|\^/| 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.
| Type ? for help.
> #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,
> 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, 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,
> 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, 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,
> 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, 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,
> 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 <> 0.0) 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, 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 relerr <> 0. 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,
> 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, 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,
> 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, 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,
> 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
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := 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))) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := 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
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := 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, 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
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := 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]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := 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
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := 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,
> 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, 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,
> 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 add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[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_tmp2[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h;
> 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 add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[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_tmp2[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h;
> 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 add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[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_tmp2[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> 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 add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[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_tmp2[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (3.0);
> 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 add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[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_tmp2[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (4.0);
> 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 NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[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_tmp2[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 - 2;
> adj3 := 2;
> while (term >= 1) do # do number 2
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 1) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary / glob_h;
> 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, 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] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp2[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary/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_tmp1[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary/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] := array_tmp1[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*2.0/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] := array_tmp1[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*3.0/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] := array_tmp1[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*4.0/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_tmp1[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_tmp2[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 - 2;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 1 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary/glob_h
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 <> 0.0) 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 rel_error <> 0. 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
> ## Comment 5
> exact_soln_y := proc(x)
> ## Comment 6
> return(2.0 - cos(x));
> ## Comment 7
> end;
exact_soln_y := proc(x) return 2.0 - 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;
> 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,
> 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/sinpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin(x);");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"## Comment 1");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=20;");
> omniout_str(ALWAYS,"## Comment 2");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"## Comment 3");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 1.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.0005;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> omniout_str(ALWAYS,"## Comment 4");
> 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,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"## Comment 5");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"## Comment 6");
> omniout_str(ALWAYS,"return(2.0 - cos(x));");
> omniout_str(ALWAYS,"## Comment 7");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 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
> ## Comment 1
> Digits:=32;
> max_terms:=20;
> ## Comment 2
> #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:= 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[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 := 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_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
> ## Comment 3
> x_start := 0.1;
> x_end := 1.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.0005;
> glob_look_poles := true;
> glob_max_iter := 1000000;
> ## Comment 4
> #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;
> #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;
> #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();
> 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 := 1;
> #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
> display_alot(current_iter)
> ;
> 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);");
> 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,"2012-12-15T03:26:23-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sin(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," 151 | ")
> ;
> logitem_str(html_log_file,"sin diffeq.mxt")
> ;
> logitem_str(html_log_file,"sin maple results")
> ;
> logitem_str(html_log_file,"Languages compared")
> ;
> 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;
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, 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/sinpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x);");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "## Comment 1");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=20;");
omniout_str(ALWAYS, "## Comment 2");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "## Comment 3");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 1.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.0005;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
omniout_str(ALWAYS, "## Comment 4");
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, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "## Comment 5");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "## Comment 6");
omniout_str(ALWAYS, "return(2.0 - cos(x));");
omniout_str(ALWAYS, "## Comment 7");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 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 := 20;
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 := 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[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 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[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 := 0.1;
x_end := 1.0;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.0005;
glob_look_poles := true;
glob_max_iter := 1000000;
glob_desired_digits_correct := 10;
glob_display_interval := 0.001;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 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;
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();
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 := 1;
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;
display_alot(current_iter)
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);");
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, "2012-12-15T03:26:23-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "sin");
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(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, " 151 | ");
logitem_str(html_log_file,
"sin diffeq.mxt");
logitem_str(html_log_file,
"sin maple results");
logitem_str(html_log_file, "Languages compared");
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/sinpostode.ode#################
diff ( y , x , 1 ) = sin(x);
!
#BEGIN FIRST INPUT BLOCK
## Comment 1
Digits:=32;
max_terms:=20;
## Comment 2
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
## Comment 3
x_start := 0.1;
x_end := 1.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.0005;
glob_look_poles := true;
glob_max_iter := 1000000;
## Comment 4
#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;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
## Comment 5
exact_soln_y := proc(x)
## Comment 6
return(2.0 - cos(x));
## Comment 7
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 = 0.9
estimated_steps = 900
step_error = 1.1111111111111111111111111111111e-13
est_needed_step_err = 1.1111111111111111111111111111111e-13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
value3 = 1.2174295054687768155749198270479e-59
max_value3 = 1.2174295054687768155749198270479e-59
value3 = 1.2174295054687768155749198270479e-59
best_h = 0.001
START of Soultion
x[1] = 0.1
y[1] (analytic) = 1.0049958347219742339044380121961
y[1] (numeric) = 1.0049958347219742339044380121961
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.101
y[1] (analytic) = 1.005096165624023340621597000171
y[1] (numeric) = 1.0050961656240233406699643058562
absolute error = 4.83673056852e-20
relative error = 4.8122067658243135951359049184283e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.102
y[1] (analytic) = 1.0051974914298239146653143235401
y[1] (numeric) = 1.0051974914298239147620440482383
absolute error = 9.67297246982e-20
relative error = 9.6229572320767191925391374928029e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.103
y[1] (analytic) = 1.0052998120380501586788328071734
y[1] (numeric) = 1.0052998120380501588239200158499
absolute error = 1.450872086765e-19
relative error = 1.4432232746802554115959902071276e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.104
y[1] (analytic) = 1.0054031273463814729626255055154
y[1] (numeric) = 1.0054031273463814731560652147781
absolute error = 1.934397092627e-19
relative error = 1.9240014676824866665069432933987e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.105
y[1] (analytic) = 1.0055074372515025577949868753959
y[1] (numeric) = 1.0055074372515025580367740535003
absolute error = 2.417871781044e-19
relative error = 2.4046284407931532749010893617440e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.106
y[1] (analytic) = 1.0056127416491035167473238881278
y[1] (numeric) = 1.0056127416491035170374534549817
absolute error = 2.901295668539e-19
relative error = 2.8851023345042024765847792310386e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.107
y[1] (analytic) = 1.0057190404338799609940437656082
y[1] (numeric) = 1.0057190404338799613325105927772
absolute error = 3.384668271690e-19
relative error = 3.3654212912483104042901073827821e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.108
y[1] (analytic) = 1.0058263334995331146169340305467
y[1] (numeric) = 1.005826333499533115003732941259
absolute error = 3.867989107123e-19
relative error = 3.8455834554114857509889324706029e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.109
y[1] (analytic) = 1.0059346207387699209039295664461
y[1] (numeric) = 1.005934620738769921339055335598
absolute error = 4.351257691519e-19
relative error = 4.3255869733595474165389586317185e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.11
y[1] (analytic) = 1.0060439020433031496421603885802
y[1] (numeric) = 1.006043902043303150125607742741
absolute error = 4.834473541608e-19
relative error = 4.8054299934516274677430909566628e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.111
y[1] (analytic) = 1.006154177303851505405172832928
y[1] (numeric) = 1.0061541773038515059369364503455
absolute error = 5.317636174175e-19
relative error = 5.2851106660655558436180354567542e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.112
y[1] (analytic) = 1.0062654464101397368342158758533
y[1] (numeric) = 1.006265446410139737414290386459
absolute error = 5.800745106057e-19
relative error = 5.7646271436142480245422983030641e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.113
y[1] (analytic) = 1.0063777092508987469134833032516
y[1] (numeric) = 1.006377709250898747541863288666
absolute error = 6.283799854144e-19
relative error = 6.2439775805660197202163014286936e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.114
y[1] (analytic) = 1.0064909657138657042392014539315
y[1] (numeric) = 1.0064909657138657049158814474699
absolute error = 6.766799935384e-19
relative error = 6.7231601334688250843944272665536e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.115
y[1] (analytic) = 1.0066052156857841552824512681535
y[1] (numeric) = 1.006605215685784156007425754831
absolute error = 7.249744866775e-19
relative error = 7.2021729609615264110954250682799e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.116
y[1] (analytic) = 1.006720459052404137645612378511
y[1] (numeric) = 1.0067204590524041384188757950483
absolute error = 7.732634165373e-19
relative error = 7.6810142238010115510705293688028e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.117
y[1] (analytic) = 1.006836695698482294312315986721
y[1] (numeric) = 1.0068366956984822951338627215497
absolute error = 8.215467348287e-19
relative error = 8.1596820848763428675952957453976e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.118
y[1] (analytic) = 1.00695392550778198889079227638
y[1] (numeric) = 1.0069539255077819897606166696485
absolute error = 8.698243932685e-19
relative error = 8.6381747092337819386911163163761e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.119
y[1] (analytic) = 1.0070721483630734218504971183478
y[1] (numeric) = 1.007072148363073422768593461927
absolute error = 9.180963435792e-19
relative error = 9.1164902640938141450305670993177e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.12
y[1] (analytic) = 1.0071913641461337477519018321424
y[1] (numeric) = 1.007191364146133748718264369631
absolute error = 9.663625374886e-19
relative error = 9.5946269188661363562533573747258e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.121
y[1] (analytic) = 1.0073115727377471934693287735644
y[1] (numeric) = 1.0073115727377471944839517002951
absolute error = 1.0146229267307e-18
relative error = 1.0072582845177500130002470317079e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.122
y[1] (analytic) = 1.007432774017705177406714525728
y[1] (numeric) = 1.007432774017705178469591988773
absolute error = 1.0628774630450e-18
relative error = 1.0550356216883613190328908353595e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.123
y[1] (analytic) = 1.0075549678648064297061814777427
y[1] (numeric) = 1.0075549678648064308173075759196
absolute error = 1.1111260981769e-18
relative error = 1.1027945210091909631631075294724e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.8MB, time=0.39
NO POLE
x[1] = 0.124
y[1] (analytic) = 1.007678154156857113449297582485
y[1] (numeric) = 1.007678154156857114608666366363
absolute error = 1.1593687838780e-18
relative error = 1.1505348003183270680482602094481e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.125
y[1] (analytic) = 1.0078023327706709468509030922118
y[1] (numeric) = 1.0078023327706709480585085641172
absolute error = 1.2076054719054e-18
relative error = 1.1982562776823766070710820311518e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.126
y[1] (analytic) = 1.0079275035820693264453820781963
y[1] (numeric) = 1.0079275035820693277012181922189
absolute error = 1.2558361140226e-18
relative error = 1.2459587713992219707818996616763e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.127
y[1] (analytic) = 1.0080536664658814512652555481279
y[1] (numeric) = 1.0080536664658814525693162101268
absolute error = 1.3040606619989e-18
relative error = 1.2936420999992833129922877011455e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.128
y[1] (analytic) = 1.0081808212959444480119719826911
y[1] (numeric) = 1.0081808212959444493642510503008
absolute error = 1.3522790676097e-18
relative error = 1.3413060822476684585473909402488e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.129
y[1] (analytic) = 1.0083089679451034972187701205446
y[1] (numeric) = 1.0083089679451034986192614031812
absolute error = 1.4004912826366e-18
relative error = 1.3889505371461186161198882003857e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.13
y[1] (analytic) = 1.0084381062852119604054878288482
y[1] (numeric) = 1.0084381062852119618541850877156
absolute error = 1.4486972588674e-18
relative error = 1.4365752839348491924192235518974e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.131
y[1] (analytic) = 1.0085682361871315082251899045384
y[1] (numeric) = 1.0085682361871315097220868526346
absolute error = 1.4968969480962e-18
relative error = 1.4841801420944840578262892420310e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.132
y[1] (analytic) = 1.008699357520732249602486659737
y[1] (numeric) = 1.0086993575207322511475769618601
absolute error = 1.5450903021231e-18
relative error = 1.5317649313475874471457328895013e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.133
y[1] (analytic) = 1.0088314701548928618634141529829
y[1] (numeric) = 1.008831470154892863456691425738
absolute error = 1.5932772727551e-18
relative error = 1.5793294716613798123378675326255e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.134
y[1] (analytic) = 1.0089645739575007218567459364203
y[1] (numeric) = 1.0089645739575007234982037482252
absolute error = 1.6414578118049e-18
relative error = 1.6268735832483658171712822631178e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.135
y[1] (analytic) = 1.0090986687954520380666051976395
y[1] (numeric) = 1.0090986687954520397562370687317
absolute error = 1.6896318710922e-18
relative error = 1.6743970865694348780525365324007e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.136
y[1] (analytic) = 1.009233754534651983716245183572
y[1] (numeric) = 1.0092337545346519854540445860148
absolute error = 1.7377994024428e-18
relative error = 1.7218998023347749176858209999829e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.137
y[1] (analytic) = 1.0093698310400148308628648026684
y[1] (numeric) = 1.0093698310400148326488251603576
absolute error = 1.7859603576892e-18
relative error = 1.7693815515062669794463110118429e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.138
y[1] (analytic) = 1.0095068981754640854833253105562
y[1] (numeric) = 1.0095068981754640873174399992266
absolute error = 1.8341146886704e-18
relative error = 1.8168421552990809308495612322067e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.139
y[1] (analytic) = 1.0096449558039326235506329934705
y[1] (numeric) = 1.0096449558039326254328953407028
absolute error = 1.8822623472323e-18
relative error = 1.8642814351838595922820219543277e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.14
y[1] (analytic) = 1.0097840037873628281010517729886
y[1] (numeric) = 1.0097840037873628300314550582156
absolute error = 1.9304032852270e-18
relative error = 1.9116992128878071573709625453143e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.141
y[1] (analytic) = 1.0099240419867067272917086649643
y[1] (numeric) = 1.009924041986706729270246119478
absolute error = 1.9785374545137e-18
relative error = 1.9590953103973563867515560337493e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.142
y[1] (analytic) = 1.0100650702619261334485540350706
y[1] (numeric) = 1.0100650702619261354752188420288
absolute error = 2.0266648069582e-18
relative error = 2.0064695499594428989578491232858e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.143
y[1] (analytic) = 1.0102070884719927831045376030009
y[1] (numeric) = 1.0102070884719927851793228974339
absolute error = 2.0747852944330e-18
relative error = 2.0538217540833676612349685675523e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.144
y[1] (analytic) = 1.0103500964748884780278601571639
y[1] (numeric) = 1.0103500964748884801507590259818
absolute error = 2.1228988688179e-18
relative error = 2.1011517455431480905737774107984e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.145
y[1] (analytic) = 1.010494094127605227240159951634
y[1] (numeric) = 1.0104940941276052294111654336331
absolute error = 2.1710054819991e-18
relative error = 2.1484593473783780044156659137295e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.146
y[1] (analytic) = 1.0106390812861453900244917671803
y[1] (numeric) = 1.0106390812861453922435968530504
absolute error = 2.2191050858701e-18
relative error = 2.1957443828968631257214266691320e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.147
y[1] (analytic) = 1.0107850578055218199229556284092
y[1] (numeric) = 1.0107850578055218221901532607404
absolute error = 2.2671976323312e-18
relative error = 2.2430066756758644686911304060840e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.148
y[1] (analytic) = 1.0109320235397580097238311794022
y[1] (numeric) = 1.0109320235397580120391142526922
absolute error = 2.3152830732900e-18
relative error = 2.2902460495643250095256831291931e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.149
y[1] (analytic) = 1.0110799783418882374380727307282
y[1] (numeric) = 1.0110799783418882398014340913892
absolute error = 2.3633613606610e-18
relative error = 2.3374623286841994257829779943102e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.15
y[1] (analytic) = 1.0112289220639577132650190013457
y[1] (numeric) = 1.0112289220639577156764514477116
absolute error = 2.4114324463659e-18
relative error = 2.3846553374324700116642796635051e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.151
y[1] (analytic) = 1.0113788545570227275471705896988
y[1] (numeric) = 1.0113788545570227300066668720325
absolute error = 2.4594962823337e-18
relative error = 2.4318249004829581507305826754132e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.152
y[1] (analytic) = 1.0115297756711507997138872192414
y[1] (numeric) = 1.0115297756711508022214400397419
absolute error = 2.5075528205005e-18
relative error = 2.4789708427878326531668700763756e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.153
y[1] (analytic) = 1.0116816852554208282138558147042
y[1] (numeric) = 1.0116816852554208307694578275139
absolute error = 2.5556020128097e-18
relative error = 2.5260929895795071514578098122214e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.154
y[1] (analytic) = 1.0118345831579232414361794766499
y[1] (numeric) = 1.0118345831579232440398232878621
absolute error = 2.6036438112122e-18
relative error = 2.5731911663725307856684579723309e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.155
y[1] (analytic) = 1.0119884692257601496199364332395
y[1] (numeric) = 1.0119884692257601522716146009058
absolute error = 2.6516781676663e-18
relative error = 2.6202651989651756957298981116481e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.156
y[1] (analytic) = 1.0121433433050454977520570596639
y[1] (numeric) = 1.0121433433050455004517620938013
absolute error = 2.6997050341374e-18
relative error = 2.6673149134408204022223756791694e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.157
y[1] (analytic) = 1.0122992052409052194533660673757
y[1] (numeric) = 1.0122992052409052222010904299744
absolute error = 2.7477243625987e-18
relative error = 2.7143401361703146786772501791887e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.158
y[1] (analytic) = 1.0124560548774773918526359770927
y[1] (numeric) = 1.0124560548774773946483720821238
absolute error = 2.7957361050311e-18
relative error = 2.7613406938135469630723750404200e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.159
y[1] (analytic) = 1.0126138920579123914484970015328
y[1] (numeric) = 1.0126138920579123942922372149555
absolute error = 2.8437402134227e-18
relative error = 2.8083164133206101428445914766488e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.16
y[1] (analytic) = 1.0127727166243730509590474759817
y[1] (numeric) = 1.012772716624373053850784115751
absolute error = 2.8917366397693e-18
relative error = 2.8552671219339484613199650750846e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.161
y[1] (analytic) = 1.0129325284180348171590079870976
y[1] (numeric) = 1.0129325284180348200987333231723
absolute error = 2.9397253360747e-18
relative error = 2.9021926471902997544685282996129e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.162
y[1] (analytic) = 1.0130933272790859097042613628125
y[1] (numeric) = 1.0130933272790859126919676171625
absolute error = 2.9877062543500e-18
relative error = 2.9490928169216435361903438987142e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.163
y[1] (analytic) = 1.0132551130467274809436196988004
y[1] (numeric) = 1.0132551130467274839792990454148
absolute error = 3.0356793466144e-18
relative error = 2.9959674592576232947564062093475e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=7.6MB, alloc=3.9MB, time=0.87
x[1] = 0.164
y[1] (analytic) = 1.0134178855591737767176586097624
y[1] (numeric) = 1.0134178855591737798013031746572
absolute error = 3.0836445648948e-18
relative error = 3.0428164026267770676701105971594e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.165
y[1] (analytic) = 1.0135816446536522981444579067051
y[1] (numeric) = 1.013581644653652301276059767931
absolute error = 3.1316018612259e-18
relative error = 3.0896394757582548093508869821806e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.166
y[1] (analytic) = 1.0137463901664039643920869144861
y[1] (numeric) = 1.0137463901664039675716381021367
absolute error = 3.1795511876506e-18
relative error = 3.1364365076838246803101704773874e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.167
y[1] (analytic) = 1.0139121219326832764376716571557
y[1] (numeric) = 1.013912121932683279665164153375
absolute error = 3.2274924962193e-18
relative error = 3.1832073277387870974906539769479e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.168
y[1] (analytic) = 1.014078839786758481812880152039
y[1] (numeric) = 1.0140788397867584850883058910299
absolute error = 3.2754257389909e-18
relative error = 3.2299517655645588839622713621658e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.169
y[1] (analytic) = 1.0142465435619117403356610670895
y[1] (numeric) = 1.0142465435619117436590119351217
absolute error = 3.3233508680322e-18
relative error = 3.2766696511096719151843546305470e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.17
y[1] (analytic) = 1.0144152330904392908280700097875
y[1] (numeric) = 1.0144152330904392941993378452054
absolute error = 3.3712678354179e-18
relative error = 3.3233608146313567875601322501998e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.171
y[1] (analytic) = 1.0145849082036516188200167297711
y[1] (numeric) = 1.0145849082036516222391933230022
absolute error = 3.4191765932311e-18
relative error = 3.3700250866976122373288486174595e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.172
y[1] (analytic) = 1.0147555687318736252387655314679
y[1] (numeric) = 1.014755568731873628705842625031
absolute error = 3.4670770935631e-18
relative error = 3.4166622981885771506386195238858e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.173
y[1] (analytic) = 1.0149272145044447960840202072392
y[1] (numeric) = 1.0149272145044447995989894957526
absolute error = 3.5149692885134e-18
relative error = 3.4632722802980927071501197823198e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.174
y[1] (analytic) = 1.0150998453497193730884238159675
y[1] (numeric) = 1.0150998453497193766512769461573
absolute error = 3.5628531301898e-18
relative error = 3.5098548645353558862412599841521e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.175
y[1] (analytic) = 1.0152734610950665253633026466005
y[1] (numeric) = 1.0152734610950665289740312173089
absolute error = 3.6107285707084e-18
relative error = 3.5564098827264671992460207871527e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.176
y[1] (analytic) = 1.0154480615668705220294827209227
y[1] (numeric) = 1.0154480615668705256880782831166
absolute error = 3.6585955621939e-18
relative error = 3.6029371670162666520607629083433e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.177
y[1] (analytic) = 1.0156236465905309058330062047525
y[1] (numeric) = 1.0156236465905309095394602615317
absolute error = 3.7064540567792e-18
relative error = 3.6494365498694729370504428219258e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.178
y[1] (analytic) = 1.0158002159904626677455741118622
y[1] (numeric) = 1.015800215990462671499878118468
absolute error = 3.7543040066058e-18
relative error = 3.6959078640726033290008730721171e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.179
y[1] (analytic) = 1.0159777695900964225495407001936
y[1] (numeric) = 1.0159777695900964263516860640173
absolute error = 3.8021453638237e-18
relative error = 3.7423509427353937473477759723381e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.18
y[1] (analytic) = 1.0161563072118785854072839753885
y[1] (numeric) = 1.0161563072118785892572620559802
absolute error = 3.8499780805917e-18
relative error = 3.7887656192926052469450751301325e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.181
y[1] (analytic) = 1.0163358286772715494147757322793
y[1] (numeric) = 1.0163358286772715533125778413564
absolute error = 3.8978021090771e-18
relative error = 3.8351517275052325000509353419224e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.182
y[1] (analytic) = 1.016516333806753864139173580784
y[1] (numeric) = 1.0165163338067538680847909822397
absolute error = 3.9456174014557e-18
relative error = 3.8815091014620003490924327811112e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.183
y[1] (analytic) = 1.0166978224198204151402564186277
y[1] (numeric) = 1.0166978224198204191336803285401
absolute error = 3.9934239099124e-18
relative error = 3.9278375755814431147821424702048e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.184
y[1] (analytic) = 1.0168802943349826044755238294719
y[1] (numeric) = 1.0168802943349826085167454161124
absolute error = 4.0412215866405e-18
relative error = 3.9741369846126974335407210128112e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.185
y[1] (analytic) = 1.0170637493697685321887789013652
y[1] (numeric) = 1.0170637493697685362777892852076
absolute error = 4.0890103838424e-18
relative error = 4.0204071636376649034420052084208e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.186
y[1] (analytic) = 1.0172481873407231787820129769491
y[1] (numeric) = 1.0172481873407231829188032306785
absolute error = 4.1367902537294e-18
relative error = 4.0666479480722817785129772963042e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.187
y[1] (analytic) = 1.0174336080634085886704098635492
y[1] (numeric) = 1.0174336080634085928549710120707
absolute error = 4.1845611485215e-18
relative error = 4.1128591736677813815617321775032e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.188
y[1] (analytic) = 1.0176200113524040546202860481617
y[1] (numeric) = 1.0176200113524040588526090686097
absolute error = 4.2323230204480e-18
relative error = 4.1590406765127353635208875328300e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.189
y[1] (analytic) = 1.0178073970213063031697824794125
y[1] (numeric) = 1.0178073970213063074498583011593
absolute error = 4.2800758217468e-18
relative error = 4.2051922930338095176148428908066e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.19
y[1] (analytic) = 1.0179957648827296810321224958101
y[1] (numeric) = 1.0179957648827296853599420004753
absolute error = 4.3278195046652e-18
relative error = 4.2513138599979862709885854757964e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.191
y[1] (analytic) = 1.0181851147483063424812494970519
y[1] (numeric) = 1.0181851147483063468568035185115
absolute error = 4.3755540214596e-18
relative error = 4.2974052145136983624840197490505e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.192
y[1] (analytic) = 1.0183754464286864377196569727608
y[1] (numeric) = 1.0183754464286864421429362971562
absolute error = 4.4232793243954e-18
relative error = 4.3434661940321516254670190896853e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.193
y[1] (analytic) = 1.0185667597335383022282225208382
y[1] (numeric) = 1.0185667597335383066992178865856
absolute error = 4.4709953657474e-18
relative error = 4.3894966363491311321460127117617e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.194
y[1] (analytic) = 1.0187590544715486470978565056148
y[1] (numeric) = 1.0187590544715486516165586034142
absolute error = 4.5187020977994e-18
relative error = 4.4354963796060139682344786737381e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.195
y[1] (analytic) = 1.0189523304504227503427750241667
y[1] (numeric) = 1.0189523304504227549091744970114
absolute error = 4.5663994728447e-18
relative error = 4.4814652622916580317285164102868e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.196
y[1] (analytic) = 1.0191465874768846491952058675394
y[1] (numeric) = 1.0191465874768846538092933107255
absolute error = 4.6140874431861e-18
relative error = 4.5274031232437919647437379615056e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.197
y[1] (analytic) = 1.019341825356677333381335182191
y[1] (numeric) = 1.0193418253566773380431011433264
absolute error = 4.6617659611354e-18
relative error = 4.5733098016499068457441038487099e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.198
y[1] (analytic) = 1.0195380438945629393783015557216
y[1] (numeric) = 1.0195380438945629440877365347359
absolute error = 4.7094349790143e-18
relative error = 4.6191851370495138711252819424346e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.199
y[1] (analytic) = 1.0197352428943229456520432699139
y[1] (numeric) = 1.0197352428943229504091377190676
absolute error = 4.7570944491537e-18
relative error = 4.6650289693348242156686829236581e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.2
y[1] (analytic) = 1.0199334221587583688758034832518
y[1] (numeric) = 1.0199334221587583736805478071459
absolute error = 4.8047443238941e-18
relative error = 4.7108411387525004007355888001232e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.201
y[1] (analytic) = 1.020132581489689961129097124429
y[1] (numeric) = 1.0201325814896899659814816800147
absolute error = 4.8523845555857e-18
relative error = 4.7566214859051053183265605072761e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.202
y[1] (analytic) = 1.0203327206879584080769422978976
y[1] (numeric) = 1.0203327206879584129769573944857
absolute error = 4.9000150965881e-18
relative error = 4.8023698517521512804096771715860e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.203
y[1] (analytic) = 1.0205338395534245281291580222406
y[1] (numeric) = 1.0205338395534245330767939215116
absolute error = 4.9476358992710e-18
relative error = 4.8480860776121214439886604420036e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.204
y[1] (analytic) = 1.020735937884969472579529142089
y[1] (numeric) = 1.0207359378849694775747760581024
absolute error = 4.9952469160134e-18
relative error = 4.8937700051630130267524506243702e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=11.4MB, alloc=4.0MB, time=1.37
x[1] = 0.205
y[1] (analytic) = 1.0209390154804949267246382744327
y[1] (numeric) = 1.0209390154804949317674863736371
absolute error = 5.0428480992044e-18
relative error = 4.9394214764444407481221822483032e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.206
y[1] (analytic) = 1.0211430721369233119621636705127
y[1] (numeric) = 1.0211430721369233170526030717555
absolute error = 5.0904394012428e-18
relative error = 4.9850403338585562741036903044187e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.207
y[1] (analytic) = 1.0213481076501979888684408950116
y[1] (numeric) = 1.021348107650197994006461669549
absolute error = 5.1380207745374e-18
relative error = 5.0306264201716455708435084262467e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.208
y[1] (analytic) = 1.0215541218152834612550852449989
y[1] (numeric) = 1.0215541218152834664406774165056
absolute error = 5.1855921715067e-18
relative error = 5.0761795785151306176129698739295e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.209
y[1] (analytic) = 1.0217611144261655812044708520248
y[1] (numeric) = 1.021761114426165586437624396604
absolute error = 5.2331535445792e-18
relative error = 5.1216996523871507316784553025777e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.21
y[1] (analytic) = 1.0219690852758517550838614319006
y[1] (numeric) = 1.0219690852758517603645662780945
absolute error = 5.2807048461939e-18
relative error = 5.1671864856543312551246525645520e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.211
y[1] (analytic) = 1.0221780341563711505379866680538
y[1] (numeric) = 1.0221780341563711558662326968529
absolute error = 5.3282460287991e-18
relative error = 5.2126399225518805249246049871162e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.212
y[1] (analytic) = 1.022387960858774904459857235895
y[1] (numeric) = 1.0223879608587749098356342807488
absolute error = 5.3757770448538e-18
relative error = 5.2580598076862233305349646800067e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.213
y[1] (analytic) = 1.0225988651731363319396104974034
y[1] (numeric) = 1.0225988651731363373629083442305
absolute error = 5.4232978468271e-18
relative error = 5.3034459860356688498162312543940e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.214
y[1] (analytic) = 1.0228107468885511361911779170994
y[1] (numeric) = 1.0228107468885511416619863042975
absolute error = 5.4708083871981e-18
relative error = 5.3487983029515601028452110133594e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.215
y[1] (analytic) = 1.0230236057931376194565642727558
y[1] (numeric) = 1.0230236057931376249748728912119
absolute error = 5.5183086184561e-18
relative error = 5.3941166041597087073133979304512e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.216
y[1] (analytic) = 1.0232374416740368948875277565849
y[1] (numeric) = 1.023237441674036900453326249686
absolute error = 5.5657984931011e-18
relative error = 5.4394007357621144924640912279224e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.217
y[1] (analytic) = 1.0234522543174130994044490852411
y[1] (numeric) = 1.0234522543174131050177270488842
absolute error = 5.6132779636431e-18
relative error = 5.4846505442375038939562249491229e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.218
y[1] (analytic) = 1.023668043508453607532176759785
y[1] (numeric) = 1.0236680435084536131929237423876
absolute error = 5.6607469826026e-18
relative error = 5.5298658764430333456775276721205e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.219
y[1] (analytic) = 1.0238848090313692462126346397834
y[1] (numeric) = 1.0238848090313692519208401422942
absolute error = 5.7082055025108e-18
relative error = 5.5750465796156909201659312681854e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.22
y[1] (analytic) = 1.0241025506693945105939770189553
y[1] (numeric) = 1.0241025506693945163496304948643
absolute error = 5.7556534759090e-18
relative error = 5.6201925013729083977962387339646e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.221
y[1] (analytic) = 1.0243212682047877807960754132258
y[1] (numeric) = 1.0243212682047877865991662685751
absolute error = 5.8030908553493e-18
relative error = 5.6653034897144350524264611823284e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.222
y[1] (analytic) = 1.0245409614188315396521202957203
y[1] (numeric) = 1.0245409614188315455026378891146
absolute error = 5.8505175933943e-18
relative error = 5.7103793930232263371872566371674e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.223
y[1] (analytic) = 1.024761630091832591426120037115
y[1] (numeric) = 1.0247616300918325973240536797322
absolute error = 5.8979336426172e-18
relative error = 5.7554200600667150868423890062203e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.224
y[1] (analytic) = 1.0249832740031222815060783338625
y[1] (numeric) = 1.0249832740031222874514172894646
absolute error = 5.9453389556021e-18
relative error = 5.8004253399982695124774643603679e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.225
y[1] (analytic) = 1.0252058929310567170726304311345
y[1] (numeric) = 1.0252058929310567230653639160782
absolute error = 5.9927334849437e-18
relative error = 5.8453950823580573458382045117070e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.226
y[1] (analytic) = 1.0254294866530169887429174718627
y[1] (numeric) = 1.02542948665301699478303465511
absolute error = 6.0401171832473e-18
relative error = 5.8903291370741946893880734578914e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.227
y[1] (analytic) = 1.0256540549454093931894773280223
y[1] (numeric) = 1.0256540549454093992769673311516
absolute error = 6.0874900031293e-18
relative error = 5.9352273544643741137830565320757e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.228
y[1] (analytic) = 1.0258795975836656567339292952864
y[1] (numeric) = 1.0258795975836656628687811925033
absolute error = 6.1348518972169e-18
relative error = 5.9800895852367040348742682803984e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.229
y[1] (analytic) = 1.0261061143422431599152290573844
y[1] (numeric) = 1.0261061143422431660974318755325
absolute error = 6.1822028181481e-18
relative error = 6.0249156804908325683029746494696e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.23
y[1] (analytic) = 1.0263336049946251630322693519284
y[1] (numeric) = 1.0263336049946251692618120705006
absolute error = 6.2295427185722e-18
relative error = 6.0697054917195502698755849174400e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.231
y[1] (analytic) = 1.0265620693133210326606007951267
y[1] (numeric) = 1.0265620693133210389374723462759
absolute error = 6.2768715511492e-18
relative error = 6.1144588708093123908684523728069e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.232
y[1] (analytic) = 1.0267915070698664691430463486806
y[1] (numeric) = 1.0267915070698664754672356172308
absolute error = 6.3241892685502e-18
relative error = 6.1591756700417275102202689194223e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.233
y[1] (analytic) = 1.0270219180348237350539819382704
y[1] (numeric) = 1.027021918034823741425477761728
absolute error = 6.3714958234576e-18
relative error = 6.2038557420948425867228324324672e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.234
y[1] (analytic) = 1.027253301977781884637054759369
y[1] (numeric) = 1.0272533019777818910558459279337
absolute error = 6.4187911685647e-18
relative error = 6.2484989400438353327338683890067e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.235
y[1] (analytic) = 1.0274856586673569942161098326828
y[1] (numeric) = 1.027485658667357000682185089259
absolute error = 6.4660752565762e-18
relative error = 6.2931051173625746945373840437436e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.236
y[1] (analytic) = 1.0277189878711923935790943983139
y[1] (numeric) = 1.0277189878711924000924424385221
absolute error = 6.5133480402082e-18
relative error = 6.3376741279246858039891339137334e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.237
y[1] (analytic) = 1.0279532893559588983347087647578
y[1] (numeric) = 1.0279532893559589048953182369455
absolute error = 6.5606094721877e-18
relative error = 6.3822058260041201592285711498021e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.238
y[1] (analytic) = 1.0281885628873550432415712561047
y[1] (numeric) = 1.0281885628873550498494307613581
absolute error = 6.6078595052534e-18
relative error = 6.4267000662769824556637884243703e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.239
y[1] (analytic) = 1.0284248082301073165096639283
y[1] (numeric) = 1.0284248082301073231647620204551
absolute error = 6.6550980921551e-18
relative error = 6.4711567038219866592035774401001e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.24
y[1] (analytic) = 1.0286620251479703950738247530366
y[1] (numeric) = 1.0286620251479704017761499386911
absolute error = 6.7023251856545e-18
relative error = 6.5155755941222654789889399675776e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.241
y[1] (analytic) = 1.0289002134037273808390509958078
y[1] (numeric) = 1.0289002134037273875885917343321
absolute error = 6.7495407385243e-18
relative error = 6.5599565930655181099314186780786e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.242
y[1] (analytic) = 1.0291393727591900378973775428355
y[1] (numeric) = 1.0291393727591900446941222463844
absolute error = 6.7967447035489e-18
relative error = 6.6042995569457054734825130624137e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.243
y[1] (analytic) = 1.0293795029751990307160929600163
y[1] (numeric) = 1.0293795029751990375600299935408
absolute error = 6.8439370335245e-18
relative error = 6.6486043424641532152970258106991e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.244
y[1] (analytic) = 1.0296206038116241632970550956892
y[1] (numeric) = 1.0296206038116241701881727769479
absolute error = 6.8911176812587e-18
relative error = 6.6928708067301605185850649924486e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.245
y[1] (analytic) = 1.0298626750273646193068670679285
y[1] (numeric) = 1.0298626750273646262451536674994
absolute error = 6.9382865995709e-18
relative error = 6.7370988072623778271277933637098e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.246
y[1] (analytic) = 1.0301057163803492031776735062069
y[1] (numeric) = 1.0301057163803492101631172474991
absolute error = 6.9854437412922e-18
relative error = 6.7812882019896901881234324412615e-16 %
Correct digits = 17
h = 0.001
memory used=15.2MB, alloc=4.1MB, time=1.86
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.247
y[1] (analytic) = 1.0303497276275365821783359466519
y[1] (numeric) = 1.0303497276275365892109250059172
absolute error = 7.0325890592653e-18
relative error = 6.8254388492520922778612117369992e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.248
y[1] (analytic) = 1.0305947085249155294557453097401
y[1] (numeric) = 1.0305947085249155365354678160852
absolute error = 7.0797225063451e-18
relative error = 6.8695506078022343246715499072357e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.249
y[1] (analytic) = 1.0308406588275051680460284191387
y[1] (numeric) = 1.0308406588275051751728724545367
absolute error = 7.1268440353980e-18
relative error = 6.9136233368056976259367308055659e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.25
y[1] (analytic) = 1.0310875782893552158554045505058
y[1] (numeric) = 1.0310875782893552230293581498084
absolute error = 7.1739535993026e-18
relative error = 6.9576568958426203511644038180466e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.251
y[1] (analytic) = 1.0313354666635462316104470294153
y[1] (numeric) = 1.0313354666635462388314981803645
absolute error = 7.2210511509492e-18
relative error = 7.0016511449081503493502713035720e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.252
y[1] (analytic) = 1.0315843237021898617775039281638
y[1] (numeric) = 1.0315843237021898690456405714042
absolute error = 7.2681366432404e-18
relative error = 7.0456059444139564883182156200058e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.253
y[1] (analytic) = 1.0318341491564290884510309420608
y[1] (numeric) = 1.0318341491564290957662409711514
absolute error = 7.3152100290906e-18
relative error = 7.0895211551886645962708269736503e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.254
y[1] (analytic) = 1.0320849427764384782105885568886
y[1] (numeric) = 1.032084942776438485572859818315
absolute error = 7.3622712614264e-18
relative error = 7.1333966384791576288172557333442e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.255
y[1] (analytic) = 1.0323367043114244319462546505563
y[1] (numeric) = 1.0323367043114244393555749437431
absolute error = 7.4093202931868e-18
relative error = 7.1772322559516730325844487865970e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.256
y[1] (analytic) = 1.0325894335096254356522027035565
y[1] (numeric) = 1.0325894335096254431085597808791
absolute error = 7.4563570773226e-18
relative error = 7.2210278696921165627030563284795e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.257
y[1] (analytic) = 1.032843130118312312188194824666
y[1] (numeric) = 1.0328431301183123196915763914629
absolute error = 7.5033815667969e-18
relative error = 7.2647833422074334611076482992214e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.258
y[1] (analytic) = 1.0330977938837884740087378304194
y[1] (numeric) = 1.0330977938837884815591315450048
absolute error = 7.5503937145854e-18
relative error = 7.3084985364267768125957898423520e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.259
y[1] (analytic) = 1.0333534245513901768596496492213
y[1] (numeric) = 1.0333534245513901844570431228972
absolute error = 7.5973934736759e-18
relative error = 7.3521733157018927680568043206394e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.26
y[1] (analytic) = 1.0336100218654867744417823535499
y[1] (numeric) = 1.0336100218654867820861631506185
absolute error = 7.6443807970686e-18
relative error = 7.3958075438082719444891854208751e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.261
y[1] (analytic) = 1.0338675855694809740416471565521
y[1] (numeric) = 1.0338675855694809817330027943283
absolute error = 7.6913556377762e-18
relative error = 7.4394010849460984153579099157882e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.262
y[1] (analytic) = 1.0341261154058090931286857424248
y[1] (numeric) = 1.0341261154058091008670036912488
absolute error = 7.7383179488240e-18
relative error = 7.4829538037411900220505873257500e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.263
y[1] (analytic) = 1.0343856111159413169189313333344
y[1] (numeric) = 1.0343856111159413247041990165839
absolute error = 7.7852676832495e-18
relative error = 7.5264655652454466235034025606692e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.264
y[1] (analytic) = 1.0346460724403819569048019292326
y[1] (numeric) = 1.0346460724403819647370067233356
absolute error = 7.8322047941030e-18
relative error = 7.5699362349382569029975711117256e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.265
y[1] (analytic) = 1.0349074991186697103507671907983
y[1] (numeric) = 1.0349074991186697182298964252458
absolute error = 7.8791292344475e-18
relative error = 7.6133656787272193687244398030589e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.266
y[1] (analytic) = 1.0351698908893779207546294698607
y[1] (numeric) = 1.0351698908893779286806704272191
absolute error = 7.9260409573584e-18
relative error = 7.6567537629486617492115560989847e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.267
y[1] (analytic) = 1.0354332474901148392741585260421
y[1] (numeric) = 1.0354332474901148472470984419663
absolute error = 7.9729399159242e-18
relative error = 7.7001003543691180629276129381290e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.268
y[1] (analytic) = 1.0356975686575238871188185030108
y[1] (numeric) = 1.0356975686575238951386445662566
absolute error = 8.0198260632458e-18
relative error = 7.7434053201854443616257745563918e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.269
y[1] (analytic) = 1.0359628541272839189063247726353
y[1] (numeric) = 1.0359628541272839269730241250723
absolute error = 8.0666993524370e-18
relative error = 7.7866685280260853006687983751577e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.27
y[1] (analytic) = 1.0362291036341094869837672905078
y[1] (numeric) = 1.0362291036341094950973270271325
absolute error = 8.1135597366247e-18
relative error = 7.8298898459520419073232128732926e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.271
y[1] (analytic) = 1.0364963169117511067130361417346
y[1] (numeric) = 1.036496316911751114873443310683
absolute error = 8.1604071689484e-18
relative error = 7.8730691424571551454857601187483e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.272
y[1] (analytic) = 1.0367644936929955227202839915894
y[1] (numeric) = 1.03676449369299553092752559415
absolute error = 8.2072416025606e-18
relative error = 7.9162062864692497590642738803804e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.273
y[1] (analytic) = 1.0370336337096659761091591915901
y[1] (numeric) = 1.0370336337096659843632221822172
absolute error = 8.2540629906271e-18
relative error = 7.9593011473511725362896493911713e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.274
y[1] (analytic) = 1.0373037366926224726375423277883
y[1] (numeric) = 1.0373037366926224809384136141146
absolute error = 8.3008712863263e-18
relative error = 8.0023535949008575306816809956050e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.275
y[1] (analytic) = 1.0375748023717620518575180345561
y[1] (numeric) = 1.0375748023717620602051844774061
absolute error = 8.3476664428500e-18
relative error = 8.0453634993528294623533182633784e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.276
y[1] (analytic) = 1.0378468304760190572183129339225
y[1] (numeric) = 1.0378468304760190656127613473255
absolute error = 8.3944484134030e-18
relative error = 8.0883307313785411193858725124318e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.277
y[1] (analytic) = 1.0381198207333654071319295975428
y[1] (numeric) = 1.0381198207333654155731467487462
absolute error = 8.4412171512034e-18
relative error = 8.1312551620873771079355622905113e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.278
y[1] (analytic) = 1.0383937728708108670012054656899
y[1] (numeric) = 1.0383937728708108754891780751723
absolute error = 8.4879726094824e-18
relative error = 8.1741366630271670827037396241867e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.279
y[1] (analytic) = 1.0386686866144033222100246952314
y[1] (numeric) = 1.038668686614403330744739436716
absolute error = 8.5347147414846e-18
relative error = 8.2169751061851721177649518657992e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.28
y[1] (analytic) = 1.0389445616892290520754099464035
y[1] (numeric) = 1.0389445616892290606568534468713
absolute error = 8.5814435004678e-18
relative error = 8.2597703639885808128963164830972e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.281
y[1] (analytic) = 1.0392213978194130047612201563121
y[1] (numeric) = 1.0392213978194130133893789960154
absolute error = 8.6281588397033e-18
relative error = 8.3025223093054782891801192882212e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.282
y[1] (analytic) = 1.0394991947281190731531793854871
y[1] (numeric) = 1.0394991947281190818280400979629
absolute error = 8.6748607124758e-18
relative error = 8.3452308154454213779876469785000e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.283
y[1] (analytic) = 1.0397779521375503716949608624835
y[1] (numeric) = 1.0397779521375503804165099345669
absolute error = 8.7215490720834e-18
relative error = 8.3878957561601015954237056384795e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.284
y[1] (analytic) = 1.0400576697689495141850493904688
y[1] (numeric) = 1.0400576697689495229532732623064
absolute error = 8.7682238718376e-18
relative error = 8.4305170056439995772784876554804e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.285
y[1] (analytic) = 1.040338347342598892534104318956
y[1] (numeric) = 1.0403383473425989013489893840199
absolute error = 8.8148850650639e-18
relative error = 8.4730944385356077132287255391897e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.286
y[1] (analytic) = 1.0406199845778209564825443233454
y[1] (numeric) = 1.0406199845778209653440769284462
absolute error = 8.8615326051008e-18
relative error = 8.5156279299171057669077293327371e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.287
y[1] (analytic) = 1.0409025811929784942780742747098
y[1] (numeric) = 1.0409025811929785031862407200108
absolute error = 8.9081664453010e-18
relative error = 8.5581173553161430761367624458006e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=19.0MB, alloc=4.1MB, time=2.35
x[1] = 0.288
y[1] (analytic) = 1.0411861369054749143128735223236
y[1] (numeric) = 1.0411861369054749232676600613541
absolute error = 8.9547865390305e-18
relative error = 8.6005625907055934186376328086465e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.289
y[1] (analytic) = 1.0414706514317545277201639517677
y[1] (numeric) = 1.0414706514317545367215567914371
absolute error = 9.0013928396694e-18
relative error = 8.6429635125049350723910341036624e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.29
y[1] (analytic) = 1.0417561244873028319298752220681
y[1] (numeric) = 1.0417561244873028409778605226794
absolute error = 9.0479853006113e-18
relative error = 8.6853199975802772136734315972494e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.291
y[1] (analytic) = 1.0420425557866467951831236262249
y[1] (numeric) = 1.0420425557866468042776875014885
absolute error = 9.0945638752636e-18
relative error = 8.7276319232452424345003918134240e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.292
y[1] (analytic) = 1.0423299450433551420052200606774
y[1] (numeric) = 1.0423299450433551511463485777253
absolute error = 9.1411285170479e-18
relative error = 8.7698991672619362156307402243813e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.293
y[1] (analytic) = 1.0426182919700386396369216307212
y[1] (numeric) = 1.0426182919700386488246008101208
absolute error = 9.1876791793996e-18
relative error = 8.8121216078411399586837461320638e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.294
y[1] (analytic) = 1.0429075962783503854236404606493
y[1] (numeric) = 1.0429075962783503946578562764172
absolute error = 9.2342158157679e-18
relative error = 8.8542991236428796960050164162785e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.295
y[1] (analytic) = 1.043197857678986095162322319432
y[1] (numeric) = 1.0431978576789861044430606990482
absolute error = 9.2807383796162e-18
relative error = 8.8964315937773697432570435271558e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.296
y[1] (analytic) = 1.0434890758816843924057067150814
y[1] (numeric) = 1.0434890758816844017329535395035
absolute error = 9.3272468244221e-18
relative error = 8.9385188978055638930205130562036e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.297
y[1] (analytic) = 1.0437812505952270987236791534653
y[1] (numeric) = 1.0437812505952271080974202571422
absolute error = 9.3737411036769e-18
relative error = 8.9805609157392190952014872580163e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.298
y[1] (analytic) = 1.0440743815274395249214253002402
y[1] (numeric) = 1.0440743815274395343416464711268
absolute error = 9.4202211708866e-18
relative error = 9.0225575280423881445981896628675e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.299
y[1] (analytic) = 1.0443684683851907632140958277764
y[1] (numeric) = 1.0443684683851907726807828073473
absolute error = 9.4666869795709e-18
relative error = 9.0645086156309872505499206809331e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.3
y[1] (analytic) = 1.044663510874393980357689772432
y[1] (numeric) = 1.044663510874393989870828255696
absolute error = 9.5131384832640e-18
relative error = 9.1064140598740798014486730668192e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.301
y[1] (analytic) = 1.0449595087000067117358632713184
y[1] (numeric) = 1.0449595087000067212954389068331
absolute error = 9.5595756355147e-18
relative error = 9.1482737425944804929100644732950e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.302
y[1] (analytic) = 1.0452564615660311564023695917739
y[1] (numeric) = 1.0452564615660311660083679816594
absolute error = 9.6059983898855e-18
relative error = 9.1900875460683941362978973613728e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.303
y[1] (analytic) = 1.0455543691755144730788354111266
y[1] (numeric) = 1.0455543691755144827312421110804
absolute error = 9.6524066999538e-18
relative error = 9.2318553530270559963328221718186e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.304
y[1] (analytic) = 1.0458532312305490771075773489994
y[1] (numeric) = 1.0458532312305490868063778683107
absolute error = 9.6988005193113e-18
relative error = 9.2735770466566406490427515139756e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.305
y[1] (analytic) = 1.0461530474322729383591617993617
y[1] (numeric) = 1.0461530474322729481043416009258
absolute error = 9.7451798015641e-18
relative error = 9.3152525105988325106755471487195e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.306
y[1] (analytic) = 1.0464538174808698800944101547946
y[1] (numeric) = 1.0464538174808698898859546551276
absolute error = 9.7915445003330e-18
relative error = 9.3568816289515789047272069755270e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.307
y[1] (analytic) = 1.0467555410755698787805505609892
y[1] (numeric) = 1.0467555410755698886184451302426
absolute error = 9.8378945692534e-18
relative error = 9.3984642862694520889699153352035e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.308
y[1] (analytic) = 1.0470582179146493648612163853508
y[1] (numeric) = 1.0470582179146493747454463473258
absolute error = 9.8842299619750e-18
relative error = 9.4400003675638120315884117660562e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.309
y[1] (analytic) = 1.0473618476954315244799906297348
y[1] (numeric) = 1.0473618476954315344105412618975
absolute error = 9.9305506321627e-18
relative error = 9.4814897583041070265768015465396e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.31
y[1] (analytic) = 1.0476664301142866021571945637978
y[1] (numeric) = 1.0476664301142866121340510972933
absolute error = 9.9768565334955e-18
relative error = 9.5229323444172554233542684111222e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.311
y[1] (analytic) = 1.0479719648666322044196179021966
y[1] (numeric) = 1.0479719648666322144427655218643
absolute error = 1.00231476196677e-17
relative error = 9.5643280122892155261106725625522e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.312
y[1] (analytic) = 1.0482784516469336043828868959338
y[1] (numeric) = 1.048278451646933614452310740322
absolute error = 1.00694238443882e-17
relative error = 9.6056766487647326283521034214739e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.313
y[1] (analytic) = 1.0485858901487040472861657555049
y[1] (numeric) = 1.0485858901487040574018509168857
absolute error = 1.01156851613808e-17
relative error = 9.6469781411480325243839734954240e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.314
y[1] (analytic) = 1.0488942800645050569788858711721
y[1] (numeric) = 1.0488942800645050671408173955563
absolute error = 1.01619315243842e-17
relative error = 9.6882323772032201553085210549772e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.315
y[1] (analytic) = 1.0492036210859467433591963436608
y[1] (numeric) = 1.0492036210859467535673592308128
absolute error = 1.02081628871520e-17
relative error = 9.7294392451546699171826424593026e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.316
y[1] (analytic) = 1.0495139129036881107638283868539
y[1] (numeric) = 1.0495139129036881210182075903067
absolute error = 1.02543792034528e-17
relative error = 9.7705986336875029243931523593460e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.317
y[1] (analytic) = 1.0498251552074373673090652126448
y[1] (numeric) = 1.0498251552074373776096456397152
absolute error = 1.03005804270704e-17
relative error = 9.8117104319481510415872865004417e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.318
y[1] (analytic) = 1.0501373476859522351825080570062
y[1] (numeric) = 1.0501373476859522455292745688096
absolute error = 1.03467665118034e-17
relative error = 9.8527745295443409163028034668620e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.319
y[1] (analytic) = 1.0504504900270402618853280555329
y[1] (numeric) = 1.0504504900270402722782654669988
absolute error = 1.03929374114659e-17
relative error = 9.8937908165461175664565964236966e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.32
y[1] (analytic) = 1.0507645819175591324246927262339
y[1] (numeric) = 1.0507645819175591428637858061209
absolute error = 1.04390930798870e-17
relative error = 9.9347591834857164668292119585503e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.321
y[1] (analytic) = 1.0510796230434169824560548671731
y[1] (numeric) = 1.051079623043416992941288338084
absolute error = 1.04852334709109e-17
relative error = 9.9756795213579990573501717864591e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.322
y[1] (analytic) = 1.0513956130895727123749907266948
y[1] (numeric) = 1.0513956130895727229063492650921
absolute error = 1.05313585383973e-17
relative error = 1.0016551721621165156649754055282e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.323
y[1] (analytic) = 1.051712551740036302358273354424
y[1] (numeric) = 1.0517125517400363129357415906451
absolute error = 1.05774682362211e-17
relative error = 1.0057375676196790859786257079329e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.324
y[1] (analytic) = 1.0520304386778691283538660919921
y[1] (numeric) = 1.0520304386778691389774286102647
absolute error = 1.06235625182726e-17
relative error = 1.0098151277470333986245087450570e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.325
y[1] (analytic) = 1.0523492735851842790195202135225
y[1] (numeric) = 1.0523492735851842896891615519801
absolute error = 1.06696413384576e-17
relative error = 1.0138878418291535934500991536070e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.326
y[1] (analytic) = 1.0526690561431468736096597773046
y[1] (numeric) = 1.0526690561431468843253644280017
absolute error = 1.07157046506971e-17
relative error = 1.0179556991974435165564045098445e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.327
y[1] (analytic) = 1.0529897860319743808102358017967
y[1] (numeric) = 1.0529897860319743915719882107247
absolute error = 1.07617524089280e-17
relative error = 1.0220186892298322685110901005369e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.328
y[1] (analytic) = 1.0533114629309369385212309311322
y[1] (numeric) = 1.0533114629309369493290154982346
absolute error = 1.08077845671024e-17
relative error = 1.0260768013507358983461709373915e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.329
y[1] (analytic) = 1.0536340865183576745864948076487
y[1] (numeric) = 1.053634086518357685440295886837
absolute error = 1.08538010791883e-17
relative error = 1.0301300250311512755132380335682e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.1MB, time=2.90
NO POLE
x[1] = 0.33
y[1] (analytic) = 1.0539576564716130284705894216338
y[1] (numeric) = 1.0539576564716130393703913208029
absolute error = 1.08998018991691e-17
relative error = 1.0341783497886351674051174758197e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.331
y[1] (analytic) = 1.0542821724671330738823227614669
y[1] (numeric) = 1.0542821724671330848281097425109
absolute error = 1.09457869810440e-17
relative error = 1.0382217651873679558497681692060e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.332
y[1] (analytic) = 1.0546076341804018423446481406519
y[1] (numeric) = 1.0546076341804018533364044194798
absolute error = 1.09917562788279e-17
relative error = 1.0422602608381690595103171581856e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.333
y[1] (analytic) = 1.0549340412859576477106056318672
y[1] (numeric) = 1.0549340412859576587483153784186
absolute error = 1.10377097465514e-17
relative error = 1.0462938263985210413633340637503e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.334
y[1] (analytic) = 1.0552613934573934116249810921192
y[1] (numeric) = 1.0552613934573934227086284303804
absolute error = 1.10836473382612e-17
relative error = 1.0503224515726308112637267742166e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.335
y[1] (analytic) = 1.0555896903673569899313573173679
y[1] (numeric) = 1.0555896903673570010609263253877
absolute error = 1.11295690080198e-17
relative error = 1.0543461261114236354145521781274e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.336
y[1] (analytic) = 1.0559189316875515000242309195995
y[1] (numeric) = 1.0559189316875515111997056295048
absolute error = 1.11754747099053e-17
relative error = 1.0583648398125458618318674888293e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.337
y[1] (analytic) = 1.056249117088735649145867574257
y[1] (numeric) = 1.0562491170887356603672319722691
absolute error = 1.12213643980121e-17
relative error = 1.0623785825204520827461018761631e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.338
y[1] (analytic) = 1.0565802462407240636275673412012
y[1] (numeric) = 1.0565802462407240748948053676517
absolute error = 1.12672380264505e-17
relative error = 1.0663873441263872589199315801683e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.339
y[1] (analytic) = 1.0569123188123876190750108179637
y[1] (numeric) = 1.0569123188123876303881063673106
absolute error = 1.13130955493469e-17
relative error = 1.0703911145684248813501955845449e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.34
y[1] (analytic) = 1.0572453344716537714973559399734
y[1] (numeric) = 1.0572453344716537828562928608172
absolute error = 1.13589369208438e-17
relative error = 1.0743898838314853789955565809047e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.341
y[1] (analytic) = 1.0575792928855068893797542986879
y[1] (numeric) = 1.0575792928855069007845163937877
absolute error = 1.14047620950998e-17
relative error = 1.0783836419473537267985652615594e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.342
y[1] (analytic) = 1.0579141937199885866989549051396
y[1] (numeric) = 1.0579141937199885981495259314294
absolute error = 1.14505710262898e-17
relative error = 1.0823723789947151607650370623604e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.343
y[1] (analytic) = 1.0582500366401980568816623833228
y[1] (numeric) = 1.0582500366401980683780260519275
absolute error = 1.14963636686047e-17
relative error = 1.0863560850991428128219396619414e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.344
y[1] (analytic) = 1.0585868213102924077053156350886
y[1] (numeric) = 1.0585868213102924192474556113407
absolute error = 1.15421399762521e-17
relative error = 1.0903347504331790704234682953939e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.345
y[1] (analytic) = 1.0589245473934869971409520758003
y[1] (numeric) = 1.0589245473934870087288519792557
absolute error = 1.15878999034554e-17
relative error = 1.0943083652162649199828471116145e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.346
y[1] (analytic) = 1.0592632145520557701378215979091
y[1] (numeric) = 1.059263214552055781771465002364
absolute error = 1.16336434044549e-17
relative error = 1.0982769197148574719240839207269e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.347
y[1] (analytic) = 1.0596028224473315963494134778678
y[1] (numeric) = 1.0596028224473316080287839113749
absolute error = 1.16793704335071e-17
relative error = 1.1022404042423766217653909210331e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.348
y[1] (analytic) = 1.0599433707397066088005585003816
y[1] (numeric) = 1.0599433707397066205256394452664
absolute error = 1.17250809448848e-17
relative error = 1.1061988091592265256752465511480e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.349
y[1] (analytic) = 1.0602848590886325434952676329222
y[1] (numeric) = 1.0602848590886325552660425257999
absolute error = 1.17707748928777e-17
relative error = 1.1101521248728634287758344265355e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.35
y[1] (analytic) = 1.0606272871526210799649676426963
y[1] (numeric) = 1.0606272871526210917814198744881
absolute error = 1.18164522317918e-17
relative error = 1.1141003418377494587685287924152e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.351
y[1] (analytic) = 1.0609706545892441827567931078597
y[1] (numeric) = 1.0609706545892441946189060238094
absolute error = 1.18621129159497e-17
relative error = 1.1180434505553905741589944652429e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.352
y[1] (analytic) = 1.0613149610551344438615933347137
y[1] (numeric) = 1.0613149610551344557693502344044
absolute error = 1.19077568996907e-17
relative error = 1.1219814415743548320673952805200e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.353
y[1] (analytic) = 1.0616602062059854260813117529063
y[1] (numeric) = 1.0616602062059854380346958902772
absolute error = 1.19533841373709e-17
relative error = 1.1259143054902898583848196330111e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.354
y[1] (analytic) = 1.0620063896965520073353944212866
y[1] (numeric) = 1.0620063896965520193343890046497
absolute error = 1.19989945833631e-17
relative error = 1.1298420329459206897291237541898e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.355
y[1] (analytic) = 1.062353511180650725905883338033
y[1] (numeric) = 1.0623535111806507379504715300897
absolute error = 1.20445881920567e-17
relative error = 1.1337646146310468581493654082917e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.356
y[1] (analytic) = 1.0627015703111601266208493099901
y[1] (numeric) = 1.0627015703111601387110142278483
absolute error = 1.20901649178582e-17
relative error = 1.1376820412825951804891389891459e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.357
y[1] (analytic) = 1.0630505667400211079758181978111
y[1] (numeric) = 1.063050566740021120111542913002
absolute error = 1.21357247151909e-17
relative error = 1.1415943036845964282459563417120e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.358
y[1] (analytic) = 1.0634005001182372701928434155077
y[1] (numeric) = 1.0634005001182372823741109540026
absolute error = 1.21812675384949e-17
relative error = 1.1455013926681894942957172366581e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.359
y[1] (analytic) = 1.0637513700958752642168766253644
y[1] (numeric) = 1.0637513700958752764436699675919
absolute error = 1.22267933422275e-17
relative error = 1.1494032991116623943863119948464e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.36
y[1] (analytic) = 1.0641031763220651416490876318753
y[1] (numeric) = 1.0641031763220651539213897127382
absolute error = 1.22723020808629e-17
relative error = 1.1533000139404266449124682925632e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.361
y[1] (analytic) = 1.064455918445000705616783541413
y[1] (numeric) = 1.0644559184450007179345772503054
absolute error = 1.23177937088924e-17
relative error = 1.1571915281270379046825911996510e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.362
y[1] (analytic) = 1.0648095961119398625795763177395
y[1] (numeric) = 1.0648095961119398749428444985637
absolute error = 1.23632681808242e-17
relative error = 1.1610778326911782517072256014928e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.363
y[1] (analytic) = 1.0651642089692049750714469272204
y[1] (numeric) = 1.0651642089692049874801723784043
absolute error = 1.24087254511839e-17
relative error = 1.1649589186997034547769879116388e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.364
y[1] (analytic) = 1.0655197566621832153783533317088
y[1] (numeric) = 1.0655197566621832278325188062231
absolute error = 1.24541654745143e-17
relative error = 1.1688347772666236973493954397388e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.365
y[1] (analytic) = 1.0658762388353269201510286515192
y[1] (numeric) = 1.0658762388353269326506168568945
absolute error = 1.24995882053753e-17
relative error = 1.1727053995530929645762807241632e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.366
y[1] (analytic) = 1.0662336551321539459526148857234
y[1] (numeric) = 1.0662336551321539584976084840676
absolute error = 1.25449935983442e-17
relative error = 1.1765707767674352102097642503913e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.367
y[1] (analytic) = 1.0665920051952480257407766421643
y[1] (numeric) = 1.06659200519524803833115825018
absolute error = 1.25903816080157e-17
relative error = 1.1804309001651415877801824443727e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.368
y[1] (analytic) = 1.0669512886662591262839383951033
y[1] (numeric) = 1.066951288666259138919690584105
absolute error = 1.26357521890017e-17
relative error = 1.1842857610488481865660256511879e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.369
y[1] (analytic) = 1.0673115051859038065112878542941
y[1] (numeric) = 1.0673115051859038191923931502257
absolute error = 1.26811052959316e-17
relative error = 1.1881353507683599041139706400355e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.37
y[1] (analytic) = 1.0676726543939655767961870955091
y[1] (numeric) = 1.0676726543939655895226279789615
absolute error = 1.27264408834524e-17
relative error = 1.1919796607206547836101680647735e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.371
y[1] (analytic) = 1.0680347359292952591726321691378
y[1] (numeric) = 1.0680347359292952719443910753662
absolute error = 1.27717589062284e-17
relative error = 1.1958186823498501363461933809703e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.1MB, time=3.39
NO POLE
x[1] = 0.372
y[1] (analytic) = 1.0683977494298113484844009704265
y[1] (numeric) = 1.0683977494298113613014602893682
absolute error = 1.28170593189417e-17
relative error = 1.1996524071472428581197674560727e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.373
y[1] (analytic) = 1.0687616945325003744665282222431
y[1] (numeric) = 1.0687616945325003873288702985349
absolute error = 1.28623420762918e-17
relative error = 1.2034808266512647010577781884391e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.374
y[1] (analytic) = 1.0691265708734172647587454889206
y[1] (numeric) = 1.0691265708734172776663526219165
absolute error = 1.29076071329959e-17
relative error = 1.2073039324475023584805541348783e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.375
y[1] (analytic) = 1.0694923780876857088505232077704
y[1] (numeric) = 1.0694923780876857218033776515596
absolute error = 1.29528544437892e-17
relative error = 1.2111217161687167571506375865556e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.376
y[1] (analytic) = 1.0698591158094985229573507932542
y[1] (numeric) = 1.0698591158094985359554347566783
absolute error = 1.29980839634241e-17
relative error = 1.2149341694947587414849263784643e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.377
y[1] (analytic) = 1.070226783672118015827889937563
y[1] (numeric) = 1.0702267836721180288711855842341
absolute error = 1.30432956466711e-17
relative error = 1.2187412841526430256490702746266e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.378
y[1] (analytic) = 1.0705953813078763554816353004824
y[1] (numeric) = 1.0705953813078763685701247488011
absolute error = 1.30884894483187e-17
relative error = 1.2225430519165278378466530623536e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.379
y[1] (analytic) = 1.070964908348175936876715850913
y[1] (numeric) = 1.070964908348175950010381174086
absolute error = 1.31336653231730e-17
relative error = 1.2263394646076658451831699273161e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.38
y[1] (analytic) = 1.0713353644234897505074691922754
y[1] (numeric) = 1.0713353644234897636862924183336
absolute error = 1.31788232260582e-17
relative error = 1.2301305140944384390680129277128e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.381
y[1] (analytic) = 1.0717067491633617519314202742562
y[1] (numeric) = 1.0717067491633617651553833860725
absolute error = 1.32239631118163e-17
relative error = 1.2339161922923145546884861805319e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.382
y[1] (analytic) = 1.0720790621964072322252949639468
y[1] (numeric) = 1.0720790621964072454943798992542
absolute error = 1.32690849353074e-17
relative error = 1.2376964911638647951092492008920e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.383
y[1] (analytic) = 1.072452303150313189369698020393
y[1] (numeric) = 1.0724523031503132026838866718028
absolute error = 1.33141886514098e-17
relative error = 1.2414714027187561309624703895872e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.384
y[1] (analytic) = 1.0728264716518387005620840879077
y[1] (numeric) = 1.0728264716518387139213583029275
absolute error = 1.33592742150198e-17
relative error = 1.2452409190137179020663470694332e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.385
y[1] (analytic) = 1.0732015673268152954576493952072
y[1] (numeric) = 1.073201567326815308861990976259
absolute error = 1.34043415810518e-17
relative error = 1.2490050321525350991115151428126e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.386
y[1] (analytic) = 1.0735775898001473303377709195101
y[1] (numeric) = 1.0735775898001473437871616239484
absolute error = 1.34493907044383e-17
relative error = 1.2527637342860316008953640702249e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.387
y[1] (analytic) = 1.0739545386958123632056188471909
y[1] (numeric) = 1.0739545386958123767000403873212
absolute error = 1.34944215401303e-17
relative error = 1.2565170176120899491624993668657e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.388
y[1] (analytic) = 1.0743324136368615298085672354074
y[1] (numeric) = 1.0743324136368615433480012785045
absolute error = 1.35394340430971e-17
relative error = 1.2602648743756144906903635884152e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.389
y[1] (analytic) = 1.0747112142454199205870268523226
y[1] (numeric) = 1.0747112142454199341714550206486
absolute error = 1.35844281683260e-17
relative error = 1.2640072968684845504748906865949e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.39
y[1] (analytic) = 1.0750909401426869585493232471189
y[1] (numeric) = 1.0750909401426869721787271179418
absolute error = 1.36294038708229e-17
relative error = 1.2677442774295906770782220935733e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.391
y[1] (analytic) = 1.0754715909489367780722421749589
y[1] (numeric) = 1.075471590948936791746603280571
absolute error = 1.36743611056121e-17
relative error = 1.2714758084447956853398574793367e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.392
y[1] (analytic) = 1.0758531662835186046268635763786
y[1] (numeric) = 1.0758531662835186183461634041151
absolute error = 1.37192998277365e-17
relative error = 1.2752018823469322222540616849300e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.393
y[1] (analytic) = 1.0762356657648571354293043853106
y[1] (numeric) = 1.076235665764857149193524377568
absolute error = 1.37642199922574e-17
relative error = 1.2789224916157624330602901832712e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.394
y[1] (analytic) = 1.0766190890104529210159895150267
y[1] (numeric) = 1.076619089010452934825111069281
absolute error = 1.38091215542543e-17
relative error = 1.2826376287779369757898172884894e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.395
y[1] (analytic) = 1.0770034356368827477430694467592
y[1] (numeric) = 1.0770034356368827615970739155851
absolute error = 1.38540044688259e-17
relative error = 1.2863472864070648072549809823937e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.396
y[1] (analytic) = 1.0773887052598000212096019216175
y[1] (numeric) = 1.0773887052598000351084706127069
absolute error = 1.38988686910894e-17
relative error = 1.2900514571236242949825657808143e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.397
y[1] (analytic) = 1.0777748974939351506041143126486
y[1] (numeric) = 1.077774897493935164547828488829
absolute error = 1.39437141761804e-17
relative error = 1.2937501335949294548457974594908e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.398
y[1] (analytic) = 1.0781620119530959339741623305114
y[1] (numeric) = 1.0781620119530959479627032097648
absolute error = 1.39885408792534e-17
relative error = 1.2974433085351511778253174120837e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.399
y[1] (analytic) = 1.0785500482501679444184997932385
y[1] (numeric) = 1.0785500482501679584518485487204
absolute error = 1.40333487554819e-17
relative error = 1.3011309747053005913349473990041e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.4
y[1] (analytic) = 1.0789390059971149172014732679482
y[1] (numeric) = 1.078939005997114931279611028006
absolute error = 1.40781377600578e-17
relative error = 1.3048131249131468455798685177044e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.401
y[1] (analytic) = 1.0793288848049791377892544701431
y[1] (numeric) = 1.0793288848049791519121623183353
absolute error = 1.41229078481922e-17
relative error = 1.3084897520132640567953959259510e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.402
y[1] (analytic) = 1.0797196842838818308075223843972
y[1] (numeric) = 1.0797196842838818449751813595121
absolute error = 1.41676589751149e-17
relative error = 1.3121608489069570170940222340468e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.403
y[1] (analytic) = 1.0801114040430235499202061487794
y[1] (numeric) = 1.0801114040430235641325972448544
absolute error = 1.42123910960750e-17
relative error = 1.3158264085422881775496514377642e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.404
y[1] (analytic) = 1.0805040436906845686288988243055
y[1] (numeric) = 1.0805040436906845828860029906458
absolute error = 1.42571041663403e-17
relative error = 1.3194864239139927850203107138550e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.405
y[1] (analytic) = 1.0808976028342252719925512500355
y[1] (numeric) = 1.0808976028342252862943493912331
absolute error = 1.43017981411976e-17
relative error = 1.3231408880634767406679659822148e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.406
y[1] (analytic) = 1.0812920810800865492670542641556
y[1] (numeric) = 1.0812920810800865636135272401087
absolute error = 1.43464729759531e-17
relative error = 1.3267897940788229852850291622359e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.407
y[1] (analytic) = 1.0816874780337901874643166514964
y[1] (numeric) = 1.0816874780337902018554452774283
absolute error = 1.43911286259319e-17
relative error = 1.3304331350947139419103186612504e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.408
y[1] (analytic) = 1.0820837932999392658304452584406
y[1] (numeric) = 1.0820837932999392802662103049189
absolute error = 1.44357650464783e-17
relative error = 1.3340709042924273355240716954568e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.409
y[1] (analytic) = 1.0824810264822185512426327970737
y[1] (numeric) = 1.0824810264822185657230149900296
absolute error = 1.44803821929559e-17
relative error = 1.3377030948998128227557737597424e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.41
y[1] (analytic) = 1.082879177183394894524357941723
y[1] (numeric) = 1.0828791771833949090493379624707
absolute error = 1.45249800207477e-17
relative error = 1.3413297001912679507651422441930e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.411
y[1] (analytic) = 1.0832782450053176276785014027179
y[1] (numeric) = 1.0832782450053176422480598879736
absolute error = 1.45695584852557e-17
relative error = 1.3449507134876672916658986081226e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.412
y[1] (analytic) = 1.0836782295489189620379807442877
y[1] (numeric) = 1.0836782295489189766520982861892
absolute error = 1.46141175419015e-17
relative error = 1.3485661281563832917905925417716e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.413
y[1] (analytic) = 1.084079130414214387333505795996
y[1] (numeric) = 1.0840791304142144019921629421221
absolute error = 1.46586571461261e-17
relative error = 1.3521759376112325605191334586715e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.2MB, time=3.85
NO POLE
x[1] = 0.414
y[1] (analytic) = 1.0844809472003030716780555899898
y[1] (numeric) = 1.0844809472003030863812328433796
absolute error = 1.47031772533898e-17
relative error = 1.3557801353124307811161852256329e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.415
y[1] (analytic) = 1.0848836795053682624676768396186
y[1] (numeric) = 1.0848836795053682772153546587912
absolute error = 1.47476778191726e-17
relative error = 1.3593787147665930928645329651337e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.416
y[1] (analytic) = 1.0852873269266776881982030586595
y[1] (numeric) = 1.0852873269266777029903618576334
absolute error = 1.47921587989739e-17
relative error = 1.3629716695266692575412798327607e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.417
y[1] (analytic) = 1.0856918890605839611974925044623
y[1] (numeric) = 1.085691889060583976034112652775
absolute error = 1.48366201483127e-17
relative error = 1.3665589931919243093676423643848e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.418
y[1] (analytic) = 1.0860973655025249812727822128099
y[1] (numeric) = 1.0860973655025249961538440355376
absolute error = 1.48810618227277e-17
relative error = 1.3701406794079093274841554077120e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.419
y[1] (analytic) = 1.0865037558470243402727544771743
y[1] (numeric) = 1.0865037558470243551982382549514
absolute error = 1.49254837777771e-17
relative error = 1.3737167218664039499241843300245e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.42
y[1] (analytic) = 1.0869110596876917275639112103343
y[1] (numeric) = 1.0869110596876917425337971793734
absolute error = 1.49698859690391e-17
relative error = 1.3772871143054227080155137227783e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.421
y[1] (analytic) = 1.087319276617223336420850712016
y[1] (numeric) = 1.0873192766172233514351190641274
absolute error = 1.50142683521114e-17
relative error = 1.3808518505091286671219188623585e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.422
y[1] (analytic) = 1.0877284062274022713300404523114
y[1] (numeric) = 1.0877284062274022863886713349231
absolute error = 1.50586308826117e-17
relative error = 1.3844109243078384875408658006387e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.423
y[1] (analytic) = 1.0881384481090989562066785671374
y[1] (numeric) = 1.088138448109098971309652083315
absolute error = 1.51029735161776e-17
relative error = 1.3879643295779716262639962301029e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.424
y[1] (analytic) = 1.088549401852271543524235848908
y[1] (numeric) = 1.0885494018522715586715320573741
absolute error = 1.51472962084661e-17
relative error = 1.3915120602419622006525668151422e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.425
y[1] (analytic) = 1.0889612670459663243562691029099
y[1] (numeric) = 1.0889612670459663395478680180647
absolute error = 1.51915989151548e-17
relative error = 1.3950541102683264585505773573969e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.426
y[1] (analytic) = 1.0893740432783181393300958276049
y[1] (numeric) = 1.0893740432783181545659774195459
absolute error = 1.52358815919410e-17
relative error = 1.3985904736715366199366479221150e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.427
y[1] (analytic) = 1.089787730136550790491919265217
y[1] (numeric) = 1.0897877301365508057720634597589
absolute error = 1.52801441945419e-17
relative error = 1.4021211445119952390649989080680e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.428
y[1] (analytic) = 1.0902023272069774540829919575135
y[1] (numeric) = 1.0902023272069774694073786362085
absolute error = 1.53243866786950e-17
relative error = 1.4056461168960272686917651115958e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.429
y[1] (analytic) = 1.0906178340750010942264050306518
y[1] (numeric) = 1.0906178340750011095950140308096
absolute error = 1.53686090001578e-17
relative error = 1.4091653849758072580544663640021e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.43
y[1] (analytic) = 1.0910342503251148775240895223366
y[1] (numeric) = 1.0910342503251148929369006370444
absolute error = 1.54128111147078e-17
relative error = 1.4126789429493135146602168419750e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.431
y[1] (analytic) = 1.09145157554090258856361515432
y[1] (numeric) = 1.0914515755409026040206081324632
absolute error = 1.54569929781432e-17
relative error = 1.4161867850603458078946607254904e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.432
y[1] (analytic) = 1.0918698093050390463343710434825
y[1] (numeric) = 1.0918698093050390618355255897644
absolute error = 1.55011545462819e-17
relative error = 1.4196889055983866389191288828277e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.433
y[1] (analytic) = 1.0922889511992905215527119353457
y[1] (numeric) = 1.0922889511992905370980077103082
absolute error = 1.55452957749625e-17
relative error = 1.4231852988986452354184225048794e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.434
y[1] (analytic) = 1.0927090008045151548956526349088
y[1] (numeric) = 1.0927090008045151704850692549525
absolute error = 1.55894166200437e-17
relative error = 1.4266759593419543259770934389942e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.435
y[1] (analytic) = 1.0931299577006633761426924011461
y[1] (numeric) = 1.0931299577006633917762094385507
absolute error = 1.56335170374046e-17
relative error = 1.4301608813547487917237393648459e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.436
y[1] (analytic) = 1.0935518214667783242253501633781
y[1] (numeric) = 1.093551821466778339902947146323
absolute error = 1.56775969829449e-17
relative error = 1.4336400594090345312741419772374e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.437
y[1] (analytic) = 1.0939745916809962681839905100158
y[1] (numeric) = 1.0939745916809962839056469226003
absolute error = 1.57216564125845e-17
relative error = 1.4371134880223018613966459921258e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.438
y[1] (analytic) = 1.0943982679205470290315194928856
y[1] (numeric) = 1.0943982679205470447972147751498
absolute error = 1.57656952822642e-17
relative error = 1.4405811617575389412283514897244e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.439
y[1] (analytic) = 1.0948228497617544025235283834771
y[1] (numeric) = 1.094822849761754418333241931422
absolute error = 1.58097135479449e-17
relative error = 1.4440430752231074691565769618022e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.44
y[1] (analytic) = 1.0952483367800365828344626110016
y[1] (numeric) = 1.0952483367800365986881737766102
absolute error = 1.58537111656086e-17
relative error = 1.4474992230727823286816364119973e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.441
y[1] (analytic) = 1.0956747285499065871393922061318
y[1] (numeric) = 1.0956747285499066030370802973892
absolute error = 1.58976880912574e-17
relative error = 1.4509496000056079210304190766689e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.442
y[1] (analytic) = 1.0961020246449726811009591686834
y[1] (numeric) = 1.0961020246449726970426034495979
absolute error = 1.59416442809145e-17
relative error = 1.4543942007659366140850289854863e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.443
y[1] (analytic) = 1.0965302246379388052610762723304
y[1] (numeric) = 1.0965302246379388212466559629542
absolute error = 1.59855796906238e-17
relative error = 1.4578330201433387438115996175984e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.444
y[1] (analytic) = 1.0969593281006050023369509146883
y[1] (numeric) = 1.0969593281006050183664451911381
absolute error = 1.60294942764498e-17
relative error = 1.4612660529725394935752719403939e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.445
y[1] (analytic) = 1.0973893346038678454210067167782
y[1] (numeric) = 1.0973893346038678614943947112561
absolute error = 1.60733879944779e-17
relative error = 1.4646932941333916922041743677432e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.446
y[1] (analytic) = 1.0978202437177208670842746719854
y[1] (numeric) = 1.0978202437177208832015354727998
absolute error = 1.61172608008144e-17
relative error = 1.4681147385508206709831108264891e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.447
y[1] (analytic) = 1.0982520550112549893828247411573
y[1] (numeric) = 1.0982520550112550055439373927439
absolute error = 1.61611126515866e-17
relative error = 1.4715303811947776789574491013175e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.448
y[1] (analytic) = 1.0986847680526589547668078874449
y[1] (numeric) = 1.0986847680526589709717513903875
absolute error = 1.62049435029426e-17
relative error = 1.4749402170801654272365681531757e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.449
y[1] (analytic) = 1.0991183824092197578916776418816
y[1] (numeric) = 1.0991183824092197741404309529331
absolute error = 1.62487533110515e-17
relative error = 1.4783442412667995279768184407015e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.45
y[1] (analytic) = 1.0995528976473230783311593885136
y[1] (numeric) = 1.099552897647323094623701420617
absolute error = 1.62925420321034e-17
relative error = 1.4817424488593511629030925038323e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.451
y[1] (analytic) = 1.0999883133324537141915346561489
y[1] (numeric) = 1.0999883133324537305278442784588
absolute error = 1.63363096223099e-17
relative error = 1.4851348350073346715880785737327e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.452
y[1] (analytic) = 1.1004246290291960166268068024775
y[1] (numeric) = 1.1004246290291960330068628403806
absolute error = 1.63800560379031e-17
relative error = 1.4885213949049581882858759482525e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.453
y[1] (analytic) = 1.100861844301234325254313575431
y[1] (numeric) = 1.1008618443012343416780948105677
absolute error = 1.64237812351367e-17
relative error = 1.4919021237911647252934411720041e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.454
y[1] (analytic) = 1.101299958711353404470351136208
y[1] (numeric) = 1.1012999587113534209378363064936
absolute error = 1.64674851702856e-17
relative error = 1.4952770169495362891557255653864e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.455
y[1] (analytic) = 1.1017389718214388806653732283767
y[1] (numeric) = 1.1017389718214388971765410280224
absolute error = 1.65111677996457e-17
relative error = 1.4986460697082157130895593818887e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.2MB, time=4.32
NO POLE
x[1] = 0.456
y[1] (analytic) = 1.1021788831924776803383282778904
y[1] (numeric) = 1.1021788831924776968931573574248
absolute error = 1.65548290795344e-17
relative error = 1.5020092774398915229731552822672e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.457
y[1] (analytic) = 1.1026196923845584691096963097179
y[1] (numeric) = 1.1026196923845584857081652760085
absolute error = 1.65984689662906e-17
relative error = 1.5053666355617368306347682794120e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.458
y[1] (analytic) = 1.1030613989568720916327866680871
y[1] (numeric) = 1.1030613989568721082748740843613
absolute error = 1.66420874162742e-17
relative error = 1.5087181395353023840822763655689e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.459
y[1] (analytic) = 1.1035040024677120124028566290802
y[1] (numeric) = 1.103504002467712029088541014947
absolute error = 1.66856843858668e-17
relative error = 1.5120637848665179596680799480453e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.46
y[1] (analytic) = 1.1039475024744747574636100964996
y[1] (numeric) = 1.1039475024744747741928699279712
absolute error = 1.67292598314716e-17
relative error = 1.5154035671056206258239905562523e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.461
y[1] (analytic) = 1.104391898533660357010634674543
y[1] (numeric) = 1.104391898533660373783448384056
absolute error = 1.67728137095130e-17
relative error = 1.5187374818470553586332703602262e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.462
y[1] (analytic) = 1.1048371902008727888913345138855
y[1] (numeric) = 1.1048371902008728057076804903227
absolute error = 1.68163459764372e-17
relative error = 1.5220655247294657533860167521879e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.463
y[1] (analytic) = 1.1052833770308204230009154312754
y[1] (numeric) = 1.1052833770308204398607720199873
absolute error = 1.68598565887119e-17
relative error = 1.5253876914356026781261950170453e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.464
y[1] (analytic) = 1.1057304585773164665739779066934
y[1] (numeric) = 1.1057304585773164834773234095199
absolute error = 1.69033455028265e-17
relative error = 1.5287039776922777152631433481450e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.465
y[1] (analytic) = 1.1061784343932794103712726665209
y[1] (numeric) = 1.106178434393279427318085341813
absolute error = 1.69468126752921e-17
relative error = 1.5320143792702979854335741949788e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.466
y[1] (analytic) = 1.1066273040307334757611726659979
y[1] (numeric) = 1.1066273040307334927514307286393
absolute error = 1.69902580626414e-17
relative error = 1.5353188919843914442648951945512e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.467
y[1] (analytic) = 1.1070770670408090626954143895363
y[1] (numeric) = 1.1070770670408090797290960109655
absolute error = 1.70336816214292e-17
relative error = 1.5386175116931859103364935781689e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.468
y[1] (analytic) = 1.107527722973743198578660493185
y[1] (numeric) = 1.1075277229737432156557438014169
absolute error = 1.70770833082319e-17
relative error = 1.5419102342990972071870407414816e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.469
y[1] (analytic) = 1.1079792713788799880314349197206
y[1] (numeric) = 1.1079792713788800051518979993684
absolute error = 1.71204630796478e-17
relative error = 1.5451970557482891374525360909766e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.47
y[1] (analytic) = 1.1084317118046710635459807234666
y[1] (numeric) = 1.1084317118046710807098016157637
absolute error = 1.71638208922971e-17
relative error = 1.5484779720306058470106409659644e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.471
y[1] (analytic) = 1.1088850437986760370345899490213
y[1] (numeric) = 1.1088850437986760542417466518433
absolute error = 1.72071567028220e-17
relative error = 1.5517529791795127316297368468225e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.472
y[1] (analytic) = 1.109339266907562952269954015601
y[1] (numeric) = 1.1093392669075629695204244834878
absolute error = 1.72504704678868e-17
relative error = 1.5550220732720368489474215413633e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.473
y[1] (analytic) = 1.1097943806771087382170821666872
y[1] (numeric) = 1.1097943806771087555108443108647
absolute error = 1.72937621441775e-17
relative error = 1.5582852504286617853479839400650e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.474
y[1] (analytic) = 1.1102503846521996632563346530956
y[1] (numeric) = 1.1102503846521996805933663414982
absolute error = 1.73370316884026e-17
relative error = 1.5615425068133302288467331564196e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.475
y[1] (analytic) = 1.1107072783768317902971164264731
y[1] (numeric) = 1.1107072783768318076773954837657
absolute error = 1.73802790572926e-17
relative error = 1.5647938386333288583546182355579e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.476
y[1] (analytic) = 1.1111650613941114327817762295659
y[1] (numeric) = 1.111165061394111450205280437166
absolute error = 1.74235042076001e-17
relative error = 1.5680392421392268809129328302913e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.477
y[1] (analytic) = 1.1116237332462556115792550793985
y[1] (numeric) = 1.1116237332462556290459621754983
absolute error = 1.74667070960998e-17
relative error = 1.5712787136248050934828848431311e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.478
y[1] (analytic) = 1.1120832934745925127680272497516
y[1] (numeric) = 1.1120832934745925302779149293406
absolute error = 1.75098876795890e-17
relative error = 1.5745122494270294510758262236463e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.479
y[1] (analytic) = 1.1125437416195619463078759700387
y[1] (numeric) = 1.1125437416195619638609218849258
absolute error = 1.75530459148871e-17
relative error = 1.5777398459259341878681602840129e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.48
y[1] (analytic) = 1.1130050772207158056000451688413
y[1] (numeric) = 1.1130050772207158231962269276771
absolute error = 1.75961817588358e-17
relative error = 1.5809614995445674943721441283030e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.481
y[1] (analytic) = 1.1134672998167185279353077019906
y[1] (numeric) = 1.11346729981671854557460287029
absolute error = 1.76392951682994e-17
relative error = 1.5841772067489456856652001937331e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.482
y[1] (analytic) = 1.1139304089453475558294896171662
y[1] (numeric) = 1.1139304089453475735118757173304
absolute error = 1.76823861001642e-17
relative error = 1.5873869640479260652176210152646e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.483
y[1] (analytic) = 1.1143944041434937992459891195241
y[1] (numeric) = 1.1143944041434938169714436308636
absolute error = 1.77254545113395e-17
relative error = 1.5905907679932230597014526953486e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.484
y[1] (analytic) = 1.1148592849471620987048280158762
y[1] (numeric) = 1.1148592849471621164733283746331
absolute error = 1.77685003587569e-17
relative error = 1.5937886151792712077867398100789e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.485
y[1] (analytic) = 1.1153250508914716892777725284065
y[1] (numeric) = 1.1153250508914717070892961277769
absolute error = 1.78115235993704e-17
relative error = 1.5969805022431596008012416739436e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.486
y[1] (analytic) = 1.115791701510656665469059482842
y[1] (numeric) = 1.1157917015106566833235836729989
absolute error = 1.78545241901569e-17
relative error = 1.6001664258646017199337813572501e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.487
y[1] (analytic) = 1.1162592363380664469812629903921
y[1] (numeric) = 1.1162592363380664648787650785079
absolute error = 1.78975020881158e-17
relative error = 1.6033463827658241074549977811287e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.488
y[1] (analytic) = 1.1167276549061662453658358576272
y[1] (numeric) = 1.1167276549061662633062931078964
absolute error = 1.79404572502692e-17
relative error = 1.6065203697115084323637497324035e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.489
y[1] (analytic) = 1.117196956746537531557859073795
y[1] (numeric) = 1.1171969567465375495412487074569
absolute error = 1.79833896336619e-17
relative error = 1.6096883835087151880836698017132e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.49
y[1] (analytic) = 1.1176671413898785042945318408633
y[1] (numeric) = 1.1176671413898785223208310362248
absolute error = 1.80262991953615e-17
relative error = 1.6128504210068159194518689281073e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.491
y[1] (analytic) = 1.1181382083660045594169337278386
y[1] (numeric) = 1.1181382083660045774861196202971
absolute error = 1.80691858924585e-17
relative error = 1.6160064790974250122423476247198e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.492
y[1] (analytic) = 1.1186101572038487600545896476376
y[1] (numeric) = 1.1186101572038487781666393297038
absolute error = 1.81120496820662e-17
relative error = 1.6191565547143131688792862628015e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.493
y[1] (analytic) = 1.1190829874314623076923674719854
y[1] (numeric) = 1.1190829874314623258472579933062
absolute error = 1.81548905213208e-17
relative error = 1.6223006448333383697570160631970e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.494
y[1] (analytic) = 1.1195566985760150141192372174827
y[1] (numeric) = 1.1195566985760150323169455848641
absolute error = 1.81977083673814e-17
relative error = 1.6254387464723674740595978333368e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.495
y[1] (analytic) = 1.1200312901637957742584198541208
y[1] (numeric) = 1.1200312901637957924989230315511
absolute error = 1.82405031774303e-17
relative error = 1.6285708566912242028466569085545e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.496
y[1] (analytic) = 1.1205067617202130398784529061372
y[1] (numeric) = 1.1205067617202130581617278148099
absolute error = 1.82832749086727e-17
relative error = 1.6316969725915831071092905945432e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.497
y[1] (analytic) = 1.1209831127697952941846991341835
y[1] (numeric) = 1.1209831127697953125107226525202
absolute error = 1.83260235183367e-17
relative error = 1.6348170913168899695712280609216e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.2MB, time=4.80
NO POLE
x[1] = 0.498
y[1] (analytic) = 1.1214603428361915272908237073372
y[1] (numeric) = 1.121460342836191545659572671011
absolute error = 1.83687489636738e-17
relative error = 1.6379312100523263977078185549673e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.499
y[1] (analytic) = 1.1219384514421717125697643935207
y[1] (numeric) = 1.1219384514421717309812155954793
absolute error = 1.84114512019586e-17
relative error = 1.6410393260247026071640763451856e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.5
y[1] (analytic) = 1.1224174381096272838837184173962
y[1] (numeric) = 1.1224174381096273023378486078849
absolute error = 1.84541301904887e-17
relative error = 1.6441414365023677046574630438253e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.501
y[1] (analytic) = 1.1228973023595716136926687557886
y[1] (numeric) = 1.1228973023595716321894546423739
absolute error = 1.84967858865853e-17
relative error = 1.6472375387951819480284728423307e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.502
y[1] (analytic) = 1.1233780437121404920409717621522
y[1] (numeric) = 1.1233780437121405105803900097448
absolute error = 1.85394182475926e-17
relative error = 1.6503276302543816670999628246212e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.503
y[1] (analytic) = 1.1238596616865926064215271335312
y[1] (numeric) = 1.1238596616865926250035543644096
absolute error = 1.85820272308784e-17
relative error = 1.6534117082725507181712786345915e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.504
y[1] (analytic) = 1.1243421558013100225170503558855
y[1] (numeric) = 1.124342155801310041141663149719
absolute error = 1.86246127938335e-17
relative error = 1.6564897702834846967690874368662e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.505
y[1] (analytic) = 1.1248255255737986658179668865485
y[1] (numeric) = 1.1248255255737986844851417804209
absolute error = 1.86671748938724e-17
relative error = 1.6595618137621704889927896471550e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.506
y[1] (analytic) = 1.1253097705206888041164464559634
y[1] (numeric) = 1.1253097705206888228261599443965
absolute error = 1.87097134884331e-17
relative error = 1.6626278362246853151070159187244e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.507
y[1] (analytic) = 1.1257948901577355308760949947039
y[1] (numeric) = 1.1257948901577355496283235296809
absolute error = 1.87522285349770e-17
relative error = 1.6656878352281043352723350135281e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.508
y[1] (analytic) = 1.1262808839998192494768208161278
y[1] (numeric) = 1.1262808839998192682715408071166
absolute error = 1.87947199909888e-17
relative error = 1.6687418083704079150072069665237e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.509
y[1] (analytic) = 1.126767751560946158334390809836
y[1] (numeric) = 1.1267677515609461771715786238134
absolute error = 1.88371878139774e-17
relative error = 1.6717897532904773029388092324378e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.51
y[1] (analytic) = 1.1272554923542487368941915264245
y[1] (numeric) = 1.1272554923542487557738234878993
absolute error = 1.88796319614748e-17
relative error = 1.6748316676679123220614565936706e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.511
y[1] (analytic) = 1.1277441058919862324987091598053
y[1] (numeric) = 1.1277441058919862514207615508422
absolute error = 1.89220523910369e-17
relative error = 1.6778675492230174381064206334074e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.512
y[1] (analytic) = 1.1282335916855451481282415596589
y[1] (numeric) = 1.1282335916855451670926906199022
absolute error = 1.89644490602433e-17
relative error = 1.6808973957166986582524295260091e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.513
y[1] (analytic) = 1.1287239492454397310143545333464
y[1] (numeric) = 1.1287239492454397500211764600437
absolute error = 1.90068219266973e-17
relative error = 1.6839212049503778469110975599727e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.514
y[1] (analytic) = 1.1292151780813124621255938238659
y[1] (numeric) = 1.1292151780813124811747647718919
absolute error = 1.90491709480260e-17
relative error = 1.6869389747659155521076058511009e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.515
y[1] (analytic) = 1.1297072777019345465249632781811
y[1] (numeric) = 1.1297072777019345656164593600615
absolute error = 1.90914960818804e-17
relative error = 1.6899507030455334666381816957458e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.516
y[1] (analytic) = 1.1302002476152064045986788484863
y[1] (numeric) = 1.1302002476152064237324761344216
absolute error = 1.91337972859353e-17
relative error = 1.6929563877117188309847418469004e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.517
y[1] (analytic) = 1.1306940873281581641557071976931
y[1] (numeric) = 1.1306940873281581833317817155828
absolute error = 1.91760745178897e-17
relative error = 1.6959560267271727439222059919654e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.518
y[1] (analytic) = 1.1311887963469501533975968096429
y[1] (numeric) = 1.1311887963469501726159245451092
absolute error = 1.92183277354663e-17
relative error = 1.6989496180946784849407779877494e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.519
y[1] (analytic) = 1.1316843741768733947581086342535
y[1] (numeric) = 1.1316843741768734140186655306653
absolute error = 1.92605568964118e-17
relative error = 1.7019371598570403136723980860422e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.52
y[1] (analytic) = 1.1321808203223500996121524280115
y[1] (numeric) = 1.1321808203223501189149143865086
absolute error = 1.93027619584971e-17
relative error = 1.7049186500970130401172238509525e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.521
y[1] (analytic) = 1.1326781342869341638535340809147
y[1] (numeric) = 1.1326781342869341831984769604319
absolute error = 1.93449428795172e-17
relative error = 1.7078940869372047383535684242734e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.522
y[1] (analytic) = 1.1331763155733116643410183521593
y[1] (numeric) = 1.1331763155733116837281179694503
absolute error = 1.93870996172910e-17
relative error = 1.7108634685399703376178508588212e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.523
y[1] (analytic) = 1.133675363683301356212210568549
y[1] (numeric) = 1.133675363683301375641442698211
absolute error = 1.94292321296620e-17
relative error = 1.7138267931073843297033003227933e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.524
y[1] (analytic) = 1.134175278117855171064759971788
y[1] (numeric) = 1.1341752781178551905361003462855
absolute error = 1.94713403744975e-17
relative error = 1.7167840588810807433763489888953e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.525
y[1] (analytic) = 1.1346760583770587160043865334936
y[1] (numeric) = 1.1346760583770587355178108431829
absolute error = 1.95134243096893e-17
relative error = 1.7197352641422251895572014019762e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.526
y[1] (analytic) = 1.135177703960131773559232189945
y[1] (numeric) = 1.1351777039601317931147160830985
absolute error = 1.95554838931535e-17
relative error = 1.7226804072114071512452630769738e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.527
y[1] (analytic) = 1.1356802143654288024600365822581
y[1] (numeric) = 1.1356802143654288220575556650886
absolute error = 1.95975190828305e-17
relative error = 1.7256194864485496245208012272811e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.528
y[1] (analytic) = 1.1361835890904394392856365218521
y[1] (numeric) = 1.1361835890904394589251663585372
absolute error = 1.96395298366851e-17
relative error = 1.7285525002528272577446541701763e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.529
y[1] (analytic) = 1.1366878276317890009732875357502
y[1] (numeric) = 1.1366878276317890206548036484569
absolute error = 1.96815161127067e-17
relative error = 1.7314794470625929646157318171445e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.53
y[1] (analytic) = 1.1371929294852389881933049814358
y[1] (numeric) = 1.1371929294852390079167828503446
absolute error = 1.97234778689088e-17
relative error = 1.7344003253552426379908339186937e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.531
y[1] (analytic) = 1.1376988941456875895875213566629
y[1] (numeric) = 1.1376988941456876093529364199927
absolute error = 1.97654150633298e-17
relative error = 1.7373151336471939523789479856795e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.532
y[1] (analytic) = 1.138205721107170186871055565808
y[1] (numeric) = 1.1382057211071702066783832198404
absolute error = 1.98073276540324e-17
relative error = 1.7402238704937416867910068284090e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.533
y[1] (analytic) = 1.1387134098628598607968890410339
y[1] (numeric) = 1.138713409862859880646104640138
absolute error = 1.98492155991041e-17
relative error = 1.7431265344890095002819534362560e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.534
y[1] (analytic) = 1.1392219599050678979827427537335
y[1] (numeric) = 1.1392219599050679178738216103904
absolute error = 1.98910788566569e-17
relative error = 1.7460231242658310812032574427884e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.535
y[1] (analytic) = 1.1397313707252442985997482894172
y[1] (numeric) = 1.1397313707252443185326656742448
absolute error = 1.99329173848276e-17
relative error = 1.7489136384956837284716170577005e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.536
y[1] (analytic) = 1.1402416418139782849224052974161
y[1] (numeric) = 1.1402416418139783048971364391938
absolute error = 1.99747311417777e-17
relative error = 1.7517980758885865023919423395225e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.537
y[1] (analytic) = 1.1407527726609988107393167654858
y[1] (numeric) = 1.1407527726609988307558368511792
absolute error = 2.00165200856934e-17
relative error = 1.7546764351930068885294969240006e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.538
y[1] (analytic) = 1.1412647627551750716241927086173
y[1] (numeric) = 1.1412647627551750916824768834031
absolute error = 2.00582841747858e-17
relative error = 1.7575487151957847123286676995479e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.539
y[1] (analytic) = 1.1417776115845170160666120010952
y[1] (numeric) = 1.1417776115845170361666353683859
absolute error = 2.01000233672907e-17
relative error = 1.7604149147220207026878942970858e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.2MB, time=5.29
NO POLE
x[1] = 0.54
y[1] (analytic) = 1.1422913186361758574620312210822
y[1] (numeric) = 1.1422913186361758776037688425511
absolute error = 2.01417376214689e-17
relative error = 1.7632750326350086065978769130968e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.541
y[1] (analytic) = 1.1428058833964445869605285177651
y[1] (numeric) = 1.1428058833964446071439554133714
absolute error = 2.01834268956063e-17
relative error = 1.7661290678361494671993340385451e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.542
y[1] (analytic) = 1.1433213053507584871737696523608
y[1] (numeric) = 1.1433213053507585073988608003745
absolute error = 2.02250911480137e-17
relative error = 1.7689770192648393767817530228129e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.543
y[1] (analytic) = 1.1438375839836956467396825060591
y[1] (numeric) = 1.1438375839836956670064128430856
absolute error = 2.02667303370265e-17
relative error = 1.7718188858983482754916967691584e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.544
y[1] (analytic) = 1.1443547187789774757443254902696
y[1] (numeric) = 1.1443547187789774960526699112755
absolute error = 2.03083444210059e-17
relative error = 1.7746546667518296432415919728731e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.545
y[1] (analytic) = 1.1448727092194692220004344373497
y[1] (numeric) = 1.1448727092194692423503677956873
absolute error = 2.03499333583376e-17
relative error = 1.7774843608781112889643886803373e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.546
y[1] (analytic) = 1.1453915547871804881821316933069
y[1] (numeric) = 1.1453915547871805085736288007396
absolute error = 2.03914971074327e-17
relative error = 1.7803079673676782718208977101088e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.547
y[1] (analytic) = 1.1459112549632657498152802778119
y[1] (numeric) = 1.1459112549632657702483159045394
absolute error = 2.04330356267275e-17
relative error = 1.7831254853485593678801451001017e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.548
y[1] (analytic) = 1.1464318092280248741229651212096
y[1] (numeric) = 1.146431809228024894597513995893
absolute error = 2.04745488746834e-17
relative error = 1.7859369139862220623335259597628e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.549
y[1] (analytic) = 1.1469532170609036397255825330915
y[1] (numeric) = 1.1469532170609036602416193428787
absolute error = 2.05160368097872e-17
relative error = 1.7887422524835021987586593900511e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.55
y[1] (analytic) = 1.1474754779404942571950182023822
y[1] (numeric) = 1.1474754779404942777525175929333
absolute error = 2.05574993905511e-17
relative error = 1.7915415000805071737909870491842e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.551
y[1] (analytic) = 1.1479985913445358904623931748063
y[1] (numeric) = 1.1479985913445359110613297503186
absolute error = 2.05989365755123e-17
relative error = 1.7943346560544840524884723923908e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.552
y[1] (analytic) = 1.1485225567499151790788564000321
y[1] (numeric) = 1.1485225567499151997192047232658
absolute error = 2.06403483232337e-17
relative error = 1.7971217197197833211120986566592e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.553
y[1] (analytic) = 1.1490473736326667613289015877443
y[1] (numeric) = 1.1490473736326667820106361800479
absolute error = 2.06817345923036e-17
relative error = 1.7999026904277352141336893381866e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.554
y[1] (analytic) = 1.1495730414679737981956852593716
y[1] (numeric) = 1.1495730414679738189187806007073
absolute error = 2.07230953413357e-17
relative error = 1.8026775675665519819577272288053e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.555
y[1] (analytic) = 1.150099559730168498177822030195
y[1] (numeric) = 1.1500995597301685189422525591643
absolute error = 2.07644305289693e-17
relative error = 1.8054463505612473238676065339315e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.556
y[1] (analytic) = 1.1506269278927326429571323050854
y[1] (numeric) = 1.1506269278927326637628724189545
absolute error = 2.08057401138691e-17
relative error = 1.8082090388735207877743902284280e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.557
y[1] (analytic) = 1.1511551454282981139168167201663
y[1] (numeric) = 1.151155145428298134763840774892
absolute error = 2.08470240547257e-17
relative error = 1.8109656320017028073531258931724e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.558
y[1] (analytic) = 1.1516842118086474195095308122717
y[1] (numeric) = 1.1516842118086474403978131225267
absolute error = 2.08882823102550e-17
relative error = 1.8137161294806038911413847629649e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.559
y[1] (analytic) = 1.1522141265047142234748325481675
y[1] (numeric) = 1.1522141265047142444043473873663
absolute error = 2.09295148391988e-17
relative error = 1.8164605308814678893144188432047e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.56
y[1] (analytic) = 1.1527448889865838739054744961337
y[1] (numeric) = 1.1527448889865838948761960964583
absolute error = 2.09707216003246e-17
relative error = 1.8191988358118555067150385364753e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.561
y[1] (analytic) = 1.153276498723493933162011573659
y[1] (numeric) = 1.1532764987234939541739141260846
absolute error = 2.10119025524256e-17
relative error = 1.8219310439155449980283676204898e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.562
y[1] (analytic) = 1.1538089551838347086351944566842
y[1] (numeric) = 1.1538089551838347296882521110052
absolute error = 2.10530576543210e-17
relative error = 1.8246571548724586589596183841925e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.563
y[1] (analytic) = 1.1543422578351497843556178880455
y[1] (numeric) = 1.154342257835149805449804752901
absolute error = 2.10941868648555e-17
relative error = 1.8273771683985197397790459680931e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.564
y[1] (analytic) = 1.1548764061441365534500922755128
y[1] (numeric) = 1.1548764061441365745853824184127
absolute error = 2.11352901428999e-17
relative error = 1.8300910842456045280200278829025e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.565
y[1] (analytic) = 1.1554113995766467514442061230971
y[1] (numeric) = 1.1554113995766467726205735704482
absolute error = 2.11763674473511e-17
relative error = 1.8327989022014421609449874707469e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.566
y[1] (analytic) = 1.1559472375976869904105459931083
y[1] (numeric) = 1.15594723759768701162796473024
absolute error = 2.12174187371317e-17
relative error = 1.8355006220894796405717382905201e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.567
y[1] (analytic) = 1.1564839196714192939620398507875
y[1] (numeric) = 1.1564839196714193152204838219779
absolute error = 2.12584439711904e-17
relative error = 1.8381962437688159292468881387571e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.568
y[1] (analytic) = 1.157021445261161633089888798216
y[1] (numeric) = 1.1570214452611616543893319067179
absolute error = 2.12994431085019e-17
relative error = 1.8408857671340925463342018274913e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.569
y[1] (analytic) = 1.1575598138293884628455513596132
y[1] (numeric) = 1.1575598138293884841859674676803
absolute error = 2.13404161080671e-17
relative error = 1.8435691921154099201627909337955e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.57
y[1] (analytic) = 1.158099024837731259866243636084
y[1] (numeric) = 1.1580990248377312812476065649972
absolute error = 2.13813629289132e-17
relative error = 1.8462465186782348742261058890847e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.571
y[1] (analytic) = 1.158639077746979060743417804361
y[1] (numeric) = 1.1586390777469790821657013344541
absolute error = 2.14222835300931e-17
relative error = 1.8489177468232474935644987134526e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.572
y[1] (analytic) = 1.1591799720170790012336805911064
y[1] (numeric) = 1.1591799720170790226968584617928
absolute error = 2.14631778706864e-17
relative error = 1.8515828765863259874943045347837e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.573
y[1] (analytic) = 1.1597217071071368563116125119018
y[1] (numeric) = 1.1597217071071368778156584217005
absolute error = 2.15040459097987e-17
relative error = 1.8542419080383845493818297335904e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.574
y[1] (analytic) = 1.1602642824754175810639478221502
y[1] (numeric) = 1.1602642824754176026088354287121
absolute error = 2.15448876065619e-17
relative error = 1.8568948412852974011191879451756e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.575
y[1] (analytic) = 1.1608076975793458524245742857562
y[1] (numeric) = 1.1608076975793458740102772058906
absolute error = 2.15857029201344e-17
relative error = 1.8595416764678139813607148913235e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.576
y[1] (analytic) = 1.1613519518755066117498110266296
y[1] (numeric) = 1.1613519518755066333763028363305
absolute error = 2.16264918097009e-17
relative error = 1.8621824137614394763845688447247e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.577
y[1] (analytic) = 1.1618970448196456082334218877795
y[1] (numeric) = 1.1618970448196456299006761222519
absolute error = 2.16672542344724e-17
relative error = 1.8648170533763324489887405377339e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.578
y[1] (analytic) = 1.162442975866669943160820883031
y[1] (numeric) = 1.1624429758666699648688110367176
absolute error = 2.17079901536866e-17
relative error = 1.8674455955572367167881799550071e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.579
y[1] (analytic) = 1.1629897444706486150019254872046
y[1] (numeric) = 1.1629897444706486367506250138121
absolute error = 2.17486995266075e-17
relative error = 1.8700680405833441870318716019746e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.58
y[1] (analytic) = 1.16353735008481306534211267195
y[1] (numeric) = 1.1635373500848130871314949844758
absolute error = 2.17893823125258e-17
relative error = 1.8726843887682263887534388865088e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.581
y[1] (analytic) = 1.1640857921615577256507317563242
y[1] (numeric) = 1.1640857921615577474807702270829
absolute error = 2.18300384707587e-17
relative error = 1.8752946404597142123372998290945e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.2MB, time=5.77
NO POLE
x[1] = 0.582
y[1] (analytic) = 1.1646350701524405648866273036464
y[1] (numeric) = 1.1646350701524405867572952642964
absolute error = 2.18706679606500e-17
relative error = 1.8778987960398033065686190193843e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.583
y[1] (analytic) = 1.165185183508183637940124459152
y[1] (numeric) = 1.1651851835081836598513952007223
absolute error = 2.19112707415703e-17
relative error = 1.8804968559245678861514384742644e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.584
y[1] (analytic) = 1.1657361316786736349109282865074
y[1] (numeric) = 1.1657361316786736568627750594241
absolute error = 2.19518467729167e-17
relative error = 1.8830888205640314542911563668162e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.585
y[1] (analytic) = 1.1662879141129624312213878253303
y[1] (numeric) = 1.1662879141129624532137838394435
absolute error = 2.19923960141132e-17
relative error = 1.8856746904420974754909642195197e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.586
y[1] (analytic) = 1.1668405302592676385645747564984
y[1] (numeric) = 1.1668405302592676605974931811091
absolute error = 2.20329184246107e-17
relative error = 1.8882544660764455307113372505364e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.587
y[1] (analytic) = 1.1673939795649731566866257272142
y[1] (numeric) = 1.1673939795649731787600396911007
absolute error = 2.20734139638865e-17
relative error = 1.8908281480183845050156172751767e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.588
y[1] (analytic) = 1.1679482614766297260027965535271
y[1] (numeric) = 1.1679482614766297481166791449725
absolute error = 2.21138825914454e-17
relative error = 1.8933957368528427551029732410279e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.589
y[1] (analytic) = 1.1685033754399554810466756843086
y[1] (numeric) = 1.1685033754399555032009999511272
absolute error = 2.21543242668186e-17
relative error = 1.8959572331981696017132813358620e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.59
y[1] (analytic) = 1.1690593208998365047520034775093
y[1] (numeric) = 1.1690593208998365269467424270738
absolute error = 2.21947389495645e-17
relative error = 1.8985126377060994850620897100715e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.591
y[1] (analytic) = 1.1696160973003273835665430069271
y[1] (numeric) = 1.1696160973003274058016696061954
absolute error = 2.22351265992683e-17
relative error = 1.9010619510616132006259129670551e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.592
y[1] (analytic) = 1.1701737040846517633974472856612
y[1] (numeric) = 1.1701737040846517856729344612037
absolute error = 2.22754871755425e-17
relative error = 1.9036051739828760202680516769703e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.593
y[1] (analytic) = 1.1707321406952029063875669609314
y[1] (numeric) = 1.1707321406952029287033875989578
absolute error = 2.23158206380264e-17
relative error = 1.9061423072210901530657521369391e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.594
y[1] (analytic) = 1.1712914065735442485221417040005
y[1] (numeric) = 1.1712914065735442708782686503871
absolute error = 2.23561269463866e-17
relative error = 1.9086733515604325853860436418979e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.595
y[1] (analytic) = 1.1718515011604099580653176885558
y[1] (numeric) = 1.1718515011604099804617237488727
absolute error = 2.23964060603169e-17
relative error = 1.9111983078179414812973114752193e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.596
y[1] (analytic) = 1.172412423895705494825932721079
y[1] (numeric) = 1.172412423895705517262590660617
absolute error = 2.24366579395380e-17
relative error = 1.9137171768433854348186213762318e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.597
y[1] (analytic) = 1.1729741742185081702520097574644
y[1] (numeric) = 1.1729741742185081927288923012625
absolute error = 2.24768825437981e-17
relative error = 1.9162299595192094125026957533703e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.598
y[1] (analytic) = 1.1735367515670677083533987114403
y[1] (numeric) = 1.173536751567067730870478544313
absolute error = 2.25170798328727e-17
relative error = 1.9187366567604122703075118664513e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.599
y[1] (analytic) = 1.1741001553788068074520056321979
y[1] (numeric) = 1.1741001553788068300092553987623
absolute error = 2.25572497665644e-17
relative error = 1.9212372695144242133052375388753e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.6
y[1] (analytic) = 1.1746643850903217027590475010446
y[1] (numeric) = 1.1746643850903217253564398057478
absolute error = 2.25973923047032e-17
relative error = 1.9237317987610267661977159175383e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.601
y[1] (analytic) = 1.1752294401373827297787700698751
y[1] (numeric) = 1.1752294401373827524162774770217
absolute error = 2.26375074071466e-17
relative error = 1.9262202455122555511512659640700e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.602
y[1] (analytic) = 1.1757953199549348885380653377883
y[1] (numeric) = 1.175795319954934911215660371568
absolute error = 2.26775950337797e-17
relative error = 1.9287026108123029424314946425358e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.603
y[1] (analytic) = 1.1763620239770984086414244362806
y[1] (numeric) = 1.1763620239770984313590795807953
absolute error = 2.27176551445147e-17
relative error = 1.9311788957373695955952437674715e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.604
y[1] (analytic) = 1.1769295516371693151506608681084
y[1] (numeric) = 1.1769295516371693379083485673999
absolute error = 2.27576876992915e-17
relative error = 1.9336491013956094695102686890316e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.605
y[1] (analytic) = 1.177497902367619995288838220145
y[1] (numeric) = 1.1774979023676200180865308782227
absolute error = 2.27976926580777e-17
relative error = 1.9361132289270236541815852932555e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.606
y[1] (analytic) = 1.1780670756000997659678356463513
y[1] (numeric) = 1.1780670756000997888055056272194
absolute error = 2.28376699808681e-17
relative error = 1.9385712795033116674261480097469e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.607
y[1] (analytic) = 1.1786370707654354421389835933405
y[1] (numeric) = 1.178637070765435465016603221026
absolute error = 2.28776196276855e-17
relative error = 1.9410232543278330853122804654344e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.608
y[1] (analytic) = 1.1792078872936319059662014179512
y[1] (numeric) = 1.1792078872936319288837429765315
absolute error = 2.29175415585803e-17
relative error = 1.9434691546354671285690489564375e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.609
y[1] (analytic) = 1.1797795246138726768210677237362
y[1] (numeric) = 1.1797795246138726997785034573666
absolute error = 2.29574357336304e-17
relative error = 1.9459089816924976946440616245760e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.61
y[1] (analytic) = 1.1803519821545204820992534213452
y[1] (numeric) = 1.1803519821545205050965555342871
absolute error = 2.29973021129419e-17
relative error = 1.9483427367965661119342414810796e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.611
y[1] (analytic) = 1.1809252593431178288577466964165
y[1] (numeric) = 1.1809252593431178518948873530648
absolute error = 2.30371406566483e-17
relative error = 1.9507704212764966258137227344923e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.612
y[1] (analytic) = 1.1814993556063875762722982477992
y[1] (numeric) = 1.1814993556063875993492495727102
absolute error = 2.30769513249110e-17
relative error = 1.9531920364922320376528018525291e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.613
y[1] (analytic) = 1.1820742703702335089145143387088
y[1] (numeric) = 1.1820742703702335320312484166282
absolute error = 2.31167340779194e-17
relative error = 1.9556075838347353099708622180174e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.614
y[1] (analytic) = 1.1826500030597409108480243837716
y[1] (numeric) = 1.1826500030597409340045132596622
absolute error = 2.31564888758906e-17
relative error = 1.9580170647258572552485776912588e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.615
y[1] (analytic) = 1.1832265530991771405431489758368
y[1] (numeric) = 1.1832265530991771637393646549069
absolute error = 2.31962156790701e-17
relative error = 1.9604204806182887466607185869625e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.616
y[1] (analytic) = 1.1838039199119922066094934379379
y[1] (numeric) = 1.1838039199119922298454078856687
absolute error = 2.32359144477308e-17
relative error = 1.9628178329953690863850647296643e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.617
y[1] (analytic) = 1.1843821029208193443458911678558
y[1] (numeric) = 1.18438210292081936762147631003
absolute error = 2.32755851421742e-17
relative error = 1.9652091233710803099546317541808e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.618
y[1] (analytic) = 1.1849611015474755931071202253905
y[1] (numeric) = 1.1849611015474756164223479481199
absolute error = 2.33152277227294e-17
relative error = 1.9675943532898554738620198157556e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.619
y[1] (analytic) = 1.1855409152129623744868157956707
y[1] (numeric) = 1.1855409152129623978416579454246
absolute error = 2.33548421497539e-17
relative error = 1.9699735243265389626668930971579e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.62
y[1] (analytic) = 1.1861215433374660713160003456393
y[1] (numeric) = 1.1861215433374660947104287292725
absolute error = 2.33944283836332e-17
relative error = 1.9723466380862453728923744836766e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.621
y[1] (analytic) = 1.1867029853403586074766524752305
y[1] (numeric) = 1.1867029853403586309106388600117
absolute error = 2.34339863847812e-17
relative error = 1.9747136962042858569154403088850e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.622
y[1] (analytic) = 1.1872852406401980285297346497202
y[1] (numeric) = 1.1872852406401980520032507633601
absolute error = 2.34735161136399e-17
relative error = 1.9770747003460353592725976038554e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.623
y[1] (analytic) = 1.1878683086547290831570991852689
y[1] (numeric) = 1.1878683086547291066701167159484
absolute error = 2.35130175306795e-17
relative error = 1.9794296522068335529973951926105e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=49.5MB, alloc=4.2MB, time=6.25
x[1] = 0.624
y[1] (analytic) = 1.1884521888008838054166910457999
y[1] (numeric) = 1.1884521888008838289691816421985
absolute error = 2.35524905963986e-17
relative error = 1.9817785535118941196902476876576e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.625
y[1] (analytic) = 1.1890368804947820978104651960589
y[1] (numeric) = 1.1890368804947821214024004673831
absolute error = 2.35919352713242e-17
relative error = 1.9841214060161971161236447355505e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.626
y[1] (analytic) = 1.189622383151732315164435442986
y[1] (numeric) = 1.1896223831517323387957869589975
absolute error = 2.36313515160115e-17
relative error = 1.9864582115043644875594434807444e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.627
y[1] (analytic) = 1.1902086961862318493202708853993
y[1] (numeric) = 1.1902086961862318729910101764437
absolute error = 2.36707392910444e-17
relative error = 1.9887889717905944050300213554098e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.628
y[1] (analytic) = 1.1907958190119677146378552804441
y[1] (numeric) = 1.1907958190119677383479538374791
absolute error = 2.37100985570350e-17
relative error = 1.9911136887185114642747074072286e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.629
y[1] (analytic) = 1.1913837510418171343082238242947
y[1] (numeric) = 1.1913837510418171580576530989187
absolute error = 2.37494292746240e-17
relative error = 1.9934323641610925169429438104516e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.63
y[1] (analytic) = 1.1919724916878481274762910342229
y[1] (numeric) = 1.1919724916878481512650224387038
absolute error = 2.37887314044809e-17
relative error = 1.9957450000205755913000148826064e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.631
y[1] (analytic) = 1.1925620403613200971727826093538
y[1] (numeric) = 1.1925620403613201210007875166572
absolute error = 2.38280049073034e-17
relative error = 1.9980515982283016507652016583010e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.632
y[1] (analytic) = 1.1931523964726844190547833382246
y[1] (numeric) = 1.1931523964726844429220330820427
absolute error = 2.38672497438181e-17
relative error = 2.0003521607446654291372074194691e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.633
y[1] (analytic) = 1.1937435594315850309543123126502
y[1] (numeric) = 1.1937435594315850548607781874302
absolute error = 2.39064658747800e-17
relative error = 2.0026466895589655420257164093663e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.634
y[1] (analytic) = 1.1943355286468590232343358993664
y[1] (numeric) = 1.1943355286468590471799891603397
absolute error = 2.39456532609733e-17
relative error = 2.0049351866893635466648928169274e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.635
y[1] (analytic) = 1.1949283035265372299516281134903
y[1] (numeric) = 1.1949283035265372539364399767006
absolute error = 2.39848118632103e-17
relative error = 2.0072176541826837760128313532638e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.636
y[1] (analytic) = 1.1955218834778448208258872309833
y[1] (numeric) = 1.1955218834778448448498288733158
absolute error = 2.40239416423325e-17
relative error = 2.0094940941143974481705302076056e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.637
y[1] (analytic) = 1.1961162679072018940145166710524
y[1] (numeric) = 1.1961162679072019180775592302625
absolute error = 2.40630425592101e-17
relative error = 2.0117645085884727186787387445850e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.638
y[1] (analytic) = 1.1967114562202240696924773737563
y[1] (numeric) = 1.1967114562202240937945919484986
absolute error = 2.41021145747423e-17
relative error = 2.0140288997372916928285770076275e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.639
y[1] (analytic) = 1.1973074478217230844366180930148
y[1] (numeric) = 1.1973074478217231085777757428719
absolute error = 2.41411576498571e-17
relative error = 2.0162872697215255904226750107044e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.64
y[1] (analytic) = 1.1979042421157073864138892207397
y[1] (numeric) = 1.1979042421157074105940609662509
absolute error = 2.41801717455112e-17
relative error = 2.0185396207300182981674810534069e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.641
y[1] (analytic) = 1.198501838505382731372844953923
y[1] (numeric) = 1.1985018385053827555920017766137
absolute error = 2.42191568226907e-17
relative error = 2.0207859549797366890249673327301e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.642
y[1] (analytic) = 1.1991002363931527794378378132311
y[1] (numeric) = 1.1991002363931528036959506556416
absolute error = 2.42581128424105e-17
relative error = 2.0230262747156123462057113390243e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.643
y[1] (analytic) = 1.1996994351806196927053087189588
y[1] (numeric) = 1.1996994351806197170023484846734
absolute error = 2.42970397657146e-17
relative error = 2.0252605822104584520313393065978e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.644
y[1] (analytic) = 1.2002994342685847336415750281037
y[1] (numeric) = 1.2002994342685847579775125817797
absolute error = 2.43359375536760e-17
relative error = 2.0274888797648532751595895073062e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.645
y[1] (analytic) = 1.2009002330570488642815181348221
y[1] (numeric) = 1.200900233057048888656324302219
absolute error = 2.43748061673969e-17
relative error = 2.0297111697070486645069217487392e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.646
y[1] (analytic) = 1.2015018309452133462275714356296
y[1] (numeric) = 1.2015018309452133706412170036383
absolute error = 2.44136455680087e-17
relative error = 2.0319274543928618498580663872052e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.647
y[1] (analytic) = 1.2021042273314803414484086604078
y[1] (numeric) = 1.2021042273314803659008643770799
absolute error = 2.44524557166721e-17
relative error = 2.0341377362055755658277730920592e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.648
y[1] (analytic) = 1.2027074216134535138767317705792
y[1] (numeric) = 1.2027074216134535383679683451561
absolute error = 2.44912365745769e-17
relative error = 2.0363420175558132137571245333593e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.649
y[1] (analytic) = 1.203311413187938631805556826712
y[1] (numeric) = 1.2033114131879386563355449296543
absolute error = 2.45299881029423e-17
relative error = 2.0385403008814556344375427933168e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.65
y[1] (analytic) = 1.2039162014509441710823954293201
y[1] (numeric) = 1.2039162014509441956511056923367
absolute error = 2.45687102630166e-17
relative error = 2.0407325886475079791799549554726e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.651
y[1] (analytic) = 1.2045217857976819191007285387257
y[1] (numeric) = 1.2045217857976819437081315548035
absolute error = 2.46074030160778e-17
relative error = 2.0429188833460413873422906429515e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.652
y[1] (analytic) = 1.2051281656225675795881686825627
y[1] (numeric) = 1.2051281656225676042342350059958
absolute error = 2.46460663234331e-17
relative error = 2.0450991874960432518170032029891e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.653
y[1] (analytic) = 1.2057353403192213781907057628076
y[1] (numeric) = 1.2057353403192214028754059092268
absolute error = 2.46847001464192e-17
relative error = 2.0472735036433339762884117275578e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.654
y[1] (analytic) = 1.2063433092804686688524308781435
y[1] (numeric) = 1.2063433092804686935757353245459
absolute error = 2.47233044464024e-17
relative error = 2.0494418343604670972037825252459e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.655
y[1] (analytic) = 1.2069520718983405409901317819836
y[1] (numeric) = 1.2069520718983405657520109667618
absolute error = 2.47618791847782e-17
relative error = 2.0516041822465879749279482702449e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.656
y[1] (analytic) = 1.207561627564074427462152801609
y[1] (numeric) = 1.207561627564074452262577124581
absolute error = 2.48004243229720e-17
relative error = 2.0537605499273837008530206925408e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.657
y[1] (analytic) = 1.2081719756681147133309112496125
y[1] (numeric) = 1.2081719756681147381698510720511
absolute error = 2.48389398224386e-17
relative error = 2.0559109400549335301800174780450e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.658
y[1] (analytic) = 1.2087831156001133454184615651814
y[1] (numeric) = 1.2087831156001133702958872098439
absolute error = 2.48774256446625e-17
relative error = 2.0580553553076256493456729020833e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.659
y[1] (analytic) = 1.2093950467489304426544976297072
y[1] (numeric) = 1.2093950467489304675703793808651
absolute error = 2.49158817511579e-17
relative error = 2.0601937983900490912195200838680e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.66
y[1] (analytic) = 1.2100077685026349072161829087698
y[1] (numeric) = 1.2100077685026349321704910122385
absolute error = 2.49543081034687e-17
relative error = 2.0623262720328856811167629730537e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.661
y[1] (analytic) = 1.2106212802485050364591972807178
y[1] (numeric) = 1.2106212802485050614519019438864
absolute error = 2.49927046631686e-17
relative error = 2.0644527789928102758016119924696e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.662
y[1] (analytic) = 1.2112355813730291356393886208484
y[1] (numeric) = 1.2112355813730291606704600127094
absolute error = 2.50310713918610e-17
relative error = 2.0665733220523745000018975245899e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.663
y[1] (analytic) = 1.2118506712619061314244164195866
y[1] (numeric) = 1.2118506712619061564938246707657
absolute error = 2.50694082511791e-17
relative error = 2.0686879040199070483773010053593e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.664
y[1] (analytic) = 1.2124665493000461861947739230711
y[1] (numeric) = 1.2124665493000462113024891258573
absolute error = 2.51077152027862e-17
relative error = 2.0707965277294304962053051874123e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.665
y[1] (analytic) = 1.2130832148715713131335744951767
y[1] (numeric) = 1.213083214871571338279566703552
absolute error = 2.51459922083753e-17
relative error = 2.0728991960405203708584436776358e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=53.4MB, alloc=4.2MB, time=6.73
x[1] = 0.666
y[1] (analytic) = 1.213700667359815992104487111237
y[1] (numeric) = 1.2137006673598160172887263409063
absolute error = 2.51842392296693e-17
relative error = 2.0749959118382138018295891969960e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.667
y[1] (analytic) = 1.2143189061473277863172051055833
y[1] (numeric) = 1.2143189061473278115396613340046
absolute error = 2.52224562284213e-17
relative error = 2.0770866780329263997611280042206e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.668
y[1] (analytic) = 1.2149379306158679597798315074841
y[1] (numeric) = 1.2149379306158679850404746738982
absolute error = 2.52606431664141e-17
relative error = 2.0791714975603032590851444642491e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.669
y[1] (analytic) = 1.2155577401464120955375635131482
y[1] (numeric) = 1.2155577401464121208363635186092
absolute error = 2.52988000054610e-17
relative error = 2.0812503733811770813083098524829e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.67
y[1] (analytic) = 1.2161783341191507146970578551619
y[1] (numeric) = 1.216178334119150740033984562567
absolute error = 2.53369267074051e-17
relative error = 2.0833233084814028095072130453746e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.671
y[1] (analytic) = 1.2167997119134898962358580450436
y[1] (numeric) = 1.2167997119134899216108812791633
absolute error = 2.53750232341197e-17
relative error = 2.0853903058717828918665158822334e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.672
y[1] (analytic) = 1.2174218729080518975962636795423
y[1] (numeric) = 1.2174218729080519230093532270505
absolute error = 2.54130895475082e-17
relative error = 2.0874513685879514275835131873983e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.673
y[1] (analytic) = 1.2180448164806757760630212168607
y[1] (numeric) = 1.2180448164806758015141468263651
absolute error = 2.54511256095044e-17
relative error = 2.0895064996902912328249195222937e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.674
y[1] (analytic) = 1.2186685420084180109242148451658
y[1] (numeric) = 1.218668542008418036413346227238
absolute error = 2.54891313820722e-17
relative error = 2.0915557022638016541578534202567e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.675
y[1] (analytic) = 1.219293048867553126414735282546
y[1] (numeric) = 1.2192930488675531519418421097518
absolute error = 2.55271068272058e-17
relative error = 2.0935989794180075239362871751981e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.676
y[1] (analytic) = 1.2199183364335743154417035649992
y[1] (numeric) = 1.219918336433574341006755471929
absolute error = 2.55650519069298e-17
relative error = 2.0956363342868599287508484937590e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.677
y[1] (analytic) = 1.2205444040811940640912260970796
y[1] (numeric) = 1.2205444040811940896941926803787
absolute error = 2.56029665832991e-17
relative error = 2.0976677700286206290600443006767e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.678
y[1] (analytic) = 1.2211712511843447769158564585004
y[1] (numeric) = 1.2211712511843448025567072768994
absolute error = 2.56408508183990e-17
relative error = 2.0996932898257629460811381239425e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.679
y[1] (analytic) = 1.221798877116179403002138679282
y[1] (numeric) = 1.2217988771161794286808432536273
absolute error = 2.56787045743453e-17
relative error = 2.1017128968848726895318795102886e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.68
y[1] (analytic) = 1.2224272812490720628176059159557
y[1] (numeric) = 1.2224272812490720885341337292399
absolute error = 2.57165278132842e-17
relative error = 2.1037265944365327670721672534484e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.681
y[1] (analytic) = 1.2230564629546186758366076818755
y[1] (numeric) = 1.2230564629546187015909281792681
absolute error = 2.57543204973926e-17
relative error = 2.1057343857352405935171062942432e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.682
y[1] (analytic) = 1.223686421603637588944338005864
y[1] (numeric) = 1.2236864216036376147364205947416
absolute error = 2.57920825888776e-17
relative error = 2.1077362740592601193834329412228e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.683
y[1] (analytic) = 1.2243171565661702056184361152149
y[1] (numeric) = 1.2243171565661702314482501651923
absolute error = 2.58298140499774e-17
relative error = 2.1097322627105884082059678991880e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.684
y[1] (analytic) = 1.2249486672114816158875304615069
y[1] (numeric) = 1.2249486672114816417550453044672
absolute error = 2.58675148429603e-17
relative error = 2.1117223550147669527246041075683e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.685
y[1] (analytic) = 1.2255809529080612270660961307334
y[1] (numeric) = 1.225580952908061252971281060859
absolute error = 2.59051849301256e-17
relative error = 2.1137065543208483486823646979038e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.686
y[1] (analytic) = 1.2262140130236233952649949029474
y[1] (numeric) = 1.2262140130236234212078191767506
absolute error = 2.59428242738032e-17
relative error = 2.1156848640012568019817037638658e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.687
y[1] (analytic) = 1.2268478469251080576770664509304
y[1] (numeric) = 1.2268478469251080836574992872842
absolute error = 2.59804328363538e-17
relative error = 2.1176572874516977225714383612479e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.688
y[1] (analytic) = 1.2274824539786813656371383923497
y[1] (numeric) = 1.2274824539786813916551489725185
absolute error = 2.60180105801688e-17
relative error = 2.1196238280910429090156933292756e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.689
y[1] (analytic) = 1.2281178335497363184558221354451
y[1] (numeric) = 1.2281178335497363445113796031155
absolute error = 2.60555574676704e-17
relative error = 2.1215844893612321265964231840234e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.69
y[1] (analytic) = 1.2287539850028933980264606845022
y[1] (numeric) = 1.2287539850028934241195341458141
absolute error = 2.60930734613119e-17
relative error = 2.1235392747271910216050225808024e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.691
y[1] (analytic) = 1.2293909077020012042045937982186
y[1] (numeric) = 1.2293909077020012303351523217957
absolute error = 2.61305585235771e-17
relative error = 2.1254881876766758392238001942222e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.692
y[1] (analytic) = 1.2300286010101370909593051215486
y[1] (numeric) = 1.2300286010101371171273177385296
absolute error = 2.61680126169810e-17
relative error = 2.1274312317202240698908639096366e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.693
y[1] (analytic) = 1.2306670642896078032958151397345
y[1] (numeric) = 1.2306670642896078295012508438041
absolute error = 2.62054357040696e-17
relative error = 2.1293684103910318772122038956846e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.694
y[1] (analytic) = 1.2313062969019501149486830319832
y[1] (numeric) = 1.231306296901950141191510779403
absolute error = 2.62428277474198e-17
relative error = 2.1312997272448397892553454131463e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.695
y[1] (analytic) = 1.2319462982079314668449797316401
y[1] (numeric) = 1.2319462982079314931251684412795
absolute error = 2.62801887096394e-17
relative error = 2.1332251858598266253270657859586e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.696
y[1] (analytic) = 1.2325870675675506063367937297397
y[1] (numeric) = 1.2325870675675506326543122831073
absolute error = 2.63175185533676e-17
relative error = 2.1351447898365440823754995538978e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.697
y[1] (analytic) = 1.2332286043400382272024303894814
y[1] (numeric) = 1.233228604340038253557247630756
absolute error = 2.63548172412746e-17
relative error = 2.1370585427977783117324079276516e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.698
y[1] (analytic) = 1.2338709078838576104156647704838
y[1] (numeric) = 1.2338709078838576368077495065454
absolute error = 2.63920847360616e-17
relative error = 2.1389664483884441131150752035047e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.699
y[1] (analytic) = 1.234513977556705265682407193618
y[1] (numeric) = 1.2345139775567052921117281940791
absolute error = 2.64293210004611e-17
relative error = 2.1408685102755035289454454778585e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.7
y[1] (analytic) = 1.2351578127155115737441400098081
y[1] (numeric) = 1.235157812715511600210666007045
absolute error = 2.64665259972369e-17
relative error = 2.1427647321478601750829908759427e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.701
y[1] (analytic) = 1.2358024127164414294474832694162
y[1] (numeric) = 1.2358024127164414559511829586001
absolute error = 2.65036996891839e-17
relative error = 2.1446551177162374900685323409662e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.702
y[1] (analytic) = 1.2364477769148948855792462226979
y[1] (numeric) = 1.2364477769148949121200882618265
absolute error = 2.65408420391286e-17
relative error = 2.1465396707131137527086408290745e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.703
y[1] (analytic) = 1.2370939046655077974663208163335
y[1] (numeric) = 1.237093904665507824044273826262
absolute error = 2.65779530099285e-17
relative error = 2.1484183948925681602735621371648e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.704
y[1] (analytic) = 1.2377407953221524683397725861917
y[1] (numeric) = 1.2377407953221524949548051506644
absolute error = 2.66150325644727e-17
relative error = 2.1502912940302241164949561190151e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.705
y[1] (analytic) = 1.2383884482379382954624835822915
y[1] (numeric) = 1.2383884482379383221145642479732
absolute error = 2.66520806656817e-17
relative error = 2.1521583719231278758014522182132e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.706
y[1] (analytic) = 1.2390368627652124170197011983717
y[1] (numeric) = 1.239036862765212443708798474879
absolute error = 2.66890972765073e-17
relative error = 2.1540196323896354189268977755885e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.707
y[1] (analytic) = 1.2396860382555603597718460155734
y[1] (numeric) = 1.2396860382555603864979283755063
absolute error = 2.67260823599329e-17
relative error = 2.1558750792693317314902053732755e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.708
y[1] (analytic) = 1.2403359740598066874689310074817
y[1] (numeric) = 1.2403359740598067142319668864552
absolute error = 2.67630358789735e-17
relative error = 2.1577247164229259323578292698934e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.2MB, time=7.22
NO POLE
x[1] = 0.709
y[1] (analytic) = 1.2409866695280156500259436921618
y[1] (numeric) = 1.2409866695280156768259014888373
absolute error = 2.67999577966755e-17
relative error = 2.1595685477321304000999191710913e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.71
y[1] (analytic) = 1.2416381240094918334585420558604
y[1] (numeric) = 1.2416381240094918602953901319775
absolute error = 2.68368480761171e-17
relative error = 2.1614065770995883891963784991090e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.711
y[1] (analytic) = 1.2422903368527808105784143127322
y[1] (numeric) = 1.24229033685278083745212099314
absolute error = 2.68737066804078e-17
relative error = 2.1632388084487292151457335073183e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.712
y[1] (analytic) = 1.2429433074056697924476518052839
y[1] (numeric) = 1.2429433074056698193581853779731
absolute error = 2.69105335726892e-17
relative error = 2.1650652457237282755098587092708e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.713
y[1] (analytic) = 1.2435970350151882805914835912195
y[1] (numeric) = 1.2435970350151883075388123073538
absolute error = 2.69473287161343e-17
relative error = 2.1668858928893463701841884406098e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.714
y[1] (analytic) = 1.2442515190276087199687205040045
y[1] (numeric) = 1.2442515190276087469528125779526
absolute error = 2.69840920739481e-17
relative error = 2.1687007539308738012388711196054e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.715
y[1] (analytic) = 1.2449067587884471526992557167609
y[1] (numeric) = 1.244906758788447179720079326128
absolute error = 2.70208236093671e-17
relative error = 2.1705098328539860833340718613391e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.716
y[1] (analytic) = 1.2455627536424638725479680820458
y[1] (numeric) = 1.2455627536424638996054913677056
absolute error = 2.70575232856598e-17
relative error = 2.1723131336846801902931730300340e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.717
y[1] (analytic) = 1.2462195029336640801643737636656
y[1] (numeric) = 1.2462195029336641072585648297921
absolute error = 2.70941910661265e-17
relative error = 2.1741106604691546305279273519374e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.718
y[1] (analytic) = 1.2468770060052985390773709209283
y[1] (numeric) = 1.2468770060052985662081978350278
absolute error = 2.71308269140995e-17
relative error = 2.1759024172737217803930930278113e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.719
y[1] (analytic) = 1.2475352621998642324444214506442
y[1] (numeric) = 1.2475352621998642596118522435872
absolute error = 2.71674307929430e-17
relative error = 2.1776884081846962477242200219899e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.72
y[1] (analytic) = 1.248194270859105020554513037748
y[1] (numeric) = 1.248194270859105047758515703801
absolute error = 2.72040026660530e-17
relative error = 2.1794686373082833904912499533394e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.721
y[1] (analytic) = 1.2488540313240122990842440116342
y[1] (numeric) = 1.2488540313240123263247865084918
absolute error = 2.72405424968576e-17
relative error = 2.1812431087705000212835975182852e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.722
y[1] (analytic) = 1.249514542934825658106372752177
y[1] (numeric) = 1.2495145429348256853834230009941
absolute error = 2.72770502488171e-17
relative error = 2.1830118267170791618007527892290e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.723
y[1] (analytic) = 1.2501758050310335418501726369398
y[1] (numeric) = 1.2501758050310335691636985223635
absolute error = 2.73135258854237e-17
relative error = 2.1847747953133429101648955813052e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.724
y[1] (analytic) = 1.2508378169513739092129327692739
y[1] (numeric) = 1.2508378169513739365629021394758
absolute error = 2.73499693702019e-17
relative error = 2.1865320187441314819571700919404e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.725
y[1] (analytic) = 1.2515005780338348950219439758613
y[1] (numeric) = 1.2515005780338349224083246425692
absolute error = 2.73863806667079e-17
relative error = 2.1882835012136523819153873844740e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.726
y[1] (analytic) = 1.2521640876156554720463088117698
y[1] (numeric) = 1.2521640876156554994690685503005
absolute error = 2.74227597385307e-17
relative error = 2.1900292469454656306370869002117e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.727
y[1] (analytic) = 1.2528283450333261137579135612673
y[1] (numeric) = 1.2528283450333261412170201105584
absolute error = 2.74591065492911e-17
relative error = 2.1917692601823012300253045305637e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.728
y[1] (analytic) = 1.2534933496225894578408994734763
y[1] (numeric) = 1.2534933496225894853363205361186
absolute error = 2.74954210626423e-17
relative error = 2.1935035451860046662525645476106e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.729
y[1] (analytic) = 1.2541591007184409704489697234547
y[1] (numeric) = 1.2541591007184409979806729657245
absolute error = 2.75317032422698e-17
relative error = 2.1952321062374265874513428484084e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.73
y[1] (analytic) = 1.2548255976551296112098678414497
y[1] (numeric) = 1.2548255976551296387778208933411
absolute error = 2.75679530518914e-17
relative error = 2.1969549476363206187524254902036e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.731
y[1] (analytic) = 1.2554928397661584989763626059028
y[1] (numeric) = 1.2554928397661585265805330611602
absolute error = 2.76041704552574e-17
relative error = 2.1986720737012572512743724603971e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.732
y[1] (analytic) = 1.2561608263842855783230736492765
y[1] (numeric) = 1.2561608263842856059634290654267
absolute error = 2.76403554161502e-17
relative error = 2.2003834887694900608894438486982e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.733
y[1] (analytic) = 1.2568295568415242867884712799312
y[1] (numeric) = 1.2568295568415243144649791783162
absolute error = 2.76765078983850e-17
relative error = 2.2020891971969096968660667605288e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.734
y[1] (analytic) = 1.2574990304691442228613832781104
y[1] (numeric) = 1.2574990304691442505740111439197
absolute error = 2.77126278658093e-17
relative error = 2.2037892033579024127281831118200e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.735
y[1] (analytic) = 1.2581692465976718147113406795812
y[1] (numeric) = 1.2581692465976718424600559618844
absolute error = 2.77487152823032e-17
relative error = 2.2054835116452724574695491689367e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.736
y[1] (analytic) = 1.2588402045568909896620938166407
y[1] (numeric) = 1.2588402045568910174468639284199
absolute error = 2.77847701117792e-17
relative error = 2.2071721264701248214467291450071e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.737
y[1] (analytic) = 1.2595119036758438444076291430284
y[1] (numeric) = 1.2595119036758438722284214612108
absolute error = 2.78207923181824e-17
relative error = 2.2088550522617799426546460015843e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.738
y[1] (analytic) = 1.2601843432828313159700166267826
y[1] (numeric) = 1.2601843432828313438267984922733
absolute error = 2.78567818654907e-17
relative error = 2.2105322934676885145559332415180e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.739
y[1] (analytic) = 1.2608575227054138533984167532507
y[1] (numeric) = 1.2608575227054138812911554709652
absolute error = 2.78927387177145e-17
relative error = 2.2122038545533067410742077649501e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.74
y[1] (analytic) = 1.2615314412704120902085754393012
y[1] (numeric) = 1.2615314412704121181372382781982
absolute error = 2.79286628388970e-17
relative error = 2.2138697400020193838011037575315e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.741
y[1] (analytic) = 1.2622060983039075175621344192991
y[1] (numeric) = 1.2622060983039075455266886124133
absolute error = 2.79645541931142e-17
relative error = 2.2155299543150391208928919155823e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.742
y[1] (analytic) = 1.2628814931312431581850839235906
y[1] (numeric) = 1.2628814931312431861854966680651
absolute error = 2.80004127444745e-17
relative error = 2.2171845020112743893674414552359e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.743
y[1] (analytic) = 1.2635576250770242410246837310994
y[1] (numeric) = 1.2635576250770242690609221882189
absolute error = 2.80362384571195e-17
relative error = 2.2188333876272924571665498207153e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.744
y[1] (analytic) = 1.2642344934651188766441779391716
y[1] (numeric) = 1.2642344934651189047162092343951
absolute error = 2.80720312952235e-17
relative error = 2.2204766157171796220584209530871e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.745
y[1] (analytic) = 1.2649120976186587333546280560096
y[1] (numeric) = 1.2649120976186587614624192790031
absolute error = 2.81077912229935e-17
relative error = 2.2221141908524412264498127296780e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.746
y[1] (analytic) = 1.2655904368600397140831882839174
y[1] (numeric) = 1.2655904368600397422267064885872
absolute error = 2.81435182046698e-17
relative error = 2.2237461176219492423588596003630e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.747
y[1] (analytic) = 1.266269510510922633977146125141
y[1] (numeric) = 1.2662695105109226621563583296663
absolute error = 2.81792122045253e-17
relative error = 2.2253724006317872026225778749638e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.748
y[1] (analytic) = 1.2669493178922338987430507063167
y[1] (numeric) = 1.2669493178922339269579238931828
absolute error = 2.82148731868661e-17
relative error = 2.2269930445051980823850674044047e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.749
y[1] (analytic) = 1.2676298583241661837202504824584
y[1] (numeric) = 1.2676298583241662119707515984894
absolute error = 2.82505011160310e-17
relative error = 2.2286080538824454166215397811878e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.75
y[1] (analytic) = 1.2683111311261791136881612469999
y[1] (numeric) = 1.2683111311261791419742572033922
absolute error = 2.82860959563923e-17
relative error = 2.2302174334207772090577675186600e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.3MB, time=7.72
NO POLE
x[1] = 0.751
y[1] (analytic) = 1.2689931356169999434065846406836
y[1] (numeric) = 1.2689931356169999717282423130386
absolute error = 2.83216576723550e-17
relative error = 2.2318211877942637202976852771863e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.752
y[1] (analytic) = 1.2696758711146242388883966190315
y[1] (numeric) = 1.2696758711146242672455828473891
absolute error = 2.83571862283576e-17
relative error = 2.2334193216937616436220465340905e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.753
y[1] (analytic) = 1.270359336936316559403924605769
y[1] (numeric) = 1.2703593369363165877966061946403
absolute error = 2.83926815888713e-17
relative error = 2.2350118398267522976714518011051e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.754
y[1] (analytic) = 1.2710435323986111402163313278786
y[1] (numeric) = 1.2710435323986111686444750462795
absolute error = 2.84281437184009e-17
relative error = 2.2365987469173139408138474579501e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.755
y[1] (analytic) = 1.2717284568173125760473225969591
y[1] (numeric) = 1.2717284568173126045108951784433
absolute error = 2.84635725814842e-17
relative error = 2.2381800477059760779243814521028e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.756
y[1] (analytic) = 1.2724141095074965052724955712377
y[1] (numeric) = 1.2724141095074965337714637139301
absolute error = 2.84989681426924e-17
relative error = 2.2397557469496526824185531968278e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.757
y[1] (analytic) = 1.2731004897835102948456433029448
y[1] (numeric) = 1.2731004897835103233799736695747
absolute error = 2.85343303666299e-17
relative error = 2.2413258494215283604958040276569e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.758
y[1] (analytic) = 1.2737875969589737259513306468032
y[1] (numeric) = 1.2737875969589737545209898647377
absolute error = 2.85696592179345e-17
relative error = 2.2428903599109761425686313586712e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.759
y[1] (analytic) = 1.274475430346779680385055877114
y[1] (numeric) = 1.2744754303467797089900105383913
absolute error = 2.86049546612773e-17
relative error = 2.2444492832234518596590784086144e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.76
y[1] (analytic) = 1.275163989259094827660311633333
y[1] (numeric) = 1.275163989259094856300528294696
absolute error = 2.86402166613630e-17
relative error = 2.2460026241804200896104245136837e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.761
y[1] (analytic) = 1.2758532730073603128418580871366
y[1] (numeric) = 1.275853273007360341517303270066
absolute error = 2.86754451829294e-17
relative error = 2.2475503876192175007409987276291e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.762
y[1] (analytic) = 1.2765432809022924451045204977583
y[1] (numeric) = 1.2765432809022924738151606885065
absolute error = 2.87106401907482e-17
relative error = 2.2490925783930183379096500646336e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.763
y[1] (analytic) = 1.2772340122538833870168225968583
y[1] (numeric) = 1.2772340122538834157626242464824
absolute error = 2.87458016496241e-17
relative error = 2.2506292013706667838383939361760e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.764
y[1] (analytic) = 1.277925466371401844548766519348
y[1] (numeric) = 1.2779254663714018733296960437439
absolute error = 2.87809295243959e-17
relative error = 2.2521602614366662325226641381807e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.765
y[1] (analytic) = 1.2786176425633937578030692724491
y[1] (numeric) = 1.2786176425633937866190930523848
absolute error = 2.88160237799357e-17
relative error = 2.2536857634910198656554397015829e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.766
y[1] (analytic) = 1.2793105401376829924691650118068
y[1] (numeric) = 1.279310540137683021320249392956
absolute error = 2.88510843811492e-17
relative error = 2.2552057124491575977138785391069e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.767
y[1] (analytic) = 1.2800041584013720319992816707128
y[1] (numeric) = 1.2800041584013720608853929636885
absolute error = 2.88861112929757e-17
relative error = 2.2567201132418396897851903418919e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.768
y[1] (analytic) = 1.2806984966608426705058997664195
y[1] (numeric) = 1.280698496660842699427004246808
absolute error = 2.89211044803885e-17
relative error = 2.2582289708150917796601872195665e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.769
y[1] (analytic) = 1.2813935542217567063799004861449
y[1] (numeric) = 1.2813935542217567353359643945391
absolute error = 2.89560639083942e-17
relative error = 2.2597322901300541504366343054195e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.77
y[1] (analytic) = 1.2820893303890566366287094346757
y[1] (numeric) = 1.2820893303890566656196989767093
absolute error = 2.89909895420336e-17
relative error = 2.2612300761629561583859057670707e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.771
y[1] (analytic) = 1.2827858244669663519337417054856
y[1] (numeric) = 1.2827858244669663809596230518666
absolute error = 2.90258813463810e-17
relative error = 2.2627223339049658895337124388772e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.772
y[1] (analytic) = 1.2834830357589918324264532179796
y[1] (numeric) = 1.2834830357589918614871925045241
absolute error = 2.90607392865445e-17
relative error = 2.2642090683621180939156266332083e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.773
y[1] (analytic) = 1.2841809635679218441823025448716
y[1] (numeric) = 1.2841809635679218732778658725378
absolute error = 2.90955633276662e-17
relative error = 2.2656902845552344442046252556305e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.774
y[1] (analytic) = 1.2848796071958286364319267357915
y[1] (numeric) = 1.2848796071958286655622801707136
absolute error = 2.91303534349221e-17
relative error = 2.2671659875198205835475999641048e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.775
y[1] (analytic) = 1.2855789659440686394888339260045
y[1] (numeric) = 1.2855789659440686686539434995265
absolute error = 2.91651095735220e-17
relative error = 2.2686361823059633881573870733689e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.776
y[1] (analytic) = 1.2862790391132831633929148026071
y[1] (numeric) = 1.286279039113283192592746511317
absolute error = 2.91998317087099e-17
relative error = 2.2701008739782673172945339803831e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.777
y[1] (analytic) = 1.2869798260033990972690742847478
y[1] (numeric) = 1.2869798260033991265035940905114
absolute error = 2.92345198057636e-17
relative error = 2.2715600676157286915992645707534e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.778
y[1] (analytic) = 1.2876813259136296094002840592981
y[1] (numeric) = 1.287681325913629638669457889293
absolute error = 2.92691738299949e-17
relative error = 2.2730137683116568602064281507283e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.779
y[1] (analytic) = 1.28838353814247484801435589898
y[1] (numeric) = 1.28838353814247487731814964573
absolute error = 2.93037937467500e-17
relative error = 2.2744619811736110329887333285907e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.78
y[1] (analytic) = 1.2890864619877226427837349762354
y[1] (numeric) = 1.2890864619877226721221144976442
absolute error = 2.93383795214088e-17
relative error = 2.2759047113232518728686300423846e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.781
y[1] (analytic) = 1.289790096746449207037611673102
y[1] (numeric) = 1.2897900967464492364105427924876
absolute error = 2.93729311193856e-17
relative error = 2.2773419638963020048621369602691e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.782
y[1] (analytic) = 1.2904944417150198406856496750424
y[1] (numeric) = 1.2904944417150198700930981811712
absolute error = 2.94074485061288e-17
relative error = 2.2787737440424290526456757890584e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.783
y[1] (analytic) = 1.2911994961890896338526274250576
y[1] (numeric) = 1.2911994961890896632945590721787
absolute error = 2.94419316471211e-17
relative error = 2.2802000569251676707015070222203e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.784
y[1] (analytic) = 1.2919052594636041712232893035015
y[1] (numeric) = 1.2919052594636042006996698113807
absolute error = 2.94763805078792e-17
relative error = 2.2816209077218030196360586756592e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.785
y[1] (analytic) = 1.2926117308328002370967021888034
y[1] (numeric) = 1.2926117308328002666074972427577
absolute error = 2.95107950539543e-17
relative error = 2.2830363016233164050799105819958e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.786
y[1] (analytic) = 1.293318909590206521149412344802
y[1] (numeric) = 1.293318909590206550694587595734
absolute error = 2.95451752509320e-17
relative error = 2.2844462438342845953655848996637e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.787
y[1] (analytic) = 1.2940267950286443249066968715924
y[1] (numeric) = 1.2940267950286443544862179360242
absolute error = 2.95795210644318e-17
relative error = 2.2858507395727484520345383244337e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.788
y[1] (analytic) = 1.2947353864402282689212032486917
y[1] (numeric) = 1.2947353864402282985350357087999
absolute error = 2.96138324601082e-17
relative error = 2.2872497940702054640268361656568e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.789
y[1] (analytic) = 1.2954446831163670006582697919461
y[1] (numeric) = 1.2954446831163670303063791955959
absolute error = 2.96481094036498e-17
relative error = 2.2886434125714478157325946653289e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.79
y[1] (analytic) = 1.296154684347763903087219138915
y[1] (numeric) = 1.2961546843477639327695709996945
absolute error = 2.96823518607795e-17
relative error = 2.2900316003344857506795913762840e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.791
y[1] (analytic) = 1.2968653894244178039779161714986
y[1] (numeric) = 1.2968653894244178336944759687534
absolute error = 2.97165597972548e-17
relative error = 2.2914143626304787969084397604797e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.792
y[1] (analytic) = 1.2975767976356236859018810793109
y[1] (numeric) = 1.2975767976356237156526142581788
absolute error = 2.97507331788679e-17
relative error = 2.2927917047436517051295443791137e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=64.8MB, alloc=4.3MB, time=8.21
x[1] = 0.793
y[1] (analytic) = 1.2982889082699733969372475627432
y[1] (numeric) = 1.2982889082699734267221195341886
absolute error = 2.97848719714454e-17
relative error = 2.2941636319711797546581574545112e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.794
y[1] (analytic) = 1.2990017206153563620768554708199
y[1] (numeric) = 1.2990017206153563918958316116684
absolute error = 2.98189761408485e-17
relative error = 2.2955301496231128301278781734842e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.795
y[1] (analytic) = 1.2997152339589602953387664658126
y[1] (numeric) = 1.2997152339589603251918121187856
absolute error = 2.98530456529730e-17
relative error = 2.2968912630222842637492715724224e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.796
y[1] (analytic) = 1.3004294475872719125784906041565
y[1] (numeric) = 1.300429447587271942465571077906
absolute error = 2.98870804737495e-17
relative error = 2.2982469775042352620175268047893e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.797
y[1] (analytic) = 1.3011443607860776450022110215024
y[1] (numeric) = 1.3011443607860776749232915906454
absolute error = 2.99210805691430e-17
relative error = 2.2995972984170933740256496625226e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.798
y[1] (analytic) = 1.3018599728404643533802932087375
y[1] (numeric) = 1.301859972840464383335339113891
absolute error = 2.99550459051535e-17
relative error = 2.3009422311215280805599849360819e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.799
y[1] (analytic) = 1.3025762830348200429603646655274
y[1] (numeric) = 1.3025762830348200729493411133431
absolute error = 2.99889764478157e-17
relative error = 2.3022817809906373441002081668646e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.8
y[1] (analytic) = 1.3032932906528345790792500183577
y[1] (numeric) = 1.3032932906528346091021221815567
absolute error = 3.00228721631990e-17
relative error = 2.3036159534098574609368475176009e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.801
y[1] (analytic) = 1.3040109949775004034730459911998
y[1] (numeric) = 1.3040109949775004335297790086075
absolute error = 3.00567330174077e-17
relative error = 2.3049447537768884586566690279498e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.802
y[1] (analytic) = 1.3047293952911132512846199187868
y[1] (numeric) = 1.3047293952911132813751788953677
absolute error = 3.00905589765809e-17
relative error = 2.3062681875015966583646433173719e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.803
y[1] (analytic) = 1.3054484908752728687678147950589
y[1] (numeric) = 1.3054484908752728988921648019517
absolute error = 3.01243500068928e-17
relative error = 2.3075862600059481123421432180322e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.804
y[1] (analytic) = 1.3061682810108837316876431526351
y[1] (numeric) = 1.3061682810108837618457492271873
absolute error = 3.01581060745522e-17
relative error = 2.3088989767238809277466013180855e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.805
y[1] (analytic) = 1.3068887649781557644157513731752
y[1] (numeric) = 1.3068887649781557946075785189784
absolute error = 3.01918271458032e-17
relative error = 2.3102063431012697485443067901991e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.806
y[1] (analytic) = 1.3076099420566050597204353332294
y[1] (numeric) = 1.3076099420566050899459485201541
absolute error = 3.02255131869247e-17
relative error = 2.3115083645957985007258143161198e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.807
y[1] (analytic) = 1.3083318115250545992504875956188
y[1] (numeric) = 1.3083318115250546295096517598493
absolute error = 3.02591641642305e-17
relative error = 2.3128050466768793356753181189435e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.808
y[1] (analytic) = 1.3090543726616349747121556625597
y[1] (numeric) = 1.3090543726616350050049357066295
absolute error = 3.02927800440698e-17
relative error = 2.3140963948256023167906061775957e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.809
y[1] (analytic) = 1.3097776247437851097384901136346
y[1] (numeric) = 1.3097776247437851400648509064612
absolute error = 3.03263607928266e-17
relative error = 2.3153824145346012085474529632152e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.81
y[1] (analytic) = 1.3105015670482529824503607593199
y[1] (numeric) = 1.3105015670482530128102671362402
absolute error = 3.03599063769203e-17
relative error = 2.3166631113080111986975261520434e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.811
y[1] (analytic) = 1.311226198851096348708418249117
y[1] (numeric) = 1.3112261988510963791018350119222
absolute error = 3.03934167628052e-17
relative error = 2.3179384906613427914955594246499e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.812
y[1] (analytic) = 1.3119515194276834660552778823829
y[1] (numeric) = 1.3119515194276834964821697993538
absolute error = 3.04268919169709e-17
relative error = 2.3192085581214246418792901465485e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.813
y[1] (analytic) = 1.3126775280526938183472016797382
y[1] (numeric) = 1.3126775280526938488075334856806
absolute error = 3.04603318059424e-17
relative error = 2.3204733192263236492589366294033e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.814
y[1] (analytic) = 1.3134042240001188410745540834314
y[1] (numeric) = 1.313404224000118871568290479711
absolute error = 3.04937363962796e-17
relative error = 2.3217327795252195585916234909507e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.815
y[1] (analytic) = 1.3141316065432626473703059662622
y[1] (numeric) = 1.3141316065432626778974116208402
absolute error = 3.05271056545780e-17
relative error = 2.3229869445783712188425181424154e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.816
y[1] (analytic) = 1.314859674954742754705860940622
y[1] (numeric) = 1.3148596749547427852663004880905
absolute error = 3.05604395474685e-17
relative error = 2.3242358199570144324528159474454e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.817
y[1] (analytic) = 1.315588428506490812273477271886
y[1] (numeric) = 1.315588428506490842867215313503
absolute error = 3.05937380416170e-17
relative error = 2.3254794112432448699481576855974e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.818
y[1] (analytic) = 1.316317866469753329054558013794
y[1] (numeric) = 1.3163178664697533596815591175191
absolute error = 3.06270011037251e-17
relative error = 2.3267177240299848694499678044132e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.819
y[1] (analytic) = 1.3170479881150924025730812975917
y[1] (numeric) = 1.3170479881150924332333099981214
absolute error = 3.06602287005297e-17
relative error = 2.3279507639208667569890456128914e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.82
y[1] (analytic) = 1.3177787927123864483334420215631
y[1] (numeric) = 1.3177787927123864790268628203663
absolute error = 3.06934207988032e-17
relative error = 2.3291785365301620173796161956842e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.821
y[1] (analytic) = 1.3185102795308309299419755031717
y[1] (numeric) = 1.3185102795308309606685528685253
absolute error = 3.07265773653536e-17
relative error = 2.3304010474827030490120304399746e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.822
y[1] (analytic) = 1.3192424478389390899114329723498
y[1] (numeric) = 1.3192424478389391206711313393741
absolute error = 3.07596983670243e-17
relative error = 2.3316183024137823722951669972974e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.823
y[1] (analytic) = 1.3199752969045426811476781015192
y[1] (numeric) = 1.3199752969045427119404618722134
absolute error = 3.07927837706942e-17
relative error = 2.3328303069690748359821062233512e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.824
y[1] (analytic) = 1.3207088259947926991178730857087
y[1] (numeric) = 1.3207088259947927299437066289867
absolute error = 3.08258335432780e-17
relative error = 2.3340370668045751617297728120290e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.825
y[1] (analytic) = 1.3214430343761601146994221046441
y[1] (numeric) = 1.3214430343761601455582697563701
absolute error = 3.08588476517260e-17
relative error = 2.3352385875864977960472161499186e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.826
y[1] (analytic) = 1.3221779213144366077089393179268
y[1] (numeric) = 1.3221779213144366386007653809507
absolute error = 3.08918260630239e-17
relative error = 2.3364348749911770337109680051350e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.827
y[1] (analytic) = 1.3229134860747353011105078643946
y[1] (numeric) = 1.322913486074735332035276608588
absolute error = 3.09247687441934e-17
relative error = 2.3376259347050278856149534671517e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.828
y[1] (analytic) = 1.3236497279214914959024956574681
y[1] (numeric) = 1.3236497279214915268601713197599
absolute error = 3.09576756622918e-17
relative error = 2.3388117724244314683368218633485e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.829
y[1] (analytic) = 1.3243866461184634066821930897261
y[1] (numeric) = 1.3243866461184634376727398741383
absolute error = 3.09905467844122e-17
relative error = 2.3399923938556660208226213794630e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.83
y[1] (analytic) = 1.3251242399287328978875370821356
y[1] (numeric) = 1.325124239928732928910919159819
absolute error = 3.10233820776834e-17
relative error = 2.3411678047148154538332355888290e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.831
y[1] (analytic) = 1.3258625086147062207151852362717
y[1] (numeric) = 1.325862508614706251771366745542
absolute error = 3.10561815092703e-17
relative error = 2.3423380107277158588966155241137e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.832
y[1] (analytic) = 1.3266014514381147507142031715169
y[1] (numeric) = 1.3266014514381147818031482178903
absolute error = 3.10889450463734e-17
relative error = 2.3435030176298342972588247731868e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.833
y[1] (analytic) = 1.3273410676600157260546274536119
y[1] (numeric) = 1.327341067660015757176300109841
absolute error = 3.11216726562291e-17
relative error = 2.3446628311662082094944604783318e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.834
y[1] (analytic) = 1.3280813565407929864701658460576
y[1] (numeric) = 1.3280813565407930176245301521673
absolute error = 3.11543643061097e-17
relative error = 2.3458174570913623846291778015128e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.835
y[1] (analytic) = 1.3288223173401577128742959417292
y[1] (numeric) = 1.3288223173401577440613159050529
absolute error = 3.11870199633237e-17
relative error = 2.3469669011692487301194194122935e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.3MB, time=8.70
NO POLE
x[1] = 0.836
y[1] (analytic) = 1.3295639493171491676490225586661
y[1] (numeric) = 1.3295639493171491988686621538816
absolute error = 3.12196395952155e-17
relative error = 2.3481111691731410635212440720905e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.837
y[1] (analytic) = 1.3303062517301354356055536113409
y[1] (numeric) = 1.3303062517301354668577767805062
absolute error = 3.12522231691653e-17
relative error = 2.3492502668855452390421484598614e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.838
y[1] (analytic) = 1.3310492238368141656161534967937
y[1] (numeric) = 1.3310492238368141969009241493833
absolute error = 3.12847706525896e-17
relative error = 2.3503842000981546019936126697192e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.839
y[1] (analytic) = 1.3317928648942133129164323638407
y[1] (numeric) = 1.3317928648942133442337143767817
absolute error = 3.13172820129410e-17
relative error = 2.3515129746117529824866593199280e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.84
y[1] (analytic) = 1.3325371741586918820773289631291
y[1] (numeric) = 1.3325371741586919134270861808372
absolute error = 3.13497572177081e-17
relative error = 2.3526365962361254701471376618779e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.841
y[1] (analytic) = 1.3332821508859406706460441061175
y[1] (numeric) = 1.333282150885940702028240340533
absolute error = 3.13821962344155e-17
relative error = 2.3537550707899769407756646326335e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.842
y[1] (analytic) = 1.3340277943309830134551810921098
y[1] (numeric) = 1.3340277943309830448697801227343
absolute error = 3.14145990306245e-17
relative error = 2.3548684041009032824696079035315e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.843
y[1] (analytic) = 1.334774103748175527599348794266
y[1] (numeric) = 1.3347741037481755590463143681981
absolute error = 3.14469655739321e-17
relative error = 2.3559766020052353104299118089268e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.844
y[1] (analytic) = 1.3355210783912088580784824280462
y[1] (numeric) = 1.3355210783912088895577782600181
absolute error = 3.14792958319719e-17
relative error = 2.3570796703480254272431207367481e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.845
y[1] (analytic) = 1.3362687175131084241071363588314
y[1] (numeric) = 1.336268717513108455618726131245
absolute error = 3.15115897724136e-17
relative error = 2.3581776149829295152251803305463e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.846
y[1] (analytic) = 1.3370170203662351660890026394896
y[1] (numeric) = 1.3370170203662351976328500024528
absolute error = 3.15438473629632e-17
relative error = 2.3592704417721415378158051519307e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.847
y[1] (analytic) = 1.3377659862022862932559083034306
y[1] (numeric) = 1.3377659862022863248319768747938
absolute error = 3.15760685713632e-17
relative error = 2.3603581565863283189708807998755e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.848
y[1] (analytic) = 1.3385156142722960319705437742155
y[1] (numeric) = 1.3385156142722960635787971396077
absolute error = 3.16082533653922e-17
relative error = 2.3614407653045196750869543111414e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.849
y[1] (analytic) = 1.3392659038266363746921740890535
y[1] (numeric) = 1.3392659038266364063325758019191
absolute error = 3.16404017128656e-17
relative error = 2.3625182738140810107597542480508e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.85
y[1] (analytic) = 1.3400168541150178296045839705385
y[1] (numeric) = 1.3400168541150178612770975521735
absolute error = 3.16725135816350e-17
relative error = 2.3635906880105889541232715619263e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.851
y[1] (analytic) = 1.3407684643864901709055071187424
y[1] (numeric) = 1.3407684643864902026100960583309
absolute error = 3.17045889395885e-17
relative error = 2.3646580137977744978600728215034e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.852
y[1] (analytic) = 1.3415207338894431897567894342973
y[1] (numeric) = 1.3415207338894432214934171889482
absolute error = 3.17366277546509e-17
relative error = 2.3657202570874588402383481181467e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.853
y[1] (analytic) = 1.3422736618716074458945352223685
y[1] (numeric) = 1.3422736618716074776631652171517
absolute error = 3.17686299947832e-17
relative error = 2.3667774237994372554713524489144e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.854
y[1] (analytic) = 1.3430272475800550198984847674316
y[1] (numeric) = 1.3430272475800550516990803954148
absolute error = 3.18005956279832e-17
relative error = 2.3678295198614452240823002139041e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.855
y[1] (analytic) = 1.3437814902612002661198710095412
y[1] (numeric) = 1.3437814902612002979523956318266
absolute error = 3.18325246222854e-17
relative error = 2.3688765512090725512367847873331e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.856
y[1] (analytic) = 1.3445363891608005662670023942965
y[1] (numeric) = 1.3445363891608005981314193400572
absolute error = 3.18644169457607e-17
relative error = 2.3699185237856628656620219063316e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.857
y[1] (analytic) = 1.3452919435239570836478183109831
y[1] (numeric) = 1.3452919435239571155440908774998
absolute error = 3.18962725665167e-17
relative error = 2.3709554435422580244670943869729e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.858
y[1] (analytic) = 1.3460481525951155180686628763995
y[1] (numeric) = 1.3460481525951155499967543290973
absolute error = 3.19280914526978e-17
relative error = 2.3719873164375278153689580991955e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.859
y[1] (analytic) = 1.3468050156180668613885221656564
y[1] (numeric) = 1.3468050156180668933483957381418
absolute error = 3.19598735724854e-17
relative error = 2.3730141484377072899780890741353e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.86
y[1] (analytic) = 1.3475625318359481537279693357761
y[1] (numeric) = 1.3475625318359481857195882298731
absolute error = 3.19916188940970e-17
relative error = 2.3740359455164526494701769102522e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.861
y[1] (analytic) = 1.3483207004912432403320614332074
y[1] (numeric) = 1.3483207004912432723553888189949
absolute error = 3.20233273857875e-17
relative error = 2.3750527136548607530721219023580e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.862
y[1] (analytic) = 1.3490795208257835290864310224247
y[1] (numeric) = 1.349079520825783561141430038273
absolute error = 3.20549990158483e-17
relative error = 2.3760644588413254585920697478542e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.863
y[1] (analytic) = 1.3498389920807487486858151195816
y[1] (numeric) = 1.3498389920807487807724488721895
absolute error = 3.20866337526079e-17
relative error = 2.3770711870715055444974660951203e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.864
y[1] (analytic) = 1.3505991134966677074542632627533
y[1] (numeric) = 1.3505991134966677395724948271848
absolute error = 3.21182315644315e-17
relative error = 2.3780729043482186726700958122989e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.865
y[1] (analytic) = 1.3513598843134190528162658986232
y[1] (numeric) = 1.3513598843134190849660583183445
absolute error = 3.21497924197213e-17
relative error = 2.3790696166813874831256739825248e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.866
y[1] (analytic) = 1.3521213037702320314180436145485
y[1] (numeric) = 1.352121303770232063599359901465
absolute error = 3.21813162869165e-17
relative error = 2.3800613300879636587064532783441e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.867
y[1] (analytic) = 1.3528833711056872498982370947791
y[1] (numeric) = 1.3528833711056872821110402292722
absolute error = 3.22128031344931e-17
relative error = 2.3810480505918374390732238482929e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.868
y[1] (analytic) = 1.3536460855577174363072370302028
y[1] (numeric) = 1.353646085557717468551489961167
absolute error = 3.22442529309642e-17
relative error = 2.3820297842237843546344907300912e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.869
y[1] (analytic) = 1.3544094463636082021743925623504
y[1] (numeric) = 1.3544094463636082344500582072307
absolute error = 3.22756656448803e-17
relative error = 2.3830065370214121183143456074728e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.87
y[1] (analytic) = 1.3551734527599988052223361945172
y[1] (numeric) = 1.3551734527599988375293774393456
absolute error = 3.23070412448284e-17
relative error = 2.3839783150290191258129717683437e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.871
y[1] (analytic) = 1.3559381039828829127276624557362
y[1] (numeric) = 1.3559381039828829450660421551694
absolute error = 3.23383796994332e-17
relative error = 2.3849451242976082880493622246592e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.872
y[1] (analytic) = 1.3567033992676093655271969569926
y[1] (numeric) = 1.3567033992676093978968779343485
absolute error = 3.23696809773559e-17
relative error = 2.3859069708847238977947181031519e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.873
y[1] (analytic) = 1.3574693378488829426690918334692
y[1] (numeric) = 1.3574693378488829750700368807647
absolute error = 3.24009450472955e-17
relative error = 2.3868638608544731954025308809801e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.874
y[1] (analytic) = 1.3582359189607651267079829217956
y[1] (numeric) = 1.3582359189607651591401547997834
absolute error = 3.24321718779878e-17
relative error = 2.3878158002773785062656403682942e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.875
y[1] (analytic) = 1.359003141836674869643443377204
y[1] (numeric) = 1.35900314183667490210680481541
absolute error = 3.24633614382060e-17
relative error = 2.3887627952303475946797252480335e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.876
y[1] (analytic) = 1.3597710057093893595009677922045
y[1] (numeric) = 1.3597710057093893919954814889651
absolute error = 3.24945136967606e-17
relative error = 2.3897048517965926224376728768091e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.877
y[1] (analytic) = 1.3605395098110447875547202358586
y[1] (numeric) = 1.3605395098110448200803488583577
absolute error = 3.25256286224991e-17
relative error = 2.3906419760655346660738037103901e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=72.4MB, alloc=4.3MB, time=9.18
x[1] = 0.878
y[1] (analytic) = 1.3613086533731371161912789909656
y[1] (numeric) = 1.3613086533731371487479851752726
absolute error = 3.25567061843070e-17
relative error = 2.3915741741328040390459090140153e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.879
y[1] (analytic) = 1.3620784356265228474136101254846
y[1] (numeric) = 1.362078435626522880001356476591
absolute error = 3.25877463511064e-17
relative error = 2.3925014521000643973847737329767e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.88
y[1] (analytic) = 1.3628488558014197919845013942779
y[1] (numeric) = 1.3628488558014198246032504861351
absolute error = 3.26187490918572e-17
relative error = 2.3934238160750282049364889928729e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.881
y[1] (analytic) = 1.3636199131274078392086873278103
y[1] (numeric) = 1.3636199131274078718584017033671
absolute error = 3.26497143755568e-17
relative error = 2.3943412721713621324804364535991e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.882
y[1] (analytic) = 1.3643916068334297273528957257406
y[1] (numeric) = 1.3643916068334297600335378969804
absolute error = 3.26806421712398e-17
relative error = 2.3952538265085927657282606667299e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.883
y[1] (analytic) = 1.3651639361477918147030451354242
y[1] (numeric) = 1.3651639361477918474145775834026
absolute error = 3.27115324479784e-17
relative error = 2.3961614852120638980745571248012e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.884
y[1] (analytic) = 1.3659369002981648512578222581931
y[1] (numeric) = 1.3659369002981648840002074330754
absolute error = 3.27423851748823e-17
relative error = 2.3970642544128573531673006093487e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.885
y[1] (analytic) = 1.3667104985115847510578675899006
y[1] (numeric) = 1.3667104985115847838310679109995
absolute error = 3.27732003210989e-17
relative error = 2.3979621402477360171965040409017e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.886
y[1] (analytic) = 1.3674847300144533651497969666091
y[1] (numeric) = 1.3674847300144533979537748224221
absolute error = 3.28039778558130e-17
relative error = 2.3988551488590504923532634876639e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.887
y[1] (analytic) = 1.3682595940325392551842860514642
y[1] (numeric) = 1.3682595940325392880190037997112
absolute error = 3.28347177482470e-17
relative error = 2.3997432863946826020408128615619e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.888
y[1] (analytic) = 1.3690350897909784676474441647341
y[1] (numeric) = 1.3690350897909785005128641323952
absolute error = 3.28654199676611e-17
relative error = 2.4006265590079890808131829400979e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.889
y[1] (analytic) = 1.369811216514275308724703225707
y[1] (numeric) = 1.3698112165142753416207877090601
absolute error = 3.28960844833531e-17
relative error = 2.4015049728577162480174114270012e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.89
y[1] (analytic) = 1.3705879734263031197964469426198
y[1] (numeric) = 1.3705879734263031527231582072781
absolute error = 3.29267112646583e-17
relative error = 2.4023785341079222617531153680271e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.891
y[1] (analytic) = 1.3713653597503050535646047550548
y[1] (numeric) = 1.371365359750305086521905036005
absolute error = 3.29573002809502e-17
relative error = 2.4032472489279579681756563016618e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.892
y[1] (analytic) = 1.3721433747088948508094344022757
y[1] (numeric) = 1.3721433747088948837972859039153
absolute error = 3.29878515016396e-17
relative error = 2.4041111234923312057494963667707e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.893
y[1] (analytic) = 1.3729220175240576177757163607833
y[1] (numeric) = 1.3729220175240576507940812569587
absolute error = 3.30183648961754e-17
relative error = 2.4049701639806953908312207044186e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.894
y[1] (analytic) = 1.373701287417150604187582764963
y[1] (numeric) = 1.373701287417150637236423199007
absolute error = 3.30488404340440e-17
relative error = 2.4058243765777362249362023726788e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.895
y[1] (analytic) = 1.3744811836089039818912027960585
y[1] (numeric) = 1.3744811836089040149704808808286
absolute error = 3.30792780847701e-17
relative error = 2.4066737674731606419325493113732e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.896
y[1] (analytic) = 1.3752617053194216241245458968532
y[1] (numeric) = 1.375261705319421657234223714769
absolute error = 3.31096778179158e-17
relative error = 2.4075183428615621786789478519706e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.897
y[1] (analytic) = 1.3760428517681818854134435423582
y[1] (numeric) = 1.3760428517681819185534831454398
absolute error = 3.31400396030816e-17
relative error = 2.4083581089424248802858339119869e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.898
y[1] (analytic) = 1.3768246221740383820931696705131
y[1] (numeric) = 1.3768246221740384152635330804188
absolute error = 3.31703634099057e-17
relative error = 2.4091930719200037196988544227795e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.899
y[1] (analytic) = 1.3776070157552207734547592513822
y[1] (numeric) = 1.3776070157552208066554084594463
absolute error = 3.32006492080641e-17
relative error = 2.4100232380032634968479976866695e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.9
y[1] (analytic) = 1.3783900317293355435152838485929
y[1] (numeric) = 1.3783900317293355767461808158641
absolute error = 3.32308969672712e-17
relative error = 2.4108486134058542216840603949192e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.901
y[1] (analytic) = 1.3791736693133667834113024028072
y[1] (numeric) = 1.3791736693133668166724090600864
absolute error = 3.32611066572792e-17
relative error = 2.4116692043459995746061471217536e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.902
y[1] (analytic) = 1.3799579277236769744147048438388
y[1] (numeric) = 1.3799579277236770077059830917172
absolute error = 3.32912782478784e-17
relative error = 2.4124850170464509691120580975335e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.903
y[1] (analytic) = 1.380742806176007771570165515639
y[1] (numeric) = 1.3807428061760078048915772245362
absolute error = 3.33214117088972e-17
relative error = 2.4132960577344200471895120099353e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.904
y[1] (analytic) = 1.3815283038854807879534227767624
y[1] (numeric) = 1.3815283038854808213049297869645
absolute error = 3.33515070102021e-17
relative error = 2.4141023326415114090445083985182e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.905
y[1] (analytic) = 1.3823144200665983795496005180982
y[1] (numeric) = 1.3823144200665984129311646397962
absolute error = 3.33815641216980e-17
relative error = 2.4149038480036772798440895242221e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.906
y[1] (analytic) = 1.3831011539332444307507867196122
y[1] (numeric) = 1.3831011539332444641623697329397
absolute error = 3.34115830133275e-17
relative error = 2.4157006100611000353198320960202e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.907
y[1] (analytic) = 1.3838885046986851404720835485838
y[1] (numeric) = 1.3838885046986851739136472036557
absolute error = 3.34415636550719e-17
relative error = 2.4164926250581979766279343447656e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.908
y[1] (analytic) = 1.3846764715755698088853428833566
y[1] (numeric) = 1.3846764715755698423568489003071
absolute error = 3.34715060169505e-17
relative error = 2.4172798992435083201251514694532e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.909
y[1] (analytic) = 1.3854650537759316247698005289301
y[1] (numeric) = 1.3854650537759316582712105979511
absolute error = 3.35014100690210e-17
relative error = 2.4180624388696499896580545613987e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.91
y[1] (analytic) = 1.3862542505111884534788217738253
y[1] (numeric) = 1.3862542505111884870100975552046
absolute error = 3.35312757813793e-17
relative error = 2.4188402501932432620433009649030e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.911
y[1] (analytic) = 1.3870440609921436255219703215436
y[1] (numeric) = 1.3870440609921436590830734457032
absolute error = 3.35611031241596e-17
relative error = 2.4196133394748513244864759795526e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.912
y[1] (analytic) = 1.387834484428986725761612014616
y[1] (numeric) = 1.3878344844289867593525040821507
absolute error = 3.35908920675347e-17
relative error = 2.4203817129789364520905536635109e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.913
y[1] (analytic) = 1.3886255200312943832232641547054
y[1] (numeric) = 1.388625520031294416843906736421
absolute error = 3.36206425817156e-17
relative error = 2.4211453769737659356381039373732e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.914
y[1] (analytic) = 1.3894171670080310615189006084766
y[1] (numeric) = 1.3894171670080310951692552454284
absolute error = 3.36503546369518e-17
relative error = 2.4219043377313687223721967598636e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.915
y[1] (analytic) = 1.390209424567549849882422275997
y[1] (numeric) = 1.3902094245675498835624504795282
absolute error = 3.36800282035312e-17
relative error = 2.4226586015274634438003414340216e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.916
y[1] (analytic) = 1.3910022919175932548165018862618
y[1] (numeric) = 1.3910022919175932885261651380422
absolute error = 3.37096632517804e-17
relative error = 2.4234081746414154577994623598610e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.917
y[1] (analytic) = 1.3917957682652939923500114730661
y[1] (numeric) = 1.3917957682652940260892712251302
absolute error = 3.37392597520641e-17
relative error = 2.4241530633561293856116554400815e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.918
y[1] (analytic) = 1.3925898528171757809052402738607
y[1] (numeric) = 1.3925898528171758146740579486467
absolute error = 3.37688176747860e-17
relative error = 2.4248932739580497425895833419586e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.919
y[1] (analytic) = 1.3933845447791541347741101844421
y[1] (numeric) = 1.3933845447791541685724471748302
absolute error = 3.37983369903881e-17
relative error = 2.4256288127370467524926946514401e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=76.2MB, alloc=4.3MB, time=9.69
x[1] = 0.92
y[1] (analytic) = 1.3941798433565371582025952933256
y[1] (numeric) = 1.3941798433565371920304129626768
absolute error = 3.38278176693512e-17
relative error = 2.4263596859863886389448190549484e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.921
y[1] (analytic) = 1.3949757477540263400825514114488
y[1] (numeric) = 1.3949757477540263739398110936432
absolute error = 3.38572596821944e-17
relative error = 2.4270859000026423411037570092291e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.922
y[1] (analytic) = 1.3957722571757173492501609054418
y[1] (numeric) = 1.3957722571757173831368239049177
absolute error = 3.38866629994759e-17
relative error = 2.4278074610856677232611475333760e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.923
y[1] (analytic) = 1.3965693708251008303901975360864
y[1] (numeric) = 1.3965693708251008643062251278787
absolute error = 3.39160275917923e-17
relative error = 2.4285243755385044146574287841116e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.924
y[1] (analytic) = 1.3973670879050632005453153977649
y[1] (numeric) = 1.3973670879050632344906688275439
absolute error = 3.39453534297790e-17
relative error = 2.4292366496673377730486793623509e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.925
y[1] (analytic) = 1.3981654076178874462295654496762
y[1] (numeric) = 1.3981654076178874802042059337864
absolute error = 3.39746404841102e-17
relative error = 2.4299442897814363735769591439672e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.926
y[1] (analytic) = 1.3989643291652539211453425253694
y[1] (numeric) = 1.3989643291652539551492312508681
absolute error = 3.40038887254987e-17
relative error = 2.4306473021930754335847300709611e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.927
y[1] (analytic) = 1.3997638517482411445029651037137
y[1] (numeric) = 1.3997638517482411785360632284102
absolute error = 3.40330981246965e-17
relative error = 2.4313456932175176710036138076086e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.928
y[1] (analytic) = 1.4005639745673265999420895217925
y[1] (numeric) = 1.4005639745673266340043581742866
absolute error = 3.40622686524941e-17
relative error = 2.4320394691729014279423223186731e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.929
y[1] (analytic) = 1.4013646968223875350541597083728
y[1] (numeric) = 1.4013646968223875691455599880937
absolute error = 3.40914002797209e-17
relative error = 2.4327286363802076923961653730470e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.93
y[1] (analytic) = 1.402166017712701761505092915567
y[1] (numeric) = 1.4021660177127017956255858928124
absolute error = 3.41204929772454e-17
relative error = 2.4334132011632129899645336256067e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.931
y[1] (analytic) = 1.4029679364369484557574013260696
y[1] (numeric) = 1.4029679364369484899069480420444
absolute error = 3.41495467159748e-17
relative error = 2.4340931698483996916270962987289e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.932
y[1] (analytic) = 1.4037704521932089603909488139114
y[1] (numeric) = 1.4037704521932089945695102807668
absolute error = 3.41785614668554e-17
relative error = 2.4347685487649236400229842868521e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.933
y[1] (analytic) = 1.4045735641789675860215415380431
y[1] (numeric) = 1.4045735641789676202290787389156
absolute error = 3.42075372008725e-17
relative error = 2.4354393442445463110386914869790e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.934
y[1] (analytic) = 1.4053772715911124138165504502244
y[1] (numeric) = 1.4053772715911124480530243392746
absolute error = 3.42364738890502e-17
relative error = 2.4361055626215601152744442673449e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.935
y[1] (analytic) = 1.4061815736259360986067632016613
y[1] (numeric) = 1.4061815736259361328721347041134
absolute error = 3.42653715024521e-17
relative error = 2.4367672102327779822314657823479e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.936
y[1] (analytic) = 1.4069864694791366725936623366093
y[1] (numeric) = 1.4069864694791367068878923487896
absolute error = 3.42942300121803e-17
relative error = 2.4374242934174021785514608328084e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.937
y[1] (analytic) = 1.4077919583458183496513260657285
y[1] (numeric) = 1.4077919583458183839743754551051
absolute error = 3.43230493893766e-17
relative error = 2.4380768185170498738544990339577e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.938
y[1] (analytic) = 1.4085980394204923302221473173594
y[1] (numeric) = 1.4085980394204923645739769225807
absolute error = 3.43518296052213e-17
relative error = 2.4387247918756082617929189389837e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.939
y[1] (analytic) = 1.409404711897077606805566171065
y[1] (numeric) = 1.4094047118970776411861368019994
absolute error = 3.43805706309344e-17
relative error = 2.4393682198392604884865054062563e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.94
y[1] (analytic) = 1.410211974968901770039010184776
y[1] (numeric) = 1.4102119749689018044482826225508
absolute error = 3.44092724377748e-17
relative error = 2.4400071087563696955378325096052e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.941
y[1] (analytic) = 1.4110198278287018153702365346646
y[1] (numeric) = 1.4110198278287018498081715317053
absolute error = 3.44379349970407e-17
relative error = 2.4406414649774485325536923363528e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.942
y[1] (analytic) = 1.4118282696686249503202692954725
y[1] (numeric) = 1.4118282696686249847868275755421
absolute error = 3.44665582800696e-17
relative error = 2.4412712948551004695594524560659e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.943
y[1] (analytic) = 1.4126372996802294023361245984231
y[1] (numeric) = 1.4126372996802294368312668566613
absolute error = 3.44951422582382e-17
relative error = 2.4418966047439542596902703721936e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.944
y[1] (analytic) = 1.41344691705448522723251581406
y[1] (numeric) = 1.4134469170544852617562027170224
absolute error = 3.45236869029624e-17
relative error = 2.4425174010006057301316452960270e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.945
y[1] (analytic) = 1.4142571209817751182217303183736
y[1] (numeric) = 1.4142571209817751527739225040712
absolute error = 3.45521921856976e-17
relative error = 2.4431336899835810143808061723843e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.946
y[1] (analytic) = 1.4150679106518952155308688124071
y[1] (numeric) = 1.4150679106518952501115268903458
absolute error = 3.45806580779387e-17
relative error = 2.4437454780532787397333261657720e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.947
y[1] (analytic) = 1.4158792852540559166056375781701
y[1] (numeric) = 1.4158792852540559512147221293897
absolute error = 3.46090845512196e-17
relative error = 2.4443527715718771294198121581231e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.948
y[1] (analytic) = 1.4166912439768826868998834671338
y[1] (numeric) = 1.4166912439768827215373550442478
absolute error = 3.46374715771140e-17
relative error = 2.4449555769033332174580380198233e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.949
y[1] (analytic) = 1.4175037860084168712500608318425
y[1] (numeric) = 1.4175037860084169059158799590772
absolute error = 3.46658191272347e-17
relative error = 2.4455539004132762772635990435611e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.95
y[1] (analytic) = 1.4183169105361165058338190262395
y[1] (numeric) = 1.4183169105361165405279461994738
absolute error = 3.46941271732343e-17
relative error = 2.4461477484690003564418729904266e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.951
y[1] (analytic) = 1.4191306167468571307118985161905
y[1] (numeric) = 1.4191306167468571654342942029951
absolute error = 3.47223956868046e-17
relative error = 2.4467371274393652637498752120233e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.952
y[1] (analytic) = 1.419944903826932602952523058373
y[1] (numeric) = 1.4199449038269326377031476980502
absolute error = 3.47506246396772e-17
relative error = 2.4473220436947824391355170672407e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.953
y[1] (analytic) = 1.4207597709620559103374748232099
y[1] (numeric) = 1.4207597709620559451162888268331
absolute error = 3.47788140036232e-17
relative error = 2.4479025036071375588533531806593e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.954
y[1] (analytic) = 1.4215752173373599856490387558386
y[1] (numeric) = 1.4215752173373600204560025062918
absolute error = 3.48069637504532e-17
relative error = 2.4484785135497345433863748973596e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.955
y[1] (analytic) = 1.4223912421373985215370018882395
y[1] (numeric) = 1.4223912421373985563720757402568
absolute error = 3.48350738520173e-17
relative error = 2.4490500798972397918153400042689e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.956
y[1] (analytic) = 1.4232078445461467859648927355918
y[1] (numeric) = 1.4232078445461468208280370157974
absolute error = 3.48631442802056e-17
relative error = 2.4496172090256617742800636148757e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.957
y[1] (analytic) = 1.4240250237470024382346453306867
y[1] (numeric) = 1.4240250237470024731258203376343
absolute error = 3.48911750069476e-17
relative error = 2.4501799073122534835711305797083e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.958
y[1] (analytic) = 1.4248427789227863455888718718004
y[1] (numeric) = 1.4248427789227863805080378760131
absolute error = 3.49191660042127e-17
relative error = 2.4507381811354924591089587456686e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.959
y[1] (analytic) = 1.4256611092557434003899273818234
y[1] (numeric) = 1.425661109255743435337044625833
absolute error = 3.49471172440096e-17
relative error = 2.4512920368749837582480061835633e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.96
y[1] (analytic) = 1.4264800139275433378749491996481
y[1] (numeric) = 1.4264800139275433728499778980355
absolute error = 3.49750286983874e-17
relative error = 2.4518414809114824722434474128806e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.961
y[1] (analytic) = 1.4272994921192815544860535488458
y[1] (numeric) = 1.4272994921192815894889538882802
absolute error = 3.50029003394344e-17
relative error = 2.4523865196267550578924174280523e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.962
y[1] (analytic) = 1.4281195430114799267748708535018
y[1] (numeric) = 1.4281195430114799618056029927809
absolute error = 3.50307321392791e-17
relative error = 2.4529271594035952323817157938112e-15 %
Correct digits = 16
memory used=80.1MB, alloc=4.3MB, time=10.19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.963
y[1] (analytic) = 1.4289401657840876308806008967442
y[1] (numeric) = 1.4289401657840876659391249668338
absolute error = 3.50585240700896e-17
relative error = 2.4534634066257278799680073752894e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.964
y[1] (analytic) = 1.4297613596164819625807683439772
y[1] (numeric) = 1.4297613596164819976670444480512
absolute error = 3.50862761040740e-17
relative error = 2.4539952676777832692973780518821e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.965
y[1] (analytic) = 1.4305831236874691579138585801337
y[1] (numeric) = 1.4305831236874691930278467936141
absolute error = 3.51139882134804e-17
relative error = 2.4545227489452434374218492584991e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.966
y[1] (analytic) = 1.4314054571752852143730132383785
y[1] (numeric) = 1.4314054571752852495146736089751
absolute error = 3.51416603705966e-17
relative error = 2.4550458568143678389600519523904e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.967
y[1] (analytic) = 1.4322283592575967126699642266353
y[1] (numeric) = 1.4322283592575967478392567743857
absolute error = 3.51692925477504e-17
relative error = 2.4555645976721611835441306106358e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.968
y[1] (analytic) = 1.4330518291115016390683844880724
y[1] (numeric) = 1.433051829111501674265269205382
absolute error = 3.51968847173096e-17
relative error = 2.4560789779063204896004098211725e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.969
y[1] (analytic) = 1.4338758659135302082858331622636
y[1] (numeric) = 1.4338758659135302435102700139458
absolute error = 3.52244368516822e-17
relative error = 2.4565890039051963090192599065559e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.97
y[1] (analytic) = 1.4347004688396456869634722451501
y[1] (numeric) = 1.434700468839645722215421168466
absolute error = 3.52519489233159e-17
relative error = 2.4570946820577053354312864015720e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.971
y[1] (analytic) = 1.4355256370652452177027312781524
y[1] (numeric) = 1.435525637065245252982152182851
absolute error = 3.52794209046986e-17
relative error = 2.4575960187533130157055317232071e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.972
y[1] (analytic) = 1.4363513697651606436680960298383
y[1] (numeric) = 1.4363513697651606789749487981968
absolute error = 3.53068527683585e-17
relative error = 2.4580930203819884146526430129614e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.973
y[1] (analytic) = 1.4371776661136593337551965674268
y[1] (numeric) = 1.4371776661136593690894410542904
absolute error = 3.53342444868636e-17
relative error = 2.4585856933341175287339778206725e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.974
y[1] (analytic) = 1.4380045252844450083233695501071
y[1] (numeric) = 1.4380045252844450436849655829294
absolute error = 3.53615960328223e-17
relative error = 2.4590740440004934359205146627248e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.975
y[1] (analytic) = 1.4388319464506585654918690116816
y[1] (numeric) = 1.4388319464506586008807763905646
absolute error = 3.53889073788830e-17
relative error = 2.4595580787722370215406423153281e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.976
y[1] (analytic) = 1.4396599287848789079988993363884
y[1] (numeric) = 1.4396599287848789434150778341228
absolute error = 3.54161784977344e-17
relative error = 2.4600378040407666432794347830414e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.977
y[1] (analytic) = 1.4404884714591237706226435689417
y[1] (numeric) = 1.4404884714591238060660529310469
absolute error = 3.54434093621052e-17
relative error = 2.4605132261977262919178298670594e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.978
y[1] (analytic) = 1.4413175736448505481634596378282
y[1] (numeric) = 1.4413175736448505836340595825929
absolute error = 3.54705999447647e-17
relative error = 2.4609843516349764867721411634511e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.979
y[1] (analytic) = 1.4421472345129571239864165097351
y[1] (numeric) = 1.4421472345129571594841667282574
absolute error = 3.54977502185223e-17
relative error = 2.4614511867445089718312248645549e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.98
y[1] (analytic) = 1.4429774532337826991233417326401
y[1] (numeric) = 1.4429774532337827346482018888678
absolute error = 3.55248601562277e-17
relative error = 2.4619137379184102617718439854017e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.981
y[1] (analytic) = 1.4438082289771086219335512655861
y[1] (numeric) = 1.4438082289771086574854809963571
absolute error = 3.55519297307710e-17
relative error = 2.4623720115488184329060267961838e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.982
y[1] (analytic) = 1.4446395609121592183224319344801
y[1] (numeric) = 1.4446395609121592539013908495628
absolute error = 3.55789589150827e-17
relative error = 2.4628260140278731867069903636166e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.983
y[1] (analytic) = 1.4454714482076026225170462954026
y[1] (numeric) = 1.445471448207602658122993977536
absolute error = 3.56059476821334e-17
relative error = 2.4632757517476453771880661425375e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.984
y[1] (analytic) = 1.4463038900315516083979291298914
y[1] (numeric) = 1.4463038900315516440308251348259
absolute error = 3.56328960049345e-17
relative error = 2.4637212311001359697059686780974e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.985
y[1] (analytic) = 1.4471368855515644213862442404742
y[1] (numeric) = 1.4471368855515644570460480970119
absolute error = 3.56598038565377e-17
relative error = 2.4641624584771921278119605286255e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.986
y[1] (analytic) = 1.4479704339346456108854696593607
y[1] (numeric) = 1.4479704339346456465721408693957
absolute error = 3.56866712100350e-17
relative error = 2.4645994402704581679537865493117e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.987
y[1] (analytic) = 1.4488045343472468632767788286789
y[1] (numeric) = 1.4488045343472468989902768672382
absolute error = 3.57134980385593e-17
relative error = 2.4650321828713681445599385175947e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.988
y[1] (analytic) = 1.4496391859552678354672847569453
y[1] (numeric) = 1.4496391859552678712075690722288
absolute error = 3.57402843152835e-17
relative error = 2.4654606926710350346127459259756e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.989
y[1] (analytic) = 1.4504743879240569889903136035916
y[1] (numeric) = 1.4504743879240570247573436170131
absolute error = 3.57670300134215e-17
relative error = 2.4658849760602713447468094574675e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.99
y[1] (analytic) = 1.4513101394184124246568735913464
y[1] (numeric) = 1.4513101394184124604506086975738
absolute error = 3.57937351062274e-17
relative error = 2.4663050394294856700569378955551e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.991
y[1] (analytic) = 1.4521464396025827177574845950707
y[1] (numeric) = 1.452146439602582753577884162067
absolute error = 3.58203995669963e-17
relative error = 2.4667208891686898408291809545927e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.992
y[1] (analytic) = 1.4529832876402677538135332052885
y[1] (numeric) = 1.4529832876402677896605565743523
absolute error = 3.58470233690638e-17
relative error = 2.4671325316674166229339481584555e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.993
y[1] (analytic) = 1.4538206826946195648773175151265
y[1] (numeric) = 1.4538206826946196007509240009325
absolute error = 3.58736064858060e-17
relative error = 2.4675399733146721442904708673461e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.994
y[1] (analytic) = 1.4546586239282431663799453306873
y[1] (numeric) = 1.454658623928243202280094221327
absolute error = 3.59001488906397e-17
relative error = 2.4679432204989022847583802764433e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.995
y[1] (analytic) = 1.4554971105031973945262489570286
y[1] (numeric) = 1.4554971105031974304528995140512
absolute error = 3.59266505570226e-17
relative error = 2.4683422796079592326379081729988e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.996
y[1] (analytic) = 1.4563361415809957442358791649033
y[1] (numeric) = 1.4563361415809957801889906233562
absolute error = 3.59531114584529e-17
relative error = 2.4687371570290270082153732424608e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.997
y[1] (analytic) = 1.4571757163226072076297403972349
y[1] (numeric) = 1.4571757163226072436092719657049
absolute error = 3.59795315684700e-17
relative error = 2.4691278591486227842677443073906e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.998
y[1] (analytic) = 1.4580158338884571130609287289657
y[1] (numeric) = 1.4580158338884571490668395896192
absolute error = 3.60059108606535e-17
relative error = 2.4695143923524816566982373063269e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.999
y[1] (analytic) = 1.4588564934384279646893335494061
y[1] (numeric) = 1.4588564934384280007215828580304
absolute error = 3.60322493086243e-17
relative error = 2.4698967630255858135279377541521e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1
y[1] (analytic) = 1.459697694131860282599063392557
y[1] (numeric) = 1.4596976941318603186576102786008
absolute error = 3.60585468860438e-17
relative error = 2.4702749775520634914167302436931e-15 %
Correct digits = 16
h = 0.001
Finished!
diff ( y , x , 1 ) = sin(x);
Iterations = 900
Total Elapsed Time = 10 Seconds
Elapsed Time(since restart) = 10 Seconds
Time to Timeout = 2 Minutes 49 Seconds
Percent Done = 100.1 %
> quit
memory used=83.5MB, alloc=4.3MB, time=10.62