|\^/| Maple 12 (IBM INTEL LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
> # Begin Function number 3
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 1
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 1;
> ret;;
> end;
check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret
end proc
> # End Function number 3
> # Begin Function number 4
> est_size_answer := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> 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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y[1]) < min_size) then # if number 1
> min_size := omniabs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> if (min_size < 1.0) then # if number 1
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
min_size := glob_large_float;
if omniabs(array_y[1]) < min_size then
min_size := omniabs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < 1.0 then
min_size := 1.0;
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
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> 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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms;
> max_value3 := 0.0;
> no_terms := glob_max_terms;
> hn_div_ho := 0.5;
> hn_div_ho_2 := 0.25;
> hn_div_ho_3 := 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,"");
> value3 := omniabs(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 (value3 > max_value3) then # if number 1
> max_value3 := value3;
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> fi;# end if 1;
> omniout_float(ALWAYS,"max_value3",32,max_value3,32,"");
> max_value3;
> end;
test_suggested_h := proc()
local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
max_value3 := 0.;
no_terms := glob_max_terms;
hn_div_ho := 0.5;
hn_div_ho_2 := 0.25;
hn_div_ho_3 := 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, "");
value3 := omniabs(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_value3 < value3 then
max_value3 := value3;
omniout_float(ALWAYS, "value3", 32, value3, 32, "")
end if;
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, "");
max_value3
end proc
> # End Function number 5
> # Begin Function number 6
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> 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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1
> ret := true;
> else
> ret := false;
> fi;# end if 1;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then
ret := true
else ret := false
end if;
return ret
end proc
> # End Function number 6
> # Begin Function number 7
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> 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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 1
> if (iter >= 0) then # if number 2
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 3
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 4
> glob_good_digits := -trunc(log10(relerr)) + 2;
> else
> glob_good_digits := Digits;
> fi;# end if 4;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 3;
> if (glob_iter = 1) then # if number 3
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 3;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 2;
> #BOTTOM DISPLAY ALOT
> fi;# end if 1;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if 0.1*10^(-33) < relerr then
glob_good_digits := -trunc(log10(relerr)) + 2
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
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 7
> # Begin Function number 8
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> 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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 2
> fi;# end if 1;
> if ( not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1;
> hnew := sz2;
> ;#END block
> return(hnew);
> #BOTTOM ADJUST FOR POLE
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y_higher[1, 1]) then
tmp := omniabs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2;
return hnew
end proc
> # End Function number 8
> # Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> 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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> 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 := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if (convfloat(percent_done) < convfloat(100.0)) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr(convfloat(glob_total_exp_sec));
> fi;# end if 1;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(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 glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec));
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(convfloat(glob_total_exp_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(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
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> 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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y_higher[1,m]) < glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (omniabs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1;
> n := n - 1;
> od;# end do number 2;
> m := n + cnt;
> if (m <= 10) then # if number 1
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> elif
> (((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-5]) <= (glob_small_float)))) then # if number 2
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> 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)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2;
> #BOTTOM RADII COMPLEX EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 1
> if ( not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if ( not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if ( not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3;
> fi;# end if 2;
> if ( not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if ( not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if ( not found ) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3;
> fi;# end if 2;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if (array_pole[1] > array_poles[1,1]) then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2;
> #BOTTOM WHICH RADIUS EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 2
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 2
> 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 / omniabs(glob_h);
> term := term + 1;
> od;# end do number 2;
> glob_h := h_new;
> fi;# end if 2;
> #BOTTOM ADJUST ALL SERIES
> if (reached_interval()) then # if number 2
> display_pole();
> fi;# end if 2
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y_higher[1, m]) < glob_small_float or
omniabs(array_y_higher[1, m - 1]) < glob_small_float or
omniabs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float
elif glob_large_float <= omniabs(array_y_higher[1, m]) or
glob_large_float <= omniabs(array_y_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y_higher[1, m - 5]) or
omniabs(array_y_higher[1, m]) <= glob_small_float or
omniabs(array_y_higher[1, m - 1]) <= glob_small_float or
omniabs(array_y_higher[1, m - 2]) <= glob_small_float or
omniabs(array_y_higher[1, m - 3]) <= glob_small_float or
omniabs(array_y_higher[1, m - 4]) <= glob_small_float or
omniabs(array_y_higher[1, m - 5]) <= glob_small_float then
rad_c := glob_large_float; ord_no := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(dr1) <= glob_small_float then
rad_c := glob_large_float; ord_no := glob_large_float
else
if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < omniabs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then
h_new := array_pole[1]*glob_ratio_of_radius;
term := 1;
ratio := 1.0;
while term <= glob_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/omniabs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_pole() end if
end proc
> # End Function number 10
> # Begin Function number 11
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> 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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 2
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 2;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 3;
> iii := iii + 1;
> od;# end do number 2
> #BOTTOM GET NORMS
> ;
> fi;# end if 2;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y[iii]) then
array_norms[iii] := omniabs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # End Function number 11
> # Begin Function number 12
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> 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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre cos 1 $eq_no = 1
> array_tmp2[1] := cos(array_x[1]);
> array_tmp2_g[1] := sin(array_x[1]);
> #emit pre div FULL - FULL $eq_no = 1 i = 1
> array_tmp3[1] := (array_tmp1[1] / (array_tmp2[1]));
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := array_tmp1_g[1] * array_x[2] / 1;
> array_tmp1_g[2] := -array_tmp1[1] * array_x[2] / 1;
> #emit pre cos ID_LINEAR iii = 2 $eq_no = 1
> array_tmp2[2] := -array_tmp2_g[1] * array_x[2] / 1;
> array_tmp2_g[2] := array_tmp2[1] * array_x[2] / 1;
> #emit pre div FULL - FULL $eq_no = 1 i = 2
> array_tmp3[2] := ((array_tmp1[2] - ats(2,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := array_tmp1_g[2] * array_x[2] / 2;
> array_tmp1_g[3] := -array_tmp1[2] * array_x[2] / 2;
> #emit pre cos ID_LINEAR iii = 3 $eq_no = 1
> array_tmp2[3] := -array_tmp2_g[2] * array_x[2] / 2;
> array_tmp2_g[3] := array_tmp2[2] * array_x[2] / 2;
> #emit pre div FULL - FULL $eq_no = 1 i = 3
> array_tmp3[3] := ((array_tmp1[3] - ats(3,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp3[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := array_tmp1_g[3] * array_x[2] / 3;
> array_tmp1_g[4] := -array_tmp1[3] * array_x[2] / 3;
> #emit pre cos ID_LINEAR iii = 4 $eq_no = 1
> array_tmp2[4] := -array_tmp2_g[3] * array_x[2] / 3;
> array_tmp2_g[4] := array_tmp2[3] * array_x[2] / 3;
> #emit pre div FULL - FULL $eq_no = 1 i = 4
> array_tmp3[4] := ((array_tmp1[4] - ats(4,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp3[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := array_tmp1_g[4] * array_x[2] / 4;
> array_tmp1_g[5] := -array_tmp1[4] * array_x[2] / 4;
> #emit pre cos ID_LINEAR iii = 5 $eq_no = 1
> array_tmp2[5] := -array_tmp2_g[4] * array_x[2] / 4;
> array_tmp2_g[5] := array_tmp2[4] * array_x[2] / 4;
> #emit pre div FULL - FULL $eq_no = 1 i = 5
> array_tmp3[5] := ((array_tmp1[5] - ats(5,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp3[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sin LINEAR $eq_no = 1
> array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / (kkk - 1);
> array_tmp1_g[kkk] := -array_tmp1[kkk - 1] * array_x[2] / (kkk - 1);
> #emit cos LINEAR $eq_no = 1
> array_tmp2[kkk] := -array_tmp2_g[kkk - 1] * array_x[2] / (kkk - 1);
> array_tmp2_g[kkk] := array_tmp2[kkk - 1] * array_x[2] / (kkk - 1);
> #emit div FULL FULL $eq_no = 1
> array_tmp3[kkk] := ((array_tmp1[kkk] - ats(kkk,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp4[kkk] := array_tmp3[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp4[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 2
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 2
> 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 glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
array_tmp1[1] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := cos(array_x[1]);
array_tmp2_g[1] := sin(array_x[1]);
array_tmp3[1] := array_tmp1[1]/array_tmp2[1];
array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp4[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_tmp1_g[1]*array_x[2];
array_tmp1_g[2] := -array_tmp1[1]*array_x[2];
array_tmp2[2] := -array_tmp2_g[1]*array_x[2];
array_tmp2_g[2] := array_tmp2[1]*array_x[2];
array_tmp3[2] :=
(array_tmp1[2] - ats(2, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[2] := array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := 1/2*array_tmp1_g[2]*array_x[2];
array_tmp1_g[3] := -1/2*array_tmp1[2]*array_x[2];
array_tmp2[3] := -1/2*array_tmp2_g[2]*array_x[2];
array_tmp2_g[3] := 1/2*array_tmp2[2]*array_x[2];
array_tmp3[3] :=
(array_tmp1[3] - ats(3, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[3] := array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp4[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := 1/3*array_tmp1_g[3]*array_x[2];
array_tmp1_g[4] := -1/3*array_tmp1[3]*array_x[2];
array_tmp2[4] := -1/3*array_tmp2_g[3]*array_x[2];
array_tmp2_g[4] := 1/3*array_tmp2[3]*array_x[2];
array_tmp3[4] :=
(array_tmp1[4] - ats(4, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[4] := array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp4[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := 1/4*array_tmp1_g[4]*array_x[2];
array_tmp1_g[5] := -1/4*array_tmp1[4]*array_x[2];
array_tmp2[5] := -1/4*array_tmp2_g[4]*array_x[2];
array_tmp2_g[5] := 1/4*array_tmp2[4]*array_x[2];
array_tmp3[5] :=
(array_tmp1[5] - ats(5, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[5] := array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp4[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp1_g[kkk] := -array_tmp1[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp2[kkk] := -array_tmp2_g[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp2_g[kkk] := array_tmp2[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp3[kkk] := (
array_tmp1[kkk] - ats(kkk, array_tmp2, array_tmp3, 2))/
array_tmp2[1];
array_tmp4[kkk] := array_tmp3[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp4[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y_higher[adj3, term] := 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
> #BEGIN ATS LIBRARY BLOCK
> # Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> # End Function number 2
> # Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> # End Function number 3
> # Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> # End Function number 4
> # Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 5
> # Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 6
> # Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> # End Function number 7
> # Begin Function number 8
> dump_series := proc(iolevel,dump_label,series_name,arr_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then # if number 0
> i := 1;
> while (i <= numb) do # do number 1
> print(dump_label,series_name
> ,i,arr_series[i]);
> i := i + 1;
> od;# end do number 1
> fi;# end if 0
> end;
dump_series := proc(iolevel, dump_label, series_name, arr_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, arr_series[i]); i := i + 1
end do
end if
end proc
> # End Function number 8
> # Begin Function number 9
> dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then # if number 0
> sub := 1;
> while (sub <= subnum) do # do number 1
> i := 1;
> while (i <= numb) do # do number 2
> print(dump_label,series_name2,sub,i,arr_series2[sub,i]);
> od;# end do number 2;
> sub := sub + 1;
> od;# end do number 1;
> fi;# end if 0;
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
arr_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> # End Function number 9
> # Begin Function number 10
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then # if number 0
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;# end if 0;
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # End Function number 10
> # Begin Function number 11
> 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 := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod 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," Unknown");
> 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 := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod 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, " Unknown")
end if;
fprintf(fd, " | \n")
end proc
> # End Function number 11
> # Begin Function number 12
> 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 := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod 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(" Unknown\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 := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod 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(" Unknown\n")
end if
end proc
> # End Function number 12
> # Begin Function number 13
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> 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;
> ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
> 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;
ret_ats := 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;
ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # End Function number 13
> # Begin Function number 14
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 7
> ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / convfp(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 glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att :=
ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # End Function number 14
> # Begin Function number 15
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 6
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 6
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # End Function number 15
> # Begin Function number 16
> 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 16
> # Begin Function number 17
> 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 17
> # Begin Function number 18
> 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 18
> # Begin Function number 19
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
> local good_digits;
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 6
> if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7
> good_digits := 1-trunc(log10(rel_error));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 7;
> else
> fprintf(file,"Unknown");
> fi;# end if 6;
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if 0.1*10^(-33) < rel_error then
good_digits := 1 - trunc(log10(rel_error));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # End Function number 19
> # Begin Function number 20
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 20
> # Begin Function number 21
> 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 21
> # Begin Function number 22
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 6
> fprintf(file,"NA");
> elif
> (pole = 1) then # if number 7
> fprintf(file,"Real");
> elif
> (pole = 2) then # if number 8
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 8
> fprintf(file," | ");
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # End Function number 22
> # Begin Function number 23
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 23
> # Begin Function number 24
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # End Function number 24
> # Begin Function number 25
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 8
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 8;
> if (glob_max_iter < 2) then # if number 8
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 8;
> if (errflag) then # if number 8
> quit;
> fi;# end if 8
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
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 25
> # Begin Function number 26
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 8
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 9
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 9
> fi;# end if 8;
> 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 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # End Function number 26
> # Begin Function number 27
> 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 8
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 8;
> 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 := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # End Function number 27
> # Begin Function number 28
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 28
> # Begin Function number 29
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 8
> if (array_fact_1[nnn] = 0) then # if number 9
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 9;
> else
> ret := factorial_2(nnn);
> fi;# end if 8;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_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 29
> # Begin Function number 30
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 8
> if (array_fact_2[mmm,nnn] = 0) then # if number 9
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 9;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 8;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_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 30
> # Begin Function number 31
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 31
> # Begin Function number 32
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 33
> # Begin Function number 34
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 34
> # Begin Function number 35
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 35
> # Begin Function number 36
> 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;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(10.0,- glob_desired_digits_correct) * omniabs(estimated_answer);
> 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 := omniabs(desired_abs_gbl_error / estimated_steps);
> 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;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer);
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 := omniabs(desired_abs_gbl_error/estimated_steps);
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
> # End Function number 36
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(2.0 - ln(abs(cos(x))));
> end;
exact_soln_y := proc(x) return 2.0 - ln(abs(cos(x))) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> 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, log10norm, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> 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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_g,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_max_terms := 30;
> glob_iolevel := 5;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_value3 := 0.0;
> glob_ratio_of_radius := 0.01;
> glob_percent_done := 0.0;
> glob_subiter_method := 3;
> glob_log10normmin := 0.1;
> glob_total_exp_sec := 0.1;
> glob_optimal_expect_sec := 0.1;
> glob_html_log := true;
> glob_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> 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_almost_1 := 0.9990;
> glob_clock_sec := 0.0;
> glob_clock_start_sec := 0.0;
> 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_disp_incr := 0.1;
> glob_h := 0.1;
> glob_hmax := 1.0;
> glob_hmin := 0.00000000001;
> glob_hmin_init := 0.001;
> glob_large_float := 9.0e100;
> glob_last_good_h := 0.1;
> glob_look_poles := false;
> glob_neg_h := false;
> glob_display_interval := 0.0;
> glob_next_display := 0.0;
> glob_dump_analytic := false;
> glob_log10_abserr := 0.1e-10;
> glob_log10_relerr := 0.1e-10;
> glob_abserr := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_max_hours := 0.0;
> glob_max_iter := 1000;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_trunc_err := 0.1e-10;
> glob_no_eqs := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_small_float := 0.1e-50;
> glob_smallish_float := 0.1e-100;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_max_sec := 10000.0;
> glob_orig_start_sec := 0.0;
> glob_start := 0;
> glob_curr_iter_when_opt := 0;
> glob_current_iter := 0;
> glob_iter := 0;
> glob_normmax := 0.0;
> glob_log10abserr := 0.0;
> glob_log10relerr := 0.0;
> glob_max_minutes := 0.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> 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/divpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := -5.0;");
> omniout_str(ALWAYS,"x_end := 5.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.05 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10000000;");
> omniout_str(ALWAYS,"glob_display_interval := 0.1;");
> omniout_str(ALWAYS,"glob_max_minutes := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.001;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> 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(2.0 - ln(abs(cos(x))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1_g:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2_g:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp2_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=max_terms) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp2_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp2_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_0D0[1] := 0.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 2
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 3
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 3;
> iiif := iiif + 1;
> od;# end do number 2;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := -5.0;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.05 ;
> glob_look_poles := true;
> glob_max_iter := 10000000;
> glob_display_interval := 0.1;
> glob_max_minutes := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.001;
> glob_look_poles:=true;
> glob_max_iter:=10000000;
> glob_max_minutes:=3;
> glob_subiter_method:=3;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := expt(10.0 , (glob_log10_abserr));
> glob_relerr := expt(10.0 , (glob_log10_relerr));
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> 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;
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> glob_check_sign := check_sign(x_start,x_end);
> glob_h := check_sign(x_start,x_end);
> if (glob_display_interval < glob_h) then # if number 2
> glob_h := glob_display_interval;
> fi;# end if 2;
> found_h := -1.0;
> best_h := 0.0;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 3
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 3;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 3
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 4
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 4;
> r_order := r_order + 1;
> od;# end do number 3
> ;
> atomall();
> 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,"");
> value3 := test_suggested_h();
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2
> best_h := glob_h;
> found_h := 1.0;
> fi;# end if 2;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> glob_h := glob_h * 0.5;
> od;# end do number 2;
> if (found_h > 0.0) then # if number 2
> glob_h := best_h ;
> else
> omniout_str(ALWAYS,"No increment to obtain desired accuracy found");
> fi;# end if 2;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2;
> #BEGIN SOLUTION CODE
> if (found_h > 0.0) then # if number 2
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := 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 , (term_no - 1)) / 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;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_log10normmin := -glob_large_float ;
> if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_y_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> if (reached_interval()) then # if number 3
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 3;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 3
> #left paren 0004C
> check_for_pole();
> fi;# end if 3;#was right paren 0004C
> if (reached_interval()) then # if number 3
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 3;
> 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 := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (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 := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4;
> term_no := term_no - 1;
> od;# end do number 3;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 2;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 3
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 3;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 3;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 3
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-01-12T22:07:05-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"div")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 4
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 4;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 4
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 4;
> log_revs(html_log_file," 156 | ")
> ;
> logitem_str(html_log_file,"div diffeq.mxt")
> ;
> logitem_str(html_log_file,"div maple results")
> ;
> logitem_str(html_log_file,"Languages compared - single equations")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 3;
> if (glob_html_log) then # if number 3
> fclose(html_log_file);
> fi;# end if 3
> ;
> ;;
> fi;# end if 2
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, 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, log10norm, max_terms, opt_iter,
tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h,
found_h, repeat_it;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, glob_total_exp_sec,
glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter,
glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2,
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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_max_terms := 30;
glob_iolevel := 5;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_value3 := 0.;
glob_ratio_of_radius := 0.01;
glob_percent_done := 0.;
glob_subiter_method := 3;
glob_log10normmin := 0.1;
glob_total_exp_sec := 0.1;
glob_optimal_expect_sec := 0.1;
glob_html_log := true;
glob_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
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_almost_1 := 0.9990;
glob_clock_sec := 0.;
glob_clock_start_sec := 0.;
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_disp_incr := 0.1;
glob_h := 0.1;
glob_hmax := 1.0;
glob_hmin := 0.1*10^(-10);
glob_hmin_init := 0.001;
glob_large_float := 0.90*10^101;
glob_last_good_h := 0.1;
glob_look_poles := false;
glob_neg_h := false;
glob_display_interval := 0.;
glob_next_display := 0.;
glob_dump_analytic := false;
glob_log10_abserr := 0.1*10^(-10);
glob_log10_relerr := 0.1*10^(-10);
glob_abserr := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_max_hours := 0.;
glob_max_iter := 1000;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_trunc_err := 0.1*10^(-10);
glob_no_eqs := 0;
glob_optimal_clock_start_sec := 0.;
glob_optimal_start := 0.;
glob_small_float := 0.1*10^(-50);
glob_smallish_float := 0.1*10^(-100);
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_max_sec := 10000.0;
glob_orig_start_sec := 0.;
glob_start := 0;
glob_curr_iter_when_opt := 0;
glob_current_iter := 0;
glob_iter := 0;
glob_normmax := 0.;
glob_log10abserr := 0.;
glob_log10relerr := 0.;
glob_max_minutes := 0.;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
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/divpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := -5.0;");
omniout_str(ALWAYS, "x_end := 5.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.05 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10000000;");
omniout_str(ALWAYS, "glob_display_interval := 0.1;");
omniout_str(ALWAYS, "glob_max_minutes := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.001;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
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(2.0 - ln(abs(cos(x))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_init := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1_g := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2_g := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 2, 0 .. 4, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp2_g[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := -5.0;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.05;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
glob_desired_digits_correct := 10;
glob_display_interval := 0.001;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 3;
glob_subiter_method := 3;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := expt(10.0, glob_log10_abserr);
glob_relerr := expt(10.0, glob_log10_relerr);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
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;
omniout_str(ALWAYS, "START of Optimize");
glob_check_sign := check_sign(x_start, x_end);
glob_h := check_sign(x_start, x_end);
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
found_h := -1.0;
best_h := 0.;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
while opt_iter <= 20 and found_h < 0. do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := 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, term_no - 1)/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;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
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, "");
value3 := test_suggested_h();
omniout_float(ALWAYS, "value3", 32, value3, 32, "");
if value3 < est_needed_step_err and found_h < 0. then
best_h := glob_h; found_h := 1.0
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1;
glob_h := glob_h*0.5
end do;
if 0. < found_h then glob_h := best_h
else omniout_str(ALWAYS,
"No increment to obtain desired accuracy found")
end if;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
if 0. < found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := 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, term_no - 1)/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;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
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_log10normmin := -glob_large_float;
if glob_small_float < omniabs(array_y_higher[1, 1]) then
tmp := omniabs(array_y_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(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();
glob_current_iter := glob_current_iter + 1;
atomall();
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 := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_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, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_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, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_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, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_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 convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(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 ) = sin ( x ) / cos ( x ) ;")
;
omniout_int(INFO, "Iterations ", 32,
glob_iter, 4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2013-01-12T22:07:05-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "div");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_total_exp_sec));
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 156 | ");
logitem_str(html_log_file,
"div diffeq.mxt");
logitem_str(html_log_file,
"div maple results");
logitem_str(html_log_file,
"Languages compared - single equations");
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/divpostode.ode#################
diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -5.0;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.05 ;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.001;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(2.0 - ln(abs(cos(x))));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
opt_iter = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 10
estimated_steps = 10000
step_error = 1.0000000000000000000000000000000e-14
est_needed_step_err = 1.0000000000000000000000000000000e-14
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
value3 = 4.5374383393035527281677287356107e-66
max_value3 = 4.5374383393035527281677287356107e-66
value3 = 4.5374383393035527281677287356107e-66
best_h = 0.001
START of Soultion
x[1] = -5
y[1] (analytic) = 3.259971236628587709130758159876
y[1] (numeric) = 3.259971236628587709130758159876
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = -5
y[1] (analytic) = 3.259971236628587709130758159876
y[1] (numeric) = 3.259971236628587709130758159876
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2876
Order of pole = 9.486e-23
TOP MAIN SOLVE Loop
x[1] = -4.999
y[1] (analytic) = 3.2633579796165452273496192122587
y[1] (numeric) = 3.2633579796165452273496192122587
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2866
Order of pole = 8.612e-23
TOP MAIN SOLVE Loop
x[1] = -4.998
y[1] (analytic) = 3.2667572350261429930154543198646
y[1] (numeric) = 3.2667572350261429930154543198646
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2856
Order of pole = 7.817e-23
TOP MAIN SOLVE Loop
x[1] = -4.997
y[1] (analytic) = 3.2701690882135694479210400994238
y[1] (numeric) = 3.2701690882135694479210400994237
absolute error = 1e-31
relative error = 3.0579458524154810286455717822906e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2846
Order of pole = 7.092e-23
TOP MAIN SOLVE Loop
x[1] = -4.996
y[1] (analytic) = 3.2735936254368717460848438747144
y[1] (numeric) = 3.2735936254368717460848438747143
absolute error = 1e-31
relative error = 3.0547469063651623482034904218018e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2836
Order of pole = 6.433e-23
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.8MB, time=0.13
x[1] = -4.995
y[1] (analytic) = 3.2770309338686958293469015044044
y[1] (numeric) = 3.2770309338686958293469015044043
absolute error = 1e-31
relative error = 3.0515427537311981597825061480434e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2826
Order of pole = 5.833e-23
TOP MAIN SOLVE Loop
x[1] = -4.994
y[1] (analytic) = 3.2804811016092523049999538571674
y[1] (numeric) = 3.2804811016092523049999538571673
absolute error = 1e-31
relative error = 3.0483333664365456955852359161215e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2816
Order of pole = 5.287e-23
TOP MAIN SOLVE Loop
x[1] = -4.993
y[1] (analytic) = 3.2839442176995129449759701733792
y[1] (numeric) = 3.283944217699512944975970173379
absolute error = 2e-31
relative error = 6.0902374322333990115324557839951e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2806
Order of pole = 4.791e-23
TOP MAIN SOLVE Loop
x[1] = -4.992
y[1] (analytic) = 3.2874203721346427465494558934324
y[1] (numeric) = 3.2874203721346427465494558934322
absolute error = 2e-31
relative error = 6.0837975482317966205799326479218e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2796
Order of pole = 4.341e-23
TOP MAIN SOLVE Loop
x[1] = -4.991
y[1] (analytic) = 3.2909096558776726184123840235942
y[1] (numeric) = 3.290909655877672618412384023594
absolute error = 2e-31
relative error = 6.0773470229665356539094214994893e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2786
Order of pole = 3.931e-23
TOP MAIN SOLVE Loop
x[1] = -4.99
y[1] (analytic) = 3.2944121608734178834329202908972
y[1] (numeric) = 3.2944121608734178834329202908971
absolute error = 1e-31
relative error = 3.0354428989688982595004436774909e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2776
Order of pole = 3.559e-23
TOP MAIN SOLVE Loop
x[1] = -4.989
y[1] (analytic) = 3.2979279800626479205470823039834
y[1] (numeric) = 3.2979279800626479205470823039832
absolute error = 2e-31
relative error = 6.0644138140397101956160400680273e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2766
Order of pole = 3.221e-23
TOP MAIN SOLVE Loop
x[1] = -4.988
y[1] (analytic) = 3.3014572073965124031690229533277
y[1] (numeric) = 3.3014572073965124031690229533275
absolute error = 2e-31
relative error = 6.0579310115522436987859675445203e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2756
Order of pole = 2.914e-23
TOP MAIN SOLVE Loop
x[1] = -4.987
y[1] (analytic) = 3.3049999378512297303660594104908
y[1] (numeric) = 3.3049999378512297303660594104906
absolute error = 2e-31
relative error = 6.0514373301329465753462812973340e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2746
Order of pole = 2.635e-23
TOP MAIN SOLVE Loop
x[1] = -4.986
y[1] (analytic) = 3.3085562674430433899577171325453
y[1] (numeric) = 3.3085562674430433899577171325451
absolute error = 2e-31
relative error = 6.0449327088085555356290912924017e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2736
Order of pole = 2.383e-23
TOP MAIN SOLVE Loop
x[1] = -4.985
y[1] (analytic) = 3.3121262932434521397974764541921
y[1] (numeric) = 3.3121262932434521397974764541919
absolute error = 2e-31
relative error = 6.0384170859664542506114589102697e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2726
Order of pole = 2.154e-23
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=3.8MB, time=0.28
x[1] = -4.984
y[1] (analytic) = 3.3157101133947200449200589667937
y[1] (numeric) = 3.3157101133947200449200589667935
absolute error = 2e-31
relative error = 6.0318903993459852714866332085106e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2716
Order of pole = 1.946e-23
TOP MAIN SOLVE Loop
x[1] = -4.983
y[1] (analytic) = 3.3193078271256725641295404948193
y[1] (numeric) = 3.319307827125672564129540494819
absolute error = 3e-31
relative error = 9.0380288790444164298033487522639e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2706
Order of pole = 1.758e-23
TOP MAIN SOLVE Loop
x[1] = -4.982
y[1] (analytic) = 3.3229195347677850401132108741722
y[1] (numeric) = 3.322919534767785040113210874172
absolute error = 2e-31
relative error = 6.0188035824339201859311213997185e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2696
Order of pole = 1.587e-23
TOP MAIN SOLVE Loop
x[1] = -4.981
y[1] (analytic) = 3.3265453377715701124473342004681
y[1] (numeric) = 3.3265453377715701124473342004678
absolute error = 3e-31
relative error = 9.0183649864507164879542175637468e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2686
Order of pole = 1.432e-23
TOP MAIN SOLVE Loop
x[1] = -4.98
y[1] (analytic) = 3.3301853387232707430739725234632
y[1] (numeric) = 3.3301853387232707430739725234629
absolute error = 3e-31
relative error = 9.0085076200297684451800098740467e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2676
Order of pole = 1.292e-23
TOP MAIN SOLVE Loop
x[1] = -4.979
y[1] (analytic) = 3.3338396413618657191389935663622
y[1] (numeric) = 3.333839641361865719138993566362
absolute error = 2e-31
relative error = 5.9990887839554414318079955235948e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2666
Order of pole = 1.166e-23
TOP MAIN SOLVE Loop
x[1] = -4.978
y[1] (analytic) = 3.3375083505963946786627059531727
y[1] (numeric) = 3.3375083505963946786627059531725
absolute error = 2e-31
relative error = 5.9924943697672271729161666133531e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2656
Order of pole = 1.051e-23
TOP MAIN SOLVE Loop
x[1] = -4.977
y[1] (analytic) = 3.3411915725236098905451743019884
y[1] (numeric) = 3.3411915725236098905451743019882
absolute error = 2e-31
relative error = 5.9858884370685613625302494663565e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2646
Order of pole = 9.474e-24
TOP MAIN SOLVE Loop
x[1] = -4.976
y[1] (analytic) = 3.3448894144459622120738565919867
y[1] (numeric) = 3.3448894144459622120738565919865
absolute error = 2e-31
relative error = 5.9792709180828754043773841525180e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2636
Order of pole = 8.536e-24
TOP MAIN SOLVE Loop
x[1] = -4.975
y[1] (analytic) = 3.3486019848899288445945304085993
y[1] (numeric) = 3.348601984889928844594530408599
absolute error = 3e-31
relative error = 8.9589626164502567379404717968170e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2626
Order of pole = 7.689e-24
TOP MAIN SOLVE Loop
x[1] = -4.974
y[1] (analytic) = 3.3523293936246907115276399501667
y[1] (numeric) = 3.3523293936246907115276399501664
absolute error = 3e-31
relative error = 8.9490012697000035012279449569379e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2616
Order of pole = 6.923e-24
TOP MAIN SOLVE Loop
x[1] = -4.973
y[1] (analytic) = 3.3560717516811674926689727494922
y[1] (numeric) = 3.3560717516811674926689727494919
absolute error = 3e-31
relative error = 8.9390222318614035613360648213104e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2606
Order of pole = 6.231e-24
memory used=11.4MB, alloc=3.9MB, time=0.44
TOP MAIN SOLVE Loop
x[1] = -4.972
y[1] (analytic) = 3.3598291713714185649217225106776
y[1] (numeric) = 3.3598291713714185649217225106773
absolute error = 3e-31
relative error = 8.9290253967747320927645803418145e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2596
Order of pole = 5.606e-24
TOP MAIN SOLVE Loop
x[1] = -4.971
y[1] (analytic) = 3.3636017663084183224905978606674
y[1] (numeric) = 3.3636017663084183224905978606671
absolute error = 3e-31
relative error = 8.9190106571163019465653429696600e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2586
Order of pole = 5.042e-24
TOP MAIN SOLVE Loop
x[1] = -4.97
y[1] (analytic) = 3.3673896514262145793604636100166
y[1] (numeric) = 3.3673896514262145793604636100163
absolute error = 3e-31
relative error = 8.9089779043817770912167765300362e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2576
Order of pole = 4.533e-24
TOP MAIN SOLVE Loop
x[1] = -4.969
y[1] (analytic) = 3.3711929430004789938238720638399
y[1] (numeric) = 3.3711929430004789938238720638396
absolute error = 3e-31
relative error = 8.8989270288691801728519706050970e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2566
Order of pole = 4.074e-24
TOP MAIN SOLVE Loop
x[1] = -4.968
y[1] (analytic) = 3.3750117586694586991650199349669
y[1] (numeric) = 3.3750117586694586991650199349666
absolute error = 3e-31
relative error = 8.8888579196615873656581994183616e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2556
Order of pole = 3.660e-24
TOP MAIN SOLVE Loop
x[1] = -4.967
y[1] (analytic) = 3.3788462174553385766132636959101
y[1] (numeric) = 3.3788462174553385766132636959098
absolute error = 3e-31
relative error = 8.8787704646095035033578217118516e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2546
Order of pole = 3.286e-24
TOP MAIN SOLVE Loop
x[1] = -4.966
y[1] (analytic) = 3.3826964397860238666187306332596
y[1] (numeric) = 3.3826964397860238666187306332593
absolute error = 3e-31
relative error = 8.8686645503129102973045641075390e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2536
Order of pole = 2.950e-24
TOP MAIN SOLVE Loop
x[1] = -4.965
y[1] (analytic) = 3.3865625475173530826578845451794
y[1] (numeric) = 3.3865625475173530826578845451791
absolute error = 3e-31
relative error = 8.8585400621029802556966195503195e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2526
Order of pole = 2.647e-24
TOP MAIN SOLVE Loop
x[1] = -4.964
y[1] (analytic) = 3.3904446639557514684414441314646
y[1] (numeric) = 3.3904446639557514684414441314643
absolute error = 3e-31
relative error = 8.8483968840234487215230181919828e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2516
Order of pole = 2.374e-24
TOP MAIN SOLVE Loop
x[1] = -4.963
y[1] (analytic) = 3.3943429138813355248757891142837
y[1] (numeric) = 3.3943429138813355248757891142833
absolute error = 4e-31
relative error = 1.1784313198415514991891973557478e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2506
Order of pole = 2.129e-24
TOP MAIN SOLVE Loop
x[1] = -4.962
y[1] (analytic) = 3.3982574235714794277390984225665
y[1] (numeric) = 3.3982574235714794277390984225662
absolute error = 3e-31
relative error = 8.8280539878791132883981575329600e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2496
Order of pole = 1.908e-24
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=3.9MB, time=0.59
x[1] = -4.961
y[1] (analytic) = 3.4021883208248544611048532366317
y[1] (numeric) = 3.4021883208248544611048532366314
absolute error = 3e-31
relative error = 8.8178540312919990757352845281195e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2486
Order of pole = 1.710e-24
TOP MAIN SOLVE Loop
x[1] = -4.96
y[1] (analytic) = 3.4061357349859529054212091224762
y[1] (numeric) = 3.4061357349859529054212091224759
absolute error = 3e-31
relative error = 8.8076349077508861168636418897831e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2476
Order of pole = 1.531e-24
TOP MAIN SOLVE Loop
x[1] = -4.959
y[1] (analytic) = 3.4100997969701081431921885401137
y[1] (numeric) = 3.4100997969701081431921885401134
absolute error = 3e-31
relative error = 8.7973964945703817817907809281524e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2466
Order of pole = 1.370e-24
TOP MAIN SOLVE Loop
x[1] = -4.958
y[1] (analytic) = 3.4140806392890230797772699690244
y[1] (numeric) = 3.4140806392890230797772699690242
absolute error = 2e-31
relative error = 5.8580924451055053359844348522998e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2456
Order of pole = 1.226e-24
TOP MAIN SOLVE Loop
x[1] = -4.957
y[1] (analytic) = 3.4180783960768193223165158346681
y[1] (numeric) = 3.4180783960768193223165158346679
absolute error = 2e-31
relative error = 5.8512408676627999850695763835409e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2446
Order of pole = 1.097e-24
TOP MAIN SOLVE Loop
x[1] = -4.956
y[1] (analytic) = 3.4220932031166199166014953974361
y[1] (numeric) = 3.4220932031166199166014953974359
absolute error = 2e-31
relative error = 5.8443761794054296356258454872808e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2436
Order of pole = 9.805e-25
TOP MAIN SOLVE Loop
x[1] = -4.955
y[1] (analytic) = 3.4261251978676788102670887108869
y[1] (numeric) = 3.4261251978676788102670887108866
absolute error = 3e-31
relative error = 8.7562474420581979792347629102496e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2426
Order of pole = 8.763e-25
TOP MAIN SOLVE Loop
x[1] = -4.954
y[1] (analytic) = 3.4301745194930705914122849128146
y[1] (numeric) = 3.4301745194930705914122849128143
absolute error = 3e-31
relative error = 8.7459106904081251626373709495733e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2416
Order of pole = 7.828e-25
TOP MAIN SOLVE Loop
x[1] = -4.953
y[1] (analytic) = 3.434241308887954445123896919125
y[1] (numeric) = 3.4342413088879544451238969191248
absolute error = 2e-31
relative error = 5.8237025884695978386061845259348e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2406
Order of pole = 6.989e-25
TOP MAIN SOLVE Loop
x[1] = -4.952
y[1] (analytic) = 3.4383257087084266768492220405603
y[1] (numeric) = 3.4383257087084266768492220405601
absolute error = 2e-31
relative error = 5.8167845906351913948777504681776e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2396
Order of pole = 6.238e-25
TOP MAIN SOLVE Loop
x[1] = -4.951
y[1] (analytic) = 3.4424278634009765716354046686103
y[1] (numeric) = 3.4424278634009765716354046686101
absolute error = 2e-31
relative error = 5.8098530437296733688504178754617e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2386
Order of pole = 5.566e-25
TOP MAIN SOLVE Loop
x[1] = -4.95
y[1] (analytic) = 3.4465479192325607924386419292941
y[1] (numeric) = 3.4465479192325607924386419292938
absolute error = 3e-31
relative error = 8.7043617854818825530728682855573e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2376
Order of pole = 4.962e-25
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.0MB, time=0.75
x[1] = -4.949
y[1] (analytic) = 3.4506860243213119695411346297333
y[1] (numeric) = 3.4506860243213119695411346297331
absolute error = 2e-31
relative error = 5.7959489385690027158462056042974e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2366
Order of pole = 4.423e-25
TOP MAIN SOLVE Loop
x[1] = -4.948
y[1] (analytic) = 3.4548423286678975971562321007678
y[1] (numeric) = 3.4548423286678975971562321007676
absolute error = 2e-31
relative error = 5.7889761955392937136101568850753e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2356
Order of pole = 3.941e-25
TOP MAIN SOLVE Loop
x[1] = -4.947
y[1] (analytic) = 3.4590169841875458331347100628465
y[1] (numeric) = 3.4590169841875458331347100628463
absolute error = 2e-31
relative error = 5.7819895338552671170396716541863e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2346
Order of pole = 3.510e-25
TOP MAIN SOLVE Loop
x[1] = -4.946
y[1] (analytic) = 3.4632101447427552939145820216199
y[1] (numeric) = 3.4632101447427552939145820216196
absolute error = 3e-31
relative error = 8.6624832875188918018336547120446e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2336
Order of pole = 3.124e-25
TOP MAIN SOLVE Loop
x[1] = -4.945
y[1] (analytic) = 3.4674219661767064501163442102562
y[1] (numeric) = 3.4674219661767064501163442102559
absolute error = 3e-31
relative error = 8.6519611090423433817159070909967e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2326
Order of pole = 2.780e-25
TOP MAIN SOLVE Loop
x[1] = -4.944
y[1] (analytic) = 3.4716526063473927591354337990077
y[1] (numeric) = 3.4716526063473927591354337990074
absolute error = 3e-31
relative error = 8.6414176191331841140005389021954e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2316
Order of pole = 2.472e-25
TOP MAIN SOLVE Loop
x[1] = -4.943
y[1] (analytic) = 3.475902225162490220412855034866
y[1] (numeric) = 3.4759022251624902204128550348657
absolute error = 3e-31
relative error = 8.6308526697978597045645227955638e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2306
Order of pole = 2.197e-25
TOP MAIN SOLVE Loop
x[1] = -4.942
y[1] (analytic) = 3.4801709846149846074922520855355
y[1] (numeric) = 3.4801709846149846074922520855352
absolute error = 3e-31
relative error = 8.6202661112407771942678286474902e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2296
Order of pole = 1.952e-25
TOP MAIN SOLVE Loop
x[1] = -4.941
y[1] (analytic) = 3.4844590488195762192474108992633
y[1] (numeric) = 3.484459048819576219247410899263
absolute error = 3e-31
relative error = 8.6096577918351615587573196359725e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2286
Order of pole = 1.735e-25
TOP MAIN SOLVE Loop
x[1] = -4.94
y[1] (analytic) = 3.4887665840498826015713750005312
y[1] (numeric) = 3.4887665840498826015713750005309
absolute error = 3e-31
relative error = 8.5990275580933098430578059356796e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2276
Order of pole = 1.539e-25
TOP MAIN SOLVE Loop
x[1] = -4.939
y[1] (analytic) = 3.4930937587764603211746638648537
y[1] (numeric) = 3.4930937587764603211746638648535
absolute error = 2e-31
relative error = 5.7255835030908184383975375905088e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2266
Order of pole = 1.365e-25
TOP MAIN SOLVE Loop
x[1] = -4.938
y[1] (analytic) = 3.4974407437056675257992493507169
y[1] (numeric) = 3.4974407437056675257992493507166
absolute error = 3e-31
relative error = 8.5777007241626324111629775665649e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2256
Order of pole = 1.210e-25
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.0MB, time=0.90
x[1] = -4.937
y[1] (analytic) = 3.5018077118193897010086645451231
y[1] (numeric) = 3.5018077118193897010086645451228
absolute error = 3e-31
relative error = 8.5670038074173071896865903864470e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2246
Order of pole = 1.073e-25
TOP MAIN SOLVE Loop
x[1] = -4.936
y[1] (analytic) = 3.5061948384156517336943677656552
y[1] (numeric) = 3.5061948384156517336943677656549
absolute error = 3e-31
relative error = 8.5562843431587887069908676701123e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2236
Order of pole = 9.504e-26
TOP MAIN SOLVE Loop
x[1] = -4.935
y[1] (analytic) = 3.5106023011501401175174900779588
y[1] (numeric) = 3.5106023011501401175174900779585
absolute error = 3e-31
relative error = 8.5455421681263722542711452282428e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2226
Order of pole = 8.406e-26
TOP MAIN SOLVE Loop
x[1] = -4.934
y[1] (analytic) = 3.5150302800786598867004032251001
y[1] (numeric) = 3.5150302800786598867004032250998
absolute error = 3e-31
relative error = 8.5347771170064160582318173467709e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2216
Order of pole = 7.454e-26
TOP MAIN SOLVE Loop
x[1] = -4.933
y[1] (analytic) = 3.5194789577005516429571999202808
y[1] (numeric) = 3.5194789577005516429571999202805
absolute error = 3e-31
relative error = 8.5239890223979269229681022650322e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2206
Order of pole = 6.589e-26
TOP MAIN SOLVE Loop
x[1] = -4.932
y[1] (analytic) = 3.5239485190030948470175203081626
y[1] (numeric) = 3.5239485190030948470175203081623
absolute error = 3e-31
relative error = 8.5131777147774084770447240420373e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2196
Order of pole = 5.814e-26
TOP MAIN SOLVE Loop
x[1] = -4.931
y[1] (analytic) = 3.5284391515069243823162487002367
y[1] (numeric) = 3.5284391515069243823162487002364
absolute error = 3e-31
relative error = 8.5023430224629527740712625987094e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2186
Order of pole = 5.150e-26
TOP MAIN SOLVE Loop
x[1] = -4.93
y[1] (analytic) = 3.5329510453124882652077845351035
y[1] (numeric) = 3.5329510453124882652077845351032
absolute error = 3e-31
relative error = 8.4914847715775554016179154794958e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2176
Order of pole = 4.548e-26
TOP MAIN SOLVE Loop
x[1] = -4.929
y[1] (analytic) = 3.5374843931475752747891809316696
y[1] (numeric) = 3.5374843931475752747891809316693
absolute error = 3e-31
relative error = 8.4806027860116336387399687930696e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2166
Order of pole = 4.011e-26
TOP MAIN SOLVE Loop
x[1] = -4.928
y[1] (analytic) = 3.5420393904159422074115915199626
y[1] (numeric) = 3.5420393904159422074115915199623
absolute error = 3e-31
relative error = 8.4696968873847265658313616209151e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2156
Order of pole = 3.527e-26
TOP MAIN SOLVE Loop
x[1] = -4.927
y[1] (analytic) = 3.5466162352470714276161564098298
y[1] (numeric) = 3.5466162352470714276161564098296
absolute error = 2e-31
relative error = 5.6391779300042369140771531605674e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2146
Order of pole = 3.113e-26
TOP MAIN SOLVE Loop
x[1] = -4.926
y[1] (analytic) = 3.5512151285470903900056897209194
y[1] (numeric) = 3.5512151285470903900056897209191
absolute error = 3e-31
relative error = 8.4478126258360214148750892772912e-30 %
Correct digits = 31
h = 0.001
memory used=26.7MB, alloc=4.0MB, time=1.06
Real estimate of pole used
Radius of convergence = 0.2136
Order of pole = 2.747e-26
TOP MAIN SOLVE Loop
x[1] = -4.925
y[1] (analytic) = 3.5558362740508858469826719773664
y[1] (numeric) = 3.5558362740508858469826719773662
absolute error = 2e-31
relative error = 5.6245559296282126030247753862279e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2126
Order of pole = 2.424e-26
TOP MAIN SOLVE Loop
x[1] = -4.924
y[1] (analytic) = 3.5604798783754465369443838864457
y[1] (numeric) = 3.5604798783754465369443838864455
absolute error = 2e-31
relative error = 5.6172203419740921999818922454241e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2116
Order of pole = 2.132e-26
TOP MAIN SOLVE Loop
x[1] = -4.923
y[1] (analytic) = 3.5651461510744692681004889188765
y[1] (numeric) = 3.5651461510744692681004889188763
absolute error = 2e-31
relative error = 5.6098681940352905384859719759560e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2106
Order of pole = 1.879e-26
TOP MAIN SOLVE Loop
x[1] = -4.922
y[1] (analytic) = 3.5698353046942644763195496222349
y[1] (numeric) = 3.5698353046942644763195496222347
absolute error = 2e-31
relative error = 5.6024993572393623562151876612208e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2096
Order of pole = 1.652e-26
TOP MAIN SOLVE Loop
x[1] = -4.921
y[1] (analytic) = 3.5745475548309985431552278302606
y[1] (numeric) = 3.5745475548309985431552278302604
absolute error = 2e-31
relative error = 5.5951137013046627006568481468670e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2086
Order of pole = 1.432e-26
TOP MAIN SOLVE Loop
x[1] = -4.92
y[1] (analytic) = 3.5792831201893114143748952609665
y[1] (numeric) = 3.5792831201893114143748952609662
absolute error = 3e-31
relative error = 8.3815666413148322741385287983886e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2076
Order of pole = 1.269e-26
TOP MAIN SOLVE Loop
x[1] = -4.919
y[1] (analytic) = 3.5840422226423493619306208816665
y[1] (numeric) = 3.5840422226423493619306208816662
absolute error = 3e-31
relative error = 8.3704371032443866861484126869643e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2066
Order of pole = 1.110e-26
TOP MAIN SOLVE Loop
x[1] = -4.918
y[1] (analytic) = 3.5888250872932540854904460637747
y[1] (numeric) = 3.5888250872932540854904460637744
absolute error = 3e-31
relative error = 8.3592817343534710081665183618152e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2056
Order of pole = 9.906e-27
TOP MAIN SOLVE Loop
x[1] = -4.917
y[1] (analytic) = 3.5936319425381507556050877525451
y[1] (numeric) = 3.5936319425381507556050877525448
absolute error = 3e-31
relative error = 8.3481003284969864897623022740592e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2046
Order of pole = 8.524e-27
TOP MAIN SOLVE Loop
x[1] = -4.916
y[1] (analytic) = 3.5984630201306790616490005282837
y[1] (numeric) = 3.5984630201306790616490005282835
absolute error = 2e-31
relative error = 5.5579284511512626647171352965718e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2036
Order of pole = 7.576e-27
TOP MAIN SOLVE Loop
x[1] = -4.915
y[1] (analytic) = 3.6033185552481128462869414305977
y[1] (numeric) = 3.6033185552481128462869414305975
absolute error = 2e-31
relative error = 5.5504390448273493739011686820559e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2026
Order of pole = 6.617e-27
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.1MB, time=1.21
x[1] = -4.914
y[1] (analytic) = 3.6081987865591154869404980979311
y[1] (numeric) = 3.6081987865591154869404980979308
absolute error = 3e-31
relative error = 8.3143977853306919863360962775950e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2016
Order of pole = 5.865e-27
TOP MAIN SOLVE Loop
x[1] = -4.913
y[1] (analytic) = 3.6131039562931798262535715035466
y[1] (numeric) = 3.6131039562931798262535715035464
absolute error = 2e-31
relative error = 5.5354067422180560179469306341303e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.2006
Order of pole = 5.186e-27
TOP MAIN SOLVE Loop
x[1] = -4.912
y[1] (analytic) = 3.6180343103118031607060936075718
y[1] (numeric) = 3.6180343103118031607060936075716
absolute error = 2e-31
relative error = 5.5278635536975863205689372752462e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1996
Order of pole = 4.431e-27
TOP MAIN SOLVE Loop
x[1] = -4.911
y[1] (analytic) = 3.6229900981814495722677128113046
y[1] (numeric) = 3.6229900981814495722677128113045
absolute error = 1e-31
relative error = 2.7601510710778574611380716454102e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1986
Order of pole = 3.823e-27
TOP MAIN SOLVE Loop
x[1] = -4.91
y[1] (analytic) = 3.6279715732483537354339393135843
y[1] (numeric) = 3.6279715732483537354339393135842
absolute error = 1e-31
relative error = 2.7563611781683184112415326762138e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1976
Order of pole = 3.486e-27
TOP MAIN SOLVE Loop
x[1] = -4.909
y[1] (analytic) = 3.632978992715222254420545848507
y[1] (numeric) = 3.6329789927152222544205458485069
absolute error = 1e-31
relative error = 2.7525620214297419712689175698378e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1966
Order of pole = 2.819e-27
TOP MAIN SOLVE Loop
x[1] = -4.908
y[1] (analytic) = 3.6380126177198905861490665942817
y[1] (numeric) = 3.6380126177198905861490665942815
absolute error = 2e-31
relative error = 5.4975070461781184169456140784006e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1956
Order of pole = 2.527e-27
TOP MAIN SOLVE Loop
x[1] = -4.907
y[1] (analytic) = 3.6430727134159956875546035605951
y[1] (numeric) = 3.643072713415995687554603560595
absolute error = 1e-31
relative error = 2.7449356042699767617865275981315e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1946
Order of pole = 2.277e-27
TOP MAIN SOLVE Loop
x[1] = -4.906
y[1] (analytic) = 3.6481595490557266944907814849447
y[1] (numeric) = 3.6481595490557266944907814849446
absolute error = 1e-31
relative error = 2.7411081849718867933234383660590e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1936
Order of pole = 1.965e-27
TOP MAIN SOLVE Loop
x[1] = -4.905
y[1] (analytic) = 3.6532733980747181980965222535611
y[1] (numeric) = 3.653273398074718198096522253561
absolute error = 1e-31
relative error = 2.7372711840482615939784039030120e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1926
Order of pole = 1.685e-27
TOP MAIN SOLVE Loop
x[1] = -4.904
y[1] (analytic) = 3.6584145381791530371345377166248
y[1] (numeric) = 3.6584145381791530371345377166247
absolute error = 1e-31
relative error = 2.7334245191845174915522600174599e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1916
Order of pole = 1.483e-27
TOP MAIN SOLVE Loop
x[1] = -4.903
y[1] (analytic) = 3.6635832514351439759415194075553
y[1] (numeric) = 3.6635832514351439759415194075553
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1906
Order of pole = 1.252e-27
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.1MB, time=1.38
x[1] = -4.902
y[1] (analytic) = 3.6687798243604661919073877911694
y[1] (numeric) = 3.6687798243604661919073877911694
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1896
Order of pole = 1.085e-27
TOP MAIN SOLVE Loop
x[1] = -4.901
y[1] (analytic) = 3.674004548018715158734656898665
y[1] (numeric) = 3.674004548018715158734656898665
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1886
Order of pole = 9.54e-28
TOP MAIN SOLVE Loop
x[1] = -4.9
y[1] (analytic) = 3.6792577181159672872889469504773
y[1] (numeric) = 3.6792577181159672872889469504773
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1876
Order of pole = 8.78e-28
TOP MAIN SOLVE Loop
x[1] = -4.899
y[1] (analytic) = 3.6845396351000235800842244405324
y[1] (numeric) = 3.6845396351000235800842244405324
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1866
Order of pole = 7.04e-28
TOP MAIN SOLVE Loop
x[1] = -4.898
y[1] (analytic) = 3.689850604262319574090396760456
y[1] (numeric) = 3.6898506042623195740903967604559
absolute error = 1e-31
relative error = 2.7101368246314717359857564677391e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1856
Order of pole = 6.01e-28
TOP MAIN SOLVE Loop
x[1] = -4.897
y[1] (analytic) = 3.695190935842587995655401876947
y[1] (numeric) = 3.6951909358425879956554018769469
absolute error = 1e-31
relative error = 2.7062201043529490652614669663720e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1846
Order of pole = 7.03e-28
TOP MAIN SOLVE Loop
x[1] = -4.896
y[1] (analytic) = 3.7005609451363638372764364559467
y[1] (numeric) = 3.7005609451363638372764364559466
absolute error = 1e-31
relative error = 2.7022930167230376352562217070279e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1836
Order of pole = 4.61e-28
TOP MAIN SOLVE Loop
x[1] = -4.895
y[1] (analytic) = 3.7059609526054249954612783054439
y[1] (numeric) = 3.7059609526054249954612783054438
absolute error = 1e-31
relative error = 2.6983554678226270078467277237532e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1826
Order of pole = 3.98e-28
TOP MAIN SOLVE Loop
x[1] = -4.894
y[1] (analytic) = 3.71139128399126518908593644501
y[1] (numeric) = 3.7113912839912651890859364450098
absolute error = 2e-31
relative error = 5.3888147246204154952880146915389e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1816
Order of pole = 3.89e-28
TOP MAIN SOLVE Loop
x[1] = -4.893
y[1] (analytic) = 3.7168522704316996159660277638794
y[1] (numeric) = 3.7168522704316996159660277638793
absolute error = 1e-31
relative error = 2.6904486033927128266357032615579e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1806
Order of pole = 2.24e-28
TOP MAIN SOLVE Loop
x[1] = -4.892
y[1] (analytic) = 3.7223442485807077097189515894089
y[1] (numeric) = 3.7223442485807077097189515894087
absolute error = 2e-31
relative error = 5.3729581855911897801531994535785e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1796
Order of pole = 2.16e-28
TOP MAIN SOLVE Loop
x[1] = -4.891
y[1] (analytic) = 3.7278675607316214377459567274415
y[1] (numeric) = 3.7278675607316214377459567274413
absolute error = 2e-31
relative error = 5.3649974614642299265964620341607e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1786
Order of pole = 2.63e-28
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.1MB, time=1.53
x[1] = -4.89
y[1] (analytic) = 3.7334225549437718431198901069061
y[1] (numeric) = 3.733422554943771843119890106906
absolute error = 1e-31
relative error = 2.6785074158718172567487952866214e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1776
Order of pole = 2.63e-28
TOP MAIN SOLVE Loop
x[1] = -4.889
y[1] (analytic) = 3.7390095851727109876356757873001
y[1] (numeric) = 3.7390095851727109876356757872999
absolute error = 2e-31
relative error = 5.3490100906163275279157805191103e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1766
Order of pole = 2.84e-28
TOP MAIN SOLVE Loop
x[1] = -4.888
y[1] (analytic) = 3.744629011404131110104944464306
y[1] (numeric) = 3.7446290114041311101049444643058
absolute error = 2e-31
relative error = 5.3409830290506026845013168350130e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1756
Order of pole = 1.07e-28
TOP MAIN SOLVE Loop
x[1] = -4.887
y[1] (analytic) = 3.7502811997916076835541259989703
y[1] (numeric) = 3.7502811997916076835541259989701
absolute error = 2e-31
relative error = 5.3329334347278658336112479135086e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1746
Order of pole = 1.34e-28
TOP MAIN SOLVE Loop
x[1] = -4.886
y[1] (analytic) = 3.7559665227982981483145012655127
y[1] (numeric) = 3.7559665227982981483145012655125
absolute error = 2e-31
relative error = 5.3248610919725267056697154213556e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.885
y[1] (analytic) = 3.7616853593427334267062755973789
y[1] (numeric) = 3.7616853593427334267062755973787
absolute error = 2e-31
relative error = 5.3167657816799787918280676447426e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1726
Order of pole = 1.12e-28
TOP MAIN SOLVE Loop
x[1] = -4.884
y[1] (analytic) = 3.767438094948844901425701695766
y[1] (numeric) = 3.7674380949488449014257016957657
absolute error = 3e-31
relative error = 7.9629709218639056529612914936114e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1716
Order of pole = 9.3e-29
TOP MAIN SOLVE Loop
x[1] = -4.883
y[1] (analytic) = 3.7732251219003753768730428670853
y[1] (numeric) = 3.7732251219003753768730428670851
absolute error = 2e-31
relative error = 5.3005053644737343740493918890243e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1706
Order of pole = 6.1e-29
TOP MAIN SOLVE Loop
x[1] = -4.882
y[1] (analytic) = 3.7790468393998286543040254502543
y[1] (numeric) = 3.779046839399828654304025450254
absolute error = 3e-31
relative error = 7.9385097022942605418583530049322e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1696
Order of pole = 9.5e-29
TOP MAIN SOLVE Loop
x[1] = -4.881
y[1] (analytic) = 3.7849036537321187524584000371182
y[1] (numeric) = 3.7849036537321187524584000371179
absolute error = 3e-31
relative error = 7.9262255382427991350610402296850e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1686
Order of pole = 7.8e-29
TOP MAIN SOLVE Loop
x[1] = -4.88
y[1] (analytic) = 3.7907959784330865106954293243597
y[1] (numeric) = 3.7907959784330865106954293243594
absolute error = 3e-31
relative error = 7.9139051984539681844167957957436e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1676
Order of pole = 9.2e-29
TOP MAIN SOLVE Loop
x[1] = -4.879
y[1] (analytic) = 3.7967242344630583380529677587405
y[1] (numeric) = 3.7967242344630583380529677587403
absolute error = 2e-31
relative error = 5.2676988806453168678999985017714e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1666
Order of pole = 7.2e-29
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.1MB, time=1.69
x[1] = -4.878
y[1] (analytic) = 3.8026888503856292364373659040857
y[1] (numeric) = 3.8026888503856292364373659040855
absolute error = 2e-31
relative error = 5.2594363585576578459629927925789e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1656
Order of pole = 7.0e-29
TOP MAIN SOLVE Loop
x[1] = -4.877
y[1] (analytic) = 3.8086902625518599477922431628017
y[1] (numeric) = 3.8086902625518599477922431628015
absolute error = 2e-31
relative error = 5.2511489833252555511201697474513e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1646
Order of pole = 5.1e-29
TOP MAIN SOLVE Loop
x[1] = -4.876
y[1] (analytic) = 3.8147289152900861731558128080091
y[1] (numeric) = 3.8147289152900861731558128080088
absolute error = 3e-31
relative error = 7.8642547520886391567470506077676e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1636
Order of pole = 1.67e-28
TOP MAIN SOLVE Loop
x[1] = -4.875
y[1] (analytic) = 3.8208052611015463067693723104409
y[1] (numeric) = 3.8208052611015463067693723104407
absolute error = 2e-31
relative error = 5.2344986549337919773666859034352e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1626
Order of pole = 6e-30
TOP MAIN SOLVE Loop
x[1] = -4.874
y[1] (analytic) = 3.8269197608620430428955411873925
y[1] (numeric) = 3.8269197608620430428955411873922
absolute error = 3e-31
relative error = 7.8392027726346344371753633047178e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.873
y[1] (analytic) = 3.8330728840298635701643666486975
y[1] (numeric) = 3.8330728840298635701643666486973
absolute error = 2e-31
relative error = 5.2177458151991089250960277209480e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.872
y[1] (analytic) = 3.8392651088601928929718715572484
y[1] (numeric) = 3.8392651088601928929718715572481
absolute error = 3e-31
relative error = 7.8139954260429927749608027395255e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.871
y[1] (analytic) = 3.8454969226262651381562904003335
y[1] (numeric) = 3.8454969226262651381562904003333
absolute error = 2e-31
relative error = 5.2008883123331401180461665145429e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.87
y[1] (analytic) = 3.8517688218475085459921917581849
y[1] (numeric) = 3.8517688218475085459921917581847
absolute error = 2e-31
relative error = 5.1924196194118837014623896964782e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1576
Order of pole = 7.1e-29
TOP MAIN SOLVE Loop
x[1] = -4.869
y[1] (analytic) = 3.8580813125249512373818705561678
y[1] (numeric) = 3.8580813125249512373818705561676
absolute error = 2e-31
relative error = 5.1839239196622439469932635021398e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.868
y[1] (analytic) = 3.8644349103841668258127714556956
y[1] (numeric) = 3.8644349103841668258127714556954
absolute error = 2e-31
relative error = 5.1754009224628867290997905521427e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.867
y[1] (analytic) = 3.8708301411260515370671312926252
y[1] (numeric) = 3.870830141126051537067131292625
absolute error = 2e-31
relative error = 5.1668503320535424584131430801604e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1546
Order of pole = 6.2e-29
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.1MB, time=1.85
x[1] = -4.866
y[1] (analytic) = 3.8772675406857377478917169128484
y[1] (numeric) = 3.8772675406857377478917169128482
absolute error = 2e-31
relative error = 5.1582718474110709111249739044682e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.865
y[1] (analytic) = 3.8837476554999627952940004709596
y[1] (numeric) = 3.8837476554999627952940004709594
absolute error = 2e-31
relative error = 5.1496651621217030411615404591555e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.864
y[1] (analytic) = 3.8902710427832265817855791307397
y[1] (numeric) = 3.8902710427832265817855791307395
absolute error = 2e-31
relative error = 5.1410299642493158383496946776282e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1516
Order of pole = 2.1e-29
TOP MAIN SOLVE Loop
x[1] = -4.863
y[1] (analytic) = 3.8968382708130869524139757674471
y[1] (numeric) = 3.8968382708130869524139757674469
absolute error = 2e-31
relative error = 5.1323659361995898850229095777894e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.862
y[1] (analytic) = 3.9034499192249580933893031377199
y[1] (numeric) = 3.9034499192249580933893031377196
absolute error = 3e-31
relative error = 7.6855091318698387837490999517492e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1496
Order of pole = 3.7e-29
TOP MAIN SOLVE Loop
x[1] = -4.861
y[1] (analytic) = 3.9101065793167943492257021423985
y[1] (numeric) = 3.9101065793167943492257021423983
absolute error = 2e-31
relative error = 5.1149500900547224482443366242693e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.86
y[1] (analytic) = 3.9168088543640599286379750350632
y[1] (numeric) = 3.9168088543640599286379750350629
absolute error = 3e-31
relative error = 7.6592964107948161555266288497339e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1476
Order of pole = 3.2e-29
TOP MAIN SOLVE Loop
x[1] = -4.859
y[1] (analytic) = 3.9235573599454040256273061409402
y[1] (numeric) = 3.92355735994540402562730614094
absolute error = 2e-31
relative error = 5.0974149643318323595910540992225e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1466
Order of pole = 2.6e-29
TOP MAIN SOLVE Loop
x[1] = -4.858
y[1] (analytic) = 3.9303527242794809818007118907229
y[1] (numeric) = 3.9303527242794809818007118907227
absolute error = 2e-31
relative error = 5.0886018133821397372382694778283e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1456
Order of pole = 2.2e-29
TOP MAIN SOLVE Loop
x[1] = -4.857
y[1] (analytic) = 3.937195588573376323713655995516
y[1] (numeric) = 3.9371955885733763237136559955157
absolute error = 3e-31
relative error = 7.6196366995499845412247715580743e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.856
y[1] (analytic) = 3.9440866073831218941118210061904
y[1] (numeric) = 3.9440866073831218941118210061901
absolute error = 3e-31
relative error = 7.6063238428490854896939014466989e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1436
Order of pole = 1.69e-28
TOP MAIN SOLVE Loop
x[1] = -4.855
y[1] (analytic) = 3.9510264489868069324202161763207
y[1] (numeric) = 3.9510264489868069324202161763204
absolute error = 3e-31
relative error = 7.5929635975211297508256530444570e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1426
Order of pole = 9e-30
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.1MB, time=2.01
x[1] = -4.854
y[1] (analytic) = 3.9580157957708169269400075257417
y[1] (numeric) = 3.9580157957708169269400075257415
absolute error = 2e-31
relative error = 5.0530369336499915607561527681398e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.853
y[1] (analytic) = 3.9650553446297584438367691949279
y[1] (numeric) = 3.9650553446297584438367691949277
absolute error = 2e-31
relative error = 5.0440657851315623352734861315451e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.852
y[1] (analytic) = 3.9721458073806560270670559192939
y[1] (numeric) = 3.9721458073806560270670559192936
absolute error = 3e-31
relative error = 7.5525928439628047153310456926741e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.851
y[1] (analytic) = 3.979287911192036756358782299909
y[1] (numeric) = 3.9792879111920367563587822999087
absolute error = 3e-31
relative error = 7.5390373025341587881785908867418e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1386
Order of pole = 7.3e-29
TOP MAIN SOLVE Loop
x[1] = -4.85
y[1] (analytic) = 3.9864823990285492517577304021098
y[1] (numeric) = 3.9864823990285492517577304021095
absolute error = 3e-31
relative error = 7.5254314448523806371119935634478e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.849
y[1] (analytic) = 3.9937300301117969352240453954106
y[1] (numeric) = 3.9937300301117969352240453954103
absolute error = 3e-31
relative error = 7.5117746502159552872962173131768e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.848
y[1] (analytic) = 4.0010315803981003226950019230733
y[1] (numeric) = 4.0010315803981003226950019230731
absolute error = 2e-31
relative error = 4.9987108569660456403552824816817e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1356
Order of pole = 5.6e-29
TOP MAIN SOLVE Loop
x[1] = -4.847
y[1] (analytic) = 4.0083878430739401532204133483018
y[1] (numeric) = 4.0083878430739401532204133483015
absolute error = 3e-31
relative error = 7.4843057045581926961892927671431e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1346
Order of pole = 3.0e-29
TOP MAIN SOLVE Loop
x[1] = -4.846
y[1] (analytic) = 4.0157996290698724041630935165322
y[1] (numeric) = 4.0157996290698724041630935165319
absolute error = 3e-31
relative error = 7.4704922483765732591346317090085e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.845
y[1] (analytic) = 4.0232677675937478424153430227217
y[1] (numeric) = 4.0232677675937478424153430227214
absolute error = 3e-31
relative error = 7.4566252441960930137511251261509e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.844
y[1] (analytic) = 4.0307931066841128817975660629393
y[1] (numeric) = 4.0307931066841128817975660629391
absolute error = 2e-31
relative error = 4.9618026702573126005389698224637e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1316
Order of pole = 9e-30
TOP MAIN SOLVE Loop
x[1] = -4.843
y[1] (analytic) = 4.0383765137847153292170779578661
y[1] (numeric) = 4.0383765137847153292170779578659
absolute error = 2e-31
relative error = 4.9524852206651363638274618059035e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1306
Order of pole = 5.1e-29
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.1MB, time=2.17
x[1] = -4.842
y[1] (analytic) = 4.0460188763410882930066238854408
y[1] (numeric) = 4.0460188763410882930066238854406
absolute error = 2e-31
relative error = 4.9431306702371291649851731874659e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1296
Order of pole = 3.8e-29
TOP MAIN SOLVE Loop
x[1] = -4.841
y[1] (analytic) = 4.0537211024202382967907754171883
y[1] (numeric) = 4.0537211024202382967907754171882
absolute error = 1e-31
relative error = 2.4668692658776126777806337429842e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1286
Order of pole = 1e-30
TOP MAIN SOLVE Loop
x[1] = -4.84
y[1] (analytic) = 4.0614841213545197075655208706915
y[1] (numeric) = 4.0614841213545197075655208706914
absolute error = 1e-31
relative error = 2.4621541538035026653283694417966e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1276
Order of pole = 2.7e-29
TOP MAIN SOLVE Loop
x[1] = -4.839
y[1] (analytic) = 4.0693088844108371807625632356911
y[1] (numeric) = 4.069308884410837180762563235691
absolute error = 1e-31
relative error = 2.4574197447407142072630304639960e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1266
Order of pole = 1.08e-28
TOP MAIN SOLVE Loop
x[1] = -4.838
y[1] (analytic) = 4.0771963654863811997494447284817
y[1] (numeric) = 4.0771963654863811997494447284816
absolute error = 1e-31
relative error = 2.4526657790265810451865849781195e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1256
Order of pole = 1.6e-29
TOP MAIN SOLVE Loop
x[1] = -4.837
y[1] (analytic) = 4.0851475618321692144647937066179
y[1] (numeric) = 4.0851475618321692144647937066178
absolute error = 1e-31
relative error = 2.4478919913274926238294433189968e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1246
Order of pole = 4.1e-29
TOP MAIN SOLVE Loop
x[1] = -4.836
y[1] (analytic) = 4.0931634948057366575950169062117
y[1] (numeric) = 4.0931634948057366575950169062116
absolute error = 1e-31
relative error = 2.4430981104688573904040886240698e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1236
Order of pole = 4.4e-29
TOP MAIN SOLVE Loop
x[1] = -4.835
y[1] (analytic) = 4.1012452106543985546282769842906
y[1] (numeric) = 4.1012452106543985546282769842904
absolute error = 2e-31
relative error = 4.8765677185170747528786536510280e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1226
Order of pole = 3.3e-29
TOP MAIN SOLVE Loop
x[1] = -4.834
y[1] (analytic) = 4.109393781330583890061298632229
y[1] (numeric) = 4.1093937813305838900612986322288
absolute error = 2e-31
relative error = 4.8668979086068953090775930881535e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1216
Order of pole = 2.2e-29
TOP MAIN SOLVE Loop
x[1] = -4.833
y[1] (analytic) = 4.1176103053408317181599987244319
y[1] (numeric) = 4.1176103053408317181599987244317
absolute error = 2e-31
relative error = 4.8571862116379944502942386043114e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.832
y[1] (analytic) = 4.1258959086301306161495541590161
y[1] (numeric) = 4.1258959086301306161495541590159
absolute error = 2e-31
relative error = 4.8474320348620595071806846335858e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1196
Order of pole = 1.53e-28
TOP MAIN SOLVE Loop
x[1] = -4.831
y[1] (analytic) = 4.1342517455033819075465233669056
y[1] (numeric) = 4.1342517455033819075465233669054
absolute error = 2e-31
relative error = 4.8376347719398065297273157845483e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.1MB, time=2.32
x[1] = -4.83
y[1] (analytic) = 4.1426789995858726075607830777096
y[1] (numeric) = 4.1426789995858726075607830777093
absolute error = 3e-31
relative error = 7.2416907037689819771223322347131e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1176
Order of pole = 4.1e-29
TOP MAIN SOLVE Loop
x[1] = -4.829
y[1] (analytic) = 4.1511788848247567755824467144763
y[1] (numeric) = 4.1511788848247567755824467144761
absolute error = 2e-31
relative error = 4.8179084917571086120621917400656e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1166
Order of pole = 3.3e-29
TOP MAIN SOLVE Loop
x[1] = -4.828
y[1] (analytic) = 4.1597526465336644605361338304908
y[1] (numeric) = 4.1597526465336644605361338304905
absolute error = 3e-31
relative error = 7.2119672848814937371421463686129e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.827
y[1] (analytic) = 4.1684015624826863006878160714432
y[1] (numeric) = 4.168401562482686300687816071443
absolute error = 2e-31
relative error = 4.7980022318406544278185234205555e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1146
Order of pole = 5.2e-29
TOP MAIN SOLVE Loop
x[1] = -4.826
y[1] (analytic) = 4.1771269440361197509124168695575
y[1] (numeric) = 4.1771269440361197509124168695573
absolute error = 2e-31
relative error = 4.7879799364381154314572360085391e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1136
Order of pole = 1.1e-29
TOP MAIN SOLVE Loop
x[1] = -4.825
y[1] (analytic) = 4.1859301373405105764632642795663
y[1] (numeric) = 4.185930137340510576463264279566
absolute error = 3e-31
relative error = 7.1668659092958976342778692605535e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.824
y[1] (analytic) = 4.1948125245656814560536984382819
y[1] (numeric) = 4.1948125245656814560536984382817
absolute error = 2e-31
relative error = 4.7677935266179127140651640988084e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.823
y[1] (analytic) = 4.2037755252016091321793637214162
y[1] (numeric) = 4.203775525201609132179363721416
absolute error = 2e-31
relative error = 4.7576279656466239963214288090083e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used
Radius of convergence = 0.101
Order of pole = 6.746e-27
TOP MAIN SOLVE Loop
x[1] = -4.822
y[1] (analytic) = 4.212820597414193464218245217077
y[1] (numeric) = 4.2128205974141934642182452170768
absolute error = 2e-31
relative error = 4.7474131730831101640109491761396e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1096
Order of pole = 2.1e-29
TOP MAIN SOLVE Loop
x[1] = -4.821
y[1] (analytic) = 4.2219492394631569964307864206525
y[1] (numeric) = 4.2219492394631569964307864206523
absolute error = 2e-31
relative error = 4.7371483799608886260914017189456e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1086
Order of pole = 1.18e-28
TOP MAIN SOLVE Loop
x[1] = -4.82
y[1] (analytic) = 4.2311629911855233590604142329946
y[1] (numeric) = 4.2311629911855233590604142329944
absolute error = 2e-31
relative error = 4.7268327979008507312821923019595e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.819
y[1] (analytic) = 4.2404634355483481905083477818901
y[1] (numeric) = 4.2404634355483481905083477818899
absolute error = 2e-31
relative error = 4.7164656184362864604056247105977e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.1MB, time=2.48
x[1] = -4.818
y[1] (analytic) = 4.249852200274618630665024343906
y[1] (numeric) = 4.2498522002746186306650243439058
absolute error = 2e-31
relative error = 4.7060460123078238081440637219806e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1056
Order of pole = 1.9e-29
TOP MAIN SOLVE Loop
x[1] = -4.817
y[1] (analytic) = 4.2593309595464982449766332201665
y[1] (numeric) = 4.2593309595464982449766332201663
absolute error = 2e-31
relative error = 4.6955731287266417669309485591255e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1046
Order of pole = 6.3e-29
TOP MAIN SOLVE Loop
x[1] = -4.816
y[1] (analytic) = 4.2689014357903750905329176478337
y[1] (numeric) = 4.2689014357903750905329176478335
absolute error = 2e-31
relative error = 4.6850460946042096352187868095990e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1036
Order of pole = 2e-30
TOP MAIN SOLVE Loop
x[1] = -4.815
y[1] (analytic) = 4.2785654015484732788886754163041
y[1] (numeric) = 4.2785654015484732788886754163038
absolute error = 3e-31
relative error = 7.0116960206200368171022497674615e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.814
y[1] (analytic) = 4.2883246814421147463315404798321
y[1] (numeric) = 4.2883246814421147463315404798319
absolute error = 2e-31
relative error = 4.6638259660120296208751875969713e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.813
y[1] (analytic) = 4.2981811542320701217290547323145
y[1] (numeric) = 4.2981811542320701217290547323143
absolute error = 2e-31
relative error = 4.6531310064275963090124118036447e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.1006
Order of pole = 2.5e-29
TOP MAIN SOLVE Loop
x[1] = -4.812
y[1] (analytic) = 4.3081367549818179066440727412812
y[1] (numeric) = 4.308136754981817906644072741281
absolute error = 2e-31
relative error = 4.6423781642661452963036697437596e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used
Radius of convergence = 0.09961
Order of pole = 1.02e-28
TOP MAIN SOLVE Loop
x[1] = -4.8100177407096553281681099049909
y[1] (analytic) = 4.3281722209962260474135195837425
y[1] (numeric) = 4.3281722209962260474135195837424
absolute error = 1e-31
relative error = 2.3104441065190043200251194049523e-30 %
Correct digits = 31
h = 0.00098614909419157040882974575830146
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.8090315916154637577592801592326
y[1] (analytic) = 4.3382926422673920384013497356244
y[1] (numeric) = 4.3382926422673920384013497356242
absolute error = 2e-31
relative error = 4.6101085494193578833539806030009e-30 %
Correct digits = 31
h = 0.00098614909419157040882974575830146
Real estimate of pole used
Radius of convergence = 0.09664
Order of pole = 9.4e-29
TOP MAIN SOLVE Loop
x[1] = -4.8080651655031560187586270083895
y[1] (analytic) = 4.3483119820236176554993442478215
y[1] (numeric) = 4.3483119820236176554993442478217
absolute error = 2e-31
relative error = 4.5994859804637106474848484030941e-30 %
Correct digits = 31
h = 0.00096642611230773900065315084313707
Complex estimate of poles used
Radius of convergence = 0.07202
Order of pole = 2.276e-26
TOP MAIN SOLVE Loop
x[1] = -4.8073449452700603778660445085668
y[1] (analytic) = 4.3558452468344652990582098043686
y[1] (numeric) = 4.3558452468344652990582098043683
absolute error = 3e-31
relative error = 6.8872970227310021450252542526072e-30 %
memory used=64.8MB, alloc=4.1MB, time=2.64
Correct digits = 31
h = 0.00072022023309564089258249982265019
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.8066247250369647369734620087441
y[1] (analytic) = 4.3634362154265243455866010897742
y[1] (numeric) = 4.3634362154265243455866010897733
absolute error = 9e-31
relative error = 2.0625946056416120169223690339441e-29 %
Correct digits = 30
h = 0.00072022023309564089258249982265019
Real estimate of pole used
Radius of convergence = 0.09424
Order of pole = 2.0e-29
TOP MAIN SOLVE Loop
x[1] = -4.8059045048038690960808795089214
y[1] (analytic) = 4.3710857705647245781490446520257
y[1] (numeric) = 4.3710857705647245781490446520243
absolute error = 1.4e-30
relative error = 3.2028655429909953716982998712875e-29 %
Correct digits = 30
h = 0.00072022023309564089258249982265019
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.804464064337677814295714509276
y[1] (analytic) = 4.3865642745550917392230461510637
y[1] (numeric) = 4.3865642745550917392230461510612
absolute error = 2.5e-30
relative error = 5.6992211752181906831513399322558e-29 %
Correct digits = 30
h = 0.00072022023309564089258249982265019
Real estimate of pole used
Radius of convergence = 0.09208
Order of pole = 1.51e-28
TOP MAIN SOLVE Loop
x[1] = -4.8037438441045821734031320094533
y[1] (analytic) = 4.3943950938924958630762805122239
y[1] (numeric) = 4.3943950938924958630762805122209
absolute error = 3.0e-30
relative error = 6.8268781843706285657650366809089e-29 %
Correct digits = 30
h = 0.00072022023309564089258249982265019
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.8023034036383908916179670098079
y[1] (analytic) = 4.4102447109560673922180281121712
y[1] (numeric) = 4.4102447109560673922180281121671
absolute error = 4.1e-30
relative error = 9.2965362892781259734790540185254e-29 %
Correct digits = 30
h = 0.00072022023309564089258249982265019
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.8015831834052952507253845099852
y[1] (analytic) = 4.4182655161730775180190217415206
y[1] (numeric) = 4.418265516173077518019021741516
absolute error = 4.6e-30
relative error = 1.0411325401702733168240153457710e-28 %
Correct digits = 29
h = 0.00072022023309564089258249982265019
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.8008629631721996098328020101625
y[1] (analytic) = 4.4263516981654598829552375265903
y[1] (numeric) = 4.4263516981654598829552375265851
absolute error = 5.2e-30
relative error = 1.1747823839111531539806229111732e-28 %
Correct digits = 29
h = 0.00072022023309564089258249982265019
Real estimate of pole used
Radius of convergence = 0.08847
Order of pole = 1.6e-29
TOP MAIN SOLVE Loop
x[1] = -4.7994225227060083280476370105171
y[1] (analytic) = 4.4427244825431142699629190090371
y[1] (numeric) = 4.4427244825431142699629190090307
absolute error = 6.4e-30
relative error = 1.4405574833973268824607343700015e-28 %
Correct digits = 29
h = 0.00072022023309564089258249982265019
NO POLE
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.1MB, time=2.79
x[1] = -4.7987023024729126871550545106944
y[1] (analytic) = 4.4510132967227909570166428750898
y[1] (numeric) = 4.4510132967227909570166428750828
absolute error = 7.0e-30
relative error = 1.5726755984202488662125773147254e-28 %
Correct digits = 29
h = 0.00072022023309564089258249982265019
Complex estimate of poles used
Radius of convergence = 0.05723
Order of pole = 8.027e-27
TOP MAIN SOLVE Loop
x[1] = -4.7975577185377326939196005824156
y[1] (analytic) = 4.4643300803402403068998651101427
y[1] (numeric) = 4.4643300803402403068998651101359
absolute error = 6.8e-30
relative error = 1.5231848625946025735815626680252e-28 %
Correct digits = 29
h = 0.00057229196758999661772696413940686
Real estimate of pole used
Radius of convergence = 0.08517
Order of pole = 4e-30
TOP MAIN SOLVE Loop
x[1] = -4.7969854265701426973018736182762
y[1] (analytic) = 4.4710560649655134047805013600758
y[1] (numeric) = 4.471056064965513404780501360069
absolute error = 6.8e-30
relative error = 1.5208934759918852499736006820465e-28 %
Correct digits = 29
h = 0.00057229196758999661772696413940686
Real estimate of pole used
Radius of convergence = 0.0846
Order of pole = 2.7e-29
TOP MAIN SOLVE Loop
x[1] = -4.7958408426349627040664196899974
y[1] (analytic) = 4.4846462851460490989602165415548
y[1] (numeric) = 4.4846462851460490989602165415482
absolute error = 6.6e-30
relative error = 1.4716879727751062306189456907632e-28 %
Correct digits = 29
h = 0.00057229196758999661772696413940686
Real estimate of pole used
Radius of convergence = 0.08345
Order of pole = 2.0e-29
TOP MAIN SOLVE Loop
x[1] = -4.794961242262060980216720291203
y[1] (analytic) = 4.495218088923505727149289989791
y[1] (numeric) = 4.4952180889235057271492899897846
absolute error = 6.4e-30
relative error = 1.4237351499741456893370471657437e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
Real estimate of pole used
Radius of convergence = 0.08257
Order of pole = 6.8e-29
memory used=72.4MB, alloc=4.1MB, time=2.95
TOP MAIN SOLVE Loop
x[1] = -4.7938856628434699349048167699105
y[1] (analytic) = 4.5083001623047747482426821655753
y[1] (numeric) = 4.5083001623047747482426821655696
absolute error = 5.7e-30
relative error = 1.2643346260879828996265331901978e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
Real estimate of pole used
Radius of convergence = 0.0815
Order of pole = 1e-30
TOP MAIN SOLVE Loop
x[1] = -4.7929637376275347532088994659455
y[1] (analytic) = 4.519652146941565767851680111687
y[1] (numeric) = 4.519652146941565767851680111682
absolute error = 5.0e-30
relative error = 1.1062798280578924854797544001052e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
NO POLE
memory used=76.2MB, alloc=4.1MB, time=3.10
TOP MAIN SOLVE Loop
x[1] = -4.791888158208943707896995944653
y[1] (analytic) = 4.5330621744207562347530152453577
y[1] (numeric) = 4.5330621744207562347530152453533
absolute error = 4.4e-30
relative error = 9.7064629398387654236184226492700e-29 %
Correct digits = 30
h = 0.00015365420265586361598621732750778
Real estimate of pole used
Radius of convergence = 0.0795
Order of pole = 7e-30
TOP MAIN SOLVE Loop
x[1] = -4.790966232993008526201078640688
y[1] (analytic) = 4.5447023044343475512083567875725
y[1] (numeric) = 4.5447023044343475512083567875686
absolute error = 3.9e-30
relative error = 8.5814201651771559392694799703666e-29 %
Correct digits = 30
h = 0.00015365420265586361598621732750778
NO POLE
memory used=80.1MB, alloc=4.1MB, time=3.25
TOP MAIN SOLVE Loop
x[1] = -4.7898906535744174808891751193955
y[1] (analytic) = 4.5584570387128803276098184854954
y[1] (numeric) = 4.5584570387128803276098184854922
absolute error = 3.2e-30
relative error = 7.0199191805996434433742002600378e-29 %
Correct digits = 30
h = 0.00015365420265586361598621732750778
NO POLE
memory used=83.9MB, alloc=4.1MB, time=3.40
TOP MAIN SOLVE Loop
x[1] = -4.7889687283584822991932578154305
y[1] (analytic) = 4.5704002247274259619539787660055
y[1] (numeric) = 4.570400224727425961953978766003
absolute error = 2.5e-30
relative error = 5.4699804767078083772344352024394e-29 %
Correct digits = 30
h = 0.00015365420265586361598621732750778
Real estimate of pole used
Radius of convergence = 0.07658
Order of pole = 2.6e-29
TOP MAIN SOLVE Loop
x[1] = -4.787893148939891253881354294138
y[1] (analytic) = 4.5845177387989343265773483577121
y[1] (numeric) = 4.5845177387989343265773483577103
absolute error = 1.8e-30
relative error = 3.9262581203831689946496237855233e-29 %
Correct digits = 30
h = 0.00015365420265586361598621732750778
NO POLE
memory used=87.7MB, alloc=4.1MB, time=3.55
TOP MAIN SOLVE Loop
x[1] = -4.786971223723956072185436990173
y[1] (analytic) = 4.5967800821760374463695756832689
y[1] (numeric) = 4.5967800821760374463695756832677
absolute error = 1.2e-30
relative error = 2.6105229716187345336628879162501e-29 %
Correct digits = 30
h = 0.00015365420265586361598621732750778
Real estimate of pole used
Radius of convergence = 0.07458
Order of pole = 1.9e-29
TOP MAIN SOLVE Loop
x[1] = -4.7858956443053650268735334688805
y[1] (analytic) = 4.6112799118087641220484589797257
y[1] (numeric) = 4.6112799118087641220484589797253
absolute error = 4e-31
relative error = 8.6743812488082273921614468572938e-30 %
Correct digits = 31
h = 0.00015365420265586361598621732750778
NO POLE
memory used=91.5MB, alloc=4.1MB, time=3.70
TOP MAIN SOLVE Loop
x[1] = -4.7849737190894298451776161649155
y[1] (analytic) = 4.6238788349029990145305040915283
y[1] (numeric) = 4.6238788349029990145305040915286
absolute error = 3e-31
relative error = 6.4880592833763880718712693206159e-30 %
Correct digits = 31
h = 0.00015365420265586361598621732750778
Real estimate of pole used
Radius of convergence = 0.07258
Order of pole = 7.1e-29
TOP MAIN SOLVE Loop
x[1] = -4.783898139670838799865712643623
y[1] (analytic) = 4.6387821408759074348877635630163
y[1] (numeric) = 4.6387821408759074348877635630174
absolute error = 1.1e-30
relative error = 2.3713120525903702265045651238455e-29 %
Correct digits = 30
h = 0.00015365420265586361598621732750778
NO POLE
memory used=95.3MB, alloc=4.1MB, time=3.84
TOP MAIN SOLVE Loop
x[1] = -4.782976214454903618169795339658
y[1] (analytic) = 4.651736535602313482244745729079
y[1] (numeric) = 4.6517365356023134822447457290805
absolute error = 1.5e-30
relative error = 3.2246022286938868094732319357852e-29 %
Correct digits = 30
h = 0.00015365420265586361598621732750778
NO POLE
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.1MB, time=3.99
x[1] = -4.7819006350363125728578918183655
y[1] (analytic) = 4.6670662890750813198870590811469
y[1] (numeric) = 4.6670662890750813198870590811492
absolute error = 2.3e-30
relative error = 4.9281494145132739162080725183310e-29 %
Correct digits = 30
h = 0.00015365420265586361598621732750778
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.7809787098203773911619745144005
y[1] (analytic) = 4.6803966869673162047928232317271
y[1] (numeric) = 4.6803966869673162047928232317301
absolute error = 3.0e-30
relative error = 6.4097131090481634106397457300672e-29 %
Correct digits = 30
h = 0.00015365420265586361598621732750778
NO POLE
memory used=103.0MB, alloc=4.1MB, time=4.14
TOP MAIN SOLVE Loop
x[1] = -4.779903130401786345850070993108
y[1] (analytic) = 4.6961778820590026412520743132157
y[1] (numeric) = 4.6961778820590026412520743132194
absolute error = 3.7e-30
relative error = 7.8787475536973565356469895258282e-29 %
Correct digits = 30
h = 0.00015365420265586361598621732750778
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.778981205185851164154153689143
y[1] (analytic) = 4.7099066496597663401430595695024
y[1] (numeric) = 4.7099066496597663401430595695069
absolute error = 4.5e-30
relative error = 9.5543294904264619533397528903149e-29 %
Correct digits = 30
h = 0.00015365420265586361598621732750778
NO POLE
memory used=106.8MB, alloc=4.1MB, time=4.29
TOP MAIN SOLVE Loop
x[1] = -4.7779056257672601188422501678505
y[1] (analytic) = 4.7261665481736428343592140050461
y[1] (numeric) = 4.7261665481736428343592140050514
absolute error = 5.3e-30
relative error = 1.1214162569129322402908129444059e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
Real estimate of pole used
Radius of convergence = 0.06552
Order of pole = 1.4e-29
TOP MAIN SOLVE Loop
x[1] = -4.7769837005513249371463328638855
y[1] (analytic) = 4.7403181124247685163417845221343
y[1] (numeric) = 4.7403181124247685163417845221403
absolute error = 6.0e-30
relative error = 1.2657378381998246822280358293586e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
NO POLE
memory used=110.6MB, alloc=4.1MB, time=4.44
TOP MAIN SOLVE Loop
x[1] = -4.775908121132733891834429342593
y[1] (analytic) = 4.7570865267347558082565267077322
y[1] (numeric) = 4.757086526734755808256526707739
absolute error = 6.8e-30
relative error = 1.4294463558281104907243745180796e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
Real estimate of pole used
Radius of convergence = 0.06352
Order of pole = 2.1e-29
TOP MAIN SOLVE Loop
x[1] = -4.774986195916798710138512038628
y[1] (analytic) = 4.7716876360694463950898520782736
y[1] (numeric) = 4.7716876360694463950898520782812
absolute error = 7.6e-30
relative error = 1.5927278941209786242165174345174e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
Real estimate of pole used
Radius of convergence = 0.0626
Order of pole = 1.07e-28
memory used=114.4MB, alloc=4.1MB, time=4.59
TOP MAIN SOLVE Loop
x[1] = -4.7739106164982076648266085173355
y[1] (analytic) = 4.7889972575391774491316466823414
y[1] (numeric) = 4.7889972575391774491316466823498
absolute error = 8.4e-30
relative error = 1.7540206327694440000175373626988e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
Real estimate of pole used
Radius of convergence = 0.06152
Order of pole = 8e-30
TOP MAIN SOLVE Loop
x[1] = -4.7729886912822724831306912133705
y[1] (analytic) = 4.8040772856848793186039033978405
y[1] (numeric) = 4.8040772856848793186039033978497
absolute error = 9.2e-30
relative error = 1.9150399656171286455998174770926e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
NO POLE
memory used=118.2MB, alloc=4.1MB, time=4.74
TOP MAIN SOLVE Loop
x[1] = -4.771913111863681437818787692078
y[1] (analytic) = 4.8219640677067258405100205882703
y[1] (numeric) = 4.8219640677067258405100205882804
absolute error = 1.01e-29
relative error = 2.0945821781711142414481019377711e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
NO POLE
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.1MB, time=4.89
x[1] = -4.770991186647746256122870388113
y[1] (analytic) = 4.8375553688665538234642295736055
y[1] (numeric) = 4.8375553688665538234642295736164
absolute error = 1.09e-29
relative error = 2.2532041845246901366017663958258e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
Real estimate of pole used
Radius of convergence = 0.0586
Order of pole = 1.4e-29
TOP MAIN SOLVE Loop
x[1] = -4.7699156072291552108109668668205
y[1] (analytic) = 4.856058975796731093128233709115
y[1] (numeric) = 4.8560589757967310931282337091267
absolute error = 1.17e-29
relative error = 2.4093611832793663776921275509065e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
NO POLE
memory used=125.8MB, alloc=4.1MB, time=5.04
TOP MAIN SOLVE Loop
x[1] = -4.7689936820132200291150495628555
y[1] (analytic) = 4.8721973020015482371701087895749
y[1] (numeric) = 4.8721973020015482371701087895873
absolute error = 1.24e-29
relative error = 2.5450529261009101175475993547027e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
Real estimate of pole used
Radius of convergence = 0.0566
Order of pole = 6.0e-29
TOP MAIN SOLVE Loop
x[1] = -4.767918102594628983803146041563
y[1] (analytic) = 4.891361638080181036440286495562
y[1] (numeric) = 4.8913616380801810364402864955753
absolute error = 1.33e-29
relative error = 2.7190792634216553109614016423876e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
NO POLE
memory used=129.7MB, alloc=4.1MB, time=5.19
TOP MAIN SOLVE Loop
x[1] = -4.766996177378693802107228737598
y[1] (analytic) = 4.9080866322441509388530250552786
y[1] (numeric) = 4.9080866322441509388530250552929
absolute error = 1.43e-29
relative error = 2.9135590040434012929540154357922e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.7659205979601027567953252163055
y[1] (analytic) = 4.9279604682334722623325897184727
y[1] (numeric) = 4.927960468233472262332589718488
absolute error = 1.53e-29
relative error = 3.1047326979643155353875915635130e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
Real estimate of pole used
Radius of convergence = 0.05353
Order of pole = 5.9e-29
memory used=133.5MB, alloc=4.1MB, time=5.35
TOP MAIN SOLVE Loop
x[1] = -4.7649986727441675750994079123405
y[1] (analytic) = 4.9453162500120325995488547110567
y[1] (numeric) = 4.9453162500120325995488547110728
absolute error = 1.61e-29
relative error = 3.2556057461362206309389803951693e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
Real estimate of pole used
Radius of convergence = 0.05261
Order of pole = 3.8e-29
TOP MAIN SOLVE Loop
x[1] = -4.763923093325576529787504391048
y[1] (analytic) = 4.9659539700488625019477143263376
y[1] (numeric) = 4.9659539700488625019477143263547
absolute error = 1.71e-29
relative error = 3.4434471408988401391426870385160e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
Real estimate of pole used
Radius of convergence = 0.05153
Order of pole = 5.9e-29
memory used=137.3MB, alloc=4.1MB, time=5.51
TOP MAIN SOLVE Loop
x[1] = -4.7628475139069854844756008697555
y[1] (analytic) = 4.9870277783271329188389425545407
y[1] (numeric) = 4.9870277783271329188389425545588
absolute error = 1.81e-29
relative error = 3.6294163186056146419188555386432e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
Real estimate of pole used
Radius of convergence = 0.05046
Order of pole = 1.8e-29
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.1MB, time=5.67
x[1] = -4.7619255886910503027796835657905
y[1] (analytic) = 5.0054523337223003295175783028361
y[1] (numeric) = 5.0054523337223003295175783028552
absolute error = 1.91e-29
relative error = 3.8158389545178829826578475650559e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.760850009272459257467780044498
y[1] (analytic) = 5.0273867746596936348448975729025
y[1] (numeric) = 5.0273867746596936348448975729225
absolute error = 2.00e-29
relative error = 3.9782099322075354271610568142163e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
NO POLE
memory used=144.9MB, alloc=4.1MB, time=5.84
TOP MAIN SOLVE Loop
x[1] = -4.759928084056524075771862740533
y[1] (analytic) = 5.0465793608590378847447778017528
y[1] (numeric) = 5.0465793608590378847447778017738
absolute error = 2.10e-29
relative error = 4.1612344715857875544439851774037e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
Real estimate of pole used
Radius of convergence = 0.04754
Order of pole = 7.4e-29
TOP MAIN SOLVE Loop
x[1] = -4.7588525046379330304599592192405
y[1] (analytic) = 5.0694475346161212193705678724383
y[1] (numeric) = 5.0694475346161212193705678724603
absolute error = 2.20e-29
relative error = 4.3397233820402734910968272640414e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
NO POLE
memory used=148.7MB, alloc=4.1MB, time=6.00
TOP MAIN SOLVE Loop
x[1] = -4.7579305794219978487640419152755
y[1] (analytic) = 5.0894748029291953893833009872726
y[1] (numeric) = 5.0894748029291953893833009872957
absolute error = 2.31e-29
relative error = 4.5387787334569433884468674502488e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
NO POLE
TOP MAIN SOLVE Loop
x[1] = -4.756855000003406803452138393983
y[1] (analytic) = 5.1133595451163619503778768506837
y[1] (numeric) = 5.1133595451163619503778768507079
absolute error = 2.42e-29
relative error = 4.7327006416188349068629014625307e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
NO POLE
memory used=152.5MB, alloc=4.1MB, time=6.17
TOP MAIN SOLVE Loop
x[1] = -4.755933074787471621756221090018
y[1] (analytic) = 5.1342972245349575811589439739614
y[1] (numeric) = 5.1342972245349575811589439739868
absolute error = 2.54e-29
relative error = 4.9471230217492175000325444393842e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
Real estimate of pole used
Radius of convergence = 0.04354
Order of pole = 5.1e-29
TOP MAIN SOLVE Loop
x[1] = -4.7548574953688805764443175687255
y[1] (analytic) = 5.1592929153665852837673034022733
y[1] (numeric) = 5.1592929153665852837673034022999
absolute error = 2.66e-29
relative error = 5.1557452612883832862121316847486e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
Complex estimate of poles used
Radius of convergence = 0.01859
Order of pole = 1.047e-27
memory used=156.4MB, alloc=4.1MB, time=6.33
TOP MAIN SOLVE Loop
x[1] = -4.7539355701529453947484002647605
y[1] (analytic) = 5.181227539496708573742333811126
y[1] (numeric) = 5.1812275394967085737423338111538
absolute error = 2.78e-29
relative error = 5.3655238624591310956701581264298e-28 %
Correct digits = 29
h = 0.00015365420265586361598621732750778
NO POLE
memory used=160.2MB, alloc=4.1MB, time=6.49
TOP MAIN SOLVE Loop
x[1] = -4.7528778758806310998951774124243
y[1] (analytic) = 5.2070007677923958894632571778411
y[1] (numeric) = 5.2070007677923958894632571778639
absolute error = 2.28e-29
relative error = 4.3787203069045217268929134874788e-28 %
Correct digits = 29
h = 0.00012506431116709460354173628016476
NO POLE
memory used=164.0MB, alloc=4.1MB, time=6.65
TOP MAIN SOLVE Loop
x[1] = -4.7519998035981998459448059890454
y[1] (analytic) = 5.228914401156607225601958107418
y[1] (numeric) = 5.228914401156607225601958107442
absolute error = 2.40e-29
relative error = 4.5898628584723688445480768573945e-28 %
Correct digits = 29
h = 5.7923690097243026679206699906218e-05
NO POLE
memory used=167.8MB, alloc=4.2MB, time=6.81
memory used=171.6MB, alloc=4.2MB, time=6.97
memory used=175.4MB, alloc=4.2MB, time=7.13
TOP MAIN SOLVE Loop
x[1] = -4.7509904472741993525784786915359
y[1] (analytic) = 5.2547133587917951954281968140459
y[1] (numeric) = 5.2547133587917951954281968140933
absolute error = 4.74e-29
relative error = 9.0204730046204801594910808852072e-28 %
Correct digits = 29
h = 2.0563939243265092369464686024901e-05
NO POLE
memory used=179.2MB, alloc=4.2MB, time=7.30
memory used=183.1MB, alloc=4.2MB, time=7.46
memory used=186.9MB, alloc=4.2MB, time=7.62
memory used=190.7MB, alloc=4.2MB, time=7.78
TOP MAIN SOLVE Loop
x[1] = -4.7499828142512793630523749219219
y[1] (analytic) = 5.2811507954329464180551764969405
y[1] (numeric) = 5.2811507954329464180551764970198
absolute error = 7.93e-29
relative error = 1.5015666674122873800411528792550e-27 %
Correct digits = 28
h = 2.0563939243265092369464686024901e-05
Real estimate of pole used
Radius of convergence = 0.03759
Order of pole = 2.0e-29
memory used=194.5MB, alloc=4.2MB, time=7.94
memory used=198.3MB, alloc=4.2MB, time=8.10
memory used=202.1MB, alloc=4.2MB, time=8.27
memory used=206.0MB, alloc=4.2MB, time=8.43
TOP MAIN SOLVE Loop
x[1] = -4.7489957451676026386186406169939
y[1] (analytic) = 5.3077455780347776596628328871988
y[1] (numeric) = 5.3077455780347776596628328873106
absolute error = 1.118e-28
relative error = 2.1063556712790776271332759675444e-27 %
Correct digits = 28
h = 2.0563939243265092369464686024901e-05
Real estimate of pole used
Radius of convergence = 0.03661
Order of pole = 4e-30
memory used=209.8MB, alloc=4.2MB, time=8.59
memory used=213.6MB, alloc=4.2MB, time=8.75
memory used=217.4MB, alloc=4.2MB, time=8.91
memory used=221.2MB, alloc=4.2MB, time=9.07
TOP MAIN SOLVE Loop
x[1] = -4.7479881121446826490925368473799
y[1] (analytic) = 5.3356452554726764699216053230618
y[1] (numeric) = 5.3356452554726764699216053232076
absolute error = 1.458e-28
relative error = 2.7325654727599353114239547034911e-27 %
Correct digits = 28
h = 2.0563939243265092369464686024901e-05
Real estimate of pole used
Radius of convergence = 0.0356
Order of pole = 2.6e-29
memory used=225.0MB, alloc=4.2MB, time=9.24
memory used=228.8MB, alloc=4.2MB, time=9.40
memory used=232.7MB, alloc=4.2MB, time=9.56
memory used=236.5MB, alloc=4.2MB, time=9.72
TOP MAIN SOLVE Loop
x[1] = -4.7469804791217626595664330777659
y[1] (analytic) = 5.3643467649343968896465389040623
y[1] (numeric) = 5.3643467649343968896465389042429
absolute error = 1.806e-28
relative error = 3.3666727360084940748651162249502e-27 %
Correct digits = 28
h = 2.0563939243265092369464686024901e-05
Real estimate of pole used
Radius of convergence = 0.03459
Order of pole = 5.7e-29
memory used=240.3MB, alloc=4.2MB, time=9.88
memory used=244.1MB, alloc=4.2MB, time=10.05
memory used=247.9MB, alloc=4.2MB, time=10.21
memory used=251.7MB, alloc=4.2MB, time=10.37
TOP MAIN SOLVE Loop
x[1] = -4.7459934100380859351326987728379
y[1] (analytic) = 5.3932856024804040899027184390921
y[1] (numeric) = 5.3932856024804040899027184393077
absolute error = 2.156e-28
relative error = 3.9975631904389465139377520371870e-27 %
Correct digits = 28
h = 2.0563939243265092369464686024901e-05
Real estimate of pole used
Radius of convergence = 0.0336
Order of pole = 3.6e-29
memory used=255.5MB, alloc=4.2MB, time=10.53
memory used=259.4MB, alloc=4.2MB, time=10.70
memory used=263.2MB, alloc=4.2MB, time=10.86
memory used=267.0MB, alloc=4.2MB, time=11.02
TOP MAIN SOLVE Loop
x[1] = -4.7449857770151659456065950032239
y[1] (analytic) = 5.423718356437575285547755968679
y[1] (numeric) = 5.4237183564375752855477559689313
absolute error = 2.523e-28
relative error = 4.6517902187995713777989764295740e-27 %
Correct digits = 28
h = 2.0563939243265092369464686024901e-05
Real estimate of pole used
Radius of convergence = 0.0326
Order of pole = 5.4e-29
memory used=270.8MB, alloc=4.2MB, time=11.18
memory used=274.6MB, alloc=4.2MB, time=11.35
memory used=278.4MB, alloc=4.2MB, time=11.51
memory used=282.2MB, alloc=4.2MB, time=11.67
TOP MAIN SOLVE Loop
x[1] = -4.7439987079314892211728606982959
y[1] (analytic) = 5.4544569066935611240873186553881
y[1] (numeric) = 5.4544569066935611240873186556777
absolute error = 2.896e-28
relative error = 5.3094195252438562443050151976523e-27 %
Correct digits = 28
h = 2.0563939243265092369464686024901e-05
NO POLE
memory used=286.1MB, alloc=4.2MB, time=11.83
memory used=289.9MB, alloc=4.2MB, time=11.99
memory used=293.7MB, alloc=4.2MB, time=12.15
memory used=297.5MB, alloc=4.2MB, time=12.31
TOP MAIN SOLVE Loop
x[1] = -4.7429910749085692316467569286819
y[1] (analytic) = 5.4868429101109461125327110253927
y[1] (numeric) = 5.4868429101109461125327110257214
absolute error = 3.287e-28
relative error = 5.9906945648887468744124757122408e-27 %
Correct digits = 28
h = 2.0563939243265092369464686024901e-05
NO POLE
memory used=301.3MB, alloc=4.2MB, time=12.48
memory used=305.1MB, alloc=4.2MB, time=12.64
memory used=309.0MB, alloc=4.2MB, time=12.80
memory used=312.8MB, alloc=4.2MB, time=12.95
TOP MAIN SOLVE Loop
x[1] = -4.7419834418856492421206531590679
y[1] (analytic) = 5.5203140229007879978565110750553
y[1] (numeric) = 5.5203140229007879978565110754246
absolute error = 3.693e-28
relative error = 6.6898368184848661289236791065232e-27 %
Correct digits = 28
h = 2.0563939243265092369464686024901e-05
NO POLE
memory used=316.6MB, alloc=4.2MB, time=13.11
memory used=320.4MB, alloc=4.2MB, time=13.26
memory used=324.2MB, alloc=4.2MB, time=13.41
memory used=328.0MB, alloc=4.2MB, time=13.56
TOP MAIN SOLVE Loop
x[1] = -4.7409963728019725176869188541399
y[1] (analytic) = 5.5542265192979478388311910936777
y[1] (numeric) = 5.5542265192979478388311910940881
absolute error = 4.104e-28
relative error = 7.3889676370612699999144528657984e-27 %
Correct digits = 28
h = 2.0563939243265092369464686024901e-05
NO POLE
memory used=331.8MB, alloc=4.2MB, time=13.71
memory used=335.7MB, alloc=4.3MB, time=13.86
memory used=339.5MB, alloc=4.3MB, time=14.01
memory used=343.3MB, alloc=4.3MB, time=14.17
TOP MAIN SOLVE Loop
x[1] = -4.7399887397790525281608150845259
y[1] (analytic) = 5.5900751849028362230011165539594
y[1] (numeric) = 5.5900751849028362230011165544134
absolute error = 4.540e-28
relative error = 8.1215365622652388650161273546676e-27 %
Correct digits = 28
h = 2.0563939243265092369464686024901e-05
NO POLE
memory used=347.1MB, alloc=4.3MB, time=14.33
memory used=350.9MB, alloc=4.3MB, time=14.49
memory used=354.7MB, alloc=4.3MB, time=14.65
memory used=358.5MB, alloc=4.3MB, time=14.82
TOP MAIN SOLVE Loop
x[1] = -4.7389811067561325386347113149119
y[1] (analytic) = 5.627257967727363608885718768677
y[1] (numeric) = 5.6272579677273636088857187691761
absolute error = 4.991e-28
relative error = 8.8693285941815030967715440615482e-27 %
Correct digits = 28
h = 2.0563939243265092369464686024901e-05
NO POLE
memory used=362.4MB, alloc=4.3MB, time=14.98
memory used=366.2MB, alloc=4.3MB, time=15.14
memory used=370.0MB, alloc=4.3MB, time=15.31
memory used=373.8MB, alloc=4.3MB, time=15.47
TOP MAIN SOLVE Loop
x[1] = -4.7379940376724558142009770099839
y[1] (analytic) = 5.6650746689182843019395709374785
y[1] (numeric) = 5.6650746689182843019395709380234
absolute error = 5.449e-28
relative error = 9.6185846055943643830194747678311e-27 %
Correct digits = 28
h = 2.0563939243265092369464686024901e-05
NO POLE
memory used=377.6MB, alloc=4.3MB, time=15.63
memory used=381.4MB, alloc=4.3MB, time=15.79
memory used=385.3MB, alloc=4.3MB, time=15.95
memory used=389.1MB, alloc=4.3MB, time=16.11
TOP MAIN SOLVE Loop
x[1] = -4.7369864046495358246748732403699
y[1] (analytic) = 5.7052143871206475071043558071628
y[1] (numeric) = 5.7052143871206475071043558077563
absolute error = 5.935e-28
relative error = 1.0402764203564526352977085859454e-26 %
Correct digits = 27
h = 2.0563939243265092369464686024901e-05
Real estimate of pole used
Radius of convergence = 0.0246
Order of pole = 5.6e-29
memory used=392.9MB, alloc=4.3MB, time=16.28
memory used=396.7MB, alloc=4.3MB, time=16.44
memory used=400.5MB, alloc=4.3MB, time=16.61
memory used=404.3MB, alloc=4.3MB, time=16.77
TOP MAIN SOLVE Loop
x[1] = -4.7359993355658591002411389354419
y[1] (analytic) = 5.7461627941945075009211355938863
y[1] (numeric) = 5.7461627941945075009211355945294
absolute error = 6.431e-28
relative error = 1.1191816574527614702195102719582e-26 %
Correct digits = 27
h = 2.0563939243265092369464686024901e-05
Real estimate of pole used
Radius of convergence = 0.02361
Order of pole = 1.35e-28
memory used=408.1MB, alloc=4.3MB, time=16.94
memory used=412.0MB, alloc=4.3MB, time=17.10
memory used=415.8MB, alloc=4.3MB, time=17.26
memory used=419.6MB, alloc=4.3MB, time=17.43
TOP MAIN SOLVE Loop
x[1] = -4.7349917025429391107150351658279
y[1] (analytic) = 5.7897700791021800738911329868594
y[1] (numeric) = 5.789770079102180073891132987555
absolute error = 6.956e-28
relative error = 1.2014294013344770430557650936059e-26 %
Correct digits = 27
h = 2.0563939243265092369464686024901e-05
Real estimate of pole used
Radius of convergence = 0.0226
Order of pole = 2e-30
memory used=423.4MB, alloc=4.3MB, time=17.59
memory used=427.2MB, alloc=4.3MB, time=17.75
memory used=431.0MB, alloc=4.3MB, time=17.91
memory used=434.8MB, alloc=4.3MB, time=18.08
TOP MAIN SOLVE Loop
x[1] = -4.7339840695200191211889313962139
y[1] (analytic) = 5.8353670708409698347827569813318
y[1] (numeric) = 5.8353670708409698347827569820825
absolute error = 7.507e-28
relative error = 1.2864657713671680113860739013686e-26 %
Correct digits = 27
h = 2.0563939243265092369464686024901e-05
Real estimate of pole used
Radius of convergence = 0.0216
Order of pole = 8.9e-29
memory used=438.7MB, alloc=4.3MB, time=18.24
memory used=442.5MB, alloc=4.3MB, time=18.40
memory used=446.3MB, alloc=4.3MB, time=18.57
memory used=450.1MB, alloc=4.3MB, time=18.73
TOP MAIN SOLVE Loop
x[1] = -4.7329970004363423967551970912859
y[1] (analytic) = 5.8821457388077878823653036617356
y[1] (numeric) = 5.882145738807787882365303662543
absolute error = 8.074e-28
relative error = 1.3726283500137254592905212165704e-26 %
Correct digits = 27
h = 2.0563939243265092369464686024901e-05
NO POLE
memory used=453.9MB, alloc=4.3MB, time=18.89
memory used=457.7MB, alloc=4.3MB, time=19.05
memory used=461.5MB, alloc=4.3MB, time=19.22
memory used=465.4MB, alloc=4.3MB, time=19.38
TOP MAIN SOLVE Loop
x[1] = -4.7319893674134224072290933216719
y[1] (analytic) = 5.9322699965919637174099961878099
y[1] (numeric) = 5.9322699965919637174099961886781
absolute error = 8.682e-28
relative error = 1.4635207104510974182798893824117e-26 %
Correct digits = 27
h = 2.0563939243265092369464686024901e-05
Real estimate of pole used
Radius of convergence = 0.0196
Order of pole = 3.6e-29
memory used=469.2MB, alloc=4.3MB, time=19.55
memory used=473.0MB, alloc=4.3MB, time=19.71
memory used=476.8MB, alloc=4.3MB, time=19.87
memory used=480.6MB, alloc=4.3MB, time=20.03
TOP MAIN SOLVE Loop
x[1] = -4.7309817343905024177029895520579
y[1] (analytic) = 5.9850409594923944854116762393729
y[1] (numeric) = 5.9850409594923944854116762403054
absolute error = 9.325e-28
relative error = 1.5580511583985676448927492157060e-26 %
Correct digits = 27
h = 2.0563939243265092369464686024901e-05
Real estimate of pole used
Radius of convergence = 0.01859
Order of pole = 1.14e-28
memory used=484.4MB, alloc=4.3MB, time=20.19
memory used=488.3MB, alloc=4.3MB, time=20.36
memory used=492.1MB, alloc=4.3MB, time=20.52
memory used=495.9MB, alloc=4.3MB, time=20.68
TOP MAIN SOLVE Loop
x[1] = -4.7299946653068256932692552471299
y[1] (analytic) = 6.0395850827113639429311901816066
y[1] (numeric) = 6.0395850827113639429311901826052
absolute error = 9.986e-28
relative error = 1.6534248401575565694406998140366e-26 %
Correct digits = 27
h = 2.0563939243265092369464686024901e-05
NO POLE
memory used=499.7MB, alloc=4.3MB, time=20.85
memory used=503.5MB, alloc=4.3MB, time=21.01
memory used=507.3MB, alloc=4.3MB, time=21.17
memory used=511.1MB, alloc=4.3MB, time=21.33
TOP MAIN SOLVE Loop
x[1] = -4.7289870322839057037431514775159
y[1] (analytic) = 6.098515862284725585897474080434
y[1] (numeric) = 6.0985158622847255858974740815042
absolute error = 1.0702e-27
relative error = 1.7548531875082541841591855786389e-26 %
Correct digits = 27
h = 2.0563939243265092369464686024901e-05
NO POLE
memory used=515.0MB, alloc=4.3MB, time=21.49
memory used=518.8MB, alloc=4.3MB, time=21.66
memory used=522.6MB, alloc=4.3MB, time=21.83
memory used=526.4MB, alloc=4.3MB, time=22.00
TOP MAIN SOLVE Loop
x[1] = -4.7279999632002289793094171725879
y[1] (analytic) = 6.1598212032607189024628147020642
y[1] (numeric) = 6.1598212032607189024628147032086
absolute error = 1.1444e-27
relative error = 1.8578461326023693670777355112909e-26 %
Correct digits = 27
h = 2.0563939243265092369464686024901e-05
Real estimate of pole used
Radius of convergence = 0.01561
Order of pole = 5.6e-29
memory used=530.2MB, alloc=4.3MB, time=22.17
memory used=534.0MB, alloc=4.3MB, time=22.34
memory used=537.8MB, alloc=4.3MB, time=22.50
memory used=541.7MB, alloc=4.3MB, time=22.65
TOP MAIN SOLVE Loop
x[1] = -4.7269923301773089897833134029739
y[1] (analytic) = 6.2265398819575840610741158724971
y[1] (numeric) = 6.2265398819575840610741158737223
absolute error = 1.2252e-27
relative error = 1.9677060184745897847448675227136e-26 %
Correct digits = 27
h = 2.0563939243265092369464686024901e-05
Real estimate of pole used
Radius of convergence = 0.0146
Order of pole = 8.0e-29
memory used=545.5MB, alloc=4.3MB, time=22.80
memory used=549.3MB, alloc=4.3MB, time=22.95
memory used=553.1MB, alloc=4.3MB, time=23.12
memory used=556.9MB, alloc=4.3MB, time=23.28
TOP MAIN SOLVE Loop
x[1] = -4.7259846971543890002572096333599
y[1] (analytic) = 6.2980312866919282551746713826171
y[1] (numeric) = 6.2980312866919282551746713839291
absolute error = 1.3120e-27
relative error = 2.0831906674905300742336005128833e-26 %
Correct digits = 27
h = 2.0563939243265092369464686024901e-05
NO POLE
memory used=560.7MB, alloc=4.3MB, time=23.44
memory used=564.6MB, alloc=4.3MB, time=23.60
memory used=568.4MB, alloc=4.3MB, time=23.75
memory used=572.2MB, alloc=4.3MB, time=23.91
TOP MAIN SOLVE Loop
x[1] = -4.7249976280707122758234753284319
y[1] (analytic) = 6.3733988726231757652436970460644
y[1] (numeric) = 6.3733988726231757652436970474679
absolute error = 1.4035e-27
relative error = 2.2021217062511337389503328570622e-26 %
Correct digits = 27
h = 2.0563939243265092369464686024901e-05
Real estimate of pole used
Radius of convergence = 0.01261
Order of pole = 3.0e-29
memory used=576.0MB, alloc=4.3MB, time=24.06
memory used=579.8MB, alloc=4.3MB, time=24.21
memory used=583.6MB, alloc=4.3MB, time=24.36
memory used=587.4MB, alloc=4.3MB, time=24.52
TOP MAIN SOLVE Loop
x[1] = -4.7239899950477922862973715588179
y[1] (analytic) = 6.4566851444289026622570463558368
y[1] (numeric) = 6.4566851444289026622570463573414
absolute error = 1.5046e-27
relative error = 2.3302979258609685452777527228259e-26 %
Correct digits = 27
h = 2.0563939243265092369464686024901e-05
NO POLE
memory used=591.3MB, alloc=4.3MB, time=24.67
memory used=595.1MB, alloc=4.3MB, time=24.83
memory used=598.9MB, alloc=4.3MB, time=24.98
memory used=602.7MB, alloc=4.3MB, time=25.13
TOP MAIN SOLVE Loop
x[1] = -4.7229823620248722967712677892039
y[1] (analytic) = 6.5475445497932186657148687954159
y[1] (numeric) = 6.5475445497932186657148687970306
absolute error = 1.6147e-27
relative error = 2.4661153318170162918271616354146e-26 %
Correct digits = 27
h = 2.0563939243265092369464686024901e-05
Real estimate of pole used
Radius of convergence = 0.01059
Order of pole = 3.6e-29
memory used=606.5MB, alloc=4.3MB, time=25.28
memory used=610.3MB, alloc=4.3MB, time=25.44
memory used=614.1MB, alloc=4.3MB, time=25.59
memory used=618.0MB, alloc=4.3MB, time=25.74
memory used=621.8MB, alloc=4.3MB, time=25.90
memory used=625.6MB, alloc=4.3MB, time=26.05
TOP MAIN SOLVE Loop
x[1] = -4.7219983527079654239304007305329
y[1] (analytic) = 6.6450317631422121351175673466982
y[1] (numeric) = 6.6450317631422121351175673486503
absolute error = 1.9521e-27
relative error = 2.9376834747843515704127000795213e-26 %
Correct digits = 27
h = 1.0532029228395596177621177743989e-05
Real estimate of pole used
Radius of convergence = 0.009609
Order of pole = 5.2e-29
memory used=629.4MB, alloc=4.3MB, time=26.21
memory used=633.2MB, alloc=4.3MB, time=26.36
memory used=637.0MB, alloc=4.3MB, time=26.52
memory used=640.8MB, alloc=4.3MB, time=26.68
memory used=644.7MB, alloc=4.3MB, time=26.83
memory used=648.5MB, alloc=4.3MB, time=26.98
memory used=652.3MB, alloc=4.3MB, time=27.14
memory used=656.1MB, alloc=4.3MB, time=27.30
TOP MAIN SOLVE Loop
x[1] = -4.7209978099312678422935267186514
y[1] (analytic) = 6.7549792629688737657774623842806
y[1] (numeric) = 6.7549792629688737657774623866922
absolute error = 2.4116e-27
relative error = 3.5701071848147765353745556156964e-26 %
Correct digits = 27
h = 1.0532029228395596177621177743989e-05
Real estimate of pole used
Radius of convergence = 0.008609
Order of pole = 6.3e-29
memory used=659.9MB, alloc=4.3MB, time=27.45
memory used=663.7MB, alloc=4.3MB, time=27.60
memory used=667.6MB, alloc=4.3MB, time=27.75
memory used=671.4MB, alloc=4.3MB, time=27.91
memory used=675.2MB, alloc=4.3MB, time=28.06
memory used=679.0MB, alloc=4.3MB, time=28.21
memory used=682.8MB, alloc=4.3MB, time=28.36
memory used=686.6MB, alloc=4.3MB, time=28.51
TOP MAIN SOLVE Loop
x[1] = -4.7199972671545702606566527067699
y[1] (analytic) = 6.8785269089373507493130593665037
y[1] (numeric) = 6.8785269089373507493130593694313
absolute error = 2.9276e-27
relative error = 4.2561438499224811599866162790539e-26 %
Correct digits = 27
h = 1.0532029228395596177621177743989e-05
NO POLE
memory used=690.4MB, alloc=4.3MB, time=28.67
memory used=694.3MB, alloc=4.3MB, time=28.81
memory used=698.1MB, alloc=4.3MB, time=28.97
memory used=701.9MB, alloc=4.3MB, time=29.12
memory used=705.7MB, alloc=4.3MB, time=29.27
memory used=709.5MB, alloc=4.3MB, time=29.42
memory used=713.3MB, alloc=4.3MB, time=29.58
TOP MAIN SOLVE Loop
x[1] = -4.7189967243778726790197786948884
y[1] (analytic) = 7.0195202625230721464405960516087
y[1] (numeric) = 7.0195202625230721464405960551258
absolute error = 3.5171e-27
relative error = 5.0104563680479009112258662424031e-26 %
Correct digits = 27
h = 1.0532029228395596177621177743989e-05
NO POLE
memory used=717.1MB, alloc=4.3MB, time=29.73
memory used=721.0MB, alloc=4.3MB, time=29.88
memory used=724.8MB, alloc=4.3MB, time=30.03
memory used=728.6MB, alloc=4.3MB, time=30.18
memory used=732.4MB, alloc=4.3MB, time=30.34
memory used=736.2MB, alloc=4.3MB, time=30.49
memory used=740.0MB, alloc=4.3MB, time=30.64
memory used=743.8MB, alloc=4.3MB, time=30.79
TOP MAIN SOLVE Loop
x[1] = -4.7179961816011750973829046830069
y[1] (analytic) = 7.1837088159506841331017260919221
y[1] (numeric) = 7.1837088159506841331017260961253
absolute error = 4.2032e-27
relative error = 5.8510166651900312713176226897866e-26 %
Correct digits = 27
h = 1.0532029228395596177621177743989e-05
NO POLE
memory used=747.7MB, alloc=4.3MB, time=30.95
memory used=751.5MB, alloc=4.3MB, time=31.10
memory used=755.3MB, alloc=4.3MB, time=31.25
memory used=759.1MB, alloc=4.3MB, time=31.40
memory used=762.9MB, alloc=4.3MB, time=31.55
memory used=766.7MB, alloc=4.3MB, time=31.70
memory used=770.5MB, alloc=4.3MB, time=31.86
TOP MAIN SOLVE Loop
memory used=774.4MB, alloc=4.3MB, time=32.01
x[1] = -4.7169956388244775157460306711254
y[1] (analytic) = 7.380256072062233013473160369383
y[1] (numeric) = 7.3802560720622330134731603744079
absolute error = 5.0249e-27
relative error = 6.8085713435088356494964773945238e-26 %
Correct digits = 27
h = 1.0532029228395596177621177743989e-05
NO POLE
memory used=778.2MB, alloc=4.3MB, time=32.16
memory used=782.0MB, alloc=4.3MB, time=32.31
memory used=785.8MB, alloc=4.3MB, time=32.46
memory used=789.6MB, alloc=4.3MB, time=32.62
memory used=793.4MB, alloc=4.3MB, time=32.77
memory used=797.3MB, alloc=4.3MB, time=32.92
memory used=801.1MB, alloc=4.3MB, time=33.06
TOP MAIN SOLVE Loop
x[1] = -4.7159950960477799341091566592439
y[1] (analytic) = 7.6251262468838746063779444906131
y[1] (numeric) = 7.6251262468838746063779444966623
absolute error = 6.0492e-27
relative error = 7.9332456986821678363038840209603e-26 %
Correct digits = 27
h = 1.0532029228395596177621177743989e-05
Real estimate of pole used
Radius of convergence = 0.003606
Order of pole = 8.4e-29
memory used=804.9MB, alloc=4.3MB, time=33.21
memory used=808.7MB, alloc=4.3MB, time=33.36
memory used=812.5MB, alloc=4.3MB, time=33.51
memory used=816.3MB, alloc=4.3MB, time=33.66
memory used=820.1MB, alloc=4.3MB, time=33.81
memory used=824.0MB, alloc=4.3MB, time=33.96
memory used=827.8MB, alloc=4.3MB, time=34.11
memory used=831.6MB, alloc=4.3MB, time=34.27
memory used=835.4MB, alloc=4.3MB, time=34.42
TOP MAIN SOLVE Loop
x[1] = -4.7149918403816523018695670193582
y[1] (analytic) = 7.9511455688253556809234777466726
y[1] (numeric) = 7.9511455688253556809234777529867
absolute error = 6.3141e-27
relative error = 7.9411198617167301255523730796187e-26 %
Correct digits = 27
h = 8.3997626540732418428655547814105e-06
Complex estimate of poles used
Radius of convergence = 0.002595
Order of pole = 8.248e-27
memory used=839.2MB, alloc=4.3MB, time=34.57
memory used=843.0MB, alloc=4.3MB, time=34.73
memory used=846.8MB, alloc=4.3MB, time=34.88
memory used=850.7MB, alloc=4.3MB, time=35.03
memory used=854.5MB, alloc=4.3MB, time=35.18
memory used=858.3MB, alloc=4.3MB, time=35.34
memory used=862.1MB, alloc=4.3MB, time=35.49
memory used=865.9MB, alloc=4.3MB, time=35.64
memory used=869.7MB, alloc=4.3MB, time=35.80
TOP MAIN SOLVE Loop
x[1] = -4.713992268625817586090266018337
y[1] (analytic) = 8.4356990363870589695801617753357
y[1] (numeric) = 8.4356990363870589695801617805754
absolute error = 5.2397e-27
relative error = 6.2113406101838843392931606754870e-26 %
Correct digits = 27
h = 8.3997626540732418428655547814105e-06
NO POLE
memory used=873.6MB, alloc=4.3MB, time=35.95
memory used=877.4MB, alloc=4.3MB, time=36.11
memory used=881.2MB, alloc=4.3MB, time=36.26
memory used=885.0MB, alloc=4.3MB, time=36.41
memory used=888.8MB, alloc=4.3MB, time=36.57
memory used=892.6MB, alloc=4.3MB, time=36.72
memory used=896.4MB, alloc=4.3MB, time=36.88
memory used=900.3MB, alloc=4.3MB, time=37.03
memory used=904.1MB, alloc=4.3MB, time=37.18
memory used=907.9MB, alloc=4.3MB, time=37.33
memory used=911.7MB, alloc=4.3MB, time=37.49
memory used=915.5MB, alloc=4.3MB, time=37.64
memory used=919.3MB, alloc=4.3MB, time=37.79
memory used=923.1MB, alloc=4.3MB, time=37.95
memory used=927.0MB, alloc=4.3MB, time=38.10
memory used=930.8MB, alloc=4.3MB, time=38.26
memory used=934.6MB, alloc=4.3MB, time=38.41
memory used=938.4MB, alloc=4.3MB, time=38.56
memory used=942.2MB, alloc=4.3MB, time=38.72
memory used=946.0MB, alloc=4.3MB, time=38.87
memory used=949.8MB, alloc=4.3MB, time=39.02
memory used=953.7MB, alloc=4.3MB, time=39.18
memory used=957.5MB, alloc=4.3MB, time=39.33
memory used=961.3MB, alloc=4.3MB, time=39.48
memory used=965.1MB, alloc=4.3MB, time=39.63
memory used=968.9MB, alloc=4.3MB, time=39.79
memory used=972.7MB, alloc=4.3MB, time=39.94
memory used=976.6MB, alloc=4.3MB, time=40.09
memory used=980.4MB, alloc=4.3MB, time=40.24
TOP MAIN SOLVE Loop
x[1] = -4.7129993869802025224804615262555
y[1] (analytic) = 9.4013853349213254506159215891454
y[1] (numeric) = 9.4013853349213254506159215896224
absolute error = 4.770e-28
relative error = 5.0737203402161339727138561487564e-27 %
Correct digits = 28
h = 1.2343788689472157317867957536685e-06
Real estimate of pole used
Radius of convergence = 0.0006104
Order of pole = 2.2e-29
memory used=984.2MB, alloc=4.3MB, time=40.39
memory used=988.0MB, alloc=4.3MB, time=40.55
memory used=991.8MB, alloc=4.3MB, time=40.70
memory used=995.6MB, alloc=4.3MB, time=40.85
memory used=999.4MB, alloc=4.3MB, time=41.00
memory used=1003.3MB, alloc=4.3MB, time=41.15
memory used=1007.1MB, alloc=4.3MB, time=41.31
memory used=1010.9MB, alloc=4.3MB, time=41.46
memory used=1014.7MB, alloc=4.3MB, time=41.61
memory used=1018.5MB, alloc=4.3MB, time=41.76
memory used=1022.3MB, alloc=4.3MB, time=41.91
memory used=1026.1MB, alloc=4.3MB, time=42.06
memory used=1030.0MB, alloc=4.3MB, time=42.22
memory used=1033.8MB, alloc=4.3MB, time=42.36
memory used=1037.6MB, alloc=4.3MB, time=42.52
memory used=1041.4MB, alloc=4.3MB, time=42.67
memory used=1045.2MB, alloc=4.3MB, time=42.82
memory used=1049.0MB, alloc=4.3MB, time=42.97
memory used=1052.9MB, alloc=4.3MB, time=43.12
memory used=1056.7MB, alloc=4.3MB, time=43.27
memory used=1060.5MB, alloc=4.3MB, time=43.42
memory used=1064.3MB, alloc=4.3MB, time=43.58
memory used=1068.1MB, alloc=4.3MB, time=43.73
memory used=1071.9MB, alloc=4.3MB, time=43.88
memory used=1075.7MB, alloc=4.3MB, time=44.03
memory used=1079.6MB, alloc=4.3MB, time=44.19
memory used=1083.4MB, alloc=4.3MB, time=44.34
memory used=1087.2MB, alloc=4.3MB, time=44.50
memory used=1091.0MB, alloc=4.3MB, time=44.65
memory used=1094.8MB, alloc=4.3MB, time=44.81
memory used=1098.6MB, alloc=4.3MB, time=44.96
memory used=1102.4MB, alloc=4.3MB, time=45.12
memory used=1106.3MB, alloc=4.3MB, time=45.27
memory used=1110.1MB, alloc=4.3MB, time=45.42
memory used=1113.9MB, alloc=4.3MB, time=45.58
memory used=1117.7MB, alloc=4.3MB, time=45.73
memory used=1121.5MB, alloc=4.3MB, time=45.89
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memory used=3830.1MB, alloc=4.3MB, time=155.60
memory used=3833.9MB, alloc=4.3MB, time=155.75
memory used=3837.7MB, alloc=4.3MB, time=155.91
memory used=3841.5MB, alloc=4.3MB, time=156.07
memory used=3845.3MB, alloc=4.3MB, time=156.22
memory used=3849.1MB, alloc=4.3MB, time=156.38
memory used=3852.9MB, alloc=4.3MB, time=156.54
memory used=3856.8MB, alloc=4.3MB, time=156.70
memory used=3860.6MB, alloc=4.3MB, time=156.85
memory used=3864.4MB, alloc=4.3MB, time=157.01
memory used=3868.2MB, alloc=4.3MB, time=157.17
memory used=3872.0MB, alloc=4.3MB, time=157.32
memory used=3875.8MB, alloc=4.3MB, time=157.48
memory used=3879.7MB, alloc=4.3MB, time=157.64
memory used=3883.5MB, alloc=4.3MB, time=157.80
memory used=3887.3MB, alloc=4.3MB, time=157.95
memory used=3891.1MB, alloc=4.3MB, time=158.11
memory used=3894.9MB, alloc=4.3MB, time=158.27
memory used=3898.7MB, alloc=4.3MB, time=158.42
memory used=3902.5MB, alloc=4.3MB, time=158.58
memory used=3906.4MB, alloc=4.3MB, time=158.74
memory used=3910.2MB, alloc=4.3MB, time=158.89
memory used=3914.0MB, alloc=4.3MB, time=159.05
memory used=3917.8MB, alloc=4.3MB, time=159.21
memory used=3921.6MB, alloc=4.3MB, time=159.37
memory used=3925.4MB, alloc=4.3MB, time=159.52
memory used=3929.2MB, alloc=4.3MB, time=159.68
memory used=3933.1MB, alloc=4.3MB, time=159.83
memory used=3936.9MB, alloc=4.3MB, time=159.99
memory used=3940.7MB, alloc=4.3MB, time=160.15
memory used=3944.5MB, alloc=4.3MB, time=160.30
memory used=3948.3MB, alloc=4.3MB, time=160.46
memory used=3952.1MB, alloc=4.3MB, time=160.62
memory used=3956.0MB, alloc=4.3MB, time=160.77
memory used=3959.8MB, alloc=4.3MB, time=160.93
memory used=3963.6MB, alloc=4.3MB, time=161.09
memory used=3967.4MB, alloc=4.3MB, time=161.24
memory used=3971.2MB, alloc=4.3MB, time=161.40
memory used=3975.0MB, alloc=4.3MB, time=161.56
memory used=3978.8MB, alloc=4.3MB, time=161.71
memory used=3982.7MB, alloc=4.3MB, time=161.87
memory used=3986.5MB, alloc=4.3MB, time=162.03
memory used=3990.3MB, alloc=4.3MB, time=162.18
memory used=3994.1MB, alloc=4.3MB, time=162.34
memory used=3997.9MB, alloc=4.3MB, time=162.50
memory used=4001.7MB, alloc=4.3MB, time=162.65
memory used=4005.5MB, alloc=4.3MB, time=162.81
memory used=4009.4MB, alloc=4.3MB, time=162.96
memory used=4013.2MB, alloc=4.3MB, time=163.12
memory used=4017.0MB, alloc=4.3MB, time=163.28
memory used=4020.8MB, alloc=4.3MB, time=163.43
memory used=4024.6MB, alloc=4.3MB, time=163.59
memory used=4028.4MB, alloc=4.3MB, time=163.75
memory used=4032.2MB, alloc=4.3MB, time=163.91
memory used=4036.1MB, alloc=4.3MB, time=164.06
memory used=4039.9MB, alloc=4.3MB, time=164.22
memory used=4043.7MB, alloc=4.3MB, time=164.38
memory used=4047.5MB, alloc=4.3MB, time=164.53
memory used=4051.3MB, alloc=4.3MB, time=164.69
memory used=4055.1MB, alloc=4.3MB, time=164.85
memory used=4059.0MB, alloc=4.3MB, time=165.01
memory used=4062.8MB, alloc=4.3MB, time=165.16
memory used=4066.6MB, alloc=4.3MB, time=165.32
memory used=4070.4MB, alloc=4.3MB, time=165.48
memory used=4074.2MB, alloc=4.3MB, time=165.63
memory used=4078.0MB, alloc=4.3MB, time=165.79
memory used=4081.8MB, alloc=4.3MB, time=165.95
memory used=4085.7MB, alloc=4.3MB, time=166.11
memory used=4089.5MB, alloc=4.3MB, time=166.26
memory used=4093.3MB, alloc=4.3MB, time=166.42
memory used=4097.1MB, alloc=4.3MB, time=166.57
memory used=4100.9MB, alloc=4.3MB, time=166.73
memory used=4104.7MB, alloc=4.3MB, time=166.89
memory used=4108.5MB, alloc=4.3MB, time=167.05
memory used=4112.4MB, alloc=4.3MB, time=167.20
memory used=4116.2MB, alloc=4.3MB, time=167.36
memory used=4120.0MB, alloc=4.3MB, time=167.52
memory used=4123.8MB, alloc=4.3MB, time=167.67
memory used=4127.6MB, alloc=4.3MB, time=167.83
memory used=4131.4MB, alloc=4.3MB, time=167.99
memory used=4135.2MB, alloc=4.3MB, time=168.14
memory used=4139.1MB, alloc=4.3MB, time=168.30
memory used=4142.9MB, alloc=4.3MB, time=168.46
memory used=4146.7MB, alloc=4.3MB, time=168.61
memory used=4150.5MB, alloc=4.3MB, time=168.77
memory used=4154.3MB, alloc=4.3MB, time=168.93
memory used=4158.1MB, alloc=4.3MB, time=169.08
memory used=4162.0MB, alloc=4.3MB, time=169.24
memory used=4165.8MB, alloc=4.3MB, time=169.40
memory used=4169.6MB, alloc=4.3MB, time=169.55
memory used=4173.4MB, alloc=4.3MB, time=169.71
memory used=4177.2MB, alloc=4.3MB, time=169.87
memory used=4181.0MB, alloc=4.3MB, time=170.02
memory used=4184.8MB, alloc=4.3MB, time=170.18
memory used=4188.7MB, alloc=4.3MB, time=170.34
memory used=4192.5MB, alloc=4.3MB, time=170.50
memory used=4196.3MB, alloc=4.3MB, time=170.65
memory used=4200.1MB, alloc=4.3MB, time=170.81
memory used=4203.9MB, alloc=4.3MB, time=170.97
memory used=4207.7MB, alloc=4.3MB, time=171.12
memory used=4211.5MB, alloc=4.3MB, time=171.28
memory used=4215.4MB, alloc=4.3MB, time=171.44
memory used=4219.2MB, alloc=4.3MB, time=171.59
memory used=4223.0MB, alloc=4.3MB, time=171.75
memory used=4226.8MB, alloc=4.3MB, time=171.91
memory used=4230.6MB, alloc=4.3MB, time=172.06
memory used=4234.4MB, alloc=4.3MB, time=172.22
memory used=4238.3MB, alloc=4.3MB, time=172.38
memory used=4242.1MB, alloc=4.3MB, time=172.53
memory used=4245.9MB, alloc=4.3MB, time=172.69
memory used=4249.7MB, alloc=4.3MB, time=172.85
memory used=4253.5MB, alloc=4.3MB, time=173.00
memory used=4257.3MB, alloc=4.3MB, time=173.16
memory used=4261.1MB, alloc=4.3MB, time=173.32
memory used=4265.0MB, alloc=4.3MB, time=173.48
memory used=4268.8MB, alloc=4.3MB, time=173.63
memory used=4272.6MB, alloc=4.3MB, time=173.79
memory used=4276.4MB, alloc=4.3MB, time=173.95
memory used=4280.2MB, alloc=4.3MB, time=174.10
memory used=4284.0MB, alloc=4.3MB, time=174.26
memory used=4287.8MB, alloc=4.3MB, time=174.42
memory used=4291.7MB, alloc=4.3MB, time=174.57
memory used=4295.5MB, alloc=4.3MB, time=174.73
memory used=4299.3MB, alloc=4.3MB, time=174.89
memory used=4303.1MB, alloc=4.3MB, time=175.04
memory used=4306.9MB, alloc=4.3MB, time=175.20
memory used=4310.7MB, alloc=4.3MB, time=175.36
memory used=4314.5MB, alloc=4.3MB, time=175.52
memory used=4318.4MB, alloc=4.3MB, time=175.68
memory used=4322.2MB, alloc=4.3MB, time=175.83
memory used=4326.0MB, alloc=4.3MB, time=175.99
memory used=4329.8MB, alloc=4.3MB, time=176.15
memory used=4333.6MB, alloc=4.3MB, time=176.30
memory used=4337.4MB, alloc=4.3MB, time=176.46
memory used=4341.3MB, alloc=4.3MB, time=176.62
memory used=4345.1MB, alloc=4.3MB, time=176.77
memory used=4348.9MB, alloc=4.3MB, time=176.93
memory used=4352.7MB, alloc=4.3MB, time=177.09
memory used=4356.5MB, alloc=4.3MB, time=177.24
memory used=4360.3MB, alloc=4.3MB, time=177.40
memory used=4364.1MB, alloc=4.3MB, time=177.56
memory used=4368.0MB, alloc=4.3MB, time=177.71
memory used=4371.8MB, alloc=4.3MB, time=177.87
memory used=4375.6MB, alloc=4.3MB, time=178.02
memory used=4379.4MB, alloc=4.3MB, time=178.18
memory used=4383.2MB, alloc=4.3MB, time=178.34
memory used=4387.0MB, alloc=4.3MB, time=178.50
memory used=4390.8MB, alloc=4.3MB, time=178.65
memory used=4394.7MB, alloc=4.3MB, time=178.81
memory used=4398.5MB, alloc=4.3MB, time=178.97
memory used=4402.3MB, alloc=4.3MB, time=179.12
memory used=4406.1MB, alloc=4.3MB, time=179.28
memory used=4409.9MB, alloc=4.3MB, time=179.43
memory used=4413.7MB, alloc=4.3MB, time=179.59
memory used=4417.5MB, alloc=4.3MB, time=179.75
memory used=4421.4MB, alloc=4.3MB, time=179.90
memory used=4425.2MB, alloc=4.3MB, time=180.06
Finished!
Maximum Time Reached before Solution Completed!
diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;
Iterations = 15609
Total Elapsed Time = 3 Minutes 0 Seconds
Elapsed Time(since restart) = 3 Minutes 0 Seconds
Expected Time Remaining = 1 Hours 41 Minutes 19 Seconds
Optimized Time Remaining = 1 Hours 41 Minutes 18 Seconds
Expected Total Time = 1 Hours 44 Minutes 18 Seconds
Time to Timeout Unknown
Percent Done = 2.876 %
> quit
memory used=4425.3MB, alloc=4.3MB, time=180.06