0228217562739998397795689187221 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=726.8MB, alloc=52.3MB, time=8.16 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (closed_form) = 0 y[1] (numeric) = -1.0474302102337382252420026464882 absolute error = 1.0474302102337382252420026464882 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=770.8MB, alloc=52.3MB, time=8.65 x[1] = 0.43 y[1] (closed_form) = 0 y[1] (numeric) = -1.0716830104836906236163278139473 absolute error = 1.0716830104836906236163278139473 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (closed_form) = 0 y[1] (numeric) = -1.0955897437327055620855894107106 absolute error = 1.0955897437327055620855894107106 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=814.9MB, alloc=52.3MB, time=9.14 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (closed_form) = 0 y[1] (numeric) = -1.1191595936436507489857870108603 absolute error = 1.1191595936436507489857870108603 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (closed_form) = 0 y[1] (numeric) = -1.1424013631735122980542500026754 absolute error = 1.1424013631735122980542500026754 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=859.0MB, alloc=52.3MB, time=9.63 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (closed_form) = 0 y[1] (numeric) = -1.1653234953853058182534120840624 absolute error = 1.1653234953853058182534120840624 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (closed_form) = 0 y[1] (numeric) = -1.1879340928555765475778349761821 absolute error = 1.1879340928555765475778349761821 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=903.0MB, alloc=52.3MB, time=10.12 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (closed_form) = 0 y[1] (numeric) = -1.2102409357897243177240648102747 absolute error = 1.2102409357897243177240648102747 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (closed_form) = 0 y[1] (numeric) = -1.2322514989470615078646244894321 absolute error = 1.2322514989470615078646244894321 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=947.0MB, alloc=52.3MB, time=10.61 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (closed_form) = 0 y[1] (numeric) = -1.2539729674682565381395192006365 absolute error = 1.2539729674682565381395192006365 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (closed_form) = 0 y[1] (numeric) = -1.2754122516895082812919592417016 absolute error = 1.2754122516895082812919592417016 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=991.1MB, alloc=52.3MB, time=11.10 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (closed_form) = 0 y[1] (numeric) = -1.2965760010203300789027122775235 absolute error = 1.2965760010203300789027122775235 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (closed_form) = 0 y[1] (numeric) = -1.3174706169551013646522199250272 absolute error = 1.3174706169551013646522199250272 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1035.1MB, alloc=52.3MB, time=11.59 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (closed_form) = 0 y[1] (numeric) = -1.3381022652824874021439818345624 absolute error = 1.3381022652824874021439818345624 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (closed_form) = 0 y[1] (numeric) = -1.3584768875513606116982057890793 absolute error = 1.3584768875513606116982057890793 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1079.2MB, alloc=52.3MB, time=12.08 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (closed_form) = 0 y[1] (numeric) = -1.3786002118469164169311276765669 absolute error = 1.3786002118469164169311276765669 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (closed_form) = 0 y[1] (numeric) = -1.3984777629262061251657456858051 absolute error = 1.3984777629262061251657456858051 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1123.4MB, alloc=52.3MB, time=12.57 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (closed_form) = 0 y[1] (numeric) = -1.4181148717582593286186838730083 absolute error = 1.4181148717582593286186838730083 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (closed_form) = 0 y[1] (numeric) = -1.4375166845102947174839089876028 absolute error = 1.4375166845102947174839089876028 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1167.5MB, alloc=52.3MB, time=13.06 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (closed_form) = 0 y[1] (numeric) = -1.4566881710181821217800944739607 absolute error = 1.4566881710181821217800944739607 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (closed_form) = 0 y[1] (numeric) = -1.4756341327762855545237516620306 absolute error = 1.4756341327762855545237516620306 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1211.6MB, alloc=52.3MB, time=13.56 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (closed_form) = 0 y[1] (numeric) = -1.4943592104790563952622792549646 absolute error = 1.4943592104790563952622792549646 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=1255.7MB, alloc=52.3MB, time=14.05 x[1] = 0.64 y[1] (closed_form) = 0 y[1] (numeric) = -1.5128678911442304105850613707012 absolute error = 1.5128678911442304105850613707012 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (closed_form) = 0 y[1] (numeric) = -1.531164514845187826148911812969 absolute error = 1.531164514845187826148911812969 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1299.8MB, alloc=52.3MB, time=14.54 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (closed_form) = 0 y[1] (numeric) = -1.5492532810779405440149355555165 absolute error = 1.5492532810779405440149355555165 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (closed_form) = 0 y[1] (numeric) = -1.567138254786295561435075306356 absolute error = 1.567138254786295561435075306356 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1344.0MB, alloc=52.3MB, time=15.03 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (closed_form) = 0 y[1] (numeric) = -1.584823372066991463739438915878 absolute error = 1.584823372066991463739438915878 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (closed_form) = 0 y[1] (numeric) = -1.6023124455750001179831369793599 absolute error = 1.6023124455750001179831369793599 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1388.1MB, alloc=52.3MB, time=15.52 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (closed_form) = 0 y[1] (numeric) = -1.6196091696477145735667011637991 absolute error = 1.6196091696477145735667011637991 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (closed_form) = 0 y[1] (numeric) = -1.6367171251653942920799403400453 absolute error = 1.6367171251653942920799403400453 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1432.2MB, alloc=52.3MB, time=16.01 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (closed_form) = 0 y[1] (numeric) = -1.6536397841639990553498278770467 absolute error = 1.6536397841639990553498278770467 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (closed_form) = 0 y[1] (numeric) = -1.6703805142154032353287563717044 absolute error = 1.6703805142154032353287563717044 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1476.3MB, alloc=52.3MB, time=16.50 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (closed_form) = 0 y[1] (numeric) = -1.6869425825889335488400528080007 absolute error = 1.6869425825889335488400528080007 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (closed_form) = 0 y[1] (numeric) = -1.703329160207207851883631767421 absolute error = 1.703329160207207851883631767421 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1520.4MB, alloc=52.3MB, time=16.99 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (closed_form) = 0 y[1] (numeric) = -1.7195433254083626345586244656457 absolute error = 1.7195433254083626345586244656457 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (closed_form) = 0 y[1] (numeric) = -1.7355880675259360510042187742223 absolute error = 1.7355880675259360510042187742223 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1564.5MB, alloc=52.3MB, time=17.48 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (closed_form) = 0 y[1] (numeric) = -1.7514662902969155863357980037719 absolute error = 1.7514662902969155863357980037719 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (closed_form) = 0 y[1] (numeric) = -1.767180815107759420049499557336 absolute error = 1.767180815107759420049499557336 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1608.7MB, alloc=52.3MB, time=17.99 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (closed_form) = 0 y[1] (numeric) = -1.7827343840875532979701989187487 absolute error = 1.7827343840875532979701989187487 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (closed_form) = 0 y[1] (numeric) = -1.7981296630568658348645274545992 absolute error = 1.7981296630568658348645274545992 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1652.8MB, alloc=52.3MB, time=18.48 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (closed_form) = 0 y[1] (numeric) = -1.8133692443403106102924026570893 absolute error = 1.8133692443403106102924026570893 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (closed_form) = 0 y[1] (numeric) = -1.8284556494503095332978653929769 absolute error = 1.8284556494503095332978653929769 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1696.9MB, alloc=52.3MB, time=18.97 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (closed_form) = 0 y[1] (numeric) = -1.843391331649075411625354908015 absolute error = 1.843391331649075411625354908015 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=1741.0MB, alloc=52.3MB, time=19.46 x[1] = 0.85 y[1] (closed_form) = 0 y[1] (numeric) = -1.8581786783953894421750268097927 absolute error = 1.8581786783953894421750268097927 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (closed_form) = 0 y[1] (numeric) = -1.8728200136823386852791035339481 absolute error = 1.8728200136823386852791035339481 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1785.2MB, alloc=52.3MB, time=19.96 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (closed_form) = 0 y[1] (numeric) = -1.8873176002717969837358742192479 absolute error = 1.8873176002717969837358742192479 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (closed_form) = 0 y[1] (numeric) = -1.9016736418310779462659968401546 absolute error = 1.9016736418310779462659968401546 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1829.4MB, alloc=52.3MB, time=20.45 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (closed_form) = 0 y[1] (numeric) = -1.9158902849768584412326376076082 absolute error = 1.9158902849768584412326376076082 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (closed_form) = 0 y[1] (numeric) = -1.9299696212311636274794958825535 absolute error = 1.9299696212311636274794958825535 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1873.6MB, alloc=52.3MB, time=20.94 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (closed_form) = 0 y[1] (numeric) = -1.9439136888939181357450436118776 absolute error = 1.9439136888939181357450436118776 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (closed_form) = 0 y[1] (numeric) = -1.9577244748363010052127345371501 absolute error = 1.9577244748363010052127345371501 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1917.7MB, alloc=52.3MB, time=21.43 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (closed_form) = 0 y[1] (numeric) = -1.9714039162188929087239098269523 absolute error = 1.9714039162188929087239098269523 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (closed_form) = 0 y[1] (numeric) = -1.9849539021383717225256606250104 absolute error = 1.9849539021383717225256606250104 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=1961.8MB, alloc=52.3MB, time=21.93 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (closed_form) = 0 y[1] (numeric) = -1.9983762752062953787101801275902 absolute error = 1.9983762752062953787101801275902 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (closed_form) = 0 y[1] (numeric) = -2.0116728330633080483259426000564 absolute error = 2.0116728330633080483259426000564 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2005.9MB, alloc=52.3MB, time=22.42 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (closed_form) = 0 y[1] (numeric) = -2.0248453298319160001149415195729 absolute error = 2.0248453298319160001149415195729 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (closed_form) = 0 y[1] (numeric) = -2.0378954775108020074171211174764 absolute error = 2.0378954775108020074171211174764 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2050.0MB, alloc=52.3MB, time=22.91 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (closed_form) = 0 y[1] (numeric) = -2.0508249473134810539235841973584 absolute error = 2.0508249473134810539235841973584 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 0 y[1] (numeric) = -2.0636353709539445073995358733992 absolute error = 2.0636353709539445073995358733992 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2094.2MB, alloc=52.3MB, time=23.40 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 0 y[1] (numeric) = -2.0763283418817941427438169986641 absolute error = 2.0763283418817941427438169986641 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (closed_form) = 0 y[1] (numeric) = -2.08890541646923071359763511073 absolute error = 2.08890541646923071359763511073 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2138.4MB, alloc=52.3MB, time=23.89 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (closed_form) = 0 y[1] (numeric) = -2.1013681151521335602725115302266 absolute error = 2.1013681151521335602725115302266 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (closed_form) = 0 y[1] (numeric) = -2.1137179235273474149577499321511 absolute error = 2.1137179235273474149577499321511 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2182.5MB, alloc=52.3MB, time=24.38 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (closed_form) = 0 y[1] (numeric) = -2.1259562934081795816253186571183 absolute error = 2.1259562934081795816253186571183 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=2226.5MB, alloc=52.3MB, time=24.87 x[1] = 1.06 y[1] (closed_form) = 0 y[1] (numeric) = -2.1380846438400045273985195537403 absolute error = 2.1380846438400045273985195537403 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (closed_form) = 0 y[1] (numeric) = -2.1501043620777731616147377080261 absolute error = 2.1501043620777731616147377080261 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2270.7MB, alloc=52.3MB, time=25.36 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (closed_form) = 0 y[1] (numeric) = -2.1620168045271302701324749906087 absolute error = 2.1620168045271302701324749906087 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (closed_form) = 0 y[1] (numeric) = -2.1738232976507553190544265582736 absolute error = 2.1738232976507553190544265582736 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2314.8MB, alloc=52.3MB, time=25.86 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = 0 y[1] (numeric) = -2.1855251388414587765493421715592 absolute error = 2.1855251388414587765493421715592 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (closed_form) = 0 y[1] (numeric) = -2.1971235972634878832471017565474 absolute error = 2.1971235972634878832471017565474 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2359.0MB, alloc=52.3MB, time=26.35 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (closed_form) = 0 y[1] (numeric) = -2.2086199146634221148132374311736 absolute error = 2.2086199146634221148132374311736 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (closed_form) = 0 y[1] (numeric) = -2.2200153061519691315574794252662 absolute error = 2.2200153061519691315574794252662 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2403.2MB, alloc=52.3MB, time=26.84 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (closed_form) = 0 y[1] (numeric) = -2.2313109609579065270052714205248 absolute error = 2.2313109609579065270052714205248 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (closed_form) = 0 y[1] (numeric) = -2.2425080431553529172719104585582 absolute error = 2.2425080431553529172719104585582 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2447.4MB, alloc=52.3MB, time=27.34 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (closed_form) = 0 y[1] (numeric) = -2.2536076923654936206428223657141 absolute error = 2.2536076923654936206428223657141 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (closed_form) = 0 y[1] (numeric) = -2.2646110244338311432347604085993 absolute error = 2.2646110244338311432347604085993 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2491.6MB, alloc=52.3MB, time=27.83 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (closed_form) = 0 y[1] (numeric) = -2.2755191320839787084281684897877 absolute error = 2.2755191320839787084281684897877 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (closed_form) = 0 y[1] (numeric) = -2.2863330855489659553886373249286 absolute error = 2.2863330855489659553886373249286 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2535.8MB, alloc=52.3MB, time=28.32 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (closed_form) = 0 y[1] (numeric) = -2.2970539331809795088780501387022 absolute error = 2.2970539331809795088780501387022 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (closed_form) = 0 y[1] (numeric) = -2.3076827020404172241407023949783 absolute error = 2.3076827020404172241407023949783 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2580.0MB, alloc=52.3MB, time=28.81 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (closed_form) = 0 y[1] (numeric) = -2.3182203984650933834959611086136 absolute error = 2.3182203984650933834959611086136 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (closed_form) = 0 y[1] (numeric) = -2.328668008620392822229037514552 absolute error = 2.328668008620392822229037514552 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2624.2MB, alloc=52.3MB, time=29.30 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (closed_form) = 0 y[1] (numeric) = -2.3390264990311347568354697941747 absolute error = 2.3390264990311347568354697941747 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (closed_form) = 0 y[1] (numeric) = -2.3492968170958718538769070816789 absolute error = 2.3492968170958718538769070816789 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2668.3MB, alloc=52.3MB, time=29.80 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (closed_form) = 0 y[1] (numeric) = -2.3594798915843166960836954977298 absolute error = 2.3594798915843166960836954977298 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=2712.4MB, alloc=52.3MB, time=30.29 x[1] = 1.27 y[1] (closed_form) = 0 y[1] (numeric) = -2.3695766331185561649459854502455 absolute error = 2.3695766331185561649459854502455 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (closed_form) = 0 y[1] (numeric) = -2.3795879346386842639928312745317 absolute error = 2.3795879346386842639928312745317 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=2756.6MB, alloc=52.3MB, time=30.78 x[1] = 1.29 y[1] (closed_form) = 0 y[1] (numeric) = -2.3895146718534554589605406622503 absolute error = 2.3895146718534554589605406622503 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (closed_form) = 0 y[1] (numeric) = -2.3993577036765336208961393938294 absolute error = 2.3993577036765336208961393938294 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2800.6MB, alloc=52.3MB, time=31.28 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (closed_form) = 0 y[1] (numeric) = -2.4091178726488860424066998994759 absolute error = 2.4091178726488860424066998994759 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (closed_form) = 0 y[1] (numeric) = -2.4187960053478476775114018188495 absolute error = 2.4187960053478476775114018188495 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2844.6MB, alloc=52.3MB, time=31.77 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (closed_form) = 0 y[1] (numeric) = -2.4283929127833576585596706698032 absolute error = 2.4283929127833576585596706698032 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (closed_form) = 0 y[1] (numeric) = -2.4379093907818482007048984798336 absolute error = 2.4379093907818482007048984798336 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2888.7MB, alloc=52.3MB, time=32.26 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (closed_form) = 0 y[1] (numeric) = -2.4473462203582451509958268680706 absolute error = 2.4473462203582451509958268680706 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (closed_form) = 0 y[1] (numeric) = -2.4567041680765196147712013242745 absolute error = 2.4567041680765196147712013242745 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2932.9MB, alloc=52.3MB, time=32.75 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (closed_form) = 0 y[1] (numeric) = -2.465983986399211239931799938048 absolute error = 2.465983986399211239931799938048 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (closed_form) = 0 y[1] (numeric) = -2.4751864140263258064922089029557 absolute error = 2.4751864140263258064922089029557 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=2977.0MB, alloc=52.3MB, time=33.24 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (closed_form) = 0 y[1] (numeric) = -2.4843121762239927044877527192272 absolute error = 2.4843121762239927044877527192272 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (closed_form) = 0 y[1] (numeric) = -2.4933619851432516407510177278022 absolute error = 2.4933619851432516407510177278022 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3021.1MB, alloc=52.3MB, time=33.74 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (closed_form) = 0 y[1] (numeric) = -2.502336540129322450016318077394 absolute error = 2.502336540129322450016318077394 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (closed_form) = 0 y[1] (numeric) = -2.5112365280216971566313815436747 absolute error = 2.5112365280216971566313815436747 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3065.2MB, alloc=52.3MB, time=34.23 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (closed_form) = 0 y[1] (numeric) = -2.5200626234453794006875554782886 absolute error = 2.5200626234453794006875554782886 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (closed_form) = 0 y[1] (numeric) = -2.5288154890935829697597384255494 absolute error = 2.5288154890935829697597384255494 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3109.3MB, alloc=52.3MB, time=34.72 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (closed_form) = 0 y[1] (numeric) = -2.5374957760021884299664710709659 absolute error = 2.5374957760021884299664710709659 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (closed_form) = 0 y[1] (numeric) = -2.5461041238162446950275307624537 absolute error = 2.5461041238162446950275307624537 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3153.4MB, alloc=52.3MB, time=35.21 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (closed_form) = 0 y[1] (numeric) = -2.5546411610487907786080616316604 absolute error = 2.5546411610487907786080616316604 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (closed_form) = 0 y[1] (numeric) = -2.563107505332261914461219703797 absolute error = 2.563107505332261914461219703797 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3197.5MB, alloc=52.3MB, time=35.70 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (closed_form) = 0 y[1] (numeric) = -2.5715037636627336733402219577052 absolute error = 2.5715037636627336733402219577052 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=3241.6MB, alloc=52.3MB, time=36.20 x[1] = 1.5 y[1] (closed_form) = 0 y[1] (numeric) = -2.5798305326372476295248919362842 absolute error = 2.5798305326372476295248919362842 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (closed_form) = 0 y[1] (numeric) = -2.5880883986844525087346822786673 absolute error = 2.5880883986844525087346822786673 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3285.7MB, alloc=52.3MB, time=36.69 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (closed_form) = 0 y[1] (numeric) = -2.5962779382887855601851113073425 absolute error = 2.5962779382887855601851113073425 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (closed_form) = 0 y[1] (numeric) = -2.6043997182084101168769279335181 absolute error = 2.6043997182084101168769279335181 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3329.8MB, alloc=52.3MB, time=37.18 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (closed_form) = 0 y[1] (numeric) = -2.612454295687116919382005736081 absolute error = 2.612454295687116919382005736081 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (closed_form) = 0 y[1] (numeric) = -2.6204422186603887600341585900993 absolute error = 2.6204422186603887600341585900993 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3374.0MB, alloc=52.3MB, time=37.67 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (closed_form) = 0 y[1] (numeric) = -2.6283640259558203382378635349785 absolute error = 2.6283640259558203382378635349785 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (closed_form) = 0 y[1] (numeric) = -2.6362202474880778862643486217726 absolute error = 2.6362202474880778862643486217726 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3418.1MB, alloc=52.3MB, time=38.16 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (closed_form) = 0 y[1] (numeric) = -2.6440114044485761120439569643268 absolute error = 2.6440114044485761120439569643268 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (closed_form) = 0 y[1] (numeric) = -2.651738009490043295601781588511 absolute error = 2.651738009490043295601781588511 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3462.2MB, alloc=52.3MB, time=38.66 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (closed_form) = 0 y[1] (numeric) = -2.6594005669061389542679967469405 absolute error = 2.6594005669061389542679967469405 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (closed_form) = 0 y[1] (numeric) = -2.6669995728062823447559541701788 absolute error = 2.6669995728062823447559541701788 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3506.3MB, alloc=52.3MB, time=39.26 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (closed_form) = 0 y[1] (numeric) = -2.674535515285844184508175769422 absolute error = 2.674535515285844184508175769422 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (closed_form) = 0 y[1] (numeric) = -2.6820088745918483379255156807464 absolute error = 2.6820088745918483379255156807464 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3550.4MB, alloc=52.3MB, time=39.74 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (closed_form) = 0 y[1] (numeric) = -2.6894201232843248134349050311232 absolute error = 2.6894201232843248134349050311232 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (closed_form) = 0 y[1] (numeric) = -2.6967697263934502436497527749833 absolute error = 2.6967697263934502436497527749833 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3594.5MB, alloc=52.3MB, time=40.24 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (closed_form) = 0 y[1] (numeric) = -2.704058141572607062549065187716 absolute error = 2.704058141572607062549065187716 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (closed_form) = 0 y[1] (numeric) = -2.7112858192474878406096487095735 absolute error = 2.7112858192474878406096487095735 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3638.6MB, alloc=52.3MB, time=40.73 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (closed_form) = 0 y[1] (numeric) = -2.7184532027613666816504651401574 absolute error = 2.7184532027613666816504651401574 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (closed_form) = 0 y[1] (numeric) = -2.7255607285166552147573527582401 absolute error = 2.7255607285166552147573527582401 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3682.7MB, alloc=52.3MB, time=41.22 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (closed_form) = 0 y[1] (numeric) = -2.73260882611285652247852598175 absolute error = 2.73260882611285652247852598175 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (closed_form) = 0 y[1] (numeric) = -2.7395979184810263243800040846542 absolute error = 2.7395979184810263243800040846542 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3726.8MB, alloc=52.3MB, time=41.71 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (closed_form) = 0 y[1] (numeric) = -2.7465284220148468752996022081494 absolute error = 2.7465284220148468752996022081494 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=3770.9MB, alloc=52.3MB, time=42.20 x[1] = 1.73 y[1] (closed_form) = 0 y[1] (numeric) = -2.7534007466984153329005799223752 absolute error = 2.7534007466984153329005799223752 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (closed_form) = 0 y[1] (numeric) = -2.7602152962308447924304148979074 absolute error = 2.7602152962308447924304148979074 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3814.9MB, alloc=52.3MB, time=42.70 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (closed_form) = 0 y[1] (numeric) = -2.7669724681477727713120203415835 absolute error = 2.7669724681477727713120203415835 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (closed_form) = 0 y[1] (numeric) = -2.7736726539398686460373929183926 absolute error = 2.7736726539398686460373929183926 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3859.2MB, alloc=52.3MB, time=43.19 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (closed_form) = 0 y[1] (numeric) = -2.7803162391684283928105178059083 absolute error = 2.7803162391684283928105178059083 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (closed_form) = 0 y[1] (numeric) = -2.7869036035781419558040318017497 absolute error = 2.7869036035781419558040318017497 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3903.4MB, alloc=52.3MB, time=43.69 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (closed_form) = 0 y[1] (numeric) = -2.7934351212071156573368927201039 absolute error = 2.7934351212071156573368927201039 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (closed_form) = 0 y[1] (numeric) = -2.7999111604942292675951231770566 absolute error = 2.7999111604942292675951231770566 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3947.5MB, alloc=52.3MB, time=44.18 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (closed_form) = 0 y[1] (numeric) = -2.8063320843839046628003927245124 absolute error = 2.8063320843839046628003927245124 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (closed_form) = 0 y[1] (numeric) = -2.8126982504283604153132295425846 absolute error = 2.8126982504283604153132295425846 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=3991.5MB, alloc=52.3MB, time=44.68 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (closed_form) = 0 y[1] (numeric) = -2.8190100108874241725937217156306 absolute error = 2.8190100108874241725937217156306 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (closed_form) = 0 y[1] (numeric) = -2.8252677128259722899989544119496 absolute error = 2.8252677128259722899989544119496 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4035.7MB, alloc=52.3MB, time=45.17 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (closed_form) = 0 y[1] (numeric) = -2.8314716982090638810399501829406 absolute error = 2.8314716982090638810399501829406 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (closed_form) = 0 y[1] (numeric) = -2.8376223039948342341084926678511 absolute error = 2.8376223039948342341084926678511 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4079.8MB, alloc=52.3MB, time=45.66 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (closed_form) = 0 y[1] (numeric) = -2.8437198622252104131532022268665 absolute error = 2.8437198622252104131532022268665 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (closed_form) = 0 y[1] (numeric) = -2.8497647001145098078429389569262 absolute error = 2.8497647001145098078429389569262 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4123.9MB, alloc=52.3MB, time=46.16 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (closed_form) = 0 y[1] (numeric) = -2.8557571401359804230746902564722 absolute error = 2.8557571401359804230746902564722 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (closed_form) = 0 y[1] (numeric) = -2.8616975001063397950872630606118 absolute error = 2.8616975001063397950872630606118 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4168.0MB, alloc=52.3MB, time=46.65 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (closed_form) = 0 y[1] (numeric) = -2.8675860932683675889022964400748 absolute error = 2.8675860932683675889022964400748 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (closed_form) = 0 y[1] (numeric) = -2.8734232283716051664401587457408 absolute error = 2.8734232283716051664401587457408 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4212.1MB, alloc=52.3MB, time=47.14 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (closed_form) = 0 y[1] (numeric) = -2.8792092097512137136919121289576 absolute error = 2.8792092097512137136919121289576 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (closed_form) = 0 y[1] (numeric) = -2.8849443374050408761367384168364 absolute error = 2.8849443374050408761367384168364 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4256.3MB, alloc=52.3MB, time=47.64 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (closed_form) = 0 y[1] (numeric) = -2.8906289070689442716631173455475 absolute error = 2.8906289070689442716631173455475 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=4300.5MB, alloc=52.3MB, time=48.13 x[1] = 1.96 y[1] (closed_form) = 0 y[1] (numeric) = -2.8962632102904187271808982385869 absolute error = 2.8962632102904187271808982385869 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (closed_form) = 0 y[1] (numeric) = -2.9018475345005726166070703453076 absolute error = 2.9018475345005726166070703453076 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4344.6MB, alloc=52.3MB, time=48.62 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (closed_form) = 0 y[1] (numeric) = -2.9073821630844972617796888073887 absolute error = 2.9073821630844972617796888073887 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (closed_form) = 0 y[1] (numeric) = -2.9128673754500719920085391189788 absolute error = 2.9128673754500719920085391189788 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4388.7MB, alloc=52.3MB, time=49.12 TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = 0 y[1] (numeric) = -2.9183034470952461404067881610605 absolute error = 2.9183034470952461404067881610605 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (closed_form) = 0 y[1] (numeric) = -2.923690649673837983952234119546 absolute error = 2.923690649673837983952234119546 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4432.9MB, alloc=52.3MB, time=49.61 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (closed_form) = 0 y[1] (numeric) = -2.9290292510598894075708368512456 absolute error = 2.9290292510598894075708368512456 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (closed_form) = 0 y[1] (numeric) = -2.9343195154106138886698111789675 absolute error = 2.9343195154106138886698111789675 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4477.0MB, alloc=52.3MB, time=50.10 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (closed_form) = 0 y[1] (numeric) = -2.9395617032279742557995297003886 absolute error = 2.9395617032279742557995297003886 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (closed_form) = 0 y[1] (numeric) = -2.9447560714189255718920277971778 absolute error = 2.9447560714189255718920277971778 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4521.2MB, alloc=52.3MB, time=50.60 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (closed_form) = 0 y[1] (numeric) = -2.9499028733543574272772071739512 absolute error = 2.9499028733543574272772071739512 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (closed_form) = 0 y[1] (numeric) = -2.9550023589267688989497737658901 absolute error = 2.9550023589267688989497737658901 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4565.3MB, alloc=52.3MB, time=51.10 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (closed_form) = 0 y[1] (numeric) = -2.9600547746067084389470151886034 absolute error = 2.9600547746067084389470151886034 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (closed_form) = 0 y[1] (numeric) = -2.9650603634980099948559020874742 absolute error = 2.9650603634980099948559020874742 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4609.5MB, alloc=52.3MB, time=51.59 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (closed_form) = 0 y[1] (numeric) = -2.9700193653918557381107721935465 absolute error = 2.9700193653918557381107721935465 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (closed_form) = 0 y[1] (numeric) = -2.9749320168196948796373764855792 absolute error = 2.9749320168196948796373764855792 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4653.6MB, alloc=52.3MB, time=52.08 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (closed_form) = 0 y[1] (numeric) = -2.9797985511050471863644430458959 absolute error = 2.9797985511050471863644430458959 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (closed_form) = 0 y[1] (numeric) = -2.9846191984142189750286329434154 absolute error = 2.9846191984142189750286329434154 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4697.8MB, alloc=52.3MB, time=52.58 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (closed_form) = 0 y[1] (numeric) = -2.9893941858059585504584261905506 absolute error = 2.9893941858059585504584261905506 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (closed_form) = 0 y[1] (numeric) = -2.9941237372800772730976528837598 absolute error = 2.9941237372800772730976528837598 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4742.0MB, alloc=52.3MB, time=53.07 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (closed_form) = 0 y[1] (numeric) = -2.9988080738250616839235664716613 absolute error = 2.9988080738250616839235664716613 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (closed_form) = 0 y[1] (numeric) = -3.0034474134647013831720150700658 absolute error = 3.0034474134647013831720150700658 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4786.2MB, alloc=52.3MB, time=53.56 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (closed_form) = 0 y[1] (numeric) = -3.008041971303756651487009562549 absolute error = 3.008041971303756651487009562549 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=4830.2MB, alloc=52.3MB, time=54.05 x[1] = 2.19 y[1] (closed_form) = 0 y[1] (numeric) = -3.0125919595726891173847987147401 absolute error = 3.0125919595726891173847987147401 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = 0 y[1] (numeric) = -3.0170975876714781124201340655787 absolute error = 3.0170975876714781124201340655787 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4874.4MB, alloc=52.3MB, time=54.55 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (closed_form) = 0 y[1] (numeric) = -3.0215590622125447143555514155391 absolute error = 3.0215590622125447143555514155391 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (closed_form) = 0 y[1] (numeric) = -3.0259765870628048581866273160167 absolute error = 3.0259765870628048581866273160167 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4918.5MB, alloc=52.3MB, time=55.04 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (closed_form) = 0 y[1] (numeric) = -3.0303503633848722943218699039187 absolute error = 3.0303503633848722943218699039187 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (closed_form) = 0 y[1] (numeric) = -3.0346805896774315918395507412808 absolute error = 3.0346805896774315918395507412808 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=4962.6MB, alloc=52.3MB, time=55.53 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (closed_form) = 0 y[1] (numeric) = -3.0389674618148008218582450936579 absolute error = 3.0389674618148008218582450936579 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (closed_form) = 0 y[1] (numeric) = -3.043211173085703011003236449717 absolute error = 3.043211173085703011003236449717 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5006.7MB, alloc=52.3MB, time=56.02 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (closed_form) = 0 y[1] (numeric) = -3.0474119142312649270934341630587 absolute error = 3.0474119142312649270934341630587 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (closed_form) = 0 y[1] (numeric) = -3.0515698734822612479041628202115 absolute error = 3.0515698734822612479041628202115 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5050.9MB, alloc=52.3MB, time=56.52 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (closed_form) = 0 y[1] (numeric) = -3.0556852365956216685950799673458 absolute error = 3.0556852365956216685950799673458 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (closed_form) = 0 y[1] (numeric) = -3.0597581868902180235673718316703 absolute error = 3.0597581868902180235673718316703 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5095.0MB, alloc=52.3MB, time=57.03 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (closed_form) = 0 y[1] (numeric) = -3.0637889052819480335899294355021 absolute error = 3.0637889052819480335899294355021 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (closed_form) = 0 y[1] (numeric) = -3.0677775703181318384910114440391 absolute error = 3.0677775703181318384910114440391 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5139.1MB, alloc=52.3MB, time=57.52 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (closed_form) = 0 y[1] (numeric) = -3.0717243582112370390505849351031 absolute error = 3.0717243582112370390505849351031 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (closed_form) = 0 y[1] (numeric) = -3.0756294428719475484689216989689 absolute error = 3.0756294428719475484689216989689 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5183.1MB, alloc=52.3MB, time=58.01 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (closed_form) = 0 y[1] (numeric) = -3.079492995941591143467318868478 absolute error = 3.079492995941591143467318868478 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (closed_form) = 0 y[1] (numeric) = -3.0833151868239402072528229709595 absolute error = 3.0833151868239402072528229709595 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5227.3MB, alloc=52.3MB, time=58.51 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (closed_form) = 0 y[1] (numeric) = -3.0870961827163997708232551160476 absolute error = 3.0870961827163997708232551160476 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (closed_form) = 0 y[1] (numeric) = -3.0908361486405965849905233514428 absolute error = 3.0908361486405965849905233514428 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5271.4MB, alloc=52.3MB, time=59.00 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (closed_form) = 0 y[1] (numeric) = -3.0945352474723825926635287648685 absolute error = 3.0945352474723825926635287648685 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (closed_form) = 0 y[1] (numeric) = -3.0981936399712658189761476782662 absolute error = 3.0981936399712658189761476782662 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5315.5MB, alloc=52.3MB, time=59.49 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (closed_form) = 0 y[1] (numeric) = -3.1018114848092813554042747979785 absolute error = 3.1018114848092813554042747979785 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=5359.6MB, alloc=52.3MB, time=59.99 x[1] = 2.42 y[1] (closed_form) = 0 y[1] (numeric) = -3.1053889385993147827358769772238 absolute error = 3.1053889385993147827358769772238 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (closed_form) = 0 y[1] (numeric) = -3.1089261559228900562996753616564 absolute error = 3.1089261559228900562996753616564 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5403.7MB, alloc=52.3MB, time=60.50 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (closed_form) = 0 y[1] (numeric) = -3.1124232893574335648942580296265 absolute error = 3.1124232893574335648942580296265 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (closed_form) = 0 y[1] (numeric) = -3.115880489503025772075000522549 absolute error = 3.115880489503025772075000522549 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5447.9MB, alloc=52.3MB, time=60.99 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (closed_form) = 0 y[1] (numeric) = -3.1192979050086515545475868628314 absolute error = 3.1192979050086515545475868628314 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (closed_form) = 0 y[1] (numeric) = -3.1226756825979600670917358780492 absolute error = 3.1226756825979600670917358780492 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5492.0MB, alloc=52.3MB, time=61.48 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (closed_form) = 0 y[1] (numeric) = -3.1260139670945446864151663890763 absolute error = 3.1260139670945446864151663890763 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (closed_form) = 0 y[1] (numeric) = -3.1293129014467533173443356853304 absolute error = 3.1293129014467533173443356853304 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5536.1MB, alloc=52.3MB, time=61.97 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = 0 y[1] (numeric) = -3.1325726267520390835333426586461 absolute error = 3.1325726267520390835333426586461 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (closed_form) = 0 y[1] (numeric) = -3.1357932822808611711633221966663 absolute error = 3.1357932822808611711633221966663 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5580.2MB, alloc=52.3MB, time=62.46 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (closed_form) = 0 y[1] (numeric) = -3.1389750055001453476684581114618 absolute error = 3.1389750055001453476684581114618 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (closed_form) = 0 y[1] (numeric) = -3.1421179320963134381269029016005 absolute error = 3.1421179320963134381269029016005 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5624.3MB, alloc=52.3MB, time=62.96 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (closed_form) = 0 y[1] (numeric) = -3.145222195997890809369274729699 absolute error = 3.145222195997890809369274729699 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (closed_form) = 0 y[1] (numeric) = -3.1482879293977006858659043357138 absolute error = 3.1482879293977006858659043357138 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5668.3MB, alloc=52.3MB, time=63.45 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (closed_form) = 0 y[1] (numeric) = -3.1513152627746539018462514612324 absolute error = 3.1513152627746539018462514612324 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (closed_form) = 0 y[1] (numeric) = -3.1543043249151424806769509361196 absolute error = 3.1543043249151424806769509361196 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5712.4MB, alloc=52.3MB, time=63.94 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (closed_form) = 0 y[1] (numeric) = -3.1572552429340452250829695694871 absolute error = 3.1572552429340452250829695694871 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (closed_form) = 0 y[1] (numeric) = -3.1601681422953533001504052189261 absolute error = 3.1601681422953533001504052189261 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5756.5MB, alloc=52.3MB, time=64.43 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (closed_form) = 0 y[1] (numeric) = -3.1630431468324235950171860369235 absolute error = 3.1630431468324235950171860369235 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (closed_form) = 0 y[1] (numeric) = -3.1658803787678674585633236036235 absolute error = 3.1658803787678674585633236036235 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5800.6MB, alloc=52.3MB, time=64.93 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (closed_form) = 0 y[1] (numeric) = -3.1686799587330822190855344261574 absolute error = 3.1686799587330822190855344261574 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=5844.7MB, alloc=52.3MB, time=65.42 x[1] = 2.63 y[1] (closed_form) = 0 y[1] (numeric) = -3.1714420057874327177179371718208 absolute error = 3.1714420057874327177179371718208 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (closed_form) = 0 y[1] (numeric) = -3.1741666374370899100827735395362 absolute error = 3.1741666374370899100827735395362 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5888.8MB, alloc=52.3MB, time=65.91 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (closed_form) = 0 y[1] (numeric) = -3.1768539696535334201697394478588 absolute error = 3.1768539696535334201697394478588 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (closed_form) = 0 y[1] (numeric) = -3.1795041168917247646018312067651 absolute error = 3.1795041168917247646018312067651 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5932.9MB, alloc=52.3MB, time=66.40 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (closed_form) = 0 y[1] (numeric) = -3.1821171921079578041069236316181 absolute error = 3.1821171921079578041069236316181 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (closed_form) = 0 y[1] (numeric) = -3.1846933067773928220397645699027 absolute error = 3.1846933067773928220397645699027 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=5976.9MB, alloc=52.3MB, time=66.89 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (closed_form) = 0 y[1] (numeric) = -3.1872325709112804770555191729327 absolute error = 3.1872325709112804770555191729327 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (closed_form) = 0 y[1] (numeric) = -3.1897350930738817283947454891519 absolute error = 3.1897350930738817283947454891519 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6021.1MB, alloc=52.3MB, time=67.38 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (closed_form) = 0 y[1] (numeric) = -3.1922009803990896875763742148151 absolute error = 3.1922009803990896875763742148151 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (closed_form) = 0 y[1] (numeric) = -3.1946303386067592094897093284312 absolute error = 3.1946303386067592094897093284312 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6065.2MB, alloc=52.3MB, time=67.87 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (closed_form) = 0 y[1] (numeric) = -3.1970232720187498988124852468086 absolute error = 3.1970232720187498988124852468086 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (closed_form) = 0 y[1] (numeric) = -3.1993798835746880742472981475599 absolute error = 3.1993798835746880742472981475599 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6109.2MB, alloc=52.3MB, time=68.37 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (closed_form) = 0 y[1] (numeric) = -3.2017002748474531031546867380705 absolute error = 3.2017002748474531031546867380705 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (closed_form) = 0 y[1] (numeric) = -3.2039845460583933926627723851689 absolute error = 3.2039845460583933926627723851689 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6153.3MB, alloc=52.3MB, time=68.86 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (closed_form) = 0 y[1] (numeric) = -3.2062327960922772001491401103127 absolute error = 3.2062327960922772001491401103127 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (closed_form) = 0 y[1] (numeric) = -3.2084451225119833060223439314258 absolute error = 3.2084451225119833060223439314258 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6197.4MB, alloc=52.3MB, time=69.35 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (closed_form) = 0 y[1] (numeric) = -3.2106216215729364748830591010282 absolute error = 3.2106216215729364748830591010282 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (closed_form) = 0 y[1] (numeric) = -3.2127623882372925173265844494422 absolute error = 3.2127623882372925173265844494422 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6241.6MB, alloc=52.3MB, time=69.84 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (closed_form) = 0 y[1] (numeric) = -3.2148675161878776537702116078276 absolute error = 3.2148675161878776537702116078276 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (closed_form) = 0 y[1] (numeric) = -3.2169370978418867736648958386568 absolute error = 3.2169370978418867736648958386568 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6285.7MB, alloc=52.3MB, time=70.34 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (closed_form) = 0 y[1] (numeric) = -3.2189712243643450781974346697023 absolute error = 3.2189712243643450781974346697023 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=6329.7MB, alloc=52.3MB, time=70.83 x[1] = 2.84 y[1] (closed_form) = 0 y[1] (numeric) = -3.220969985681337492026413739094 absolute error = 3.220969985681337492026413739094 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (closed_form) = 0 y[1] (numeric) = -3.2229334704930101296445267890965 absolute error = 3.2229334704930101296445267890965 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6373.8MB, alloc=52.3MB, time=71.32 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (closed_form) = 0 y[1] (numeric) = -3.2248617662863480045460244094564 absolute error = 3.2248617662863480045460244094564 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (closed_form) = 0 y[1] (numeric) = -3.2267549593477330744279053616543 absolute error = 3.2267549593477330744279053616543 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6417.8MB, alloc=52.3MB, time=71.81 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (closed_form) = 0 y[1] (numeric) = -3.2286131347752866230962678934034 absolute error = 3.2286131347752866230962678934034 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (closed_form) = 0 y[1] (numeric) = -3.2304363764909998895164594384175 absolute error = 3.2304363764909998895164594384175 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6461.9MB, alloc=52.3MB, time=72.30 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (closed_form) = 0 y[1] (numeric) = -3.2322247672526567664709368395508 absolute error = 3.2322247672526567664709368395508 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (closed_form) = 0 y[1] (numeric) = -3.2339783886655523055077983321573 absolute error = 3.2339783886655523055077983321573 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6506.0MB, alloc=52.3MB, time=72.79 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (closed_form) = 0 y[1] (numeric) = -3.2356973211940106812135106139342 absolute error = 3.2356973211940106812135106139342 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (closed_form) = 0 y[1] (numeric) = -3.2373816441727061862651125810739 absolute error = 3.2373816441727061862651125810739 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6550.2MB, alloc=52.3MB, time=73.29 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (closed_form) = 0 y[1] (numeric) = -3.2390314358177907491516935455841 absolute error = 3.2390314358177907491516935455841 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (closed_form) = 0 y[1] (numeric) = -3.2406467732378313888455940296946 absolute error = 3.2406467732378313888455940296946 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6594.3MB, alloc=52.3MB, time=73.78 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (closed_form) = 0 y[1] (numeric) = -3.2422277324445609449956898728895 absolute error = 3.2422277324445609449956898728895 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (closed_form) = 0 y[1] (numeric) = -3.2437743883634453483551162471957 absolute error = 3.2437743883634453483551162471957 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6638.4MB, alloc=52.3MB, time=74.27 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (closed_form) = 0 y[1] (numeric) = -3.2452868148440706240923231782778 absolute error = 3.2452868148440706240923231782778 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (closed_form) = 0 y[1] (numeric) = -3.2467650846703527503174639245414 absolute error = 3.2467650846703527503174639245414 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6682.5MB, alloc=52.3MB, time=74.76 TOP MAIN SOLVE Loop x[1] = 3 y[1] (closed_form) = 0 y[1] (numeric) = -3.2482092695705734255373640400991 absolute error = 3.2482092695705734255373640400991 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (closed_form) = 0 y[1] (numeric) = -3.2496194402272447317847390822555 absolute error = 3.2496194402272447317847390822555 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6726.6MB, alloc=52.3MB, time=75.25 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (closed_form) = 0 y[1] (numeric) = -3.2509956662868056148053851359331 absolute error = 3.2509956662868056148053851359331 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (closed_form) = 0 y[1] (numeric) = -3.2523380163691530388865988065146 absolute error = 3.2523380163691530388865988065146 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6770.6MB, alloc=52.3MB, time=75.74 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (closed_form) = 0 y[1] (numeric) = -3.2536465580770106116282640767192 absolute error = 3.2536465580770106116282640767192 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=6814.7MB, alloc=52.3MB, time=76.23 x[1] = 3.05 y[1] (closed_form) = 0 y[1] (numeric) = -3.2549213580051374131533319345492 absolute error = 3.2549213580051374131533319345492 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (closed_form) = 0 y[1] (numeric) = -3.2561624817493797048865192605413 absolute error = 3.2561624817493797048865192605413 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6858.7MB, alloc=52.3MB, time=76.72 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (closed_form) = 0 y[1] (numeric) = -3.2573699939155681350598740485777 absolute error = 3.2573699939155681350598740485777 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (closed_form) = 0 y[1] (numeric) = -3.2585439581282630014934665020118 absolute error = 3.2585439581282630014934665020118 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6902.9MB, alloc=52.3MB, time=77.22 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (closed_form) = 0 y[1] (numeric) = -3.2596844370393500769120674423546 absolute error = 3.2596844370393500769120674423546 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (closed_form) = 0 y[1] (numeric) = -3.2607914923364894480585531004585 absolute error = 3.2607914923364894480585531004585 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6947.0MB, alloc=52.3MB, time=77.70 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (closed_form) = 0 y[1] (numeric) = -3.2618651847514197671172682064436 absolute error = 3.2618651847514197671172682064436 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (closed_form) = 0 y[1] (numeric) = -3.262905574068120262432045664074 absolute error = 3.262905574068120262432045664074 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=6991.0MB, alloc=52.3MB, time=78.20 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (closed_form) = 0 y[1] (numeric) = -3.2639127191308328051613650094324 absolute error = 3.2639127191308328051613650094324 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (closed_form) = 0 y[1] (numeric) = -3.2648866778519462793255310914586 absolute error = 3.2648866778519462793255310914586 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7035.2MB, alloc=52.3MB, time=78.68 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (closed_form) = 0 y[1] (numeric) = -3.2658275072197454546369896769965 absolute error = 3.2658275072197454546369896769965 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (closed_form) = 0 y[1] (numeric) = -3.2667352633060265145350818510363 absolute error = 3.2667352633060265145350818510363 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7079.2MB, alloc=52.3MB, time=79.18 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (closed_form) = 0 y[1] (numeric) = -3.2676100012735813459416524866331 absolute error = 3.2676100012735813459416524866331 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (closed_form) = 0 y[1] (numeric) = -3.2684517753835526523857847731846 absolute error = 3.2684517753835526523857847731846 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7123.2MB, alloc=52.3MB, time=79.66 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (closed_form) = 0 y[1] (numeric) = -3.2692606390026619082871578790266 absolute error = 3.2692606390026619082871578790266 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (closed_form) = 0 y[1] (numeric) = -3.2700366446103121293115275069956 absolute error = 3.2700366446103121293115275069956 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7167.2MB, alloc=52.3MB, time=80.15 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (closed_form) = 0 y[1] (numeric) = -3.2707798438055673917927778240023 absolute error = 3.2707798438055673917927778240023 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (closed_form) = 0 y[1] (numeric) = -3.2714902873140109932287915938152 absolute error = 3.2714902873140109932287915938152 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7211.3MB, alloc=52.3MB, time=80.64 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (closed_form) = 0 y[1] (numeric) = -3.2721680249944841057786487891566 absolute error = 3.2721680249944841057786487891566 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=7255.3MB, alloc=52.3MB, time=81.13 x[1] = 3.24 y[1] (closed_form) = 0 y[1] (numeric) = -3.2728131058457067354926974048519 absolute error = 3.2728131058457067354926974048519 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (closed_form) = 0 y[1] (numeric) = -3.27342557801278276167181627041 absolute error = 3.27342557801278276167181627041 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7299.3MB, alloc=52.3MB, time=81.62 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (closed_form) = 0 y[1] (numeric) = -3.2740054887935907932553277749787 absolute error = 3.2740054887935907932553277749787 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (closed_form) = 0 y[1] (numeric) = -3.2745528846450625424567645039243 absolute error = 3.2745528846450625424567645039243 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7343.4MB, alloc=52.3MB, time=82.11 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (closed_form) = 0 y[1] (numeric) = -3.2750678111893503799819007409649 absolute error = 3.2750678111893503799819007409649 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (closed_form) = 0 y[1] (numeric) = -3.2755503132198857010535685670335 absolute error = 3.2755503132198857010535685670335 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7387.5MB, alloc=52.3MB, time=82.60 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (closed_form) = 0 y[1] (numeric) = -3.2760004347073296971127996278011 absolute error = 3.2760004347073296971127996278011 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (closed_form) = 0 y[1] (numeric) = -3.2764182188054180944463304145708 absolute error = 3.2764182188054180944463304145708 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7431.6MB, alloc=52.3MB, time=83.09 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (closed_form) = 0 y[1] (numeric) = -3.2768037078567013880875790340325 absolute error = 3.2768037078567013880875790340325 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (closed_form) = 0 y[1] (numeric) = -3.277156943398182067133461412464 absolute error = 3.277156943398182067133461412464 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7475.7MB, alloc=52.3MB, time=83.58 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (closed_form) = 0 y[1] (numeric) = -3.2774779661668502960949837711242 absolute error = 3.2774779661668502960949837711242 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (closed_form) = 0 y[1] (numeric) = -3.2777668161051194860380322766823 absolute error = 3.2777668161051194860380322766823 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7519.7MB, alloc=52.3MB, time=84.07 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (closed_form) = 0 y[1] (numeric) = -3.2780235323661631590552585228526 absolute error = 3.2780235323661631590552585228526 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (closed_form) = 0 y[1] (numeric) = -3.2782481533191544800239672722212 absolute error = 3.2782481533191544800239672722212 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7563.7MB, alloc=52.3MB, time=84.56 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (closed_form) = 0 y[1] (numeric) = -3.2784407165544098006324308861875 absolute error = 3.2784407165544098006324308861875 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (closed_form) = 0 y[1] (numeric) = -3.2786012588884375322824936722173 absolute error = 3.2786012588884375322824936722173 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7607.8MB, alloc=52.3MB, time=85.05 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (closed_form) = 0 y[1] (numeric) = -3.2787298163688936366845168679254 absolute error = 3.2787298163688936366845168679254 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (closed_form) = 0 y[1] (numeric) = -3.2788264242794449957368837220098 absolute error = 3.2788264242794449957368837220098 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7651.8MB, alloc=52.3MB, time=85.53 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (closed_form) = 0 y[1] (numeric) = -3.2788911171445418956120591312256 absolute error = 3.2788911171445418956120591312256 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=7695.7MB, alloc=52.3MB, time=86.02 x[1] = 3.43 y[1] (closed_form) = 0 y[1] (numeric) = -3.2789239287341008338405851737072 absolute error = 3.2789239287341008338405851737072 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (closed_form) = 0 y[1] (numeric) = -3.2789248920680988325797674282475 absolute error = 3.2789248920680988325797674282475 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7739.7MB, alloc=52.3MB, time=86.51 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (closed_form) = 0 y[1] (numeric) = -3.2788940394210804161619000510958 absolute error = 3.2788940394210804161619000510958 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (closed_form) = 0 y[1] (numeric) = -3.2788314023265783864247704089058 absolute error = 3.2788314023265783864247704089058 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7783.7MB, alloc=52.3MB, time=87.00 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (closed_form) = 0 y[1] (numeric) = -3.2787370115814495052222938106994 absolute error = 3.2787370115814495052222938106994 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (closed_form) = 0 y[1] (numeric) = -3.2786108972501261698831996164368 absolute error = 3.2786108972501261698831996164368 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7827.7MB, alloc=52.3MB, time=87.49 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (closed_form) = 0 y[1] (numeric) = -3.2784530886687851442187829597768 absolute error = 3.2784530886687851442187829597768 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (closed_form) = 0 y[1] (numeric) = -3.2782636144494343849652204716403 absolute error = 3.2782636144494343849652204716403 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7871.8MB, alloc=52.3MB, time=87.98 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (closed_form) = 0 y[1] (numeric) = -3.278042502483918981270491286473 absolute error = 3.278042502483918981270491286473 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (closed_form) = 0 y[1] (numeric) = -3.2777897799478472029895035561185 absolute error = 3.2777897799478472029895035561185 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7915.8MB, alloc=52.3MB, time=88.46 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (closed_form) = 0 y[1] (numeric) = -3.2775054733044376321228401602546 absolute error = 3.2775054733044376321228401602546 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (closed_form) = 0 y[1] (numeric) = -3.2771896083082883307141166270345 absolute error = 3.2771896083082883307141166270345 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=7959.8MB, alloc=52.3MB, time=88.95 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (closed_form) = 0 y[1] (numeric) = -3.2768422100090689778980656214409 absolute error = 3.2768422100090689778980656214409 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (closed_form) = 0 y[1] (numeric) = -3.2764633027551368885561589007993 absolute error = 3.2764633027551368885561589007993 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8003.8MB, alloc=52.3MB, time=89.44 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (closed_form) = 0 y[1] (numeric) = -3.2760529101970778061791320182909 absolute error = 3.2760529101970778061791320182909 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (closed_form) = 0 y[1] (numeric) = -3.2756110552911723430467140544522 absolute error = 3.2756110552911723430467140544522 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8047.9MB, alloc=52.3MB, time=89.93 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (closed_form) = 0 y[1] (numeric) = -3.2751377603027889217049440874913 absolute error = 3.2751377603027889217049440874913 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (closed_form) = 0 y[1] (numeric) = -3.2746330468097040529416659410267 absolute error = 3.2746330468097040529416659410267 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8092.0MB, alloc=52.3MB, time=90.42 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (closed_form) = 0 y[1] (numeric) = -3.274096935705350767022342414002 absolute error = 3.274096935705350767022342414002 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=8136.0MB, alloc=52.3MB, time=90.91 x[1] = 3.62 y[1] (closed_form) = 0 y[1] (numeric) = -3.2735294472019959968426441470289 absolute error = 3.2735294472019959968426441470289 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (closed_form) = 0 y[1] (numeric) = -3.2729306008338476938729796835148 absolute error = 3.2729306008338476938729796835148 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8180.1MB, alloc=52.3MB, time=91.40 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (closed_form) = 0 y[1] (numeric) = -3.2723004154600924403050779517852 absolute error = 3.2723004154600924403050779517852 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (closed_form) = 0 y[1] (numeric) = -3.2716389092678643036539448672246 absolute error = 3.2716389092678643036539448672246 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8224.2MB, alloc=52.3MB, time=91.90 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (closed_form) = 0 y[1] (numeric) = -3.2709460997751456632122155749594 absolute error = 3.2709460997751456632122155749594 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (closed_form) = 0 y[1] (numeric) = -3.2702220038336007211905220110143 absolute error = 3.2702220038336007211905220110143 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8268.3MB, alloc=52.3MB, time=92.38 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (closed_form) = 0 y[1] (numeric) = -3.2694666376313423950995809895334 absolute error = 3.2694666376313423950995809895334 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (closed_form) = 0 y[1] (numeric) = -3.2686800166956332719300447759963 absolute error = 3.2686800166956332719300447759963 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8312.2MB, alloc=52.3MB, time=92.88 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (closed_form) = 0 y[1] (numeric) = -3.2678621558955212889576776645128 absolute error = 3.2678621558955212889576776645128 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (closed_form) = 0 y[1] (numeric) = -3.2670130694444107905372268248006 absolute error = 3.2670130694444107905372268248006 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8356.3MB, alloc=52.3MB, time=93.37 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (closed_form) = 0 y[1] (numeric) = -3.2661327709025695950417020164455 absolute error = 3.2661327709025695950417020164455 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (closed_form) = 0 y[1] (numeric) = -3.2652212731795726911480804416229 absolute error = 3.2652212731795726911480804416229 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8400.3MB, alloc=52.3MB, time=93.86 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (closed_form) = 0 y[1] (numeric) = -3.2642785885366831679592746263743 absolute error = 3.2642785885366831679592746263743 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (closed_form) = 0 y[1] (numeric) = -3.2633047285891709689792538498131 absolute error = 3.2633047285891709689792538498131 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8444.4MB, alloc=52.3MB, time=94.35 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (closed_form) = 0 y[1] (numeric) = -3.2622997043085700457173465468533 absolute error = 3.2622997043085700457173465468533 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (closed_form) = 0 y[1] (numeric) = -3.2612635260248744726829636229379 absolute error = 3.2612635260248744726829636229379 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8488.5MB, alloc=52.3MB, time=94.84 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (closed_form) = 0 y[1] (numeric) = -3.2601962034286740717373961108558 absolute error = 3.2601962034286740717373961108558 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (closed_form) = 0 y[1] (numeric) = -3.2590977455732300801892105770288 absolute error = 3.2590977455732300801892105770288 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8532.5MB, alloc=52.3MB, time=95.33 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (closed_form) = 0 y[1] (numeric) = -3.2579681608764913836484739919435 absolute error = 3.2579681608764913836484739919435 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (closed_form) = 0 y[1] (numeric) = -3.2568074571230518214870909069156 absolute error = 3.2568074571230518214870909069156 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8576.6MB, alloc=52.3MB, time=95.82 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (closed_form) = 0 y[1] (numeric) = -3.2556156414660490597825532744328 absolute error = 3.2556156414660490597825532744328 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=8620.6MB, alloc=52.3MB, time=96.31 x[1] = 3.83 y[1] (closed_form) = 0 y[1] (numeric) = -3.2543927204290055138451262268399 absolute error = 3.2543927204290055138451262268399 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (closed_form) = 0 y[1] (numeric) = -3.2531386999076117898387728770342 absolute error = 3.2531386999076117898387728770342 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8664.7MB, alloc=52.3MB, time=96.80 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (closed_form) = 0 y[1] (numeric) = -3.2518535851714531025989178872746 absolute error = 3.2518535851714531025989178872746 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (closed_form) = 0 y[1] (numeric) = -3.250537380865679114520528992591 absolute error = 3.250537380865679114520528992591 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8708.7MB, alloc=52.3MB, time=97.30 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (closed_form) = 0 y[1] (numeric) = -3.2491900910126176283331262259616 absolute error = 3.2491900910126176283331262259616 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (closed_form) = 0 y[1] (numeric) = -3.2478117190133325546904781333961 absolute error = 3.2478117190133325546904781333961 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8752.8MB, alloc=52.3MB, time=97.78 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (closed_form) = 0 y[1] (numeric) = -3.2464022676491265637772771867406 absolute error = 3.2464022676491265637772771867406 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (closed_form) = 0 y[1] (numeric) = -3.2449617390829888185684609564321 absolute error = 3.2449617390829888185684609564321 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8796.9MB, alloc=52.3MB, time=98.28 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (closed_form) = 0 y[1] (numeric) = -3.2434901348609881759646103043509 absolute error = 3.2434901348609881759646103043509 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (closed_form) = 0 y[1] (numeric) = -3.2419874559136122307646479281982 absolute error = 3.2419874559136122307646479281982 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8841.0MB, alloc=52.3MB, time=98.77 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (closed_form) = 0 y[1] (numeric) = -3.2404537025570525663206025237618 absolute error = 3.2404537025570525663206025237618 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (closed_form) = 0 y[1] (numeric) = -3.2388888744944365647443009885237 absolute error = 3.2388888744944365647443009885237 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8885.0MB, alloc=52.3MB, time=99.26 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (closed_form) = 0 y[1] (numeric) = -3.237292970817006118698389170138 absolute error = 3.237292970817006118698389170138 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (closed_form) = 0 y[1] (numeric) = -3.2356659900052435761000242476461 absolute error = 3.2356659900052435761000242476461 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8929.1MB, alloc=52.3MB, time=99.75 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (closed_form) = 0 y[1] (numeric) = -3.2340079299299452384909679835583 absolute error = 3.2340079299299452384909679835583 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (closed_form) = 0 y[1] (numeric) = -3.2323187878532427233787520031253 absolute error = 3.2323187878532427233787520031253 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=8973.3MB, alloc=52.3MB, time=100.24 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (closed_form) = 0 y[1] (numeric) = -3.2305985604295724905262670030454 absolute error = 3.2305985604295724905262670030454 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4 y[1] (closed_form) = 0 y[1] (numeric) = -3.228847243706593821957799056768 absolute error = 3.228847243706593821957799056768 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9017.3MB, alloc=52.3MB, time=100.73 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (closed_form) = 0 y[1] (numeric) = -3.2270648331260555353545161174163 absolute error = 3.2270648331260555353545161174163 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (closed_form) = 0 y[1] (numeric) = -3.2252513235246117005280789105629 memory used=9061.4MB, alloc=52.3MB, time=101.27 absolute error = 3.2252513235246117005280789105629 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (closed_form) = 0 y[1] (numeric) = -3.2234067091345866187838574141858 absolute error = 3.2234067091345866187838574141858 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=9105.4MB, alloc=52.3MB, time=101.76 x[1] = 4.04 y[1] (closed_form) = 0 y[1] (numeric) = -3.2215309835846893152116820454823 absolute error = 3.2215309835846893152116820454823 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (closed_form) = 0 y[1] (numeric) = -3.2196241399006777842687107893003 absolute error = 3.2196241399006777842687107893003 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9149.5MB, alloc=52.3MB, time=102.25 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (closed_form) = 0 y[1] (numeric) = -3.2176861705059732194424694291774 absolute error = 3.2176861705059732194424694291774 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (closed_form) = 0 y[1] (numeric) = -3.2157170672222244482990958551702 absolute error = 3.2157170672222244482990958551702 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9193.5MB, alloc=52.3MB, time=102.74 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (closed_form) = 0 y[1] (numeric) = -3.2137168212698227848290178126438 absolute error = 3.2137168212698227848290178126438 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (closed_form) = 0 y[1] (numeric) = -3.2116854232683675016964939241826 absolute error = 3.2116854232683675016964939241826 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9237.6MB, alloc=52.3MB, time=103.23 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (closed_form) = 0 y[1] (numeric) = -3.2096228632370821157774769120228 absolute error = 3.2096228632370821157774769120228 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (closed_form) = 0 y[1] (numeric) = -3.2075291305951816712289895424899 absolute error = 3.2075291305951816712289895424899 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9281.7MB, alloc=52.3MB, time=103.72 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (closed_form) = 0 y[1] (numeric) = -3.2054042141621911952695574118317 absolute error = 3.2054042141621911952695574118317 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (closed_form) = 0 y[1] (numeric) = -3.2032481021582154928611817788374 absolute error = 3.2032481021582154928611817788374 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9325.8MB, alloc=52.3MB, time=104.21 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (closed_form) = 0 y[1] (numeric) = -3.2010607822041604375658660672751 absolute error = 3.2010607822041604375658660672751 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (closed_form) = 0 y[1] (numeric) = -3.1988422413219059070008780256024 absolute error = 3.1988422413219059070008780256024 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9369.8MB, alloc=52.3MB, time=104.70 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (closed_form) = 0 y[1] (numeric) = -3.1965924659344305025338216732178 absolute error = 3.1965924659344305025338216732178 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (closed_form) = 0 y[1] (numeric) = -3.1943114418658881841383326016689 absolute error = 3.1943114418658881841383326016689 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9413.9MB, alloc=52.3MB, time=105.20 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (closed_form) = 0 y[1] (numeric) = -3.1919991543416369426709566479069 absolute error = 3.1919991543416369426709566479069 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (closed_form) = 0 y[1] (numeric) = -3.1896555879882196232267198500443 absolute error = 3.1896555879882196232267198500443 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9458.0MB, alloc=52.3MB, time=105.69 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (closed_form) = 0 y[1] (numeric) = -3.1872807268332970046822746497297 absolute error = 3.1872807268332970046822746497297 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (closed_form) = 0 y[1] (numeric) = -3.1848745543055332320385730983634 absolute error = 3.1848745543055332320385730983634 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9502.0MB, alloc=52.3MB, time=106.18 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (closed_form) = 0 y[1] (numeric) = -3.1824370532344336897270624072749 absolute error = 3.1824370532344336897270624072749 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (closed_form) = 0 y[1] (numeric) = -3.1799682058501353956417407075438 absolute error = 3.1799682058501353956417407075438 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9546.1MB, alloc=52.3MB, time=106.67 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (closed_form) = 0 y[1] (numeric) = -3.1774679937831499873013982624236 absolute error = 3.1774679937831499873013982624236 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=9590.2MB, alloc=52.3MB, time=107.16 x[1] = 4.25 y[1] (closed_form) = 0 y[1] (numeric) = -3.174936398064059363229374945055 absolute error = 3.174936398064059363229374945055 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (closed_form) = 0 y[1] (numeric) = -3.1723733991231640343595870245361 absolute error = 3.1723733991231640343595870245361 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9634.3MB, alloc=52.3MB, time=107.65 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (closed_form) = 0 y[1] (numeric) = -3.1697789767900842320348375058537 absolute error = 3.1697789767900842320348375058537 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (closed_form) = 0 y[1] (numeric) = -3.1671531102933138109539693324793 absolute error = 3.1671531102933138109539693324793 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9678.4MB, alloc=52.3MB, time=108.14 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (closed_form) = 0 y[1] (numeric) = -3.1644957782597269772457159030359 absolute error = 3.1644957782597269772457159030359 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (closed_form) = 0 y[1] (numeric) = -3.1618069587140378636966348924304 absolute error = 3.1618069587140378636966348924304 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9722.6MB, alloc=52.3MB, time=108.64 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (closed_form) = 0 y[1] (numeric) = -3.1590866290782129660357845041615 absolute error = 3.1590866290782129660357845041615 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (closed_form) = 0 y[1] (numeric) = -3.1563347661708364460773388992167 absolute error = 3.1563347661708364460773388992167 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9766.7MB, alloc=52.3MB, time=109.13 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (closed_form) = 0 y[1] (numeric) = -3.1535513462064282994416810321006 absolute error = 3.1535513462064282994416810321006 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (closed_form) = 0 y[1] (numeric) = -3.1507363447947153775132111872437 absolute error = 3.1507363447947153775132111872437 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9810.8MB, alloc=52.3MB, time=109.62 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (closed_form) = 0 y[1] (numeric) = -3.1478897369398552452467370287615 absolute error = 3.1478897369398552452467370287615 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (closed_form) = 0 y[1] (numeric) = -3.1450114970396128484014478538491 absolute error = 3.1450114970396128484014478538491 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9855.0MB, alloc=52.3MB, time=110.12 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (closed_form) = 0 y[1] (numeric) = -3.1421015988844899557597157609239 absolute error = 3.1421015988844899557597157609239 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (closed_form) = 0 y[1] (numeric) = -3.1391600156568073338749141537344 absolute error = 3.1391600156568073338749141537344 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9899.0MB, alloc=52.3MB, time=110.61 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (closed_form) = 0 y[1] (numeric) = -3.1361867199297396038857135918249 absolute error = 3.1361867199297396038857135918249 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (closed_form) = 0 y[1] (numeric) = -3.1331816836663027219315291927417 absolute error = 3.1331816836663027219315291927417 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9943.1MB, alloc=52.3MB, time=111.10 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (closed_form) = 0 y[1] (numeric) = -3.1301448782182940167025827572474 absolute error = 3.1301448782182940167025827572474 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (closed_form) = 0 y[1] (numeric) = -3.1270762743251847096560430373161 absolute error = 3.1270762743251847096560430373161 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=9987.2MB, alloc=52.3MB, time=111.59 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (closed_form) = 0 y[1] (numeric) = -3.1239758421129648354245608716475 absolute error = 3.1239758421129648354245608716475 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (closed_form) = 0 y[1] (numeric) = -3.1208435510929404719328682319107 absolute error = 3.1208435510929404719328682319107 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10031.4MB, alloc=52.3MB, time=112.08 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (closed_form) = 0 y[1] (numeric) = -3.1176793701604831817196106216856 absolute error = 3.1176793701604831817196106216856 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=10075.4MB, alloc=52.3MB, time=112.58 x[1] = 4.46 y[1] (closed_form) = 0 y[1] (numeric) = -3.1144832675937315579328818565903 absolute error = 3.1144832675937315579328818565903 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (closed_form) = 0 y[1] (numeric) = -3.1112552110522447604266811114831 absolute error = 3.1112552110522447604266811114831 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10119.5MB, alloc=52.3MB, time=113.07 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (closed_form) = 0 y[1] (numeric) = -3.107995167575607919329366245599 absolute error = 3.107995167575607919329366245599 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (closed_form) = 0 y[1] (numeric) = -3.1047031035819892753817856598671 absolute error = 3.1047031035819892753817856598671 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10163.7MB, alloc=52.3MB, time=113.56 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (closed_form) = 0 y[1] (numeric) = -3.1013789848666489182497819496518 absolute error = 3.1013789848666489182497819496518 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (closed_form) = 0 y[1] (numeric) = -3.0980227766003989759008197777749 absolute error = 3.0980227766003989759008197777749 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10207.9MB, alloc=52.3MB, time=114.05 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (closed_form) = 0 y[1] (numeric) = -3.0946344433280150999952387774338 absolute error = 3.0946344433280150999952387774338 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (closed_form) = 0 y[1] (numeric) = -3.0912139489665990840767056002084 absolute error = 3.0912139489665990840767056002084 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10252.1MB, alloc=52.3MB, time=114.54 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (closed_form) = 0 y[1] (numeric) = -3.0877612568038924431514667181364 absolute error = 3.0877612568038924431514667181364 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (closed_form) = 0 y[1] (numeric) = -3.0842763294965407750196070489383 absolute error = 3.0842763294965407750196070489383 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10296.2MB, alloc=52.3MB, time=115.04 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (closed_form) = 0 y[1] (numeric) = -3.0807591290683087154613121274867 absolute error = 3.0807591290683087154613121274867 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (closed_form) = 0 y[1] (numeric) = -3.0772096169082452910847170073329 absolute error = 3.0772096169082452910847170073329 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10340.3MB, alloc=52.3MB, time=115.53 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (closed_form) = 0 y[1] (numeric) = -3.0736277537687994653068962737005 absolute error = 3.0736277537687994653068962737005 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (closed_form) = 0 y[1] (numeric) = -3.0700134997638856645634876591939 absolute error = 3.0700134997638856645634876591939 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10384.4MB, alloc=52.3MB, time=116.02 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (closed_form) = 0 y[1] (numeric) = -3.0663668143668990634229151189157 absolute error = 3.0663668143668990634229151189157 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (closed_form) = 0 y[1] (numeric) = -3.0626876564086803988157402713152 absolute error = 3.0626876564086803988157402713152 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10428.6MB, alloc=52.3MB, time=116.52 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (closed_form) = 0 y[1] (numeric) = -3.0589759840754300750758632694492 absolute error = 3.0589759840754300750758632694492 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (closed_form) = 0 y[1] (numeric) = -3.055231754906571312925638758686 absolute error = 3.055231754906571312925638758686 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10472.7MB, alloc=52.3MB, time=117.02 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (closed_form) = 0 y[1] (numeric) = -3.0514549257925620869189757212909 absolute error = 3.0514549257925620869189757212909 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (closed_form) = 0 y[1] (numeric) = -3.0476454529726555871826395090871 absolute error = 3.0476454529726555871826395090871 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10516.9MB, alloc=52.3MB, time=117.54 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (closed_form) = 0 y[1] (numeric) = -3.0438032920326089325637385875943 absolute error = 3.0438032920326089325637385875943 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (closed_form) = 0 y[1] (numeric) = -3.0399283979023398534982052540397 absolute error = 3.0399283979023398534982052540397 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10561.0MB, alloc=52.3MB, time=118.04 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (closed_form) = 0 y[1] (numeric) = -3.0360207248535310540583949310397 absolute error = 3.0360207248535310540583949310397 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=10605.1MB, alloc=52.3MB, time=118.54 x[1] = 4.69 y[1] (closed_form) = 0 y[1] (numeric) = -3.0320802264971819537151357961425 absolute error = 3.0320802264971819537151357961425 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (closed_form) = 0 y[1] (numeric) = -3.0281068557811075003580386729582 absolute error = 3.0281068557811075003580386729582 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10649.3MB, alloc=52.3MB, time=119.03 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (closed_form) = 0 y[1] (numeric) = -3.0241005649873837370549802619157 absolute error = 3.0241005649873837370549802619157 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (closed_form) = 0 y[1] (numeric) = -3.0200613057297397958947285071881 absolute error = 3.0200613057297397958947285071881 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10693.3MB, alloc=52.3MB, time=119.52 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (closed_form) = 0 y[1] (numeric) = -3.0159890289508959830429871542725 absolute error = 3.0159890289508959830429871542725 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (closed_form) = 0 y[1] (numeric) = -3.0118836849198476098489684961727 absolute error = 3.0118836849198476098489684961727 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10737.4MB, alloc=52.3MB, time=120.02 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (closed_form) = 0 y[1] (numeric) = -3.0077452232290942154642000171282 absolute error = 3.0077452232290942154642000171282 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (closed_form) = 0 y[1] (numeric) = -3.0035735927918138169748418858118 absolute error = 3.0035735927918138169748418858118 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10781.5MB, alloc=52.3MB, time=120.51 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (closed_form) = 0 y[1] (numeric) = -2.9993687418389818135005152008312 absolute error = 2.9993687418389818135005152008312 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (closed_form) = 0 y[1] (numeric) = -2.995130617916434161073658848341 absolute error = 2.995130617916434161073658848341 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10825.6MB, alloc=52.3MB, time=121.01 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (closed_form) = 0 y[1] (numeric) = -2.9908591678818744253808539066946 absolute error = 2.9908591678818744253808539066946 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (closed_form) = 0 y[1] (numeric) = -2.9865543379018243096184503239454 absolute error = 2.9865543379018243096184503239454 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10869.7MB, alloc=52.3MB, time=121.50 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (closed_form) = 0 y[1] (numeric) = -2.9822160734485172447862348347489 absolute error = 2.9822160734485172447862348347489 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (closed_form) = 0 y[1] (numeric) = -2.977844319296734619711786273486 absolute error = 2.977844319296734619711786273486 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10913.8MB, alloc=52.3MB, time=122.00 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (closed_form) = 0 y[1] (numeric) = -2.9734390195205842179615284521104 absolute error = 2.9734390195205842179615284521104 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (closed_form) = 0 y[1] (numeric) = -2.9690001174902204185492234312927 absolute error = 2.9690001174902204185492234312927 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=10958.0MB, alloc=52.3MB, time=122.49 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (closed_form) = 0 y[1] (numeric) = -2.9645275558685057069956176627102 absolute error = 2.9645275558685057069956176627102 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (closed_form) = 0 y[1] (numeric) = -2.9600212766076130328209835064126 absolute error = 2.9600212766076130328209835064126 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=11002.1MB, alloc=52.3MB, time=122.99 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (closed_form) = 0 y[1] (numeric) = -2.9554812209455685389621659713795 absolute error = 2.9554812209455685389621659713795 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (closed_form) = 0 y[1] (numeric) = -2.9509073294027341778941781639098 absolute error = 2.9509073294027341778941781639098 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=11046.3MB, alloc=52.3MB, time=123.48 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (closed_form) = 0 y[1] (numeric) = -2.9462995417782297184000683155124 absolute error = 2.9462995417782297184000683155124 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (closed_form) = 0 y[1] (numeric) = -2.9416577971462936359683347630795 absolute error = 2.9416577971462936359683347630795 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=11090.4MB, alloc=52.3MB, time=123.98 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (closed_form) = 0 y[1] (numeric) = -2.9369820338525823687011685292477 absolute error = 2.9369820338525823687011685292477 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop memory used=11134.6MB, alloc=52.3MB, time=124.47 x[1] = 4.92 y[1] (closed_form) = 0 y[1] (numeric) = -2.9322721895104074093857775156209 absolute error = 2.9322721895104074093857775156209 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (closed_form) = 0 y[1] (numeric) = -2.9275282009969096930114570739461 absolute error = 2.9275282009969096930114570739461 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=11178.8MB, alloc=52.3MB, time=124.96 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (closed_form) = 0 y[1] (numeric) = -2.9227500044491707275033264333754 absolute error = 2.9227500044491707275033264333754 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (closed_form) = 0 y[1] (numeric) = -2.917937535260259903786097241445 absolute error = 2.917937535260259903786097241445 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=11222.8MB, alloc=52.3MB, time=125.45 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (closed_form) = 0 y[1] (numeric) = -2.9130907280752174094841661822506 absolute error = 2.9130907280752174094841661822506 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (closed_form) = 0 y[1] (numeric) = -2.9082095167869721586039520655826 absolute error = 2.9082095167869721586039520655826 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=11267.0MB, alloc=52.3MB, time=125.95 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (closed_form) = 0 y[1] (numeric) = -2.9032938345321941374268878168601 absolute error = 2.9032938345321941374268878168601 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (closed_form) = 0 y[1] (numeric) = -2.8983436136870805545629215093772 absolute error = 2.8983436136870805545629215093772 relative error = -1 % Desired digits = 8 Estimated correct digits = 12 Correct digits = -16 h = 0.001 memory used=11311.2MB, alloc=52.3MB, time=126.44 Finished! diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations = 4900 Total Elapsed Time = 2 Minutes 6 Seconds Elapsed Time(since restart) = 2 Minutes 6 Seconds Time to Timeout = 53 Seconds Percent Done = 100 % > quit memory used=11317.1MB, alloc=52.3MB, time=126.51