|\^/| 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_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 1 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > if (min_size < 1.0) then # if number 1 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 4 > # Begin Function number 5 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms; > max_value3 := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > value3 := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (value3 > max_value3) then # if number 1 > max_value3 := value3; > omniout_float(ALWAYS,"value3",32,value3,32,""); > fi;# end if 1; > omniout_float(ALWAYS,"max_value3",32,max_value3,32,""); > max_value3; > end; test_suggested_h := proc() local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; max_value3 := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); value3 := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_value3 < value3 then max_value3 := value3; omniout_float(ALWAYS, "value3", 32, value3, 32, "") end if; omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""); max_value3 end proc > # End Function number 5 > # Begin Function number 6 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1 > ret := true; > else > ret := false; > fi;# end if 1; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 6 > # Begin Function number 7 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 1 > if (iter >= 0) then # if number 2 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 3 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr <> 0.0) 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_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 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_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 2 > fi;# end if 1; > if ( not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 8 > # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 1; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 9 > # Begin Function number 10 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) < glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2; > if (m > 10) then # if number 1 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (omniabs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1; > n := n - 1; > od;# end do number 2; > m := n + cnt; > if (m <= 10) then # if number 1 > 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_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) < glob_small_float or omniabs(array_y_higher[1, m - 1]) < glob_small_float or omniabs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then 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_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 2 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 3; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 2; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 11 > # Begin Function number 12 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre sin 1 $eq_no = 1 > array_tmp1[1] := sin(array_x[1]); > array_tmp1_g[1] := cos(array_x[1]); > #emit pre cos 1 $eq_no = 1 > array_tmp2[1] := cos(array_x[1]); > array_tmp2_g[1] := sin(array_x[1]); > #emit pre div FULL - FULL $eq_no = 1 i = 1 > array_tmp3[1] := (array_tmp1[1] / (array_tmp2[1])); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h; > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp1[2] := array_tmp1_g[1] * array_x[2] / 1; > array_tmp1_g[2] := -array_tmp1[1] * array_x[2] / 1; > #emit pre cos ID_LINEAR iii = 2 $eq_no = 1 > array_tmp2[2] := -array_tmp2_g[1] * array_x[2] / 1; > array_tmp2_g[2] := array_tmp2[1] * array_x[2] / 1; > #emit pre div FULL - FULL $eq_no = 1 i = 2 > array_tmp3[2] := ((array_tmp1[2] - ats(2,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp3[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h; > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sin ID_LINEAR iii = 3 $eq_no = 1 > array_tmp1[3] := array_tmp1_g[2] * array_x[2] / 2; > array_tmp1_g[3] := -array_tmp1[2] * array_x[2] / 2; > #emit pre cos ID_LINEAR iii = 3 $eq_no = 1 > array_tmp2[3] := -array_tmp2_g[2] * array_x[2] / 2; > array_tmp2_g[3] := array_tmp2[2] * array_x[2] / 2; > #emit pre div FULL - FULL $eq_no = 1 i = 3 > array_tmp3[3] := ((array_tmp1[3] - ats(3,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp4[3] := array_tmp3[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (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 cos ID_LINEAR iii = 4 $eq_no = 1 > array_tmp2[4] := -array_tmp2_g[3] * array_x[2] / 3; > array_tmp2_g[4] := array_tmp2[3] * array_x[2] / 3; > #emit pre div FULL - FULL $eq_no = 1 i = 4 > array_tmp3[4] := ((array_tmp1[4] - ats(4,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp4[4] := array_tmp3[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (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 cos ID_LINEAR iii = 5 $eq_no = 1 > array_tmp2[5] := -array_tmp2_g[4] * array_x[2] / 4; > array_tmp2_g[5] := array_tmp2[4] * array_x[2] / 4; > #emit pre div FULL - FULL $eq_no = 1 i = 5 > array_tmp3[5] := ((array_tmp1[5] - ats(5,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp4[5] := array_tmp3[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (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 cos LINEAR $eq_no = 1 > array_tmp2[kkk] := -array_tmp2_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp2_g[kkk] := array_tmp2[kkk - 1] * array_x[2] / (kkk - 1); > #emit div FULL FULL $eq_no = 1 > array_tmp3[kkk] := ((array_tmp1[kkk] - ats(kkk,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp4[kkk] := array_tmp3[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp4[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 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_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; array_tmp1[1] := sin(array_x[1]); array_tmp1_g[1] := cos(array_x[1]); array_tmp2[1] := cos(array_x[1]); array_tmp2_g[1] := sin(array_x[1]); array_tmp3[1] := array_tmp1[1]/array_tmp2[1]; array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_tmp1_g[1]*array_x[2]; array_tmp1_g[2] := -array_tmp1[1]*array_x[2]; array_tmp2[2] := -array_tmp2_g[1]*array_x[2]; array_tmp2_g[2] := array_tmp2[1]*array_x[2]; array_tmp3[2] := (array_tmp1[2] - ats(2, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[2] := array_tmp3[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := 1/2*array_tmp1_g[2]*array_x[2]; array_tmp1_g[3] := -1/2*array_tmp1[2]*array_x[2]; array_tmp2[3] := -1/2*array_tmp2_g[2]*array_x[2]; array_tmp2_g[3] := 1/2*array_tmp2[2]*array_x[2]; array_tmp3[3] := (array_tmp1[3] - ats(3, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[3] := array_tmp3[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*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] := -1/3*array_tmp2_g[3]*array_x[2]; array_tmp2_g[4] := 1/3*array_tmp2[3]*array_x[2]; array_tmp3[4] := (array_tmp1[4] - ats(4, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[4] := array_tmp3[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*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] := -1/4*array_tmp2_g[4]*array_x[2]; array_tmp2_g[5] := 1/4*array_tmp2[4]*array_x[2]; array_tmp3[5] := (array_tmp1[5] - ats(5, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[5] := array_tmp3[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*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_tmp2_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp2_g[kkk] := array_tmp2[kkk - 1]*array_x[2]/(kkk - 1); array_tmp3[kkk] := ( array_tmp1[kkk] - ats(kkk, array_tmp2, array_tmp3, 2))/ array_tmp2[1]; array_tmp4[kkk] := array_tmp3[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp4[kkk]*expt(glob_h, order_d)/ factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 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 > exact_soln_y := proc(x) > return(2.0 - ln(abs(cos(x)))); > end; exact_soln_y := proc(x) return 2.0 - ln(abs(cos(x))) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h; > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_value3 := 0.0; > glob_ratio_of_radius := 0.01; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_log10normmin := 0.1; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_hmax := 1.0; > glob_hmin := 0.00000000001; > glob_hmin_init := 0.001; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_log10_abserr := 0.1e-10; > glob_log10_relerr := 0.1e-10; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.1e-50; > glob_smallish_float := 0.1e-100; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_log10abserr := 0.0; > glob_log10relerr := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/divpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := -5.0;"); > omniout_str(ALWAYS,"x_end := 5.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.05 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10000000;"); > omniout_str(ALWAYS,"glob_display_interval := 0.1;"); > omniout_str(ALWAYS,"glob_max_minutes := 10;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.001;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(2.0 - ln(abs(cos(x))));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1_g:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2_g:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2_g[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp1_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp2_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2_g[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3; > iiif := iiif + 1; > od;# end do number 2; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := -5.0; > x_end := 5.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.05 ; > glob_look_poles := true; > glob_max_iter := 10000000; > glob_display_interval := 0.1; > glob_max_minutes := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.001; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := expt(10.0 , (glob_log10_abserr)); > glob_relerr := expt(10.0 , (glob_log10_relerr)); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > if (glob_display_interval < glob_h) then # if number 2 > glob_h := glob_display_interval; > fi;# end if 2; > found_h := -1.0; > best_h := 0.0; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 3 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 3; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 3 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 4 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 4; > r_order := r_order + 1; > od;# end do number 3 > ; > atomall(); > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > value3 := test_suggested_h(); > omniout_float(ALWAYS,"value3",32,value3,32,""); > if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2 > best_h := glob_h; > found_h := 1.0; > fi;# end if 2; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > glob_h := glob_h * 0.5; > od;# end do number 2; > if (found_h > 0.0) then # if number 2 > glob_h := best_h ; > else > omniout_str(ALWAYS,"No increment to obtain desired accuracy found"); > fi;# end if 2; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2; > #BEGIN SOLUTION CODE > if (found_h > 0.0) then # if number 2 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_log10normmin := -glob_large_float ; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_y_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > if (reached_interval()) then # if number 3 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 3; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > 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 ) / cos ( x ) ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 3 > logstart(html_log_file); > logitem_str(html_log_file,"2012-12-14T21:36:31-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"div") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 4 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 4; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 4 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 4; > log_revs(html_log_file," 151 ") > ; > logitem_str(html_log_file,"div diffeq.mxt") > ; > logitem_str(html_log_file,"div 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_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_value3 := 0.; glob_ratio_of_radius := 0.01; glob_percent_done := 0.; glob_subiter_method := 3; glob_log10normmin := 0.1; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_hmax := 1.0; glob_hmin := 0.1*10^(-10); glob_hmin_init := 0.001; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_log10_abserr := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.1*10^(-50); glob_smallish_float := 0.1*10^(-100); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_log10abserr := 0.; glob_log10relerr := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/divpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := -5.0;"); omniout_str(ALWAYS, "x_end := 5.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.05 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10000000;"); omniout_str(ALWAYS, "glob_display_interval := 0.1;"); omniout_str(ALWAYS, "glob_max_minutes := 10;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.001;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(2.0 - ln(abs(cos(x))));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1_g := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2_g := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2_g[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := -5.0; x_end := 5.0; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.05; glob_look_poles := true; glob_max_iter := 10000000; glob_display_interval := 0.1; glob_max_minutes := 10; glob_desired_digits_correct := 10; glob_display_interval := 0.001; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := expt(10.0, glob_log10_abserr); glob_relerr := expt(10.0, glob_log10_relerr); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); if glob_display_interval < glob_h then glob_h := glob_display_interval end if; found_h := -1.0; best_h := 0.; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; while opt_iter <= 20 and found_h < 0. do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer) ; omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); value3 := test_suggested_h(); omniout_float(ALWAYS, "value3", 32, value3, 32, ""); if value3 < est_needed_step_err and found_h < 0. then best_h := glob_h; found_h := 1.0 end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1; glob_h := glob_h*0.5 end do; if 0. < found_h then glob_h := best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found") end if; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; if 0. < found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_log10normmin := -glob_large_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); 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 ) / cos ( x ) ;") ; omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-12-14T21:36:31-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "div"); logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 151 "); logitem_str(html_log_file, "div diffeq.mxt"); logitem_str(html_log_file, "div 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/divpostode.ode################# diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -5.0; x_end := 5.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.05 ; glob_look_poles := true; glob_max_iter := 10000000; glob_display_interval := 0.1; glob_max_minutes := 10; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.001; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(2.0 - ln(abs(cos(x)))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 10 estimated_steps = 10000 step_error = 1.0000000000000000000000000000000e-14 est_needed_step_err = 1.0000000000000000000000000000000e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 3.0677116042050893868093673224158e-63 max_value3 = 3.0677116042050893868093673224158e-63 value3 = 3.0677116042050893868093673224158e-63 best_h = 0.001 START of Soultion x[1] = -5 y[1] (analytic) = 3.259971236628587709130758159876 y[1] (numeric) = 3.259971236628587709130758159876 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2881 Order of pole = 2.082 x[1] = -4.999 y[1] (analytic) = 3.2633579796165452273496192122587 y[1] (numeric) = 3.2633579796165555755010007360666 absolute error = 1.03481513815238079e-14 relative error = 3.1710132465270475976155012333618e-13 % Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2871 Order of pole = 2.082 x[1] = -4.998 y[1] (analytic) = 3.2667572350261429930154543198646 y[1] (numeric) = 3.2667572350261639079988415279477 absolute error = 2.09149833872080831e-14 relative error = 6.4023684291436813874155333406339e-13 % Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2861 Order of pole = 2.082 x[1] = -4.997 y[1] (analytic) = 3.2701690882135694479210400994238 y[1] (numeric) = 3.2701690882136011538275334890504 absolute error = 3.17059064933896266e-14 relative error = 9.6954945258533876725312699028381e-13 % Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.285 Order of pole = 2.082 x[1] = -4.996 y[1] (analytic) = 3.2735936254368717460848438747144 y[1] (numeric) = 3.2735936254369144725695484939883 absolute error = 4.27264847046192739e-14 relative error = 1.3051859697129415433921084429803e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.284 Order of pole = 2.082 x[1] = -4.995 y[1] (analytic) = 3.2770309338686958293469015044044 y[1] (numeric) = 3.2770309338687498117873736865034 absolute error = 5.39824404721820990e-14 relative error = 1.6472972505161304343360678005742e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.8MB, time=0.36 Real estimate of pole used Radius of convergence = 0.283 Order of pole = 2.082 x[1] = -4.994 y[1] (analytic) = 3.2804811016092523049999538571674 y[1] (numeric) = 3.2804811016093177846597421800323 absolute error = 6.54796597883228649e-14 relative error = 1.9960383175565794988435826002571e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.282 Order of pole = 2.082 x[1] = -4.993 y[1] (analytic) = 3.2839442176995129449759701733792 y[1] (numeric) = 3.2839442176995901691734332792453 absolute error = 7.72241974631058661e-14 relative error = 2.3515684903199541802763797196982e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.281 Order of pole = 2.082 x[1] = -4.992 y[1] (analytic) = 3.2874203721346427465494558934324 y[1] (numeric) = 3.2874203721347319688320470309145 absolute error = 8.92222825911374821e-14 relative error = 2.7140515203780336185796365785140e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.28 Order of pole = 2.082 x[1] = -4.991 y[1] (analytic) = 3.2909096558776726184123840235942 y[1] (numeric) = 3.2909096558777740987365997165684 absolute error = 1.014803242156929742e-13 relative error = 3.0836557313096026697272387134140e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.279 Order of pole = 2.082 x[1] = -4.99 y[1] (analytic) = 3.2944121608734178834329202908972 y[1] (numeric) = 3.2944121608735318883501184079311 absolute error = 1.140049171981170339e-13 relative error = 3.4605541635656157537232803443863e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.278 Order of pole = 2.082 x[1] = -4.989 y[1] (analytic) = 3.2979279800626479205470823039834 y[1] (numeric) = 3.2979279800627747233953830150504 absolute error = 1.268028483007110670e-13 relative error = 3.8449247244720699332408591420123e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.277 Order of pole = 2.082 x[1] = -4.988 y[1] (analytic) = 3.3014572073965124031690229533277 y[1] (numeric) = 3.3014572073966522842715146333101 absolute error = 1.398811024916799824e-13 relative error = 4.2369503435723299614957929038167e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.276 Order of pole = 2.082 x[1] = -4.987 y[1] (analytic) = 3.3049999378512297303660594104908 y[1] (numeric) = 3.3049999378513829772355404986574 absolute error = 1.532468694810881666e-13 relative error = 4.6368191335193415343227420089939e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.275 Order of pole = 2.082 x[1] = -4.986 y[1] (analytic) = 3.3085562674430433899577171325453 y[1] (numeric) = 3.3085562674432102975082143018109 absolute error = 1.669075504971692656e-13 relative error = 5.0447245567372708946527877149332e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.274 Order of pole = 2.082 x[1] = -4.985 y[1] (analytic) = 3.3121262932434521397974764541921 y[1] (numeric) = 3.312126293243633010562789202471 absolute error = 1.808707653127482789e-13 relative error = 5.4608655980816394778097910044044e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.273 Order of pole = 2.082 x[1] = -4.984 y[1] (analytic) = 3.3157101133947200449200589667937 y[1] (numeric) = 3.3157101133949151892795909350806 absolute error = 1.951443595319682869e-13 relative error = 5.8854469437370035876817033990415e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.8MB, time=0.76 Real estimate of pole used Radius of convergence = 0.272 Order of pole = 2.082 x[1] = -4.983 y[1] (analytic) = 3.3193078271256725641295404948193 y[1] (numeric) = 3.3193078271258823005416884637446 absolute error = 2.097364121479689253e-13 relative error = 6.3186791666016843689445674098939e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.271 Order of pole = 2.082 x[1] = -4.982 y[1] (analytic) = 3.3229195347677850401132108741722 y[1] (numeric) = 3.3229195347680096953565935147449 absolute error = 2.246552433826405727e-13 relative error = 6.7607789184200066028214406958351e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.27 Order of pole = 2.082 x[1] = -4.981 y[1] (analytic) = 3.3265453377715701124473342004681 y[1] (numeric) = 3.3265453377718100218701542787596 absolute error = 2.399094228200782915e-13 relative error = 7.2119691289339819144096350819104e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.269 Order of pole = 2.082 x[1] = -4.98 y[1] (analytic) = 3.3301853387232707430739725234632 y[1] (numeric) = 3.3301853387235262508518184075586 absolute error = 2.555077778458840954e-13 relative error = 7.6724792123384004277519276335943e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.268 Order of pole = 2.082 x[1] = -4.979 y[1] (analytic) = 3.3338396413618657191389935663622 y[1] (numeric) = 3.3338396413621371785413985827275 absolute error = 2.714594024050163653e-13 relative error = 8.1425452813359023005712604476081e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.267 Order of pole = 2.082 x[1] = -4.978 y[1] (analytic) = 3.3375083505963946786627059531727 y[1] (numeric) = 3.3375083505966824523287974157833 absolute error = 2.877736660914626106e-13 relative error = 8.6224103691018185463480674427480e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.266 Order of pole = 2.082 x[1] = -4.977 y[1] (analytic) = 3.3411915725236098905451743019884 y[1] (numeric) = 3.341191572523914350768757919665 absolute error = 3.044602235836176766e-13 relative error = 9.1123246594824298037695134703849e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.265 Order of pole = 2.082 x[1] = -4.976 y[1] (analytic) = 3.3448894144459622120738565919867 y[1] (numeric) = 3.3448894144462837410982964774677 absolute error = 3.215290244398854810e-13 relative error = 9.6125457257648267185663144967489e-12 % Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.264 Order of pole = 2.082 x[1] = -4.975 y[1] (analytic) = 3.3486019848899288445945304085993 y[1] (numeric) = 3.3486019848902678349178000986301 absolute error = 3.389903232696900308e-13 relative error = 1.0123338778371801829979617384995e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.263 Order of pole = 2.082 x[1] = -4.974 y[1] (analytic) = 3.3523293936246907115276399501667 y[1] (numeric) = 3.3523293936250475662179357326959 absolute error = 3.568546902957825292e-13 relative error = 1.0644976921851197905984970925957e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.262 Order of pole = 2.082 x[1] = -4.973 y[1] (analytic) = 3.3560717516811674926689727494922 y[1] (numeric) = 3.3560717516815426256912972171254 absolute error = 3.751330223244676332e-13 relative error = 1.1177741421545921299399371993276e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.261 Order of pole = 2.082 x[1] = -4.972 y[1] (analytic) = 3.3598291713714185649217225106776 y[1] (numeric) = 3.3598291713718124014758636559697 absolute error = 3.938365541411452921e-13 relative error = 1.1721921980348443664945662047363e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=3.9MB, time=1.18 Real estimate of pole used Radius of convergence = 0.26 Order of pole = 2.082 x[1] = -4.971 y[1] (analytic) = 3.3636017663084183224905978606674 y[1] (numeric) = 3.3636017663088312993609472377496 absolute error = 4.129768703493770822e-13 relative error = 1.2277817025962105077871536100773e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.259 Order of pole = 2.082 x[1] = -4.97 y[1] (analytic) = 3.3673896514262145793604636100166 y[1] (numeric) = 3.3673896514266471452781361497354 absolute error = 4.325659176725397188e-13 relative error = 1.2845734009110944067200370794235e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.258 Order of pole = 2.082 x[1] = -4.969 y[1] (analytic) = 3.3711929430004789938238720638399 y[1] (numeric) = 3.3711929430009316098416100895623 absolute error = 4.526160177380257224e-13 relative error = 1.3425989713160164643192309393483e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.257 Order of pole = 2.082 x[1] = -4.968 y[1] (analytic) = 3.3750117586694586991650199349669 y[1] (numeric) = 3.375011758669931839045384829417 absolute error = 4.731398803648944501e-13 relative error = 1.4018910575630760031363271645682e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.256 Order of pole = 2.082 x[1] = -4.967 y[1] (analytic) = 3.3788462174553385766132636959101 y[1] (numeric) = 3.3788462174558327272306405643259 absolute error = 4.941506173768684158e-13 relative error = 1.4624833022114303264990475738742e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.255 Order of pole = 2.082 x[1] = -4.966 y[1] (analytic) = 3.3826964397860238666187306332596 y[1] (numeric) = 3.3826964397865395283756942459675 absolute error = 5.156617569636127079e-13 relative error = 1.5244103813117545120541042928079e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.254 Order of pole = 2.082 x[1] = -4.965 y[1] (analytic) = 3.3865625475173530826578845451794 y[1] (numeric) = 3.386562547517890769916498877406 absolute error = 5.376872586143322266e-13 relative error = 1.5877080404391292693635601282861e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.253 Order of pole = 2.082 x[1] = -4.964 y[1] (analytic) = 3.3904446639557514684414441314646 y[1] (numeric) = 3.3904446639563117099700930068932 absolute error = 5.602415286488754286e-13 relative error = 1.6524131321324143400397739935589e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.252 Order of pole = 2.082 x[1] = -4.963 y[1] (analytic) = 3.3943429138813355248757891142837 y[1] (numeric) = 3.3943429138819188643121618617825 absolute error = 5.833394363727474988e-13 relative error = 1.7185636548009089697012549410719e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.251 Order of pole = 2.082 x[1] = -4.962 y[1] (analytic) = 3.3982574235714794277390984225665 y[1] (numeric) = 3.3982574235720864240699821363279 absolute error = 6.069963308837137614e-13 relative error = 1.7861987931619863483942781379519e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.25 Order of pole = 2.082 x[1] = -4.961 y[1] (analytic) = 3.4021883208248544611048532366317 y[1] (numeric) = 3.4021883208254856891634122559441 absolute error = 6.312280585590193124e-13 relative error = 1.8553589602764235016435333272338e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.249 Order of pole = 2.082 memory used=15.2MB, alloc=3.9MB, time=1.60 x[1] = -4.96 y[1] (analytic) = 3.4061357349859529054212091224762 y[1] (numeric) = 3.4061357349866089564024627896099 absolute error = 6.560509812536671337e-13 relative error = 1.9260858412513402807709680333083e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.248 Order of pole = 2.082 x[1] = -4.959 y[1] (analytic) = 3.4100997969701081431921885401137 y[1] (numeric) = 3.4100997969707896251874302284995 absolute error = 6.814819952416883858e-13 relative error = 1.9984224386840196675272433656187e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.247 Order of pole = 2.082 x[1] = -4.958 y[1] (analytic) = 3.4140806392890230797772699690244 y[1] (numeric) = 3.414080639289730618328203878532 absolute error = 7.075385509339095076e-13 relative error = 2.0724131199234160366617261881720e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.246 Order of pole = 2.082 x[1] = -4.957 y[1] (analytic) = 3.4180783960768193223165158346681 y[1] (numeric) = 3.4180783960775535609899232104041 absolute error = 7.342386734073757360e-13 relative error = 2.1481036662298782137396586601309e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.245 Order of pole = 2.082 x[1] = -4.956 y[1] (analytic) = 3.4220932031166199166014953974361 y[1] (numeric) = 3.4220932031173815175852787320139 absolute error = 7.616009837833345778e-13 relative error = 2.2255413239175307565144525109849e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.244 Order of pole = 2.082 x[1] = -4.955 y[1] (analytic) = 3.4261251978676788102670887108869 y[1] (numeric) = 3.4261251978684684549885812316607 absolute error = 7.896447214925207738e-13 relative error = 2.3047748575678810582741241617105e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.243 Order of pole = 2.082 x[1] = -4.954 y[1] (analytic) = 3.4301745194930705914122849128146 y[1] (numeric) = 3.4301745194938889811797533347086 absolute error = 8.183897674684218940e-13 relative error = 2.3858546054075635790378189128618e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.242 Order of pole = 2.082 x[1] = -4.953 y[1] (analytic) = 3.434241308887954445123896919125 y[1] (numeric) = 3.4342413088888023017922081658402 absolute error = 8.478566683112467152e-13 relative error = 2.4688325369477083718517705493417e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.241 Order of pole = 2.082 x[1] = -4.952 y[1] (analytic) = 3.4383257087084266768492220405603 y[1] (numeric) = 3.4383257087093047435106895137334 absolute error = 8.780666614674731731e-13 relative error = 2.5537623129872425635098281613366e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.24 Order of pole = 2.082 x[1] = -4.951 y[1] (analytic) = 3.4424278634009765716354046686103 y[1] (numeric) = 3.4424278634018856133368767941478 absolute error = 9.090417014721255375e-13 relative error = 2.6406993480875148272305336620192e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.239 Order of pole = 2.082 x[1] = -4.95 y[1] (analytic) = 3.4465479192325607924386419292941 y[1] (numeric) = 3.4465479192335015969259452578382 absolute error = 9.408044873033285441e-13 relative error = 2.7297008756309893169492886909210e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.238 Order of pole = 2.082 x[1] = -4.949 y[1] (analytic) = 3.4506860243213119695411346297333 y[1] (numeric) = 3.4506860243222853480320358467405 absolute error = 9.733784909012170072e-13 relative error = 2.8208260155824031903287259808021e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.0MB, time=2.04 Real estimate of pole used Radius of convergence = 0.237 Order of pole = 2.082 x[1] = -4.948 y[1] (analytic) = 3.4548423286678975971562321007678 y[1] (numeric) = 3.4548423286689043851431380516199 absolute error = 1.0067879869059508521e-12 relative error = 2.9141358450767378094617349991731e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.236 Order of pole = 2.082 x[1] = -4.947 y[1] (analytic) = 3.4590169841875458331347100628465 y[1] (numeric) = 3.4590169841885868912183824688688 absolute error = 1.0410580836724060223e-12 relative error = 3.0096934719646362838790542766646e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.235 Order of pole = 2.082 x[1] = -4.946 y[1] (analytic) = 3.4632101447427552939145820216199 y[1] (numeric) = 3.4632101447438315086702041119281 absolute error = 1.0762147556220903082e-12 relative error = 3.1075641114525285321639639570009e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.234 Order of pole = 2.082 x[1] = -4.945 y[1] (analytic) = 3.4674219661767064501163442102562 y[1] (numeric) = 3.4674219661778187349933401896751 absolute error = 1.1122848769959794189e-12 relative error = 3.2078151659817201949368970275841e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.233 Order of pole = 2.082 x[1] = -4.944 y[1] (analytic) = 3.4716526063473927591354337990077 y[1] (numeric) = 3.4716526063485420553925090917717 absolute error = 1.1492962570752927640e-12 relative error = 3.3105163084980854347118391241134e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.232 Order of pole = 2.082 x[1] = -4.943 y[1] (analytic) = 3.475902225162490220412855034866 y[1] (numeric) = 3.4759022251636774980897957761917 absolute error = 1.1872776769407413257e-12 relative error = 3.4157395692717993474388120354202e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.231 Order of pole = 2.082 x[1] = -4.942 y[1] (analytic) = 3.4801709846149846074922520855355 y[1] (numeric) = 3.4801709846162108664200965787901 absolute error = 1.2262589278444932546e-12 relative error = 3.5235594264347782215629158949706e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.23 Order of pole = 2.082 x[1] = -4.941 y[1] (analytic) = 3.4844590488195762192474108992633 y[1] (numeric) = 3.4844590488208424900986839280622 absolute error = 1.2662708512730287989e-12 relative error = 3.6340529004121918015249660083656e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.229 Order of pole = 2.082 x[1] = -4.94 y[1] (analytic) = 3.4887665840498826015713750005312 y[1] (numeric) = 3.4887665840511899469521582085666 absolute error = 1.3073453807832080354e-12 relative error = 3.7472996524335992374516227450040e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.228 Order of pole = 2.082 x[1] = -4.939 y[1] (analytic) = 3.4930937587764603211746638648537 y[1] (numeric) = 3.4930937587778098367603621315388 absolute error = 1.3495155856982666851e-12 relative error = 3.8633820873189696829946553996204e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.227 Order of pole = 2.082 x[1] = -4.938 y[1] (analytic) = 3.4974407437056675257992493507169 y[1] (numeric) = 3.4974407437070603415160044527768 absolute error = 1.3928157167551020599e-12 relative error = 3.9823854607451116160732314761142e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.226 Order of pole = 2.082 x[1] = -4.937 y[1] (analytic) = 3.5018077118193897010086645451231 y[1] (numeric) = 3.5018077118208269822624636740385 absolute error = 1.4372812537991289154e-12 relative error = 4.1043979912088861441092381592044e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.0MB, time=2.46 Real estimate of pole used Radius of convergence = 0.225 Order of pole = 2.082 x[1] = -4.936 y[1] (analytic) = 3.5061948384156517336943677656552 y[1] (numeric) = 3.5061948384171346826499959564155 absolute error = 1.4829489556281907603e-12 relative error = 4.2295109769150552929899379958026e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.224 Order of pole = 2.082 x[1] = -4.935 y[1] (analytic) = 3.5106023011501401175174900779588 y[1] (numeric) = 3.510602301151669974429582602225 absolute error = 1.5298569120925242662e-12 relative error = 4.3578189178287555670229275570925e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.223 Order of pole = 2.082 x[1] = -4.934 y[1] (analytic) = 3.5150302800786598867004032251001 y[1] (numeric) = 3.5150302800802379312989668374084 absolute error = 1.5780445985636123083e-12 relative error = 4.4894196431454314079250593787616e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.222 Order of pole = 2.082 x[1] = -4.933 y[1] (analytic) = 3.5194789577005516429571999202808 y[1] (numeric) = 3.5194789577021791958900908659786 absolute error = 1.6275529328909456978e-12 relative error = 4.6244144444446569939327779385288e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.221 Order of pole = 2.082 x[1] = -4.932 y[1] (analytic) = 3.5239485190030948470175203081626 y[1] (numeric) = 3.5239485190047732713524925752633 absolute error = 1.6784243349722671007e-12 relative error = 4.7629082148086654652734092414354e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2199 Order of pole = 2.082 x[1] = -4.931 y[1] (analytic) = 3.5284391515069243823162487002367 y[1] (numeric) = 3.5284391515086550851053185170179 absolute error = 1.7307027890698167812e-12 relative error = 4.9050095942016427459156879077570e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2189 Order of pole = 2.082 x[1] = -4.93 y[1] (analytic) = 3.5329510453124882652077845351035 y[1] (numeric) = 3.5329510453142726991167969992288 absolute error = 1.7844339090124641253e-12 relative error = 5.0508311214219827373830354575672e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2179 Order of pole = 2.082 x[1] = -4.929 y[1] (analytic) = 3.5374843931475752747891809316696 y[1] (numeric) = 3.5374843931494149397956123502946 absolute error = 1.8396650064314186250e-12 relative error = 5.2004893929567995690648915801904e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2169 Order of pole = 2.082 x[1] = -4.928 y[1] (analytic) = 3.5420393904159422074115915199626 y[1] (numeric) = 3.542039390417838652573777018248 absolute error = 1.8964451621854982854e-12 relative error = 5.3541052290861125929771146406555e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2159 Order of pole = 2.082 x[1] = -4.927 y[1] (analytic) = 3.5466162352470714276161564098298 y[1] (numeric) = 3.5466162352490262529172971332826 absolute error = 1.9548253011407234528e-12 relative error = 5.5118038476033269730499675007537e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2149 Order of pole = 2.082 x[1] = -4.926 y[1] (analytic) = 3.5512151285470903900056897209194 y[1] (numeric) = 3.5512151285491052482761680541836 absolute error = 2.0148582704783332642e-12 relative error = 5.6737150455389977334414306748856e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2139 Order of pole = 2.082 x[1] = -4.925 y[1] (analytic) = 3.5558362740508858469826719773664 y[1] (numeric) = 3.5558362740529624459043872034339 absolute error = 2.0765989217152260675e-12 relative error = 5.8399733892964636207908215702118e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.1MB, time=2.88 Real estimate of pole used Radius of convergence = 0.2129 Order of pole = 2.082 x[1] = -4.924 y[1] (analytic) = 3.5604798783754465369443838864457 y[1] (numeric) = 3.5604798783775866411410152290405 absolute error = 2.1401041966313425948e-12 relative error = 6.0107184136308500533686927211815e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2119 Order of pole = 2.082 x[1] = -4.923 y[1] (analytic) = 3.5651461510744692681004889188765 y[1] (numeric) = 3.5651461510766747013177986013726 absolute error = 2.2054332173096824961e-12 relative error = 6.1860948299272545044718136948758e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2109 Order of pole = 2.082 x[1] = -4.922 y[1] (analytic) = 3.5698353046942644763195496222349 y[1] (numeric) = 3.5698353046965371237000561373223 absolute error = 2.2726473805065150874e-12 relative error = 6.3662527442597356716568062005301e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2099 Order of pole = 2.082 x[1] = -4.921 y[1] (analytic) = 3.5745475548309985431552278302606 y[1] (numeric) = 3.5745475548333403536118097913804 absolute error = 2.3418104565819611198e-12 relative error = 6.5513478857401292944854946422864e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2089 Order of pole = 2.082 x[1] = -4.92 y[1] (analytic) = 3.5792831201893114143748952609665 y[1] (numeric) = 3.5792831201917244030681297956616 absolute error = 2.4129886932345346951e-12 relative error = 6.7415418456948150357896171855631e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2079 Order of pole = 2.082 x[1] = -4.919 y[1] (analytic) = 3.5840422226423493619306208816665 y[1] (numeric) = 3.5840422226448356128549183792309 absolute error = 2.4862509242974975644e-12 relative error = 6.9370023282384748158094618070664e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2069 Order of pole = 2.082 x[1] = -4.918 y[1] (analytic) = 3.5888250872932540854904460637747 y[1] (numeric) = 3.5888250872958157541743161141109 absolute error = 2.5616686838700503362e-12 relative error = 7.1379034128467359391111212922996e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2059 Order of pole = 2.082 x[1] = -4.917 y[1] (analytic) = 3.5936319425381507556050877525451 y[1] (numeric) = 3.5936319425407900719311602818699 absolute error = 2.6393163260725293248e-12 relative error = 7.3444258295645138548065402934028e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2049 Order of pole = 2.082 x[1] = -4.916 y[1] (analytic) = 3.5984630201306790616490005282837 y[1] (numeric) = 3.5984630201333983327997324895327 absolute error = 2.7192711507319612490e-12 relative error = 7.5567572475240005505973713153039e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2039 Order of pole = 2.082 x[1] = -4.915 y[1] (analytic) = 3.6033185552481128462869414305977 y[1] (numeric) = 3.6033185552509144598222640537703 absolute error = 2.8016135353226231726e-12 relative error = 7.7750925774857369990302015031113e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2029 Order of pole = 2.082 x[1] = -4.914 y[1] (analytic) = 3.6081987865591154869404980979311 y[1] (numeric) = 3.6081987865620019140140038377209 absolute error = 2.8864270735057397898e-12 relative error = 7.9996342891582244651504613538143e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.2019 Order of pole = 2.082 x[1] = -4.913 y[1] (analytic) = 3.6131039562931798262535715035466 y[1] (numeric) = 3.6131039562961536249742047116577 absolute error = 2.9737987206332081111e-12 relative error = 8.2305927440962446972344896115718e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.1MB, time=3.30 Real estimate of pole used Radius of convergence = 0.2009 Order of pole = 2.082 x[1] = -4.912 y[1] (analytic) = 3.6180343103118031607060936075718 y[1] (numeric) = 3.6180343103148669796526959684311 absolute error = 3.0638189466023608593e-12 relative error = 8.4681865450256609818639846556894e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1999 Order of pole = 2.082 x[1] = -4.911 y[1] (analytic) = 3.6229900981814495722677128113046 y[1] (numeric) = 3.6229900981846061541641851726507 absolute error = 3.1565818964723613461e-12 relative error = 8.7126429024931627436706540405000e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1989 Order of pole = 2.082 x[1] = -4.91 y[1] (analytic) = 3.6279715732483537354339393135843 y[1] (numeric) = 3.6279715732516059209932172821775 absolute error = 3.2521855592779685932e-12 relative error = 8.9641980197934130474000778521915e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1979 Order of pole = 2.082 x[1] = -4.909 y[1] (analytic) = 3.632978992715222254420545848507 y[1] (numeric) = 3.6329789927185729863660490828687 absolute error = 3.3507319455032343617e-12 relative error = 9.2230974971835947881318922091344e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1969 Order of pole = 2.082 x[1] = -4.908 y[1] (analytic) = 3.6380126177198905861490665942817 y[1] (numeric) = 3.63801261772334291342277290887 absolute error = 3.4523272737063145883e-12 relative error = 9.4895967564566790263212878193644e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1959 Order of pole = 2.082 x[1] = -4.907 y[1] (analytic) = 3.6430727134159956875546035605951 y[1] (numeric) = 3.6430727134195527697214206875667 absolute error = 3.5570821668171269716e-12 relative error = 9.7639614870101287061394297585413e-11 % Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1949 Order of pole = 2.082 x[1] = -4.906 y[1] (analytic) = 3.6481595490557266944907814849447 y[1] (numeric) = 3.6481595490593918063494436896905 absolute error = 3.6651118586622047458e-12 relative error = 1.0046468114616494531682936858894e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1939 Order of pole = 2.082 x[1] = -4.905 y[1] (analytic) = 3.6532733980747181980965222535611 y[1] (numeric) = 3.6532733980784947345078281893029 absolute error = 3.7765364113059357418e-12 relative error = 1.0337404294176771381111909925144e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1929 Order of pole = 2.082 x[1] = -4.904 y[1] (analytic) = 3.6584145381791530371345377166248 y[1] (numeric) = 3.6584145381830445180783723159487 absolute error = 3.8914809438345993239e-12 relative error = 1.0637069427816801974668864224323e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1919 Order of pole = 2.082 x[1] = -4.903 y[1] (analytic) = 3.6635832514351439759415194075553 y[1] (numeric) = 3.6635832514391540518147688059692 absolute error = 4.0100758732493984139e-12 relative error = 1.0945775209771804908401077898283e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1909 Order of pole = 2.082 x[1] = -4.902 y[1] (analytic) = 3.6687798243604661919073877911694 y[1] (numeric) = 3.6687798243645986490755650114878 absolute error = 4.1324571681772203184e-12 relative error = 1.1263846199594660504816821752334e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1899 Order of pole = 2.082 x[1] = -4.901 y[1] (analytic) = 3.674004548018715158734656898665 y[1] (numeric) = 3.6740045480229739253508102532312 absolute error = 4.2587666161533545662e-12 relative error = 1.1591620425320335407964834890035e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.1MB, time=3.71 Real estimate of pole used Radius of convergence = 0.1889 Order of pole = 2.082 x[1] = -4.9 y[1] (analytic) = 3.6792577181159672872889469504773 y[1] (numeric) = 3.6792577181203564393942260216153 absolute error = 4.3891521052790711380e-12 relative error = 1.1929450018322224369531401535921e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1879 Order of pole = 2.082 x[1] = -4.899 y[1] (analytic) = 3.6845396351000235800842244405324 y[1] (numeric) = 3.6845396351045473480053334996416 absolute error = 4.5237679211090591092e-12 relative error = 1.2277701881706730885684955780020e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1869 Order of pole = 2.082 x[1] = -4.898 y[1] (analytic) = 3.689850604262319574090396760456 y[1] (numeric) = 3.6898506042669823491500762646805 absolute error = 4.6627750596795042245e-12 relative error = 1.2636758394210632698327918737276e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1859 Order of pole = 2.082 x[1] = -4.897 y[1] (analytic) = 3.695190935842587995655401876947 y[1] (numeric) = 3.695190935847394337213049202996 absolute error = 4.8063415576473260490e-12 relative error = 1.3007018151692262455745655971170e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1849 Order of pole = 2.082 x[1] = -4.896 y[1] (analytic) = 3.7005609451363638372764364559467 y[1] (numeric) = 3.7005609451413184801170115620089 absolute error = 4.9546428405751060622e-12 relative error = 1.3388896748442903778330915368613e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1839 Order of pole = 2.082 x[1] = -4.895 y[1] (analytic) = 3.7059609526054249954612783054439 y[1] (numeric) = 3.7059609526105328575517431531062 absolute error = 5.1078620904648476623e-12 relative error = 1.3782827600689735568862204106353e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1829 Order of pole = 2.082 x[1] = -4.894 y[1] (analytic) = 3.71139128399126518908593644501 y[1] (numeric) = 3.711391283996531379719653720323 absolute error = 5.2661906337172753130e-12 relative error = 1.4189262814816885165077457968161e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1819 Order of pole = 2.082 x[1] = -4.893 y[1] (analytic) = 3.7168522704316996159660277638794 y[1] (numeric) = 3.7168522704371294443168000546644 absolute error = 5.4298283507722907850e-12 relative error = 1.4608674102997466953391488543957e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1809 Order of pole = 2.082 x[1] = -4.892 y[1] (analytic) = 3.7223442485807077097189515894089 y[1] (numeric) = 3.7223442485863066938277224695048 absolute error = 5.5989841087708800959e-12 relative error = 1.5041553749107746342632501960930e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1799 Order of pole = 2.082 x[1] = -4.891 y[1] (analytic) = 3.7278675607316214377459567274415 y[1] (numeric) = 3.727867560737395313964626388902 absolute error = 5.7738762186696614605e-12 relative error = 1.5488415627985710333241063251566e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1789 Order of pole = 2.082 x[1] = -4.89 y[1] (analytic) = 3.7334225549437718431198901069061 y[1] (numeric) = 3.7334225549497265760382269842237 absolute error = 5.9547329183368773176e-12 relative error = 1.5949796281301354280673114412979e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1779 Order of pole = 2.082 x[1] = -4.889 y[1] (analytic) = 3.7390095851727109876356757873001 y[1] (numeric) = 3.73900958517885278051893928707 absolute error = 6.1417928832634997699e-12 relative error = 1.6426256053526004211310152534225e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.1MB, time=4.13 Real estimate of pole used Radius of convergence = 0.1769 Order of pole = 2.082 x[1] = -4.888 y[1] (analytic) = 3.744629011404131110104944464306 y[1] (numeric) = 3.7446290114104664158715802866346 absolute error = 6.3353057666358223286e-12 relative error = 1.6918380291724172479720153512772e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1759 Order of pole = 2.082 x[1] = -4.887 y[1] (analytic) = 3.7502811997916076835541259989703 y[1] (numeric) = 3.7502811997981432163247630850996 absolute error = 6.5355327706370861293e-12 relative error = 1.7426780613145080553737504211057e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1749 Order of pole = 2.082 x[1] = -4.886 y[1] (analytic) = 3.7559665227982981483145012655127 y[1] (numeric) = 3.755966522805040895565477291064 absolute error = 6.7427472509760255513e-12 relative error = 1.7952096244863476001547219223992e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1739 Order of pole = 2.082 x[1] = -4.885 y[1] (analytic) = 3.7616853593427334267062755973789 y[1] (numeric) = 3.7616853593496906620630560640899 absolute error = 6.9572353567804667110e-12 relative error = 1.8494995440012242115310756596685e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1729 Order of pole = 2.082 x[1] = -4.884 y[1] (analytic) = 3.767438094948844901425701695766 y[1] (numeric) = 3.7674380949560241981338467848913 absolute error = 7.1792967081450891253e-12 relative error = 1.9056176975464201188056719729448e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1719 Order of pole = 2.082 x[1] = -4.883 y[1] (analytic) = 3.7732251219003753768730428670853 y[1] (numeric) = 3.7732251219077846219868279220561 absolute error = 7.4092451137850549708e-12 relative error = 1.9636371736159244155958870885381e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1709 Order of pole = 2.082 x[1] = -4.882 y[1] (analytic) = 3.7790468393998286543040254502543 y[1] (numeric) = 3.7790468394074760636354478404358 absolute error = 7.6474093314223901815e-12 relative error = 2.0236344391637436243181422842298e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1699 Order of pole = 2.082 x[1] = -4.881 y[1] (analytic) = 3.7849036537321187524584000371182 y[1] (numeric) = 3.7849036537400128863321208596866 absolute error = 7.8941338737208225684e-12 relative error = 2.0856895170731179933538102165037e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1689 Order of pole = 2.082 x[1] = -4.88 y[1] (analytic) = 3.7907959784330865106954293243597 y[1] (numeric) = 3.7907959784412362905582177193519 absolute error = 8.1497798627883949922e-12 relative error = 2.1498861740792182223518453429843e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1679 Order of pole = 2.082 x[1] = -4.879 y[1] (analytic) = 3.7967242344630583380529677587405 y[1] (numeric) = 3.7967242344714730639894545906021 absolute error = 8.4147259364868318616e-12 relative error = 2.2163121198284399958834599533669e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1669 Order of pole = 2.082 x[1] = -4.878 y[1] (analytic) = 3.8026888503856292364373659040857 y[1] (numeric) = 3.8026888503943186056473896192418 absolute error = 8.6893692100237151561e-12 relative error = 2.2850592178065080225333481398977e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1659 Order of pole = 2.082 x[1] = -4.877 y[1] (analytic) = 3.8086902625518599477922431628017 y[1] (numeric) = 3.8086902625608340740888026810742 absolute error = 8.9741262965595182725e-12 relative error = 2.3562237089205477585008882939085e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.1MB, time=4.55 Real estimate of pole used Radius of convergence = 0.1649 Order of pole = 2.082 x[1] = -4.876 y[1] (analytic) = 3.8147289152900861731558128080091 y[1] (numeric) = 3.8147289152993556075466508953217 absolute error = 9.2694343908380873126e-12 relative error = 2.4299064485774096086210486087527e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1639 Order of pole = 2.082 x[1] = -4.875 y[1] (analytic) = 3.8208052611015463067693723104409 y[1] (numeric) = 3.820805261111122059189520347861 absolute error = 9.5757524201480374201e-12 relative error = 2.5062131581621952571719473233920e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1629 Order of pole = 2.082 x[1] = -4.874 y[1] (analytic) = 3.8269197608620430428955411873925 y[1] (numeric) = 3.8269197608719366051627868888941 absolute error = 9.8935622672457015016e-12 relative error = 2.5852546918875301112520056507651e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1619 Order of pole = 2.082 x[1] = -4.873 y[1] (analytic) = 3.8330728840298635701643666486975 y[1] (numeric) = 3.8330728840400869402345865183932 absolute error = 1.02233700702198696957e-11 relative error = 2.6671473200560772730062189096251e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1609 Order of pole = 2.082 x[1] = -4.872 y[1] (analytic) = 3.8392651088601928929718715572484 y[1] (numeric) = 3.8392651088707586005765284902676 absolute error = 1.05657076046569330192e-11 relative error = 2.7520130298565646666855275953202e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1599 Order of pole = 2.082 x[1] = -4.871 y[1] (analytic) = 3.8454969226262651381562904003335 y[1] (numeric) = 3.8454969226371862719101651607185 absolute error = 1.09211337538747603850e-11 relative error = 2.8399798448977096893055465716077e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1589 Order of pole = 2.082 x[1] = -4.87 y[1] (analytic) = 3.8517688218475085459921917581849 y[1] (numeric) = 3.8517688218587987820656292663155 absolute error = 1.12902360734375081306e-11 relative error = 2.9311821647754353106055545856806e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1579 Order of pole = 2.082 x[1] = -4.869 y[1] (analytic) = 3.8580813125249512373818705561678 y[1] (numeric) = 3.8580813125366248698385152273843 absolute error = 1.16736324566446712165e-11 relative error = 3.0257611260672917018471105753184e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1569 Order of pole = 2.082 x[1] = -4.868 y[1] (analytic) = 3.8644349103841668258127714556956 y[1] (numeric) = 3.8644349103962387987209808775412 absolute error = 1.20719729082094218456e-11 relative error = 3.1238649862547009621033763505127e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1559 Order of pole = 2.082 x[1] = -4.867 y[1] (analytic) = 3.8708301411260515370671312926252 y[1] (numeric) = 3.8708301411385374785010386557059 absolute error = 1.24859414339073630807e-11 relative error = 3.2256495321892671495366631429373e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1548 Order of pole = 2.082 x[1] = -4.866 y[1] (analytic) = 3.8772675406857377478917169128484 y[1] (numeric) = 3.8772675406986540059463082506494 absolute error = 1.29162580545913378010e-11 relative error = 3.3312785148447492417895666304884e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1538 Order of pole = 2.082 x[1] = -4.865 y[1] (analytic) = 3.8837476554999627952940004709596 y[1] (numeric) = 3.8837476555133264762476358397156 absolute error = 1.33636809536353687560e-11 relative error = 3.4409241122322698173483229006010e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.1MB, time=4.96 Real estimate of pole used Radius of convergence = 0.1528 Order of pole = 2.082 x[1] = -4.864 y[1] (analytic) = 3.8902710427832265817855791307397 y[1] (numeric) = 3.8902710427970555905531752352973 absolute error = 1.38290087675961045576e-11 relative error = 3.5547674225039038347368532371308e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1518 Order of pole = 2.082 x[1] = -4.863 y[1] (analytic) = 3.8968382708130869524139757674471 y[1] (numeric) = 3.8968382708274000354446445152248 absolute error = 1.43130830306687477777e-11 relative error = 3.6729989894300335495228856979171e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1508 Order of pole = 2.082 x[1] = -4.862 y[1] (analytic) = 3.9034499192249580933893031377199 y[1] (numeric) = 3.9034499192397748841736754725714 absolute error = 1.48167907843723348515e-11 relative error = 3.7958193626099483626645361158083e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1498 Order of pole = 2.082 x[1] = -4.861 y[1] (analytic) = 3.9101065793167943492257021423985 y[1] (numeric) = 3.9101065793321354165905351669771 absolute error = 1.53410673648330245786e-11 relative error = 3.9234396949644121334083619451398e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1488 Order of pole = 2.082 x[1] = -4.86 y[1] (analytic) = 3.9168088543640599286379750350632 y[1] (numeric) = 3.9168088543799468280190260475168 absolute error = 1.58868993810510124536e-11 relative error = 4.0560823802647468667336372233369e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1478 Order of pole = 2.082 x[1] = -4.859 y[1] (analytic) = 3.9235573599454040256273061409402 y[1] (numeric) = 3.9235573599618593535259509958942 absolute error = 1.64553278986448549540e-11 relative error = 4.1939817336769684624290477893572e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1468 Order of pole = 2.082 x[1] = -4.858 y[1] (analytic) = 3.9303527242794809818007118907229 y[1] (numeric) = 3.9303527242965284336454871220913 absolute error = 1.70474518447752313684e-11 relative error = 4.3373847185433972843639585048896e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1458 Order of pole = 2.082 x[1] = -4.857 y[1] (analytic) = 3.937195588573376323713655995516 y[1] (numeric) = 3.9371955885910407553649242871661 absolute error = 1.76644316512682916501e-11 relative error = 4.4865517228898736429952117431896e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1448 Order of pole = 2.082 x[1] = -4.856 y[1] (analytic) = 3.9440866073831218941118210061904 y[1] (numeric) = 3.9440866074014293872662185797389 absolute error = 1.83074931543975735485e-11 relative error = 4.6417573894363559206324501853036e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1438 Order of pole = 2.082 x[1] = -4.855 y[1] (analytic) = 3.9510264489868069324202161763207 y[1] (numeric) = 3.9510264490057848641915711868834 absolute error = 1.89779317713550105627e-11 relative error = 4.8032915032046095807108022330734e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1428 Order of pole = 2.082 x[1] = -4.854 y[1] (analytic) = 3.9580157957708169269400075257417 y[1] (numeric) = 3.9580157957904940439151665944234 absolute error = 1.96771169751590686817e-11 relative error = 4.9714599411614988786189375998221e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1418 Order of pole = 2.082 x[1] = -4.853 y[1] (analytic) = 3.9650553446297584438367691949279 y[1] (numeric) = 3.9650553446501649409283954469176 absolute error = 2.04064970916262519897e-11 relative error = 5.1465856887129357040579947510769e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.1MB, time=5.38 Real estimate of pole used Radius of convergence = 0.1408 Order of pole = 2.082 x[1] = -4.852 y[1] (analytic) = 3.9721458073806560270670559192939 y[1] (numeric) = 3.9721458074018236315111433310322 absolute error = 2.11676044440874117383e-11 relative error = 5.3290099282749949644036175718708e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1398 Order of pole = 2.082 x[1] = -4.851 y[1] (analytic) = 3.979287911192036756358782299909 y[1] (numeric) = 3.9792879112139988172325628729582 absolute error = 2.19620608737805730492e-11 relative error = 5.5190932055985893934365919020811e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1388 Order of pole = 2.082 x[1] = -4.85 y[1] (analytic) = 3.9864823990285492517577304021098 y[1] (numeric) = 3.9864823990513408354240478489078 absolute error = 2.27915836663174467980e-11 relative error = 5.7172166800163074141917762576434e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1378 Order of pole = 2.082 x[1] = -4.849 y[1] (analytic) = 3.9937300301117969352240453954106 y[1] (numeric) = 3.9937300301354549271413691383773 absolute error = 2.36579919173237429667e-11 relative error = 5.9237834653188818900576696713399e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1368 Order of pole = 2.082 x[1] = -4.848 y[1] (analytic) = 4.0010315803981003226950019230733 y[1] (numeric) = 4.0010315804226635360683205898757 absolute error = 2.45632133733186668024e-11 relative error = 6.1392200685590792842507378327410e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1358 Order of pole = 2.082 x[1] = -4.847 y[1] (analytic) = 4.0083878430739401532204133483018 y[1] (numeric) = 4.0083878430994494450075675299776 absolute error = 2.55092917871541816758e-11 relative error = 6.3639779347279165401397731343580e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1348 Order of pole = 2.082 x[1] = -4.846 y[1] (analytic) = 4.0157996290698724041630935165322 y[1] (numeric) = 4.0157996290963707989940040400165 absolute error = 2.64983948309105234843e-11 relative error = 6.5985351059579641124799117884782e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1338 Order of pole = 2.082 x[1] = -4.845 y[1] (analytic) = 4.0232677675937478424153430227217 y[1] (numeric) = 4.0232677676212806650284183577241 absolute error = 2.75328226130753350024e-11 relative error = 6.8433980046876860538641903693580e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1328 Order of pole = 2.082 x[1] = -4.844 y[1] (analytic) = 4.0307931066841128817975660629393 y[1] (numeric) = 4.0307931067127278986487239589749 absolute error = 2.86150168511578960356e-11 relative error = 7.0991033510766622770730188421758e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1318 Order of pole = 2.082 x[1] = -4.843 y[1] (analytic) = 4.0383765137847153292170779578661 y[1] (numeric) = 4.0383765138144628999727279037265 absolute error = 2.97475707556499458604e-11 relative error = 7.3662202259023389706272164298723e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1308 Order of pole = 2.082 x[1] = -4.842 y[1] (analytic) = 4.0460188763410882930066238854408 y[1] (numeric) = 4.0460188763720215326931121071363 absolute error = 3.09332396864882216955e-11 relative error = 7.6453522912038143276964311716042e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1298 Order of pole = 2.082 x[1] = -4.841 y[1] (analytic) = 4.0537211024202382967907754171883 y[1] (numeric) = 4.0537211024524132494397298162683 absolute error = 3.21749526489543990800e-11 relative error = 7.9371401820773087828710241344216e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.1MB, time=5.79 Real estimate of pole used Radius of convergence = 0.1288 Order of pole = 2.082 x[1] = -4.84 y[1] (analytic) = 4.0614841213545197075655208706915 y[1] (numeric) = 4.0614841213879955322678461664978 absolute error = 3.34758247023252958063e-11 relative error = 8.2422640842828130198818673312358e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1278 Order of pole = 2.082 x[1] = -4.839 y[1] (analytic) = 4.0693088844108371807625632356911 y[1] (numeric) = 4.0693088844456763511241900685218 absolute error = 3.48391703616268328307e-11 relative error = 8.5614465137047267414463675196367e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1268 Order of pole = 2.082 x[1] = -4.838 y[1] (analytic) = 4.0771963654863811997494447284817 y[1] (numeric) = 4.0771963655226497178300689924199 absolute error = 3.62685180806242639382e-11 relative error = 8.8954553152353950236238458698134e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1258 Order of pole = 2.082 x[1] = -4.837 y[1] (analytic) = 4.0851475618321692144647937066179 y[1] (numeric) = 4.0851475618699368403775763687035 absolute error = 3.77676259127826620856e-11 relative error = 9.2451069003353361948985664652665e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1248 Order of pole = 2.082 x[1] = -4.836 y[1] (analytic) = 4.0931634948057366575950169062117 y[1] (numeric) = 4.0931634948450771560514669014006 absolute error = 3.93404984564499951889e-11 relative error = 9.6112697443855983998997904280268e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1238 Order of pole = 2.082 x[1] = -4.835 y[1] (analytic) = 4.1012452106543985546282769842906 y[1] (numeric) = 4.1012452106953899598293334402375 absolute error = 4.09914052010564559469e-11 relative error = 9.9948681670062416640313343555809e-10 % Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.1218 Order of pole = 0.9933 x[1] = -4.834 y[1] (analytic) = 4.109393781330583890061298632229 y[1] (numeric) = 4.1093937813733087904641060483143 absolute error = 4.27249004028074160853e-11 relative error = 1.0396886420793065615385165388414e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1218 Order of pole = 2.082 x[1] = -4.833 y[1] (analytic) = 4.1176103053408317181599987244319 y[1] (numeric) = 4.1176103053853775627913066198922 absolute error = 4.45458446313078954603e-11 relative error = 1.0818373116447854519182124931017e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1208 Order of pole = 2.082 x[1] = -4.832 y[1] (analytic) = 4.1258959086301306161495541590161 y[1] (numeric) = 4.1258959086765900442924994650019 absolute error = 4.64594281429453059858e-11 relative error = 1.1260446015074249953715136493695e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1198 Order of pole = 2.082 x[1] = -4.831 y[1] (analytic) = 4.1342517455033819075465233669056 y[1] (numeric) = 4.1342517455518531037993687848187 absolute error = 4.84711962528454179131e-11 relative error = 1.1724297221514172406327857055660e-09 % Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.04491 Order of pole = 0.5717 memory used=57.2MB, alloc=4.1MB, time=6.20 x[1] = -4.8296525755274864345490528200464 y[1] (analytic) = 4.1456237715032203184121785102041 y[1] (numeric) = 4.1456237715517445426877138258143 absolute error = 4.85242242755353156102e-11 relative error = 1.1704927159354895169062381743946e-09 % Correct digits = 10 h = 0.00044914149083785515031572665119202 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1174 Order of pole = 2.082 x[1] = -4.828754292545810724248421366744 y[1] (analytic) = 4.1532786274171284382411765424338 y[1] (numeric) = 4.1532786274656900958650829196684 absolute error = 4.85616576239063772346e-11 relative error = 1.1692366917869475864279959038427e-09 % Correct digits = 10 h = 0.00044914149083785515031572665119202 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1165 Order of pole = 2.082 x[1] = -4.8278560095641350139477899134416 y[1] (analytic) = 4.1609933456142907400109606593014 y[1] (numeric) = 4.1609933456628916034971471622267 absolute error = 4.86008634861865029253e-11 relative error = 1.1680110841179804625056811675407e-09 % Correct digits = 10 h = 0.00044914149083785515031572665119202 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1156 Order of pole = 2.082 x[1] = -4.8269577265824593036471584601392 y[1] (analytic) = 4.1687688569267151589016117156764 y[1] (numeric) = 4.168768856975357099459830148688 absolute error = 4.86419405582184330116e-11 relative error = 1.1668178838314885646746588905358e-09 % Correct digits = 10 h = 0.00044914149083785515031572665119202 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.09036 Order of pole = 0.8111 x[1] = -4.8256103021099457381962112801856 y[1] (analytic) = 4.1805482014481943307448482941916 y[1] (numeric) = 4.180548201496901627018840761854 absolute error = 4.87072962739924676624e-11 relative error = 1.1650935218763809332639858689307e-09 % Correct digits = 10 h = 0.00044914149083785515031572665119202 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.03124 Order of pole = 0.5381 memory used=61.0MB, alloc=4.1MB, time=6.60 x[1] = -4.8249855924239036540539159454918 y[1] (analytic) = 4.1860575453708736478825215815762 y[1] (numeric) = 4.1860575454195861476351685288687 absolute error = 4.87124997526469472925e-11 relative error = 1.1636844268066828118331861968711e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1128 Order of pole = 2.082 x[1] = -4.8237361730518194857693252761042 y[1] (analytic) = 4.1971693182529418539565180065317 y[1] (numeric) = 4.197169318301665295612628024083 absolute error = 4.87234416561100175513e-11 relative error = 1.1608643340695865103716171115032e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1115 Order of pole = 2.082 x[1] = -4.8227991085227563595558822740635 y[1] (analytic) = 4.2055859679257372228757730224932 y[1] (numeric) = 4.2055859679744693673223525108243 absolute error = 4.87321444465794883311e-11 relative error = 1.1587480274625076168735652021170e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1106 Order of pole = 2.082 x[1] = -4.8218620439936932333424392720228 y[1] (analytic) = 4.2140749448907615994166456129243 y[1] (numeric) = 4.2140749449395029009214510471979 absolute error = 4.87413015048054342736e-11 relative error = 1.1566311027263640559403457584431e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.03321 Order of pole = 0.546 memory used=64.8MB, alloc=4.1MB, time=7.00 x[1] = -4.8209249794646301071289962699821 y[1] (analytic) = 4.222637487646454711842528171673 y[1] (numeric) = 4.2226374876952056525791801133608 absolute error = 4.87509407366519416878e-11 relative error = 1.1545139946129723631362970536442e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1087 Order of pole = 2.082 x[1] = -4.8199879149355669809155532679414 y[1] (analytic) = 4.231274866909928562203916051582 y[1] (numeric) = 4.2312748669586896542283568300405 absolute error = 4.87610920244407784585e-11 relative error = 1.1523971748035048927717644232617e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1078 Order of pole = 2.082 x[1] = -4.8187384955634828126309625985538 y[1] (analytic) = 4.2429100438253052609351545350066 y[1] (numeric) = 4.2429100438740807402095860693739 absolute error = 4.87754792744315343673e-11 relative error = 1.1495760874170393633159255524535e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1065 Order of pole = 2.082 x[1] = -4.8178014310344196864175195965131 y[1] (analytic) = 4.251727172808752471922931520367 y[1] (numeric) = 4.2517271728575394258124616335199 absolute error = 4.87869538895301131529e-11 relative error = 1.1474620055947932733035595309582e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.1MB, time=7.39 Real estimate of pole used Radius of convergence = 0.1056 Order of pole = 2.082 x[1] = -4.8168643665053565602040765944724 y[1] (analytic) = 4.2606236215658305769481458922821 y[1] (numeric) = 4.2606236216146296335410001493482 absolute error = 4.87990565928542570661e-11 relative error = 1.1453500925510058338321952597996e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1046 Order of pole = 2.082 x[1] = -4.8159273019762934339906335924317 y[1] (analytic) = 4.269600814113245227620592647929 y[1] (numeric) = 4.2696008141620570554828676879187 absolute error = 4.88118278622750399897e-11 relative error = 1.1432410191820891407408107144902e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.07113 Order of pole = 0.736 x[1] = -4.814990237447230307777190590391 y[1] (analytic) = 4.2786602133087501668176714810901 y[1] (numeric) = 4.2786602133575754780022559980735 absolute error = 4.88253111845845169834e-11 relative error = 1.1411355132317738731051978151030e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1028 Order of pole = 2.082 memory used=72.4MB, alloc=4.1MB, time=7.79 x[1] = -4.8137408180751461394925999210034 y[1] (analytic) = 4.2908698932218013359670051790857 y[1] (numeric) = 4.2908698932706458138587433494499 absolute error = 4.88444778917381703642e-11 relative error = 1.1383350953823322536911212837718e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.1015 Order of pole = 2.082 x[1] = -4.8128037535460830132791569189627 y[1] (analytic) = 4.3001270258108467016623750142362 y[1] (numeric) = 4.3001270258597065123009592476873 absolute error = 4.88598106385842334511e-11 relative error = 1.1362411004444934964499926835777e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.0525 Order of pole = 0.6367 x[1] = -4.811866689017019887065713916922 y[1] (analytic) = 4.3094715405637443841840956899506 y[1] (numeric) = 4.3094715406126204097556181144336 absolute error = 4.88760255715224244830e-11 relative error = 1.1341535757103224167460203581481e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.09963 Order of pole = 2.082 x[1] = -4.8109296244879567608522709148813 y[1] (analytic) = 4.3189050859976427763802211422487 y[1] (numeric) = 4.3189050860465359588593366151983 absolute error = 4.88931824791154729496e-11 relative error = 1.1320735581254715828896408526553e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.09869 Order of pole = 2.082 memory used=76.2MB, alloc=4.1MB, time=8.19 x[1] = -4.8099925599588936346388279128406 y[1] (analytic) = 4.3284293578855401391704696185213 y[1] (numeric) = 4.3284293579344514849964457913206 absolute error = 4.89113458259761727993e-11 relative error = 1.1300021735798782953026583049571e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.08708 Order of pole = 0.898 x[1] = -4.808743140586809466354237243453 y[1] (analytic) = 4.3412725402097656853675785887477 y[1] (numeric) = 4.3412725402587029355718080515979 absolute error = 4.89372502042294628502e-11 relative error = 1.1272558852493713010853792436056e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.0965 Order of pole = 2.082 x[1] = -4.8078060760577463401407942414123 y[1] (analytic) = 4.3510153811153538095176910135373 y[1] (numeric) = 4.3510153811643118515845183040517 absolute error = 4.89580420668272905144e-11 relative error = 1.1252095839357208283394938661424e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.09556 Order of pole = 2.082 x[1] = -4.8068690115286832139273512393716 y[1] (analytic) = 4.3608549664334686750478339456202 y[1] (numeric) = 4.3608549664824487697240250241311 absolute error = 4.89800946761910785109e-11 relative error = 1.1231764196058443409003950514589e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.1MB, time=8.58 Real estimate of pole used Radius of convergence = 0.09463 Order of pole = 2.082 x[1] = -4.8059319469996200877139082373309 y[1] (analytic) = 4.3707932189653530485951100860079 y[1] (numeric) = 4.3707932190143565467233460279013 absolute error = 4.90034981282359418934e-11 relative error = 1.1211580066429216486604420509281e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.09369 Order of pole = 2.082 x[1] = -4.8049948824705569615004652352902 y[1] (analytic) = 4.3808321195903408873484256836359 y[1] (numeric) = 4.3808321196393692373011743850645 absolute error = 4.90283499527487014286e-11 relative error = 1.1191561012690307425486248897121e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.09275 Order of pole = 2.082 x[1] = -4.8037454630984727932158745659026 y[1] (analytic) = 4.3943774213456147706087868871104 y[1] (numeric) = 4.3943774213946786932413493716998 absolute error = 4.90639226325624845894e-11 relative error = 1.1165159003920624031772108914837e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.0915 Order of pole = 2.082 memory used=83.9MB, alloc=4.1MB, time=8.98 x[1] = -4.8028083985694096670024315638619 y[1] (analytic) = 4.4046592151217763403213765174026 y[1] (numeric) = 4.4046592151708689207243671139052 absolute error = 4.90925804029905965026e-11 relative error = 1.1145602419013323333649882873723e-09 % Correct digits = 10 h = 0.000312354843021042071147667346868 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.0666 Order of pole = 0.7712 x[1] = -4.8019758043950241983254860920317 y[1] (analytic) = 4.4138850144784348769910455009565 y[1] (numeric) = 4.4138850145275484752144236104715 absolute error = 4.91135982233781095150e-11 relative error = 1.1127067891953592281967445721427e-09 % Correct digits = 10 h = 0.00020788448834338453465013713644828 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.08972 Order of pole = 2.082 x[1] = -4.8009363819533072756522354063497 y[1] (analytic) = 4.4255243748341590096840007387642 y[1] (numeric) = 4.4255243748832773043263329577351 absolute error = 4.91182946423322189709e-11 relative error = 1.1098864333827754733224109349636e-09 % Correct digits = 10 h = 0.00020788448834338453465013713644828 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.08868 Order of pole = 2.082 memory used=87.7MB, alloc=4.1MB, time=9.37 x[1] = -4.7998969595115903529789847206677 y[1] (analytic) = 4.4373019000899706146098712130298 y[1] (numeric) = 4.4373019001390939481529052719705 absolute error = 4.91233335430340589407e-11 relative error = 1.1070541209296134559615093998818e-09 % Correct digits = 10 h = 0.00020788448834338453465013713644828 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.08764 Order of pole = 2.082 x[1] = -4.7988575370698734303057340349857 y[1] (analytic) = 4.4492208835924681838098421861586 y[1] (numeric) = 4.4492208836415969282299951732577 absolute error = 4.91287444201529870991e-11 relative error = 1.1042100562219017579297930609766e-09 % Correct digits = 10 h = 0.00020788448834338453465013713644828 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.0866 Order of pole = 2.082 memory used=91.5MB, alloc=4.1MB, time=9.77 x[1] = -4.7978764186806806087824004848729 y[1] (analytic) = 4.4606041482166051812243696708491 y[1] (numeric) = 4.4606041482657383227508683000673 absolute error = 4.91331415264986292182e-11 relative error = 1.1014907374406347615268609386859e-09 % Correct digits = 10 h = 0.00017873246208133395969156935178515 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.08562 Order of pole = 2.082 x[1] = -4.7969827563702739389839426381139 y[1] (analytic) = 4.471087554104553105333282292957 y[1] (numeric) = 4.4710875541536887516191998735538 absolute error = 4.91356462859175805968e-11 relative error = 1.0989640818106998654128686377732e-09 % Correct digits = 10 h = 0.00017873246208133395969156935178515 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.08472 Order of pole = 2.082 x[1] = -4.7959103615977859352257932220031 memory used=95.3MB, alloc=4.1MB, time=10.15 y[1] (analytic) = 4.4838155247894101117752900742547 y[1] (numeric) = 4.4838155248385489810910566151963 absolute error = 4.91388693157665409416e-11 relative error = 1.0959163918340380438867313742311e-09 % Correct digits = 10 h = 0.00017873246208133395969156935178515 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.08365 Order of pole = 2.082 x[1] = -4.7948379668252979314676438058923 y[1] (analytic) = 4.4967087524678636520854264520144 y[1] (numeric) = 4.4967087525170060023978755833313 absolute error = 4.91423503124491313169e-11 relative error = 1.0928515280310081386828216208155e-09 % Correct digits = 10 h = 0.00017873246208133395969156935178515 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.08258 Order of pole = 2.082 x[1] = -4.7939443045148912616691859591333 y[1] (analytic) = 4.5075824563757587900072686873683 y[1] (numeric) = 4.507582456424904255742633770964 absolute error = 4.91454657353650835957e-11 relative error = 1.0902843422387356177886636705606e-09 % Correct digits = 10 h = 0.00017873246208133395969156935178515 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.1MB, time=10.55 Real estimate of pole used Radius of convergence = 0.08168 Order of pole = 2.082 x[1] = -4.7928719097424032579110365430225 y[1] (analytic) = 4.5207899915622685804963513689908 y[1] (numeric) = 4.520789991611418065493945821968 absolute error = 4.91494849975944529772e-11 relative error = 1.0871879713352855147799766644342e-09 % Correct digits = 10 h = 0.00017873246208133395969156935178515 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.08061 Order of pole = 2.082 x[1] = -4.7919782474319965881125786962635 y[1] (analytic) = 4.5319319962248598560425267729474 y[1] (numeric) = 4.5319319962740129444621044337642 absolute error = 4.91530884195776608168e-11 relative error = 1.0845945715982196089523842761978e-09 % Correct digits = 10 h = 0.00017873246208133395969156935178515 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.07971 Order of pole = 2.082 memory used=103.0MB, alloc=4.1MB, time=10.94 x[1] = -4.7909058526595085843544292801527 y[1] (analytic) = 4.545469438283810713543332912954 y[1] (numeric) = 4.5454694383329684591359965042215 absolute error = 4.91577455926635912675e-11 relative error = 1.0814668596963135594238532302032e-09 % Correct digits = 10 h = 0.00017873246208133395969156935178515 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.07864 Order of pole = 2.082 x[1] = -4.7898334578870205805962798640419 y[1] (analytic) = 4.5591938264671337022021662420929 y[1] (numeric) = 4.5591938265162965024559477620791 absolute error = 4.91628002537815199862e-11 relative error = 1.0783222237313214299131478108287e-09 % Correct digits = 10 h = 0.00017873246208133395969156935178515 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.03871 Order of pole = 0.6249 memory used=106.8MB, alloc=4.1MB, time=11.33 x[1] = -4.7889397955766139107978220172829 y[1] (analytic) = 4.5707773698578924001524925962967 y[1] (numeric) = 4.5707773699070597450882418929207 absolute error = 4.91673449357492966240e-11 relative error = 1.0756889027233004854376898042795e-09 % Correct digits = 10 h = 0.00017873246208133395969156935178515 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.07667 Order of pole = 2.082 x[1] = -4.7879604475285427281907921453889 y[1] (analytic) = 4.5836285081428735975127276162216 y[1] (numeric) = 4.5836285081920451440829893760695 absolute error = 4.91715465702617598479e-11 relative error = 1.0727646554014551999527559775832e-09 % Correct digits = 10 h = 0.00013220909987292338413179724343189 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.02087 Order of pole = 0.5381 memory used=110.6MB, alloc=4.1MB, time=11.71 x[1] = -4.7869027747295593411177377674417 y[1] (analytic) = 4.5976965673304483222934767688554 y[1] (numeric) = 4.597696567379621260353945306272 absolute error = 4.91729380604685374166e-11 relative error = 1.0695124686973356631925403094274e-09 % Correct digits = 10 h = 0.00013220909987292338413179724343189 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.07463 Order of pole = 2.082 memory used=114.4MB, alloc=4.1MB, time=12.09 x[1] = -4.7859773110304488774288151867379 y[1] (analytic) = 4.6101715201996327530273049796206 y[1] (numeric) = 4.6101715202488070096413550845975 absolute error = 4.91742566140501049769e-11 relative error = 1.0666470086544790461166977898925e-09 % Correct digits = 10 h = 0.00013220909987292338413179724343189 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.0737 Order of pole = 2.082 x[1] = -4.7849196382314654903557608087907 y[1] (analytic) = 4.6246228761746640023269824900898 y[1] (numeric) = 4.6246228762238398928912526524551 absolute error = 4.91758905642701623653e-11 relative error = 1.0633492044857686269429124211369e-09 % Correct digits = 10 h = 0.00013220909987292338413179724343189 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.07264 Order of pole = 2.082 memory used=118.2MB, alloc=4.1MB, time=12.49 x[1] = -4.7839941745323550266668382280869 y[1] (analytic) = 4.6374423604219961062395308548146 y[1] (numeric) = 4.6374423604711735484797074478754 absolute error = 4.91774422401765930608e-11 relative error = 1.0604432016207650296504936833716e-09 % Correct digits = 10 h = 0.00013220909987292338413179724343189 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.07172 Order of pole = 2.082 memory used=122.0MB, alloc=4.1MB, time=12.87 x[1] = -4.7829365017333716395937838501397 y[1] (analytic) = 4.652298364341036903406680138397 y[1] (numeric) = 4.652298364390216272802176187922 absolute error = 4.91793693954960495250e-11 relative error = 1.0570983532020723603632710183719e-09 % Correct digits = 10 h = 0.00013220909987292338413179724343189 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.04091 Order of pole = 0.6682 x[1] = -4.7818788289343882525207294721925 y[1] (analytic) = 4.6673795372039081579881344508504 y[1] (numeric) = 4.6673795372530896358506625953148 absolute error = 4.91814778625281444644e-11 relative error = 1.0537278460108119427484070807882e-09 % Correct digits = 10 h = 0.00013220909987292338413179724343189 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.0696 Order of pole = 2.082 memory used=125.8MB, alloc=4.1MB, time=13.25 x[1] = -4.780926006575447998780726606947 y[1] (analytic) = 4.6811641613601374533251724633761 y[1] (numeric) = 4.6811641614093204906689543043986 absolute error = 4.91830373437818410225e-11 relative error = 1.0506582475734293558891955702907e-09 % Correct digits = 10 h = 9.7258953191878939781293009462920e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.06864 Order of pole = 2.082 memory used=129.7MB, alloc=4.1MB, time=13.65 x[1] = -4.779953417043529209382913676852 y[1] (analytic) = 4.6954344606143572600019049687235 y[1] (numeric) = 4.6954344606635407933887525828339 absolute error = 4.91835333868476141104e-11 relative error = 1.0474756659772942781042499859976e-09 % Correct digits = 10 h = 9.7258953191878939781293009462920e-05 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.03844 Order of pole = 0.6618 memory used=133.5MB, alloc=4.1MB, time=14.03 x[1] = -4.778980827511610419985100746757 y[1] (analytic) = 4.7099123127365110978560252714518 y[1] (numeric) = 4.7099123127856951720197446529608 absolute error = 4.91840741637193815090e-11 relative error = 1.0442673004912673403844102932084e-09 % Correct digits = 10 h = 9.7258953191878939781293009462920e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.06669 Order of pole = 2.082 memory used=137.3MB, alloc=4.2MB, time=14.42 x[1] = -4.7779109790264997516475065236525 y[1] (analytic) = 4.7260849600747256038467699382884 y[1] (numeric) = 4.7260849601239103302523302590532 absolute error = 4.91847264055603207648e-11 relative error = 1.0407076220818223655022908812609e-09 % Correct digits = 10 h = 9.7258953191878939781293009462920e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.06562 Order of pole = 2.082 x[1] = -4.7769383894945809622496935935575 y[1] (analytic) = 4.7410188498992334779600689209844 y[1] (numeric) = 4.7410188499484188553450027605326 absolute error = 4.91853773849338395482e-11 relative error = 1.0374431940083772283027775007295e-09 % Correct digits = 10 h = 9.7258953191878939781293009462920e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.06465 Order of pole = 2.082 memory used=141.1MB, alloc=4.2MB, time=14.80 x[1] = -4.7759657999626621728518806634625 y[1] (analytic) = 4.7561801065704029677413261981475 y[1] (numeric) = 4.7561801066195890576792855169644 absolute error = 4.91860899379593188169e-11 relative error = 1.0341511220319731543383105274473e-09 % Correct digits = 10 h = 9.7258953191878939781293009462920e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.06367 Order of pole = 2.082 memory used=144.9MB, alloc=4.2MB, time=15.19 x[1] = -4.7749932104307433834540677333675 y[1] (analytic) = 4.7715757308341501592652679116245 y[1] (numeric) = 4.7715757308833370302328297148952 absolute error = 4.91868709675618032707e-11 relative error = 1.0308307725205720823792574786291e-09 % Correct digits = 10 h = 9.7258953191878939781293009462920e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.0627 Order of pole = 2.082 memory used=148.7MB, alloc=4.2MB, time=15.58 x[1] = -4.773923361945632715116473510263 y[1] (analytic) = 4.7887903702989104704196640058069 y[1] (numeric) = 4.7887903703480982889515402943915 absolute error = 4.91878185318762885846e-11 relative error = 1.0271449516134498236104748702885e-09 % Correct digits = 10 h = 9.7258953191878939781293009462920e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.06163 Order of pole = 2.082 memory used=152.5MB, alloc=4.2MB, time=15.97 x[1] = -4.772950772413713925718660580168 y[1] (analytic) = 4.8047024425171297379246968921607 y[1] (numeric) = 4.8047024425663185079183051351341 absolute error = 4.91887699936082429734e-11 relative error = 1.0237630858954669811441984416467e-09 % Correct digits = 10 h = 9.7258953191878939781293009462920e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.06066 Order of pole = 2.082 memory used=156.4MB, alloc=4.2MB, time=16.36 x[1] = -4.771978182881795136320847650073 y[1] (analytic) = 4.8208727697191888669031330563427 y[1] (numeric) = 4.8208727697683786845685190000501 absolute error = 4.91898176653859437074e-11 relative error = 1.0203508786698638091491612337817e-09 % Correct digits = 10 h = 9.7258953191878939781293009462920e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.05968 Order of pole = 2.082 memory used=160.2MB, alloc=4.2MB, time=16.75 x[1] = -4.7709083343966844679832534269685 y[1] (analytic) = 4.8389685592787224432501578347124 y[1] (numeric) = 4.8389685593279135383009391746689 absolute error = 4.91910950507813399565e-11 relative error = 1.0165615760502806502031323993199e-09 % Correct digits = 10 h = 9.7258953191878939781293009462920e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.05861 Order of pole = 2.082 x[1] = -4.7699357448647656785854404968735 y[1] (analytic) = 4.8557093657089410120089295569022 y[1] (numeric) = 4.855709365758133396275818992283 absolute error = 4.91923842668894353808e-11 relative error = 1.0130833738585437734013356144937e-09 % Correct digits = 10 h = 9.7258953191878939781293009462920e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.05764 Order of pole = 2.082 memory used=164.0MB, alloc=4.2MB, time=17.14 x[1] = -4.7689631553328468891876275667785 y[1] (analytic) = 4.8727361673662536651335877169504 y[1] (numeric) = 4.8727361674154474761610996469443 absolute error = 4.91938110275119299939e-11 relative error = 1.0095726371760758047226488555555e-09 % Correct digits = 10 h = 9.7258953191878939781293009462920e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.05666 Order of pole = 2.082 memory used=167.8MB, alloc=4.2MB, time=17.53 x[1] = -4.7679905658009280997898146366835 y[1] (analytic) = 4.8900588726099097297793661545893 y[1] (numeric) = 4.8900588726591051225401949621953 absolute error = 4.91953927608288076060e-11 relative error = 1.0060286397855240595880719143819e-09 % Correct digits = 10 h = 9.7258953191878939781293009462920e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.05569 Order of pole = 2.082 memory used=171.6MB, alloc=4.2MB, time=17.91 x[1] = -4.766920717315817431452220413579 y[1] (analytic) = 4.9094680853147499109687477587319 y[1] (numeric) = 4.9094680853639472465845623950937 absolute error = 4.91973356158146363618e-11 relative error = 1.0020909548831613592917240717859e-09 % Correct digits = 10 h = 9.7258953191878939781293009462920e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.05462 Order of pole = 2.082 memory used=175.4MB, alloc=4.2MB, time=18.30 x[1] = -4.765948127783898642054407483484 y[1] (analytic) = 4.9274468196653139905600385091078 y[1] (numeric) = 4.9274468197145133020465824831694 absolute error = 4.91993114865439740616e-11 relative error = 9.9847473320647079660283455197793e-10 % Correct digits = 11 h = 9.7258953191878939781293009462920e-05 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.03463 Order of pole = 0.709 memory used=179.2MB, alloc=4.2MB, time=18.69 x[1] = -4.7649629575947850625611077705289 y[1] (analytic) = 4.9459947244679556294482724970461 y[1] (numeric) = 4.945994724517156310715430214634 absolute error = 4.92006812671577175879e-11 relative error = 9.9475806198823375933377813286720e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.05265 Order of pole = 2.082 memory used=183.1MB, alloc=4.2MB, time=19.08 x[1] = -4.7639675100460034908409806372033 y[1] (analytic) = 4.9650932150325797591063129647465 y[1] (numeric) = 4.9650932150817805907782997376101 absolute error = 4.92008316719867728636e-11 relative error = 9.9093470235410129605536870893077e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.05166 Order of pole = 2.082 memory used=186.9MB, alloc=4.2MB, time=19.47 memory used=190.7MB, alloc=4.2MB, time=19.85 x[1] = -4.7629720624972219191208535038777 y[1] (analytic) = 4.9845645819391607257921096731994 y[1] (numeric) = 4.9845645819883617263324355752286 absolute error = 4.92010005403259020292e-11 relative error = 9.8706716969017749464849584331990e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.05066 Order of pole = 2.082 memory used=194.5MB, alloc=4.2MB, time=20.23 x[1] = -4.7619766149484403474007263705521 y[1] (analytic) = 5.0044236353290151790991988436285 y[1] (numeric) = 5.0044236353782163696705315978719 absolute error = 4.92011905713327542434e-11 relative error = 9.8315398848319179891674198222066e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.04966 Order of pole = 2.082 memory used=198.3MB, alloc=4.2MB, time=20.62 memory used=202.1MB, alloc=4.2MB, time=21.00 x[1] = -4.7609811673996587756805992372265 y[1] (analytic) = 5.0246860864261692919734952574697 y[1] (numeric) = 5.0246860864753706968981652811796 absolute error = 4.92014049246700237099e-11 relative error = 9.7919360689186347806323865451345e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.04867 Order of pole = 2.082 memory used=206.0MB, alloc=4.2MB, time=21.39 x[1] = -4.7599857198508772039604721039009 y[1] (analytic) = 5.0453686221517126502856328299268 y[1] (numeric) = 5.0453686222009142975964380468218 absolute error = 4.92016473108052168950e-11 relative error = 9.7518439177635450893055210596804e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.02628 Order of pole = 0.6524 memory used=209.8MB, alloc=4.2MB, time=21.78 memory used=213.6MB, alloc=4.2MB, time=22.16 x[1] = -4.7589902723020956322403449705753 y[1] (analytic) = 5.0664889876247768287438720819154 y[1] (numeric) = 5.066488987673978750845291556813 absolute error = 4.92019221014194748976e-11 relative error = 9.7112462341472199616326985362822e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.02399 Order of pole = 0.6325 memory used=217.4MB, alloc=4.2MB, time=22.55 x[1] = -4.7579948247533140605202178372497 y[1] (analytic) = 5.088066077572106801325083512935 y[1] (numeric) = 5.0880660776213090357900462352278 absolute error = 4.92022344649627222928e-11 relative error = 9.6701248990934395973186584658369e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.04568 Order of pole = 2.082 memory used=221.2MB, alloc=4.2MB, time=22.94 memory used=225.0MB, alloc=4.2MB, time=23.32 x[1] = -4.7569993772045324888000907039241 y[1] (analytic) = 5.1101200378261108153178729639308 y[1] (numeric) = 5.110120037875313405851673737827 absolute error = 4.92025905338007738962e-11 relative error = 9.6284608129737752153977522321888e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.04468 Order of pole = 2.082 memory used=228.8MB, alloc=4.2MB, time=23.71 x[1] = -4.7559486270141519408732898409693 y[1] (analytic) = 5.1339403536946814660176078116677 y[1] (numeric) = 5.1339403537438844879076745997165 absolute error = 4.92030218900667880488e-11 relative error = 9.5838709646592285831621039681422e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.04363 Order of pole = 2.082 memory used=232.7MB, alloc=4.2MB, time=24.10 memory used=236.5MB, alloc=4.2MB, time=24.49 x[1] = -4.7549531794653703691531627076437 y[1] (analytic) = 5.15704374628325282057010677678 y[1] (numeric) = 5.1570437463324563128864843372105 absolute error = 4.92034923163775604305e-11 relative error = 9.5410267465423663856984946092281e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.04263 Order of pole = 2.082 memory used=240.3MB, alloc=4.2MB, time=24.87 x[1] = -4.7539577319165887974330355743181 y[1] (analytic) = 5.1806945691865597957759048039201 y[1] (numeric) = 5.1806945692357638293831274494537 absolute error = 4.92040336072226455336e-11 relative error = 9.4975746881268769001264484861421e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.04163 Order of pole = 2.082 memory used=244.1MB, alloc=4.2MB, time=25.27 memory used=247.9MB, alloc=4.2MB, time=25.65 x[1] = -4.7529622843678072257129084409925 y[1] (analytic) = 5.2049193465648025800120400162962 y[1] (numeric) = 5.2049193466140072385466797110155 absolute error = 4.92046585346396947193e-11 relative error = 9.4534910645857179005557677496700e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.04064 Order of pole = 2.082 memory used=251.7MB, alloc=4.2MB, time=26.04 x[1] = -4.7519668368190256539927813076669 y[1] (analytic) = 5.2297465794920829781040153002736 y[1] (numeric) = 5.2297465795412883606743543908972 absolute error = 4.92053825703390906236e-11 relative error = 9.4087508490933331868315506690462e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.03964 Order of pole = 2.082 memory used=255.5MB, alloc=4.2MB, time=26.43 memory used=259.4MB, alloc=4.2MB, time=26.81 x[1] = -4.7509713892702440822726541743413 y[1] (analytic) = 5.2552069474317547393761881064212 y[1] (numeric) = 5.2552069474809609639211230307251 absolute error = 4.92062245449349243039e-11 relative error = 9.3633276552471917738951212104855e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.03864 Order of pole = 2.082 memory used=263.2MB, alloc=4.2MB, time=27.20 x[1] = -4.7499759417214625105525270410157 y[1] (analytic) = 5.2813335360507826117696616713128 y[1] (numeric) = 5.281333536099989819260642004297 absolute error = 4.92072074909803329842e-11 relative error = 9.3171936888833490167803510972901e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.03764 Order of pole = 2.082 memory used=267.0MB, alloc=4.2MB, time=27.60 memory used=270.8MB, alloc=4.3MB, time=27.99 x[1] = -4.7489804941726809388323999076901 y[1] (analytic) = 5.3081620956162802068441426996382 y[1] (numeric) = 5.3081620956654885665719233712144 absolute error = 4.92083597277806715762e-11 relative error = 9.2703197154471140965511375234982e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.03665 Order of pole = 2.082 memory used=274.6MB, alloc=4.3MB, time=28.37 x[1] = -4.7479850466238993671122727743645 y[1] (analytic) = 5.3357313350369474763502010963423 y[1] (numeric) = 5.3357313350861571926166896603939 absolute error = 4.92097162664885640516e-11 relative error = 9.2226750517504850126116515352391e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.03565 Order of pole = 2.082 memory used=278.4MB, alloc=4.3MB, time=28.76 memory used=282.3MB, alloc=4.3MB, time=29.14 x[1] = -4.7469895990751177953921456410389 y[1] (analytic) = 5.3640832576177311017463400165026 y[1] (numeric) = 5.3640832576669424223889690395983 absolute error = 4.92113206426290230957e-11 relative error = 9.1742275947604325888480449756715e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.03465 Order of pole = 2.082 memory used=286.1MB, alloc=4.3MB, time=29.52 x[1] = -4.7459941515263362236720185077133 y[1] (analytic) = 5.3932635458365931021653769268239 y[1] (numeric) = 5.3932635458858063294888976622766 absolute error = 4.92132273235207354527e-11 relative error = 9.1249439055340786843903796223954e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.03366 Order of pole = 2.082 memory used=289.9MB, alloc=4.3MB, time=29.91 memory used=293.7MB, alloc=4.3MB, time=30.29 x[1] = -4.7449987039775546519518913743877 y[1] (analytic) = 5.4233220039914180266548651836933 y[1] (numeric) = 5.4233220040406335315502040137178 absolute error = 4.92155048953388300245e-11 relative error = 9.0747893743203062860257798414926e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.03266 Order of pole = 2.082 memory used=297.5MB, alloc=4.3MB, time=30.67 x[1] = -4.7439479537871741040250905114329 y[1] (analytic) = 5.4560633122834929664165089056153 y[1] (numeric) = 5.4560633123327113742223442221244 absolute error = 4.92184078058353165091e-11 relative error = 9.0208644930911250529697372494008e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.03161 Order of pole = 2.082 memory used=301.3MB, alloc=4.3MB, time=31.06 memory used=305.1MB, alloc=4.3MB, time=31.46 x[1] = -4.7429525062383925323049633781073 y[1] (analytic) = 5.4881036395785260216837704598778 y[1] (numeric) = 5.4881036396277477692763736884278 absolute error = 4.92217475926032285500e-11 relative error = 8.9688079572023803326856165211990e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.03061 Order of pole = 2.082 memory used=309.0MB, alloc=4.3MB, time=31.84 x[1] = -4.7419570586896109605848362447817 y[1] (analytic) = 5.5212056513492200517335011836232 y[1] (numeric) = 5.5212056513984458600287043935806 absolute error = 4.92258082952032099574e-11 relative error = 8.9157715549272960333975089944484e-10 % Correct digits = 11 h = 5.5302641598976206673729629206565e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.02961 Order of pole = 2.082 memory used=312.8MB, alloc=4.3MB, time=32.22 memory used=316.6MB, alloc=4.3MB, time=32.59 x[1] = -4.7409841226076536412929619798753 y[1] (analytic) = 5.5546547120012488436773303547305 y[1] (numeric) = 5.5546547120504789898859298521535 absolute error = 4.92301462085994974230e-11 relative error = 8.8628634471615432235747167706726e-10 % Correct digits = 11 h = 5.2488708245944653142121076783578e-05 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.02085 Order of pole = 0.7659 memory used=320.4MB, alloc=4.3MB, time=32.97 x[1] = -4.7399868371509806928832616794161 y[1] (analytic) = 5.5901441061754117183446464583163 y[1] (numeric) = 5.5901441062246465702856165786169 absolute error = 4.92348519409701203006e-11 relative error = 8.8074387718521530957137996907168e-10 % Correct digits = 11 h = 5.2488708245944653142121076783578e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.02764 Order of pole = 2.082 memory used=324.2MB, alloc=4.3MB, time=33.35 memory used=328.0MB, alloc=4.3MB, time=33.72 x[1] = -4.7389895516943077444735613789569 y[1] (analytic) = 5.6269405201339813854204269250456 y[1] (numeric) = 5.6269405201832220828042189375895 absolute error = 4.92406973837920125439e-11 relative error = 8.7508828656713003843704186596063e-10 % Correct digits = 11 h = 5.2488708245944653142121076783578e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.02664 Order of pole = 2.082 memory used=331.8MB, alloc=4.3MB, time=34.10 memory used=335.7MB, alloc=4.3MB, time=34.48 x[1] = -4.7379922662376347960638610784977 y[1] (analytic) = 5.6651438391977432666342005957168 y[1] (numeric) = 5.6651438392469912845605184599593 absolute error = 4.92480179263178642425e-11 relative error = 8.6931628435566805781208066290577e-10 % Correct digits = 11 h = 5.2488708245944653142121076783578e-05 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.01398 Order of pole = 0.6491 memory used=339.5MB, alloc=4.3MB, time=34.86 x[1] = -4.7369949807809618476541607780385 y[1] (analytic) = 5.7048658584853326924906001739418 y[1] (numeric) = 5.7048658585345899591201829558528 absolute error = 4.92572666295827819110e-11 relative error = 8.6342550116788908515877369211294e-10 % Correct digits = 11 h = 5.2488708245944653142121076783578e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.02464 Order of pole = 2.082 memory used=343.3MB, alloc=4.3MB, time=35.24 memory used=347.1MB, alloc=4.3MB, time=35.62 x[1] = -4.7359976953242888992444604775793 y[1] (analytic) = 5.7462322549777423128725907064105 y[1] (numeric) = 5.7462322550270113756417554053571 absolute error = 4.92690627691646989466e-11 relative error = 8.5741509536940114015475866482689e-10 % Correct digits = 11 h = 5.2488708245944653142121076783578e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.02365 Order of pole = 2.082 memory used=350.9MB, alloc=4.3MB, time=36.00 x[1] = -4.7349479211593700061816180560433 y[1] (analytic) = 5.7917086240051430868574342786901 y[1] (numeric) = 5.7917086240544282657675870223865 absolute error = 4.92851789101527436964e-11 relative error = 8.5096095314391938297648997219027e-10 % Correct digits = 11 h = 5.2488708245944653142121076783578e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.02259 Order of pole = 2.082 memory used=354.7MB, alloc=4.3MB, time=36.38 memory used=358.5MB, alloc=4.3MB, time=36.75 x[1] = -4.7339506357026970577719177555841 y[1] (analytic) = 5.8369162439796400460902742592316 y[1] (numeric) = 5.8369162440289453187478870712977 absolute error = 4.93052726576128120661e-11 relative error = 8.4471441077242902323890323612577e-10 % Correct digits = 11 h = 5.2488708245944653142121076783578e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.02159 Order of pole = 2.082 memory used=362.4MB, alloc=4.3MB, time=37.13 x[1] = -4.7329533502460241093622174551249 y[1] (analytic) = 5.8842658022968526600500685173149 y[1] (numeric) = 5.8842658023461844584185813465295 absolute error = 4.93317983685128292146e-11 relative error = 8.3836794641834080194479328520902e-10 % Correct digits = 11 h = 5.2488708245944653142121076783578e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.0206 Order of pole = 2.082 memory used=366.2MB, alloc=4.3MB, time=37.51 memory used=370.0MB, alloc=4.3MB, time=37.89 x[1] = -4.7319560647893511609525171546657 y[1] (analytic) = 5.9339703041855679610180754283681 y[1] (numeric) = 5.9339703042349352517840590730855 absolute error = 4.93672907659836447174e-11 relative error = 8.3194367742558598079533876648905e-10 % Correct digits = 11 h = 5.2488708245944653142121076783578e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.0196 Order of pole = 2.082 memory used=373.8MB, alloc=4.3MB, time=38.27 x[1] = -4.7309798152051447929397390238625 y[1] (analytic) = 5.9851441751469122056768395591791 y[1] (numeric) = 5.9851441751963151751038961451668 absolute error = 4.94029694270565859877e-11 relative error = 8.2542655584138762418820174330728e-10 % Correct digits = 11 h = 4.3298135656879021884084735185316e-05 TOP MAIN SOLVE Loop memory used=377.6MB, alloc=4.3MB, time=38.65 Real estimate of pole used Radius of convergence = 0.01862 Order of pole = 2.082 memory used=381.4MB, alloc=4.3MB, time=39.03 x[1] = -4.7299839580850365754364050749529 y[1] (analytic) = 6.040193373334376600361833343574 y[1] (numeric) = 6.0401933733838047935946586457528 absolute error = 4.94281932328253021788e-11 relative error = 8.1832137115072833940397514033446e-10 % Correct digits = 11 h = 4.3298135656879021884084735185316e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.01762 Order of pole = 2.082 memory used=385.3MB, alloc=4.3MB, time=39.41 memory used=389.1MB, alloc=4.3MB, time=39.80 x[1] = -4.7289881009649283579330711260433 y[1] (analytic) = 6.098451484339484181775442705819 y[1] (numeric) = 6.0984514843889478153899451647163 absolute error = 4.94636336145024588973e-11 relative error = 8.1108513762096124194312367683334e-10 % Correct digits = 11 h = 4.3298135656879021884084735185316e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.01662 Order of pole = 2.082 memory used=392.9MB, alloc=4.3MB, time=40.19 memory used=396.7MB, alloc=4.3MB, time=40.57 x[1] = -4.7279929840991768443010604133752 y[1] (analytic) = 6.1602683304420055280100557575989 y[1] (numeric) = 6.1602683304915197247437923912666 absolute error = 4.95141967337366336677e-11 relative error = 8.0376688283290964394183185720311e-10 % Correct digits = 11 h = 4.3051384204644398109672654727477e-05 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.006662 Order of pole = 0.5911 memory used=400.5MB, alloc=4.3MB, time=40.95 memory used=404.3MB, alloc=4.3MB, time=41.34 x[1] = -4.7269851836894433413612729412016 y[1] (analytic) = 6.2270293401497046676902319592127 y[1] (numeric) = 6.2270293401992908547599463819462 absolute error = 4.95861870697144227335e-11 relative error = 7.9630565974693666678270925352183e-10 % Correct digits = 11 h = 1.7618573026681783265001115523024e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.01462 Order of pole = 2.082 memory used=408.1MB, alloc=4.3MB, time=41.72 memory used=412.0MB, alloc=4.3MB, time=42.11 memory used=415.8MB, alloc=4.3MB, time=42.50 memory used=419.6MB, alloc=4.3MB, time=42.90 memory used=423.4MB, alloc=4.3MB, time=43.28 x[1] = -4.7259985435999491614984328787336 y[1] (analytic) = 6.2970134259868076249899414610283 y[1] (numeric) = 6.2970134260363950617680426641197 absolute error = 4.95874367781012030914e-11 relative error = 7.8747548120925810155630734384344e-10 % Correct digits = 11 h = 1.7618573026681783265001115523024e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.01363 Order of pole = 2.082 memory used=427.2MB, alloc=4.3MB, time=43.67 memory used=431.0MB, alloc=4.3MB, time=44.06 memory used=434.8MB, alloc=4.3MB, time=44.45 memory used=438.7MB, alloc=4.3MB, time=44.84 x[1] = -4.7249942849374282998523278151501 y[1] (analytic) = 6.3736640397937534947522494470501 y[1] (numeric) = 6.373664039843342908056937166632 absolute error = 4.95894133046877195819e-11 relative error = 7.7803619699874221873439707845527e-10 % Correct digits = 11 h = 1.7618573026681783265001115523024e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.01262 Order of pole = 2.082 memory used=442.5MB, alloc=4.3MB, time=45.23 memory used=446.3MB, alloc=4.3MB, time=45.61 memory used=450.1MB, alloc=4.3MB, time=46.00 memory used=453.9MB, alloc=4.3MB, time=46.38 memory used=457.7MB, alloc=4.3MB, time=46.77 x[1] = -4.7239900262749074382062227515666 y[1] (analytic) = 6.456682452796047159421662832135 y[1] (numeric) = 6.4566824528456397664302477275913 absolute error = 4.95926070085848954563e-11 relative error = 7.6808186512423209359569760134097e-10 % Correct digits = 11 h = 1.7618573026681783265001115523024e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.01162 Order of pole = 2.082 memory used=461.5MB, alloc=4.3MB, time=47.15 memory used=465.4MB, alloc=4.3MB, time=47.54 memory used=469.2MB, alloc=4.3MB, time=47.93 memory used=473.0MB, alloc=4.3MB, time=48.31 memory used=476.8MB, alloc=4.3MB, time=48.70 memory used=480.6MB, alloc=4.3MB, time=49.09 memory used=484.4MB, alloc=4.3MB, time=49.47 x[1] = -4.7229969637576144986885993091561 y[1] (analytic) = 6.5461671679044798626213222026821 y[1] (numeric) = 6.5461671679540733433744256092548 absolute error = 4.95934807531034065727e-11 relative error = 7.5759569655137568009660741100843e-10 % Correct digits = 11 h = 1.0024869800935120605922746941677e-05 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.01062 Order of pole = 2.082 memory used=488.3MB, alloc=4.3MB, time=49.86 memory used=492.1MB, alloc=4.3MB, time=50.24 memory used=495.9MB, alloc=4.3MB, time=50.63 memory used=499.7MB, alloc=4.3MB, time=51.03 memory used=503.5MB, alloc=4.3MB, time=51.42 memory used=507.3MB, alloc=4.3MB, time=51.81 memory used=511.1MB, alloc=4.3MB, time=52.21 memory used=515.0MB, alloc=4.3MB, time=52.60 memory used=518.8MB, alloc=4.3MB, time=52.99 memory used=522.6MB, alloc=4.3MB, time=53.39 x[1] = -4.7219965967783425751783065104262 y[1] (analytic) = 6.6452145051540442839687407649135 y[1] (numeric) = 6.645214505203637967804265017016 absolute error = 4.95936838355242521025e-11 relative error = 7.4630674144618314659548805197333e-10 % Correct digits = 11 h = 7.4018747485616897726593803398376e-06 TOP MAIN SOLVE Loop memory used=526.4MB, alloc=4.3MB, time=53.78 Real estimate of pole used Radius of convergence = 0.009622 Order of pole = 2.082 memory used=530.2MB, alloc=4.3MB, time=54.17 memory used=534.0MB, alloc=4.3MB, time=54.56 memory used=537.8MB, alloc=4.3MB, time=54.95 memory used=541.7MB, alloc=4.3MB, time=55.34 memory used=545.5MB, alloc=4.3MB, time=55.72 memory used=549.3MB, alloc=4.3MB, time=56.11 memory used=553.1MB, alloc=4.3MB, time=56.50 memory used=556.9MB, alloc=4.3MB, time=56.89 memory used=560.7MB, alloc=4.3MB, time=57.28 memory used=564.5MB, alloc=4.3MB, time=57.68 x[1] = -4.7209973436872867470589974940857 y[1] (analytic) = 6.7550334219096229834510093720759 y[1] (numeric) = 6.7550334219592168986356459224286 absolute error = 4.95939151846365503527e-11 relative error = 7.3417719923903106043810740742646e-10 % Correct digits = 11 h = 7.4018747485616897726593803398376e-06 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.008622 Order of pole = 2.082 memory used=568.4MB, alloc=4.3MB, time=58.07 memory used=572.2MB, alloc=4.3MB, time=58.46 memory used=576.0MB, alloc=4.3MB, time=58.85 memory used=579.8MB, alloc=4.3MB, time=59.24 memory used=583.6MB, alloc=4.3MB, time=59.63 memory used=587.4MB, alloc=4.3MB, time=60.02 memory used=591.3MB, alloc=4.3MB, time=60.43 memory used=595.1MB, alloc=4.3MB, time=60.82 memory used=598.9MB, alloc=4.3MB, time=61.21 memory used=602.7MB, alloc=4.3MB, time=61.60 memory used=606.5MB, alloc=4.3MB, time=61.99 x[1] = -4.7199980905962309189396884777452 y[1] (analytic) = 6.8784186873049523298209435611473 y[1] (numeric) = 6.8784186873545467120925982331782 absolute error = 4.95943822716546720309e-11 relative error = 7.2101429887057880005657801551500e-10 % Correct digits = 11 h = 7.4018747485616897726593803398376e-06 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.007621 Order of pole = 2.082 memory used=610.3MB, alloc=4.3MB, time=62.39 memory used=614.1MB, alloc=4.3MB, time=62.78 memory used=618.0MB, alloc=4.3MB, time=63.17 memory used=621.8MB, alloc=4.3MB, time=63.56 memory used=625.6MB, alloc=4.3MB, time=63.96 memory used=629.4MB, alloc=4.3MB, time=64.35 memory used=633.2MB, alloc=4.3MB, time=64.73 memory used=637.0MB, alloc=4.3MB, time=65.12 memory used=640.8MB, alloc=4.3MB, time=65.50 memory used=644.7MB, alloc=4.3MB, time=65.89 memory used=648.5MB, alloc=4.3MB, time=66.29 x[1] = -4.7189988375051750908203794614047 y[1] (analytic) = 7.0192005227249552414036362756673 y[1] (numeric) = 7.0192005227745506599128321604946 absolute error = 4.95954185091958848273e-11 relative error = 7.0656791109797537882219576295106e-10 % Correct digits = 11 h = 7.4018747485616897726593803398376e-06 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.00662 Order of pole = 2.082 memory used=652.3MB, alloc=4.3MB, time=66.69 memory used=656.1MB, alloc=4.3MB, time=67.07 memory used=659.9MB, alloc=4.3MB, time=67.45 memory used=663.7MB, alloc=4.3MB, time=67.84 memory used=667.5MB, alloc=4.3MB, time=68.22 memory used=671.4MB, alloc=4.3MB, time=68.61 memory used=675.2MB, alloc=4.3MB, time=69.01 memory used=679.0MB, alloc=4.3MB, time=69.40 memory used=682.8MB, alloc=4.3MB, time=69.79 memory used=686.6MB, alloc=4.3MB, time=70.18 x[1] = -4.7179995844141192627010704450642 y[1] (analytic) = 7.1831021415986267633341966659173 y[1] (numeric) = 7.1831021416482247839212188116595 absolute error = 4.95980205870221457422e-11 relative error = 6.9048190613622427474943593099295e-10 % Correct digits = 11 h = 7.4018747485616897726593803398376e-06 TOP MAIN SOLVE Loop memory used=690.4MB, alloc=4.3MB, time=70.59 Real estimate of pole used Radius of convergence = 0.005619 Order of pole = 2.082 memory used=694.3MB, alloc=4.3MB, time=71.00 memory used=698.1MB, alloc=4.3MB, time=71.41 memory used=701.9MB, alloc=4.3MB, time=71.82 memory used=705.7MB, alloc=4.3MB, time=72.22 memory used=709.5MB, alloc=4.3MB, time=72.63 memory used=713.3MB, alloc=4.3MB, time=73.03 memory used=717.1MB, alloc=4.3MB, time=73.44 memory used=721.0MB, alloc=4.3MB, time=73.84 memory used=724.8MB, alloc=4.3MB, time=74.24 memory used=728.6MB, alloc=4.3MB, time=74.64 x[1] = -4.7169936008708515074926050232893 y[1] (analytic) = 7.3806985598570312191783175925078 y[1] (numeric) = 7.3806985599066370375591692258577 absolute error = 4.96058183808516333499e-11 relative error = 6.7210194236428115691500425329160e-10 % Correct digits = 11 h = 7.1780672363501562339080650281135e-06 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.004612 Order of pole = 2.082 memory used=732.4MB, alloc=4.3MB, time=75.04 memory used=736.2MB, alloc=4.3MB, time=75.44 memory used=740.0MB, alloc=4.3MB, time=75.81 memory used=743.8MB, alloc=4.3MB, time=76.20 memory used=747.7MB, alloc=4.3MB, time=76.58 memory used=751.5MB, alloc=4.3MB, time=76.97 memory used=755.3MB, alloc=4.3MB, time=77.35 memory used=759.1MB, alloc=4.3MB, time=77.75 memory used=762.9MB, alloc=4.3MB, time=78.15 memory used=766.7MB, alloc=4.3MB, time=78.55 memory used=770.6MB, alloc=4.3MB, time=78.93 x[1] = -4.7159958495249988357760918022543 y[1] (analytic) = 7.6249173253415716821830046569482 y[1] (numeric) = 7.6249173253912030949886541689929 absolute error = 4.96314128056495120447e-11 relative error = 6.5091083205188962447076720745528e-10 % Correct digits = 11 h = 7.1780672363501562339080650281135e-06 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.003612 Order of pole = 2.082 memory used=774.4MB, alloc=4.3MB, time=79.32 memory used=778.2MB, alloc=4.3MB, time=79.71 memory used=782.0MB, alloc=4.3MB, time=80.09 memory used=785.8MB, alloc=4.3MB, time=80.48 memory used=789.6MB, alloc=4.3MB, time=80.86 memory used=793.4MB, alloc=4.3MB, time=81.25 memory used=797.3MB, alloc=4.3MB, time=81.63 memory used=801.1MB, alloc=4.3MB, time=82.01 memory used=804.9MB, alloc=4.3MB, time=82.40 memory used=808.7MB, alloc=4.3MB, time=82.79 memory used=812.5MB, alloc=4.3MB, time=83.17 memory used=816.3MB, alloc=4.3MB, time=83.56 memory used=820.1MB, alloc=4.3MB, time=83.94 x[1] = -4.7149947765985868566853158310973 y[1] (analytic) = 7.9500181338446667189489927543672 y[1] (numeric) = 7.9500181338943634682180205879029 absolute error = 4.96967492690278335357e-11 relative error = 6.2511491712779588795355432351531e-10 % Correct digits = 11 h = 6.0128808010874226107974205801600e-06 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 0.0008903 Order of pole = 0.5584 memory used=824.0MB, alloc=4.3MB, time=84.33 memory used=827.8MB, alloc=4.3MB, time=84.72 memory used=831.6MB, alloc=4.3MB, time=85.11 memory used=835.4MB, alloc=4.3MB, time=85.50 memory used=839.2MB, alloc=4.3MB, time=85.89 memory used=843.0MB, alloc=4.3MB, time=86.28 memory used=846.8MB, alloc=4.3MB, time=86.67 memory used=850.7MB, alloc=4.3MB, time=87.05 memory used=854.5MB, alloc=4.3MB, time=87.44 memory used=858.3MB, alloc=4.3MB, time=87.83 memory used=862.1MB, alloc=4.3MB, time=88.22 memory used=865.9MB, alloc=4.3MB, time=88.61 memory used=869.7MB, alloc=4.3MB, time=88.99 memory used=873.6MB, alloc=4.3MB, time=89.39 memory used=877.4MB, alloc=4.3MB, time=89.79 memory used=881.2MB, alloc=4.3MB, time=90.19 memory used=885.0MB, alloc=4.3MB, time=90.59 memory used=888.8MB, alloc=4.3MB, time=90.99 memory used=892.6MB, alloc=4.3MB, time=91.39 memory used=896.4MB, alloc=4.3MB, time=91.80 memory used=900.3MB, alloc=4.3MB, time=92.19 memory used=904.1MB, alloc=4.3MB, time=92.58 memory used=907.9MB, alloc=4.3MB, time=92.97 memory used=911.7MB, alloc=4.3MB, time=93.37 memory used=915.5MB, alloc=4.3MB, time=93.77 memory used=919.3MB, alloc=4.3MB, time=94.16 memory used=923.1MB, alloc=4.3MB, time=94.55 memory used=927.0MB, alloc=4.3MB, time=94.93 memory used=930.8MB, alloc=4.3MB, time=95.33 memory used=934.6MB, alloc=4.3MB, time=95.73 memory used=938.4MB, alloc=4.3MB, time=96.12 memory used=942.2MB, alloc=4.3MB, time=96.50 memory used=946.0MB, alloc=4.3MB, time=96.88 memory used=949.8MB, alloc=4.3MB, time=97.26 memory used=953.7MB, alloc=4.3MB, time=97.64 memory used=957.5MB, alloc=4.3MB, time=98.02 memory used=961.3MB, alloc=4.3MB, time=98.39 memory used=965.1MB, alloc=4.3MB, time=98.77 memory used=968.9MB, alloc=4.3MB, time=99.15 memory used=972.7MB, alloc=4.3MB, time=99.53 memory used=976.6MB, alloc=4.3MB, time=99.91 memory used=980.4MB, alloc=4.3MB, time=100.30 memory used=984.2MB, alloc=4.3MB, time=100.69 memory used=988.0MB, alloc=4.3MB, time=101.07 memory used=991.8MB, alloc=4.3MB, time=101.46 memory used=995.6MB, alloc=4.3MB, time=101.86 memory used=999.4MB, alloc=4.3MB, time=102.25 memory used=1003.3MB, alloc=4.3MB, time=102.64 memory used=1007.1MB, alloc=4.3MB, time=103.02 memory used=1010.9MB, alloc=4.3MB, time=103.42 memory used=1014.7MB, alloc=4.3MB, time=103.81 memory used=1018.5MB, alloc=4.3MB, time=104.20 memory used=1022.3MB, alloc=4.3MB, time=104.59 memory used=1026.1MB, alloc=4.3MB, time=104.98 memory used=1030.0MB, alloc=4.3MB, time=105.37 memory used=1033.8MB, alloc=4.3MB, time=105.75 memory used=1037.6MB, alloc=4.3MB, time=106.14 memory used=1041.4MB, alloc=4.3MB, time=106.53 memory used=1045.2MB, alloc=4.3MB, time=106.91 memory used=1049.0MB, alloc=4.3MB, time=107.30 memory used=1052.8MB, alloc=4.3MB, time=107.68 memory used=1056.7MB, alloc=4.3MB, time=108.08 memory used=1060.5MB, alloc=4.3MB, time=108.47 memory used=1064.3MB, alloc=4.3MB, time=108.86 memory used=1068.1MB, alloc=4.3MB, time=109.25 memory used=1071.9MB, alloc=4.3MB, time=109.64 memory used=1075.7MB, alloc=4.3MB, time=110.04 memory used=1079.6MB, alloc=4.3MB, time=110.43 memory used=1083.4MB, alloc=4.3MB, time=110.82 memory used=1087.2MB, alloc=4.3MB, time=111.22 memory used=1091.0MB, alloc=4.3MB, time=111.61 memory used=1094.8MB, alloc=4.3MB, time=112.00 memory used=1098.6MB, alloc=4.3MB, time=112.40 memory used=1102.4MB, alloc=4.3MB, time=112.79 memory used=1106.3MB, alloc=4.3MB, time=113.19 memory used=1110.1MB, alloc=4.3MB, time=113.59 memory used=1113.9MB, alloc=4.3MB, time=113.99 memory used=1117.7MB, alloc=4.3MB, time=114.39 memory used=1121.5MB, alloc=4.3MB, time=114.79 memory used=1125.3MB, alloc=4.3MB, time=115.18 memory used=1129.1MB, alloc=4.3MB, time=115.57 memory used=1133.0MB, alloc=4.3MB, time=115.96 memory used=1136.8MB, alloc=4.3MB, time=116.35 memory used=1140.6MB, alloc=4.3MB, time=116.73 memory used=1144.4MB, alloc=4.3MB, time=117.13 memory used=1148.2MB, alloc=4.3MB, time=117.54 memory used=1152.0MB, alloc=4.3MB, time=117.94 memory used=1155.9MB, alloc=4.3MB, time=118.33 memory used=1159.7MB, alloc=4.3MB, time=118.73 memory used=1163.5MB, alloc=4.3MB, time=119.12 memory used=1167.3MB, alloc=4.3MB, time=119.51 memory used=1171.1MB, alloc=4.3MB, time=119.91 memory used=1174.9MB, alloc=4.3MB, time=120.31 memory used=1178.7MB, alloc=4.3MB, time=120.69 memory used=1182.6MB, alloc=4.3MB, time=121.09 memory used=1186.4MB, alloc=4.3MB, time=121.48 memory used=1190.2MB, alloc=4.3MB, time=121.87 x[1] = -4.7139996865112451801785718190537 y[1] (analytic) = 8.4310830406105166121529591692184 y[1] (numeric) = 8.4310830406602573330214607326495 absolute error = 4.97407208685015634311e-11 relative error = 5.8996834248829446582897726334475e-10 % Correct digits = 11 h = 6.0671232888829560077972685025699e-07 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.001613 Order of pole = 2.082 memory used=1194.0MB, alloc=4.3MB, time=122.26 memory used=1197.8MB, alloc=4.3MB, time=122.66 memory used=1201.6MB, alloc=4.3MB, time=123.06 memory used=1205.4MB, alloc=4.3MB, time=123.46 memory used=1209.3MB, alloc=4.3MB, time=123.87 memory used=1213.1MB, alloc=4.3MB, time=124.27 memory used=1216.9MB, alloc=4.3MB, time=124.68 memory used=1220.7MB, alloc=4.3MB, time=125.08 memory used=1224.5MB, alloc=4.3MB, time=125.49 memory used=1228.3MB, alloc=4.3MB, time=125.89 memory used=1232.1MB, alloc=4.3MB, time=126.28 memory used=1236.0MB, alloc=4.3MB, time=126.68 memory used=1239.8MB, alloc=4.3MB, time=127.08 memory used=1243.6MB, alloc=4.3MB, time=127.48 memory used=1247.4MB, alloc=4.3MB, time=127.88 memory used=1251.2MB, alloc=4.3MB, time=128.27 memory used=1255.0MB, alloc=4.3MB, time=128.67 memory used=1258.9MB, alloc=4.3MB, time=129.07 memory used=1262.7MB, alloc=4.3MB, time=129.47 memory used=1266.5MB, alloc=4.3MB, time=129.87 memory used=1270.3MB, alloc=4.3MB, time=130.27 memory used=1274.1MB, alloc=4.3MB, time=130.68 memory used=1277.9MB, alloc=4.3MB, time=131.07 memory used=1281.7MB, alloc=4.3MB, time=131.46 memory used=1285.6MB, alloc=4.3MB, time=131.85 memory used=1289.4MB, alloc=4.3MB, time=132.24 memory used=1293.2MB, alloc=4.3MB, time=132.64 memory used=1297.0MB, alloc=4.3MB, time=133.03 memory used=1300.8MB, alloc=4.3MB, time=133.42 memory used=1304.6MB, alloc=4.3MB, time=133.81 memory used=1308.4MB, alloc=4.3MB, time=134.20 memory used=1312.3MB, alloc=4.3MB, time=134.60 memory used=1316.1MB, alloc=4.3MB, time=135.00 memory used=1319.9MB, alloc=4.3MB, time=135.40 memory used=1323.7MB, alloc=4.3MB, time=135.79 memory used=1327.5MB, alloc=4.3MB, time=136.18 memory used=1331.3MB, alloc=4.3MB, time=136.57 memory used=1335.1MB, alloc=4.3MB, time=136.98 memory used=1339.0MB, alloc=4.3MB, time=137.41 memory used=1342.8MB, alloc=4.3MB, time=137.83 memory used=1346.6MB, alloc=4.3MB, time=138.24 memory used=1350.4MB, alloc=4.3MB, time=138.65 memory used=1354.2MB, alloc=4.3MB, time=139.06 memory used=1358.0MB, alloc=4.3MB, time=139.47 memory used=1361.9MB, alloc=4.3MB, time=139.88 memory used=1365.7MB, alloc=4.3MB, time=140.28 memory used=1369.5MB, alloc=4.3MB, time=140.67 memory used=1373.3MB, alloc=4.3MB, time=141.08 memory used=1377.1MB, alloc=4.3MB, time=141.48 memory used=1380.9MB, alloc=4.3MB, time=141.88 memory used=1384.7MB, alloc=4.3MB, time=142.28 memory used=1388.6MB, alloc=4.3MB, time=142.69 memory used=1392.4MB, alloc=4.3MB, time=143.09 memory used=1396.2MB, alloc=4.3MB, time=143.50 memory used=1400.0MB, alloc=4.3MB, time=143.90 memory used=1403.8MB, alloc=4.3MB, time=144.31 memory used=1407.6MB, alloc=4.3MB, time=144.71 memory used=1411.4MB, alloc=4.3MB, time=145.12 memory used=1415.3MB, alloc=4.3MB, time=145.52 memory used=1419.1MB, alloc=4.3MB, time=145.93 memory used=1422.9MB, alloc=4.3MB, time=146.34 memory used=1426.7MB, alloc=4.3MB, time=146.75 memory used=1430.5MB, alloc=4.3MB, time=147.16 memory used=1434.3MB, alloc=4.3MB, time=147.56 memory used=1438.2MB, alloc=4.3MB, time=147.97 memory used=1442.0MB, alloc=4.3MB, time=148.37 memory used=1445.8MB, alloc=4.3MB, time=148.77 memory used=1449.6MB, alloc=4.3MB, time=149.18 memory used=1453.4MB, alloc=4.3MB, time=149.58 memory used=1457.2MB, alloc=4.3MB, time=149.97 memory used=1461.0MB, alloc=4.3MB, time=150.37 memory used=1464.9MB, alloc=4.3MB, time=150.77 memory used=1468.7MB, alloc=4.3MB, time=151.17 memory used=1472.5MB, alloc=4.3MB, time=151.56 memory used=1476.3MB, alloc=4.3MB, time=151.96 memory used=1480.1MB, alloc=4.3MB, time=152.35 memory used=1483.9MB, alloc=4.3MB, time=152.75 memory used=1487.7MB, alloc=4.3MB, time=153.16 memory used=1491.6MB, alloc=4.3MB, time=153.55 memory used=1495.4MB, alloc=4.3MB, time=153.95 memory used=1499.2MB, alloc=4.3MB, time=154.35 memory used=1503.0MB, alloc=4.3MB, time=154.75 memory used=1506.8MB, alloc=4.3MB, time=155.15 memory used=1510.6MB, alloc=4.3MB, time=155.55 memory used=1514.4MB, alloc=4.3MB, time=155.95 memory used=1518.3MB, alloc=4.3MB, time=156.35 memory used=1522.1MB, alloc=4.3MB, time=156.76 memory used=1525.9MB, alloc=4.3MB, time=157.16 memory used=1529.7MB, alloc=4.3MB, time=157.57 memory used=1533.5MB, alloc=4.3MB, time=157.97 memory used=1537.3MB, alloc=4.3MB, time=158.38 memory used=1541.2MB, alloc=4.3MB, time=158.78 memory used=1545.0MB, alloc=4.3MB, time=159.18 memory used=1548.8MB, alloc=4.3MB, time=159.58 memory used=1552.6MB, alloc=4.3MB, time=159.98 memory used=1556.4MB, alloc=4.3MB, time=160.37 memory used=1560.2MB, alloc=4.3MB, time=160.76 memory used=1564.0MB, alloc=4.3MB, time=161.16 memory used=1567.9MB, alloc=4.3MB, time=161.55 memory used=1571.7MB, alloc=4.3MB, time=161.95 memory used=1575.5MB, alloc=4.3MB, time=162.34 memory used=1579.3MB, alloc=4.3MB, time=162.74 memory used=1583.1MB, alloc=4.3MB, time=163.13 memory used=1586.9MB, alloc=4.3MB, time=163.52 memory used=1590.7MB, alloc=4.3MB, time=163.91 memory used=1594.6MB, alloc=4.3MB, time=164.31 memory used=1598.4MB, alloc=4.3MB, time=164.72 memory used=1602.2MB, alloc=4.3MB, time=165.11 memory used=1606.0MB, alloc=4.3MB, time=165.51 memory used=1609.8MB, alloc=4.3MB, time=165.90 memory used=1613.6MB, alloc=4.3MB, time=166.30 memory used=1617.4MB, alloc=4.3MB, time=166.69 memory used=1621.3MB, alloc=4.3MB, time=167.09 memory used=1625.1MB, alloc=4.3MB, time=167.48 memory used=1628.9MB, alloc=4.3MB, time=167.87 memory used=1632.7MB, alloc=4.3MB, time=168.26 memory used=1636.5MB, alloc=4.3MB, time=168.65 memory used=1640.3MB, alloc=4.3MB, time=169.04 memory used=1644.2MB, alloc=4.3MB, time=169.43 memory used=1648.0MB, alloc=4.3MB, time=169.82 memory used=1651.8MB, alloc=4.3MB, time=170.21 memory used=1655.6MB, alloc=4.3MB, time=170.60 memory used=1659.4MB, alloc=4.3MB, time=170.99 memory used=1663.2MB, alloc=4.3MB, time=171.37 memory used=1667.0MB, alloc=4.3MB, time=171.76 memory used=1670.9MB, alloc=4.3MB, time=172.14 memory used=1674.7MB, alloc=4.3MB, time=172.53 x[1] = -4.7129998245932372690284868291225 y[1] (analytic) = 9.400668671320971091078683888934 y[1] (numeric) = 9.4006686713707129291421200970322 absolute error = 4.97418380634362080982e-11 relative error = 5.2913085018287898591904428043226e-10 % Correct digits = 11 h = 6.0671232888829560077972685025699e-07 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.0006118 Order of pole = 2.082 memory used=1678.5MB, alloc=4.3MB, time=172.92 memory used=1682.3MB, alloc=4.3MB, time=173.30 memory used=1686.1MB, alloc=4.3MB, time=173.68 memory used=1689.9MB, alloc=4.3MB, time=174.06 memory used=1693.7MB, alloc=4.3MB, time=174.44 memory used=1697.6MB, alloc=4.3MB, time=174.83 memory used=1701.4MB, alloc=4.3MB, time=175.21 memory used=1705.2MB, alloc=4.3MB, time=175.59 memory used=1709.0MB, alloc=4.3MB, time=175.98 memory used=1712.8MB, alloc=4.3MB, time=176.37 memory used=1716.6MB, alloc=4.3MB, time=176.76 memory used=1720.5MB, alloc=4.3MB, time=177.14 memory used=1724.3MB, alloc=4.3MB, time=177.52 memory used=1728.1MB, alloc=4.3MB, time=177.90 memory used=1731.9MB, alloc=4.3MB, time=178.28 memory used=1735.7MB, alloc=4.3MB, time=178.66 memory used=1739.5MB, alloc=4.3MB, time=179.04 memory used=1743.3MB, alloc=4.3MB, time=179.43 memory used=1747.2MB, alloc=4.3MB, time=179.82 Finished! Maximum Time Reached before Solution Completed! diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; Iterations = 5786 Total Elapsed Time = 3 Minutes 0 Seconds Elapsed Time(since restart) = 2 Minutes 59 Seconds Expected Time Remaining = 1 Hours 41 Minutes 29 Seconds Optimized Time Remaining = 1 Hours 41 Minutes 27 Seconds Expected Total Time = 1 Hours 44 Minutes 27 Seconds Time to Timeout Unknown Percent Done = 2.872 % > quit memory used=1750.5MB, alloc=4.3MB, time=180.12