|\^/| 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 > 0.0000000000000000000000000000000001) then # if number 4 > glob_good_digits := -trunc(log10(relerr)) + 2; > else > glob_good_digits := Digits; > fi;# end if 4; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 3; > if (glob_iter = 1) then # if number 3 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 3; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 2; > #BOTTOM DISPLAY ALOT > fi;# end if 1; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 2 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 7 > # Begin Function number 8 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 2 > fi;# end if 1; > if ( not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 8 > # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 1; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 9 > # Begin Function number 10 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) < glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2; > if (m > 10) then # if number 1 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (omniabs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1; > n := n - 1; > od;# end do number 2; > m := n + cnt; > if (m <= 10) then # if number 1 > rad_c := glob_large_float; > ord_no := glob_large_float; > elif > (((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-5]) <= (glob_small_float)))) then # if number 2 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2; > #BOTTOM RADII COMPLEX EQ = 1 > found := false; > #TOP WHICH RADII EQ = 1 > if ( not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if ( not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if ( not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3; > fi;# end if 2; > if ( not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if ( not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if ( not found ) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3; > fi;# end if 2; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if (array_pole[1] > array_poles[1,1]) then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2; > #BOTTOM WHICH RADIUS EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 2 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 2 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 2; > #BOTTOM ADJUST ALL SERIES > if (reached_interval()) then # if number 2 > display_pole(); > fi;# end if 2 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) < glob_small_float or omniabs(array_y_higher[1, m - 1]) < glob_small_float or omniabs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float elif glob_large_float <= omniabs(array_y_higher[1, m]) or glob_large_float <= omniabs(array_y_higher[1, m - 1]) or glob_large_float <= omniabs(array_y_higher[1, m - 2]) or glob_large_float <= omniabs(array_y_higher[1, m - 3]) or glob_large_float <= omniabs(array_y_higher[1, m - 4]) or glob_large_float <= omniabs(array_y_higher[1, m - 5]) or omniabs(array_y_higher[1, m]) <= glob_small_float or omniabs(array_y_higher[1, m - 1]) <= glob_small_float or omniabs(array_y_higher[1, m - 2]) <= glob_small_float or omniabs(array_y_higher[1, m - 3]) <= glob_small_float or omniabs(array_y_higher[1, m - 4]) <= glob_small_float or omniabs(array_y_higher[1, m - 5]) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(dr1) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used") end if end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used") end if end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_pole() end if end proc > # End Function number 10 > # Begin Function number 11 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 2 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 3; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 2; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 11 > # Begin Function number 12 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre sin 1 $eq_no = 1 > array_tmp1[1] := sin(array_x[1]); > array_tmp1_g[1] := cos(array_x[1]); > #emit pre cos 1 $eq_no = 1 > array_tmp2[1] := cos(array_x[1]); > array_tmp2_g[1] := sin(array_x[1]); > #emit pre div FULL - FULL $eq_no = 1 i = 1 > array_tmp3[1] := (array_tmp1[1] / (array_tmp2[1])); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp1[2] := array_tmp1_g[1] * array_x[2] / 1; > array_tmp1_g[2] := -array_tmp1[1] * array_x[2] / 1; > #emit pre cos ID_LINEAR iii = 2 $eq_no = 1 > array_tmp2[2] := -array_tmp2_g[1] * array_x[2] / 1; > array_tmp2_g[2] := array_tmp2[1] * array_x[2] / 1; > #emit pre div FULL - FULL $eq_no = 1 i = 2 > array_tmp3[2] := ((array_tmp1[2] - ats(2,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp3[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sin ID_LINEAR iii = 3 $eq_no = 1 > array_tmp1[3] := array_tmp1_g[2] * array_x[2] / 2; > array_tmp1_g[3] := -array_tmp1[2] * array_x[2] / 2; > #emit pre cos ID_LINEAR iii = 3 $eq_no = 1 > array_tmp2[3] := -array_tmp2_g[2] * array_x[2] / 2; > array_tmp2_g[3] := array_tmp2[2] * array_x[2] / 2; > #emit pre div FULL - FULL $eq_no = 1 i = 3 > array_tmp3[3] := ((array_tmp1[3] - ats(3,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp4[3] := array_tmp3[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sin ID_LINEAR iii = 4 $eq_no = 1 > array_tmp1[4] := array_tmp1_g[3] * array_x[2] / 3; > array_tmp1_g[4] := -array_tmp1[3] * array_x[2] / 3; > #emit pre cos ID_LINEAR iii = 4 $eq_no = 1 > array_tmp2[4] := -array_tmp2_g[3] * array_x[2] / 3; > array_tmp2_g[4] := array_tmp2[3] * array_x[2] / 3; > #emit pre div FULL - FULL $eq_no = 1 i = 4 > array_tmp3[4] := ((array_tmp1[4] - ats(4,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp4[4] := array_tmp3[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sin ID_LINEAR iii = 5 $eq_no = 1 > array_tmp1[5] := array_tmp1_g[4] * array_x[2] / 4; > array_tmp1_g[5] := -array_tmp1[4] * array_x[2] / 4; > #emit pre cos ID_LINEAR iii = 5 $eq_no = 1 > array_tmp2[5] := -array_tmp2_g[4] * array_x[2] / 4; > array_tmp2_g[5] := array_tmp2[4] * array_x[2] / 4; > #emit pre div FULL - FULL $eq_no = 1 i = 5 > array_tmp3[5] := ((array_tmp1[5] - ats(5,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp4[5] := array_tmp3[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sin LINEAR $eq_no = 1 > array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp1_g[kkk] := -array_tmp1[kkk - 1] * array_x[2] / (kkk - 1); > #emit cos LINEAR $eq_no = 1 > array_tmp2[kkk] := -array_tmp2_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp2_g[kkk] := array_tmp2[kkk - 1] * array_x[2] / (kkk - 1); > #emit div FULL FULL $eq_no = 1 > array_tmp3[kkk] := ((array_tmp1[kkk] - ats(kkk,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp4[kkk] := array_tmp3[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp4[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 2 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; array_tmp1[1] := sin(array_x[1]); array_tmp1_g[1] := cos(array_x[1]); array_tmp2[1] := cos(array_x[1]); array_tmp2_g[1] := sin(array_x[1]); array_tmp3[1] := array_tmp1[1]/array_tmp2[1]; array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_tmp1_g[1]*array_x[2]; array_tmp1_g[2] := -array_tmp1[1]*array_x[2]; array_tmp2[2] := -array_tmp2_g[1]*array_x[2]; array_tmp2_g[2] := array_tmp2[1]*array_x[2]; array_tmp3[2] := (array_tmp1[2] - ats(2, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[2] := array_tmp3[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := 1/2*array_tmp1_g[2]*array_x[2]; array_tmp1_g[3] := -1/2*array_tmp1[2]*array_x[2]; array_tmp2[3] := -1/2*array_tmp2_g[2]*array_x[2]; array_tmp2_g[3] := 1/2*array_tmp2[2]*array_x[2]; array_tmp3[3] := (array_tmp1[3] - ats(3, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[3] := array_tmp3[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := 1/3*array_tmp1_g[3]*array_x[2]; array_tmp1_g[4] := -1/3*array_tmp1[3]*array_x[2]; array_tmp2[4] := -1/3*array_tmp2_g[3]*array_x[2]; array_tmp2_g[4] := 1/3*array_tmp2[3]*array_x[2]; array_tmp3[4] := (array_tmp1[4] - ats(4, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[4] := array_tmp3[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := 1/4*array_tmp1_g[4]*array_x[2]; array_tmp1_g[5] := -1/4*array_tmp1[4]*array_x[2]; array_tmp2[5] := -1/4*array_tmp2_g[4]*array_x[2]; array_tmp2_g[5] := 1/4*array_tmp2[4]*array_x[2]; array_tmp3[5] := (array_tmp1[5] - ats(5, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[5] := array_tmp3[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp1_g[kkk] := -array_tmp1[kkk - 1]*array_x[2]/(kkk - 1); array_tmp2[kkk] := -array_tmp2_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp2_g[kkk] := array_tmp2[kkk - 1]*array_x[2]/(kkk - 1); array_tmp3[kkk] := ( array_tmp1[kkk] - ats(kkk, array_tmp2, array_tmp3, 2))/ array_tmp2[1]; array_tmp4[kkk] := array_tmp3[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp4[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 12 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, "\n") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 6 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 6 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 8 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 8 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 8; > if (glob_max_iter < 2) then # if number 8 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 8; > if (errflag) then # if number 8 > quit; > fi;# end if 8 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 8 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 9 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 9 > fi;# end if 8; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 8 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 8; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 8 > if (array_fact_1[nnn] = 0) then # if number 9 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 9; > else > ret := factorial_2(nnn); > fi;# end if 8; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 8 > if (array_fact_2[mmm,nnn] = 0) then # if number 9 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 9; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 8; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0,- glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(2.0 - ln(abs(cos(x)))); > end; exact_soln_y := proc(x) return 2.0 - ln(abs(cos(x))) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_value3 := 0.0; > glob_ratio_of_radius := 0.01; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_log10normmin := 0.1; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_hmax := 1.0; > glob_hmin := 0.00000000001; > glob_hmin_init := 0.001; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_log10_abserr := 0.1e-10; > glob_log10_relerr := 0.1e-10; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.1e-50; > glob_smallish_float := 0.1e-100; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_log10abserr := 0.0; > glob_log10relerr := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/divpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := -5.0;"); > omniout_str(ALWAYS,"x_end := 5.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.05 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10000000;"); > omniout_str(ALWAYS,"glob_display_interval := 0.1;"); > omniout_str(ALWAYS,"glob_max_minutes := 10;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.001;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(2.0 - ln(abs(cos(x))));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1_g:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2_g:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2_g[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp1_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp2_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2_g[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3; > iiif := iiif + 1; > od;# end do number 2; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := -5.0; > x_end := 5.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.05 ; > glob_look_poles := true; > glob_max_iter := 10000000; > glob_display_interval := 0.1; > glob_max_minutes := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.001; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := expt(10.0 , (glob_log10_abserr)); > glob_relerr := expt(10.0 , (glob_log10_relerr)); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > if (glob_display_interval < glob_h) then # if number 2 > glob_h := glob_display_interval; > fi;# end if 2; > found_h := -1.0; > best_h := 0.0; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 3 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 3; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 3 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 4 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 4; > r_order := r_order + 1; > od;# end do number 3 > ; > atomall(); > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > value3 := test_suggested_h(); > omniout_float(ALWAYS,"value3",32,value3,32,""); > if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2 > best_h := glob_h; > found_h := 1.0; > fi;# end if 2; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > glob_h := glob_h * 0.5; > od;# end do number 2; > if (found_h > 0.0) then # if number 2 > glob_h := best_h ; > else > omniout_str(ALWAYS,"No increment to obtain desired accuracy found"); > fi;# end if 2; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2; > #BEGIN SOLUTION CODE > if (found_h > 0.0) then # if number 2 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_log10normmin := -glob_large_float ; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_y_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > if (reached_interval()) then # if number 3 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 3; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 3 > #left paren 0004C > check_for_pole(); > fi;# end if 3;#was right paren 0004C > if (reached_interval()) then # if number 3 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 3; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4; > term_no := term_no - 1; > od;# end do number 3; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 2;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 3 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 3; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 3; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 3 > logstart(html_log_file); > logitem_str(html_log_file,"2013-01-12T22:07:05-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"div") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 4 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 4; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 4 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 4; > log_revs(html_log_file," 156 ") > ; > logitem_str(html_log_file,"div diffeq.mxt") > ; > logitem_str(html_log_file,"div maple results") > ; > logitem_str(html_log_file,"Languages compared - single equations") > ; > logend(html_log_file) > ; > ; > fi;# end if 3; > if (glob_html_log) then # if number 3 > fclose(html_log_file); > fi;# end if 3 > ; > ;; > fi;# end if 2 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_value3 := 0.; glob_ratio_of_radius := 0.01; glob_percent_done := 0.; glob_subiter_method := 3; glob_log10normmin := 0.1; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_hmax := 1.0; glob_hmin := 0.1*10^(-10); glob_hmin_init := 0.001; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_log10_abserr := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.1*10^(-50); glob_smallish_float := 0.1*10^(-100); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_log10abserr := 0.; glob_log10relerr := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/divpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := -5.0;"); omniout_str(ALWAYS, "x_end := 5.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.05 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10000000;"); omniout_str(ALWAYS, "glob_display_interval := 0.1;"); omniout_str(ALWAYS, "glob_max_minutes := 10;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.001;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(2.0 - ln(abs(cos(x))));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1_g := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2_g := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2_g[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := -5.0; x_end := 5.0; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.05; glob_look_poles := true; glob_max_iter := 10000000; glob_display_interval := 0.1; glob_max_minutes := 10; glob_desired_digits_correct := 10; glob_display_interval := 0.001; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := expt(10.0, glob_log10_abserr); glob_relerr := expt(10.0, glob_log10_relerr); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); if glob_display_interval < glob_h then glob_h := glob_display_interval end if; found_h := -1.0; best_h := 0.; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; while opt_iter <= 20 and found_h < 0. do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer) ; omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); value3 := test_suggested_h(); omniout_float(ALWAYS, "value3", 32, value3, 32, ""); if value3 < est_needed_step_err and found_h < 0. then best_h := glob_h; found_h := 1.0 end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1; glob_h := glob_h*0.5 end do; if 0. < found_h then glob_h := best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found") end if; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; if 0. < found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_log10normmin := -glob_large_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;") ; omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-01-12T22:07:05-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "div"); logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 156 "); logitem_str(html_log_file, "div diffeq.mxt"); logitem_str(html_log_file, "div maple results"); logitem_str(html_log_file, "Languages compared - single equations"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 12 > main(); ##############ECHO OF PROBLEM################# ##############temp/divpostode.ode################# diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -5.0; x_end := 5.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.05 ; glob_look_poles := true; glob_max_iter := 10000000; glob_display_interval := 0.1; glob_max_minutes := 10; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.001; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(2.0 - ln(abs(cos(x)))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 10 estimated_steps = 10000 step_error = 1.0000000000000000000000000000000e-14 est_needed_step_err = 1.0000000000000000000000000000000e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 4.5374383393035527281677287356107e-66 max_value3 = 4.5374383393035527281677287356107e-66 value3 = 4.5374383393035527281677287356107e-66 best_h = 0.001 START of Soultion x[1] = -5 y[1] (analytic) = 3.259971236628587709130758159876 y[1] (numeric) = 3.259971236628587709130758159876 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = -5 y[1] (analytic) = 3.259971236628587709130758159876 y[1] (numeric) = 3.259971236628587709130758159876 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.2876 Order of pole = 9.486e-23 TOP MAIN SOLVE Loop x[1] = -4.999 y[1] (analytic) = 3.2633579796165452273496192122587 y[1] (numeric) = 3.2633579796165452273496192122587 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.2866 Order of pole = 8.612e-23 TOP MAIN SOLVE Loop x[1] = -4.998 y[1] (analytic) = 3.2667572350261429930154543198646 y[1] (numeric) = 3.2667572350261429930154543198646 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.2856 Order of pole = 7.817e-23 TOP MAIN SOLVE Loop x[1] = -4.997 y[1] (analytic) = 3.2701690882135694479210400994238 y[1] (numeric) = 3.2701690882135694479210400994237 absolute error = 1e-31 relative error = 3.0579458524154810286455717822906e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2846 Order of pole = 7.092e-23 TOP MAIN SOLVE Loop x[1] = -4.996 y[1] (analytic) = 3.2735936254368717460848438747144 y[1] (numeric) = 3.2735936254368717460848438747143 absolute error = 1e-31 relative error = 3.0547469063651623482034904218018e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2836 Order of pole = 6.433e-23 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.8MB, time=0.13 x[1] = -4.995 y[1] (analytic) = 3.2770309338686958293469015044044 y[1] (numeric) = 3.2770309338686958293469015044043 absolute error = 1e-31 relative error = 3.0515427537311981597825061480434e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2826 Order of pole = 5.833e-23 TOP MAIN SOLVE Loop x[1] = -4.994 y[1] (analytic) = 3.2804811016092523049999538571674 y[1] (numeric) = 3.2804811016092523049999538571673 absolute error = 1e-31 relative error = 3.0483333664365456955852359161215e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2816 Order of pole = 5.287e-23 TOP MAIN SOLVE Loop x[1] = -4.993 y[1] (analytic) = 3.2839442176995129449759701733792 y[1] (numeric) = 3.283944217699512944975970173379 absolute error = 2e-31 relative error = 6.0902374322333990115324557839951e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2806 Order of pole = 4.791e-23 TOP MAIN SOLVE Loop x[1] = -4.992 y[1] (analytic) = 3.2874203721346427465494558934324 y[1] (numeric) = 3.2874203721346427465494558934322 absolute error = 2e-31 relative error = 6.0837975482317966205799326479218e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2796 Order of pole = 4.341e-23 TOP MAIN SOLVE Loop x[1] = -4.991 y[1] (analytic) = 3.2909096558776726184123840235942 y[1] (numeric) = 3.290909655877672618412384023594 absolute error = 2e-31 relative error = 6.0773470229665356539094214994893e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2786 Order of pole = 3.931e-23 TOP MAIN SOLVE Loop x[1] = -4.99 y[1] (analytic) = 3.2944121608734178834329202908972 y[1] (numeric) = 3.2944121608734178834329202908971 absolute error = 1e-31 relative error = 3.0354428989688982595004436774909e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2776 Order of pole = 3.559e-23 TOP MAIN SOLVE Loop x[1] = -4.989 y[1] (analytic) = 3.2979279800626479205470823039834 y[1] (numeric) = 3.2979279800626479205470823039832 absolute error = 2e-31 relative error = 6.0644138140397101956160400680273e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2766 Order of pole = 3.221e-23 TOP MAIN SOLVE Loop x[1] = -4.988 y[1] (analytic) = 3.3014572073965124031690229533277 y[1] (numeric) = 3.3014572073965124031690229533275 absolute error = 2e-31 relative error = 6.0579310115522436987859675445203e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2756 Order of pole = 2.914e-23 TOP MAIN SOLVE Loop x[1] = -4.987 y[1] (analytic) = 3.3049999378512297303660594104908 y[1] (numeric) = 3.3049999378512297303660594104906 absolute error = 2e-31 relative error = 6.0514373301329465753462812973340e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2746 Order of pole = 2.635e-23 TOP MAIN SOLVE Loop x[1] = -4.986 y[1] (analytic) = 3.3085562674430433899577171325453 y[1] (numeric) = 3.3085562674430433899577171325451 absolute error = 2e-31 relative error = 6.0449327088085555356290912924017e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2736 Order of pole = 2.383e-23 TOP MAIN SOLVE Loop x[1] = -4.985 y[1] (analytic) = 3.3121262932434521397974764541921 y[1] (numeric) = 3.3121262932434521397974764541919 absolute error = 2e-31 relative error = 6.0384170859664542506114589102697e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2726 Order of pole = 2.154e-23 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.8MB, time=0.28 x[1] = -4.984 y[1] (analytic) = 3.3157101133947200449200589667937 y[1] (numeric) = 3.3157101133947200449200589667935 absolute error = 2e-31 relative error = 6.0318903993459852714866332085106e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2716 Order of pole = 1.946e-23 TOP MAIN SOLVE Loop x[1] = -4.983 y[1] (analytic) = 3.3193078271256725641295404948193 y[1] (numeric) = 3.319307827125672564129540494819 absolute error = 3e-31 relative error = 9.0380288790444164298033487522639e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2706 Order of pole = 1.758e-23 TOP MAIN SOLVE Loop x[1] = -4.982 y[1] (analytic) = 3.3229195347677850401132108741722 y[1] (numeric) = 3.322919534767785040113210874172 absolute error = 2e-31 relative error = 6.0188035824339201859311213997185e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2696 Order of pole = 1.587e-23 TOP MAIN SOLVE Loop x[1] = -4.981 y[1] (analytic) = 3.3265453377715701124473342004681 y[1] (numeric) = 3.3265453377715701124473342004678 absolute error = 3e-31 relative error = 9.0183649864507164879542175637468e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2686 Order of pole = 1.432e-23 TOP MAIN SOLVE Loop x[1] = -4.98 y[1] (analytic) = 3.3301853387232707430739725234632 y[1] (numeric) = 3.3301853387232707430739725234629 absolute error = 3e-31 relative error = 9.0085076200297684451800098740467e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2676 Order of pole = 1.292e-23 TOP MAIN SOLVE Loop x[1] = -4.979 y[1] (analytic) = 3.3338396413618657191389935663622 y[1] (numeric) = 3.333839641361865719138993566362 absolute error = 2e-31 relative error = 5.9990887839554414318079955235948e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2666 Order of pole = 1.166e-23 TOP MAIN SOLVE Loop x[1] = -4.978 y[1] (analytic) = 3.3375083505963946786627059531727 y[1] (numeric) = 3.3375083505963946786627059531725 absolute error = 2e-31 relative error = 5.9924943697672271729161666133531e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2656 Order of pole = 1.051e-23 TOP MAIN SOLVE Loop x[1] = -4.977 y[1] (analytic) = 3.3411915725236098905451743019884 y[1] (numeric) = 3.3411915725236098905451743019882 absolute error = 2e-31 relative error = 5.9858884370685613625302494663565e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2646 Order of pole = 9.474e-24 TOP MAIN SOLVE Loop x[1] = -4.976 y[1] (analytic) = 3.3448894144459622120738565919867 y[1] (numeric) = 3.3448894144459622120738565919865 absolute error = 2e-31 relative error = 5.9792709180828754043773841525180e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2636 Order of pole = 8.536e-24 TOP MAIN SOLVE Loop x[1] = -4.975 y[1] (analytic) = 3.3486019848899288445945304085993 y[1] (numeric) = 3.348601984889928844594530408599 absolute error = 3e-31 relative error = 8.9589626164502567379404717968170e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2626 Order of pole = 7.689e-24 TOP MAIN SOLVE Loop x[1] = -4.974 y[1] (analytic) = 3.3523293936246907115276399501667 y[1] (numeric) = 3.3523293936246907115276399501664 absolute error = 3e-31 relative error = 8.9490012697000035012279449569379e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2616 Order of pole = 6.923e-24 TOP MAIN SOLVE Loop x[1] = -4.973 y[1] (analytic) = 3.3560717516811674926689727494922 y[1] (numeric) = 3.3560717516811674926689727494919 absolute error = 3e-31 relative error = 8.9390222318614035613360648213104e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2606 Order of pole = 6.231e-24 memory used=11.4MB, alloc=3.9MB, time=0.44 TOP MAIN SOLVE Loop x[1] = -4.972 y[1] (analytic) = 3.3598291713714185649217225106776 y[1] (numeric) = 3.3598291713714185649217225106773 absolute error = 3e-31 relative error = 8.9290253967747320927645803418145e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2596 Order of pole = 5.606e-24 TOP MAIN SOLVE Loop x[1] = -4.971 y[1] (analytic) = 3.3636017663084183224905978606674 y[1] (numeric) = 3.3636017663084183224905978606671 absolute error = 3e-31 relative error = 8.9190106571163019465653429696600e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2586 Order of pole = 5.042e-24 TOP MAIN SOLVE Loop x[1] = -4.97 y[1] (analytic) = 3.3673896514262145793604636100166 y[1] (numeric) = 3.3673896514262145793604636100163 absolute error = 3e-31 relative error = 8.9089779043817770912167765300362e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2576 Order of pole = 4.533e-24 TOP MAIN SOLVE Loop x[1] = -4.969 y[1] (analytic) = 3.3711929430004789938238720638399 y[1] (numeric) = 3.3711929430004789938238720638396 absolute error = 3e-31 relative error = 8.8989270288691801728519706050970e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2566 Order of pole = 4.074e-24 TOP MAIN SOLVE Loop x[1] = -4.968 y[1] (analytic) = 3.3750117586694586991650199349669 y[1] (numeric) = 3.3750117586694586991650199349666 absolute error = 3e-31 relative error = 8.8888579196615873656581994183616e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2556 Order of pole = 3.660e-24 TOP MAIN SOLVE Loop x[1] = -4.967 y[1] (analytic) = 3.3788462174553385766132636959101 y[1] (numeric) = 3.3788462174553385766132636959098 absolute error = 3e-31 relative error = 8.8787704646095035033578217118516e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2546 Order of pole = 3.286e-24 TOP MAIN SOLVE Loop x[1] = -4.966 y[1] (analytic) = 3.3826964397860238666187306332596 y[1] (numeric) = 3.3826964397860238666187306332593 absolute error = 3e-31 relative error = 8.8686645503129102973045641075390e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2536 Order of pole = 2.950e-24 TOP MAIN SOLVE Loop x[1] = -4.965 y[1] (analytic) = 3.3865625475173530826578845451794 y[1] (numeric) = 3.3865625475173530826578845451791 absolute error = 3e-31 relative error = 8.8585400621029802556966195503195e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2526 Order of pole = 2.647e-24 TOP MAIN SOLVE Loop x[1] = -4.964 y[1] (analytic) = 3.3904446639557514684414441314646 y[1] (numeric) = 3.3904446639557514684414441314643 absolute error = 3e-31 relative error = 8.8483968840234487215230181919828e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2516 Order of pole = 2.374e-24 TOP MAIN SOLVE Loop x[1] = -4.963 y[1] (analytic) = 3.3943429138813355248757891142837 y[1] (numeric) = 3.3943429138813355248757891142833 absolute error = 4e-31 relative error = 1.1784313198415514991891973557478e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used Radius of convergence = 0.2506 Order of pole = 2.129e-24 TOP MAIN SOLVE Loop x[1] = -4.962 y[1] (analytic) = 3.3982574235714794277390984225665 y[1] (numeric) = 3.3982574235714794277390984225662 absolute error = 3e-31 relative error = 8.8280539878791132883981575329600e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2496 Order of pole = 1.908e-24 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=3.9MB, time=0.59 x[1] = -4.961 y[1] (analytic) = 3.4021883208248544611048532366317 y[1] (numeric) = 3.4021883208248544611048532366314 absolute error = 3e-31 relative error = 8.8178540312919990757352845281195e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2486 Order of pole = 1.710e-24 TOP MAIN SOLVE Loop x[1] = -4.96 y[1] (analytic) = 3.4061357349859529054212091224762 y[1] (numeric) = 3.4061357349859529054212091224759 absolute error = 3e-31 relative error = 8.8076349077508861168636418897831e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2476 Order of pole = 1.531e-24 TOP MAIN SOLVE Loop x[1] = -4.959 y[1] (analytic) = 3.4100997969701081431921885401137 y[1] (numeric) = 3.4100997969701081431921885401134 absolute error = 3e-31 relative error = 8.7973964945703817817907809281524e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2466 Order of pole = 1.370e-24 TOP MAIN SOLVE Loop x[1] = -4.958 y[1] (analytic) = 3.4140806392890230797772699690244 y[1] (numeric) = 3.4140806392890230797772699690242 absolute error = 2e-31 relative error = 5.8580924451055053359844348522998e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2456 Order of pole = 1.226e-24 TOP MAIN SOLVE Loop x[1] = -4.957 y[1] (analytic) = 3.4180783960768193223165158346681 y[1] (numeric) = 3.4180783960768193223165158346679 absolute error = 2e-31 relative error = 5.8512408676627999850695763835409e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2446 Order of pole = 1.097e-24 TOP MAIN SOLVE Loop x[1] = -4.956 y[1] (analytic) = 3.4220932031166199166014953974361 y[1] (numeric) = 3.4220932031166199166014953974359 absolute error = 2e-31 relative error = 5.8443761794054296356258454872808e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2436 Order of pole = 9.805e-25 TOP MAIN SOLVE Loop x[1] = -4.955 y[1] (analytic) = 3.4261251978676788102670887108869 y[1] (numeric) = 3.4261251978676788102670887108866 absolute error = 3e-31 relative error = 8.7562474420581979792347629102496e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2426 Order of pole = 8.763e-25 TOP MAIN SOLVE Loop x[1] = -4.954 y[1] (analytic) = 3.4301745194930705914122849128146 y[1] (numeric) = 3.4301745194930705914122849128143 absolute error = 3e-31 relative error = 8.7459106904081251626373709495733e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2416 Order of pole = 7.828e-25 TOP MAIN SOLVE Loop x[1] = -4.953 y[1] (analytic) = 3.434241308887954445123896919125 y[1] (numeric) = 3.4342413088879544451238969191248 absolute error = 2e-31 relative error = 5.8237025884695978386061845259348e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2406 Order of pole = 6.989e-25 TOP MAIN SOLVE Loop x[1] = -4.952 y[1] (analytic) = 3.4383257087084266768492220405603 y[1] (numeric) = 3.4383257087084266768492220405601 absolute error = 2e-31 relative error = 5.8167845906351913948777504681776e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2396 Order of pole = 6.238e-25 TOP MAIN SOLVE Loop x[1] = -4.951 y[1] (analytic) = 3.4424278634009765716354046686103 y[1] (numeric) = 3.4424278634009765716354046686101 absolute error = 2e-31 relative error = 5.8098530437296733688504178754617e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2386 Order of pole = 5.566e-25 TOP MAIN SOLVE Loop x[1] = -4.95 y[1] (analytic) = 3.4465479192325607924386419292941 y[1] (numeric) = 3.4465479192325607924386419292938 absolute error = 3e-31 relative error = 8.7043617854818825530728682855573e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2376 Order of pole = 4.962e-25 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.0MB, time=0.75 x[1] = -4.949 y[1] (analytic) = 3.4506860243213119695411346297333 y[1] (numeric) = 3.4506860243213119695411346297331 absolute error = 2e-31 relative error = 5.7959489385690027158462056042974e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2366 Order of pole = 4.423e-25 TOP MAIN SOLVE Loop x[1] = -4.948 y[1] (analytic) = 3.4548423286678975971562321007678 y[1] (numeric) = 3.4548423286678975971562321007676 absolute error = 2e-31 relative error = 5.7889761955392937136101568850753e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2356 Order of pole = 3.941e-25 TOP MAIN SOLVE Loop x[1] = -4.947 y[1] (analytic) = 3.4590169841875458331347100628465 y[1] (numeric) = 3.4590169841875458331347100628463 absolute error = 2e-31 relative error = 5.7819895338552671170396716541863e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2346 Order of pole = 3.510e-25 TOP MAIN SOLVE Loop x[1] = -4.946 y[1] (analytic) = 3.4632101447427552939145820216199 y[1] (numeric) = 3.4632101447427552939145820216196 absolute error = 3e-31 relative error = 8.6624832875188918018336547120446e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2336 Order of pole = 3.124e-25 TOP MAIN SOLVE Loop x[1] = -4.945 y[1] (analytic) = 3.4674219661767064501163442102562 y[1] (numeric) = 3.4674219661767064501163442102559 absolute error = 3e-31 relative error = 8.6519611090423433817159070909967e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2326 Order of pole = 2.780e-25 TOP MAIN SOLVE Loop x[1] = -4.944 y[1] (analytic) = 3.4716526063473927591354337990077 y[1] (numeric) = 3.4716526063473927591354337990074 absolute error = 3e-31 relative error = 8.6414176191331841140005389021954e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2316 Order of pole = 2.472e-25 TOP MAIN SOLVE Loop x[1] = -4.943 y[1] (analytic) = 3.475902225162490220412855034866 y[1] (numeric) = 3.4759022251624902204128550348657 absolute error = 3e-31 relative error = 8.6308526697978597045645227955638e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2306 Order of pole = 2.197e-25 TOP MAIN SOLVE Loop x[1] = -4.942 y[1] (analytic) = 3.4801709846149846074922520855355 y[1] (numeric) = 3.4801709846149846074922520855352 absolute error = 3e-31 relative error = 8.6202661112407771942678286474902e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2296 Order of pole = 1.952e-25 TOP MAIN SOLVE Loop x[1] = -4.941 y[1] (analytic) = 3.4844590488195762192474108992633 y[1] (numeric) = 3.484459048819576219247410899263 absolute error = 3e-31 relative error = 8.6096577918351615587573196359725e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2286 Order of pole = 1.735e-25 TOP MAIN SOLVE Loop x[1] = -4.94 y[1] (analytic) = 3.4887665840498826015713750005312 y[1] (numeric) = 3.4887665840498826015713750005309 absolute error = 3e-31 relative error = 8.5990275580933098430578059356796e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2276 Order of pole = 1.539e-25 TOP MAIN SOLVE Loop x[1] = -4.939 y[1] (analytic) = 3.4930937587764603211746638648537 y[1] (numeric) = 3.4930937587764603211746638648535 absolute error = 2e-31 relative error = 5.7255835030908184383975375905088e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2266 Order of pole = 1.365e-25 TOP MAIN SOLVE Loop x[1] = -4.938 y[1] (analytic) = 3.4974407437056675257992493507169 y[1] (numeric) = 3.4974407437056675257992493507166 absolute error = 3e-31 relative error = 8.5777007241626324111629775665649e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2256 Order of pole = 1.210e-25 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.0MB, time=0.90 x[1] = -4.937 y[1] (analytic) = 3.5018077118193897010086645451231 y[1] (numeric) = 3.5018077118193897010086645451228 absolute error = 3e-31 relative error = 8.5670038074173071896865903864470e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2246 Order of pole = 1.073e-25 TOP MAIN SOLVE Loop x[1] = -4.936 y[1] (analytic) = 3.5061948384156517336943677656552 y[1] (numeric) = 3.5061948384156517336943677656549 absolute error = 3e-31 relative error = 8.5562843431587887069908676701123e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2236 Order of pole = 9.504e-26 TOP MAIN SOLVE Loop x[1] = -4.935 y[1] (analytic) = 3.5106023011501401175174900779588 y[1] (numeric) = 3.5106023011501401175174900779585 absolute error = 3e-31 relative error = 8.5455421681263722542711452282428e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2226 Order of pole = 8.406e-26 TOP MAIN SOLVE Loop x[1] = -4.934 y[1] (analytic) = 3.5150302800786598867004032251001 y[1] (numeric) = 3.5150302800786598867004032250998 absolute error = 3e-31 relative error = 8.5347771170064160582318173467709e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2216 Order of pole = 7.454e-26 TOP MAIN SOLVE Loop x[1] = -4.933 y[1] (analytic) = 3.5194789577005516429571999202808 y[1] (numeric) = 3.5194789577005516429571999202805 absolute error = 3e-31 relative error = 8.5239890223979269229681022650322e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2206 Order of pole = 6.589e-26 TOP MAIN SOLVE Loop x[1] = -4.932 y[1] (analytic) = 3.5239485190030948470175203081626 y[1] (numeric) = 3.5239485190030948470175203081623 absolute error = 3e-31 relative error = 8.5131777147774084770447240420373e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2196 Order of pole = 5.814e-26 TOP MAIN SOLVE Loop x[1] = -4.931 y[1] (analytic) = 3.5284391515069243823162487002367 y[1] (numeric) = 3.5284391515069243823162487002364 absolute error = 3e-31 relative error = 8.5023430224629527740712625987094e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2186 Order of pole = 5.150e-26 TOP MAIN SOLVE Loop x[1] = -4.93 y[1] (analytic) = 3.5329510453124882652077845351035 y[1] (numeric) = 3.5329510453124882652077845351032 absolute error = 3e-31 relative error = 8.4914847715775554016179154794958e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2176 Order of pole = 4.548e-26 TOP MAIN SOLVE Loop x[1] = -4.929 y[1] (analytic) = 3.5374843931475752747891809316696 y[1] (numeric) = 3.5374843931475752747891809316693 absolute error = 3e-31 relative error = 8.4806027860116336387399687930696e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2166 Order of pole = 4.011e-26 TOP MAIN SOLVE Loop x[1] = -4.928 y[1] (analytic) = 3.5420393904159422074115915199626 y[1] (numeric) = 3.5420393904159422074115915199623 absolute error = 3e-31 relative error = 8.4696968873847265658313616209151e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2156 Order of pole = 3.527e-26 TOP MAIN SOLVE Loop x[1] = -4.927 y[1] (analytic) = 3.5466162352470714276161564098298 y[1] (numeric) = 3.5466162352470714276161564098296 absolute error = 2e-31 relative error = 5.6391779300042369140771531605674e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2146 Order of pole = 3.113e-26 TOP MAIN SOLVE Loop x[1] = -4.926 y[1] (analytic) = 3.5512151285470903900056897209194 y[1] (numeric) = 3.5512151285470903900056897209191 absolute error = 3e-31 relative error = 8.4478126258360214148750892772912e-30 % Correct digits = 31 h = 0.001 memory used=26.7MB, alloc=4.0MB, time=1.06 Real estimate of pole used Radius of convergence = 0.2136 Order of pole = 2.747e-26 TOP MAIN SOLVE Loop x[1] = -4.925 y[1] (analytic) = 3.5558362740508858469826719773664 y[1] (numeric) = 3.5558362740508858469826719773662 absolute error = 2e-31 relative error = 5.6245559296282126030247753862279e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2126 Order of pole = 2.424e-26 TOP MAIN SOLVE Loop x[1] = -4.924 y[1] (analytic) = 3.5604798783754465369443838864457 y[1] (numeric) = 3.5604798783754465369443838864455 absolute error = 2e-31 relative error = 5.6172203419740921999818922454241e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2116 Order of pole = 2.132e-26 TOP MAIN SOLVE Loop x[1] = -4.923 y[1] (analytic) = 3.5651461510744692681004889188765 y[1] (numeric) = 3.5651461510744692681004889188763 absolute error = 2e-31 relative error = 5.6098681940352905384859719759560e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2106 Order of pole = 1.879e-26 TOP MAIN SOLVE Loop x[1] = -4.922 y[1] (analytic) = 3.5698353046942644763195496222349 y[1] (numeric) = 3.5698353046942644763195496222347 absolute error = 2e-31 relative error = 5.6024993572393623562151876612208e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2096 Order of pole = 1.652e-26 TOP MAIN SOLVE Loop x[1] = -4.921 y[1] (analytic) = 3.5745475548309985431552278302606 y[1] (numeric) = 3.5745475548309985431552278302604 absolute error = 2e-31 relative error = 5.5951137013046627006568481468670e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2086 Order of pole = 1.432e-26 TOP MAIN SOLVE Loop x[1] = -4.92 y[1] (analytic) = 3.5792831201893114143748952609665 y[1] (numeric) = 3.5792831201893114143748952609662 absolute error = 3e-31 relative error = 8.3815666413148322741385287983886e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2076 Order of pole = 1.269e-26 TOP MAIN SOLVE Loop x[1] = -4.919 y[1] (analytic) = 3.5840422226423493619306208816665 y[1] (numeric) = 3.5840422226423493619306208816662 absolute error = 3e-31 relative error = 8.3704371032443866861484126869643e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2066 Order of pole = 1.110e-26 TOP MAIN SOLVE Loop x[1] = -4.918 y[1] (analytic) = 3.5888250872932540854904460637747 y[1] (numeric) = 3.5888250872932540854904460637744 absolute error = 3e-31 relative error = 8.3592817343534710081665183618152e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2056 Order of pole = 9.906e-27 TOP MAIN SOLVE Loop x[1] = -4.917 y[1] (analytic) = 3.5936319425381507556050877525451 y[1] (numeric) = 3.5936319425381507556050877525448 absolute error = 3e-31 relative error = 8.3481003284969864897623022740592e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2046 Order of pole = 8.524e-27 TOP MAIN SOLVE Loop x[1] = -4.916 y[1] (analytic) = 3.5984630201306790616490005282837 y[1] (numeric) = 3.5984630201306790616490005282835 absolute error = 2e-31 relative error = 5.5579284511512626647171352965718e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2036 Order of pole = 7.576e-27 TOP MAIN SOLVE Loop x[1] = -4.915 y[1] (analytic) = 3.6033185552481128462869414305977 y[1] (numeric) = 3.6033185552481128462869414305975 absolute error = 2e-31 relative error = 5.5504390448273493739011686820559e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2026 Order of pole = 6.617e-27 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.1MB, time=1.21 x[1] = -4.914 y[1] (analytic) = 3.6081987865591154869404980979311 y[1] (numeric) = 3.6081987865591154869404980979308 absolute error = 3e-31 relative error = 8.3143977853306919863360962775950e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2016 Order of pole = 5.865e-27 TOP MAIN SOLVE Loop x[1] = -4.913 y[1] (analytic) = 3.6131039562931798262535715035466 y[1] (numeric) = 3.6131039562931798262535715035464 absolute error = 2e-31 relative error = 5.5354067422180560179469306341303e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.2006 Order of pole = 5.186e-27 TOP MAIN SOLVE Loop x[1] = -4.912 y[1] (analytic) = 3.6180343103118031607060936075718 y[1] (numeric) = 3.6180343103118031607060936075716 absolute error = 2e-31 relative error = 5.5278635536975863205689372752462e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1996 Order of pole = 4.431e-27 TOP MAIN SOLVE Loop x[1] = -4.911 y[1] (analytic) = 3.6229900981814495722677128113046 y[1] (numeric) = 3.6229900981814495722677128113045 absolute error = 1e-31 relative error = 2.7601510710778574611380716454102e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1986 Order of pole = 3.823e-27 TOP MAIN SOLVE Loop x[1] = -4.91 y[1] (analytic) = 3.6279715732483537354339393135843 y[1] (numeric) = 3.6279715732483537354339393135842 absolute error = 1e-31 relative error = 2.7563611781683184112415326762138e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1976 Order of pole = 3.486e-27 TOP MAIN SOLVE Loop x[1] = -4.909 y[1] (analytic) = 3.632978992715222254420545848507 y[1] (numeric) = 3.6329789927152222544205458485069 absolute error = 1e-31 relative error = 2.7525620214297419712689175698378e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1966 Order of pole = 2.819e-27 TOP MAIN SOLVE Loop x[1] = -4.908 y[1] (analytic) = 3.6380126177198905861490665942817 y[1] (numeric) = 3.6380126177198905861490665942815 absolute error = 2e-31 relative error = 5.4975070461781184169456140784006e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1956 Order of pole = 2.527e-27 TOP MAIN SOLVE Loop x[1] = -4.907 y[1] (analytic) = 3.6430727134159956875546035605951 y[1] (numeric) = 3.643072713415995687554603560595 absolute error = 1e-31 relative error = 2.7449356042699767617865275981315e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1946 Order of pole = 2.277e-27 TOP MAIN SOLVE Loop x[1] = -4.906 y[1] (analytic) = 3.6481595490557266944907814849447 y[1] (numeric) = 3.6481595490557266944907814849446 absolute error = 1e-31 relative error = 2.7411081849718867933234383660590e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1936 Order of pole = 1.965e-27 TOP MAIN SOLVE Loop x[1] = -4.905 y[1] (analytic) = 3.6532733980747181980965222535611 y[1] (numeric) = 3.653273398074718198096522253561 absolute error = 1e-31 relative error = 2.7372711840482615939784039030120e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1926 Order of pole = 1.685e-27 TOP MAIN SOLVE Loop x[1] = -4.904 y[1] (analytic) = 3.6584145381791530371345377166248 y[1] (numeric) = 3.6584145381791530371345377166247 absolute error = 1e-31 relative error = 2.7334245191845174915522600174599e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1916 Order of pole = 1.483e-27 TOP MAIN SOLVE Loop x[1] = -4.903 y[1] (analytic) = 3.6635832514351439759415194075553 y[1] (numeric) = 3.6635832514351439759415194075553 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.1906 Order of pole = 1.252e-27 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.1MB, time=1.38 x[1] = -4.902 y[1] (analytic) = 3.6687798243604661919073877911694 y[1] (numeric) = 3.6687798243604661919073877911694 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.1896 Order of pole = 1.085e-27 TOP MAIN SOLVE Loop x[1] = -4.901 y[1] (analytic) = 3.674004548018715158734656898665 y[1] (numeric) = 3.674004548018715158734656898665 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.1886 Order of pole = 9.54e-28 TOP MAIN SOLVE Loop x[1] = -4.9 y[1] (analytic) = 3.6792577181159672872889469504773 y[1] (numeric) = 3.6792577181159672872889469504773 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.1876 Order of pole = 8.78e-28 TOP MAIN SOLVE Loop x[1] = -4.899 y[1] (analytic) = 3.6845396351000235800842244405324 y[1] (numeric) = 3.6845396351000235800842244405324 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used Radius of convergence = 0.1866 Order of pole = 7.04e-28 TOP MAIN SOLVE Loop x[1] = -4.898 y[1] (analytic) = 3.689850604262319574090396760456 y[1] (numeric) = 3.6898506042623195740903967604559 absolute error = 1e-31 relative error = 2.7101368246314717359857564677391e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1856 Order of pole = 6.01e-28 TOP MAIN SOLVE Loop x[1] = -4.897 y[1] (analytic) = 3.695190935842587995655401876947 y[1] (numeric) = 3.6951909358425879956554018769469 absolute error = 1e-31 relative error = 2.7062201043529490652614669663720e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1846 Order of pole = 7.03e-28 TOP MAIN SOLVE Loop x[1] = -4.896 y[1] (analytic) = 3.7005609451363638372764364559467 y[1] (numeric) = 3.7005609451363638372764364559466 absolute error = 1e-31 relative error = 2.7022930167230376352562217070279e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1836 Order of pole = 4.61e-28 TOP MAIN SOLVE Loop x[1] = -4.895 y[1] (analytic) = 3.7059609526054249954612783054439 y[1] (numeric) = 3.7059609526054249954612783054438 absolute error = 1e-31 relative error = 2.6983554678226270078467277237532e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1826 Order of pole = 3.98e-28 TOP MAIN SOLVE Loop x[1] = -4.894 y[1] (analytic) = 3.71139128399126518908593644501 y[1] (numeric) = 3.7113912839912651890859364450098 absolute error = 2e-31 relative error = 5.3888147246204154952880146915389e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1816 Order of pole = 3.89e-28 TOP MAIN SOLVE Loop x[1] = -4.893 y[1] (analytic) = 3.7168522704316996159660277638794 y[1] (numeric) = 3.7168522704316996159660277638793 absolute error = 1e-31 relative error = 2.6904486033927128266357032615579e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1806 Order of pole = 2.24e-28 TOP MAIN SOLVE Loop x[1] = -4.892 y[1] (analytic) = 3.7223442485807077097189515894089 y[1] (numeric) = 3.7223442485807077097189515894087 absolute error = 2e-31 relative error = 5.3729581855911897801531994535785e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1796 Order of pole = 2.16e-28 TOP MAIN SOLVE Loop x[1] = -4.891 y[1] (analytic) = 3.7278675607316214377459567274415 y[1] (numeric) = 3.7278675607316214377459567274413 absolute error = 2e-31 relative error = 5.3649974614642299265964620341607e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1786 Order of pole = 2.63e-28 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.1MB, time=1.53 x[1] = -4.89 y[1] (analytic) = 3.7334225549437718431198901069061 y[1] (numeric) = 3.733422554943771843119890106906 absolute error = 1e-31 relative error = 2.6785074158718172567487952866214e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1776 Order of pole = 2.63e-28 TOP MAIN SOLVE Loop x[1] = -4.889 y[1] (analytic) = 3.7390095851727109876356757873001 y[1] (numeric) = 3.7390095851727109876356757872999 absolute error = 2e-31 relative error = 5.3490100906163275279157805191103e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1766 Order of pole = 2.84e-28 TOP MAIN SOLVE Loop x[1] = -4.888 y[1] (analytic) = 3.744629011404131110104944464306 y[1] (numeric) = 3.7446290114041311101049444643058 absolute error = 2e-31 relative error = 5.3409830290506026845013168350130e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1756 Order of pole = 1.07e-28 TOP MAIN SOLVE Loop x[1] = -4.887 y[1] (analytic) = 3.7502811997916076835541259989703 y[1] (numeric) = 3.7502811997916076835541259989701 absolute error = 2e-31 relative error = 5.3329334347278658336112479135086e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1746 Order of pole = 1.34e-28 TOP MAIN SOLVE Loop x[1] = -4.886 y[1] (analytic) = 3.7559665227982981483145012655127 y[1] (numeric) = 3.7559665227982981483145012655125 absolute error = 2e-31 relative error = 5.3248610919725267056697154213556e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.885 y[1] (analytic) = 3.7616853593427334267062755973789 y[1] (numeric) = 3.7616853593427334267062755973787 absolute error = 2e-31 relative error = 5.3167657816799787918280676447426e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1726 Order of pole = 1.12e-28 TOP MAIN SOLVE Loop x[1] = -4.884 y[1] (analytic) = 3.767438094948844901425701695766 y[1] (numeric) = 3.7674380949488449014257016957657 absolute error = 3e-31 relative error = 7.9629709218639056529612914936114e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1716 Order of pole = 9.3e-29 TOP MAIN SOLVE Loop x[1] = -4.883 y[1] (analytic) = 3.7732251219003753768730428670853 y[1] (numeric) = 3.7732251219003753768730428670851 absolute error = 2e-31 relative error = 5.3005053644737343740493918890243e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1706 Order of pole = 6.1e-29 TOP MAIN SOLVE Loop x[1] = -4.882 y[1] (analytic) = 3.7790468393998286543040254502543 y[1] (numeric) = 3.779046839399828654304025450254 absolute error = 3e-31 relative error = 7.9385097022942605418583530049322e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1696 Order of pole = 9.5e-29 TOP MAIN SOLVE Loop x[1] = -4.881 y[1] (analytic) = 3.7849036537321187524584000371182 y[1] (numeric) = 3.7849036537321187524584000371179 absolute error = 3e-31 relative error = 7.9262255382427991350610402296850e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1686 Order of pole = 7.8e-29 TOP MAIN SOLVE Loop x[1] = -4.88 y[1] (analytic) = 3.7907959784330865106954293243597 y[1] (numeric) = 3.7907959784330865106954293243594 absolute error = 3e-31 relative error = 7.9139051984539681844167957957436e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1676 Order of pole = 9.2e-29 TOP MAIN SOLVE Loop x[1] = -4.879 y[1] (analytic) = 3.7967242344630583380529677587405 y[1] (numeric) = 3.7967242344630583380529677587403 absolute error = 2e-31 relative error = 5.2676988806453168678999985017714e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1666 Order of pole = 7.2e-29 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.1MB, time=1.69 x[1] = -4.878 y[1] (analytic) = 3.8026888503856292364373659040857 y[1] (numeric) = 3.8026888503856292364373659040855 absolute error = 2e-31 relative error = 5.2594363585576578459629927925789e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1656 Order of pole = 7.0e-29 TOP MAIN SOLVE Loop x[1] = -4.877 y[1] (analytic) = 3.8086902625518599477922431628017 y[1] (numeric) = 3.8086902625518599477922431628015 absolute error = 2e-31 relative error = 5.2511489833252555511201697474513e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1646 Order of pole = 5.1e-29 TOP MAIN SOLVE Loop x[1] = -4.876 y[1] (analytic) = 3.8147289152900861731558128080091 y[1] (numeric) = 3.8147289152900861731558128080088 absolute error = 3e-31 relative error = 7.8642547520886391567470506077676e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1636 Order of pole = 1.67e-28 TOP MAIN SOLVE Loop x[1] = -4.875 y[1] (analytic) = 3.8208052611015463067693723104409 y[1] (numeric) = 3.8208052611015463067693723104407 absolute error = 2e-31 relative error = 5.2344986549337919773666859034352e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1626 Order of pole = 6e-30 TOP MAIN SOLVE Loop x[1] = -4.874 y[1] (analytic) = 3.8269197608620430428955411873925 y[1] (numeric) = 3.8269197608620430428955411873922 absolute error = 3e-31 relative error = 7.8392027726346344371753633047178e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.873 y[1] (analytic) = 3.8330728840298635701643666486975 y[1] (numeric) = 3.8330728840298635701643666486973 absolute error = 2e-31 relative error = 5.2177458151991089250960277209480e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.872 y[1] (analytic) = 3.8392651088601928929718715572484 y[1] (numeric) = 3.8392651088601928929718715572481 absolute error = 3e-31 relative error = 7.8139954260429927749608027395255e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.871 y[1] (analytic) = 3.8454969226262651381562904003335 y[1] (numeric) = 3.8454969226262651381562904003333 absolute error = 2e-31 relative error = 5.2008883123331401180461665145429e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.87 y[1] (analytic) = 3.8517688218475085459921917581849 y[1] (numeric) = 3.8517688218475085459921917581847 absolute error = 2e-31 relative error = 5.1924196194118837014623896964782e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1576 Order of pole = 7.1e-29 TOP MAIN SOLVE Loop x[1] = -4.869 y[1] (analytic) = 3.8580813125249512373818705561678 y[1] (numeric) = 3.8580813125249512373818705561676 absolute error = 2e-31 relative error = 5.1839239196622439469932635021398e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.868 y[1] (analytic) = 3.8644349103841668258127714556956 y[1] (numeric) = 3.8644349103841668258127714556954 absolute error = 2e-31 relative error = 5.1754009224628867290997905521427e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.867 y[1] (analytic) = 3.8708301411260515370671312926252 y[1] (numeric) = 3.870830141126051537067131292625 absolute error = 2e-31 relative error = 5.1668503320535424584131430801604e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1546 Order of pole = 6.2e-29 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.1MB, time=1.85 x[1] = -4.866 y[1] (analytic) = 3.8772675406857377478917169128484 y[1] (numeric) = 3.8772675406857377478917169128482 absolute error = 2e-31 relative error = 5.1582718474110709111249739044682e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.865 y[1] (analytic) = 3.8837476554999627952940004709596 y[1] (numeric) = 3.8837476554999627952940004709594 absolute error = 2e-31 relative error = 5.1496651621217030411615404591555e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.864 y[1] (analytic) = 3.8902710427832265817855791307397 y[1] (numeric) = 3.8902710427832265817855791307395 absolute error = 2e-31 relative error = 5.1410299642493158383496946776282e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1516 Order of pole = 2.1e-29 TOP MAIN SOLVE Loop x[1] = -4.863 y[1] (analytic) = 3.8968382708130869524139757674471 y[1] (numeric) = 3.8968382708130869524139757674469 absolute error = 2e-31 relative error = 5.1323659361995898850229095777894e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.862 y[1] (analytic) = 3.9034499192249580933893031377199 y[1] (numeric) = 3.9034499192249580933893031377196 absolute error = 3e-31 relative error = 7.6855091318698387837490999517492e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1496 Order of pole = 3.7e-29 TOP MAIN SOLVE Loop x[1] = -4.861 y[1] (analytic) = 3.9101065793167943492257021423985 y[1] (numeric) = 3.9101065793167943492257021423983 absolute error = 2e-31 relative error = 5.1149500900547224482443366242693e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.86 y[1] (analytic) = 3.9168088543640599286379750350632 y[1] (numeric) = 3.9168088543640599286379750350629 absolute error = 3e-31 relative error = 7.6592964107948161555266288497339e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1476 Order of pole = 3.2e-29 TOP MAIN SOLVE Loop x[1] = -4.859 y[1] (analytic) = 3.9235573599454040256273061409402 y[1] (numeric) = 3.92355735994540402562730614094 absolute error = 2e-31 relative error = 5.0974149643318323595910540992225e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1466 Order of pole = 2.6e-29 TOP MAIN SOLVE Loop x[1] = -4.858 y[1] (analytic) = 3.9303527242794809818007118907229 y[1] (numeric) = 3.9303527242794809818007118907227 absolute error = 2e-31 relative error = 5.0886018133821397372382694778283e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1456 Order of pole = 2.2e-29 TOP MAIN SOLVE Loop x[1] = -4.857 y[1] (analytic) = 3.937195588573376323713655995516 y[1] (numeric) = 3.9371955885733763237136559955157 absolute error = 3e-31 relative error = 7.6196366995499845412247715580743e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.856 y[1] (analytic) = 3.9440866073831218941118210061904 y[1] (numeric) = 3.9440866073831218941118210061901 absolute error = 3e-31 relative error = 7.6063238428490854896939014466989e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1436 Order of pole = 1.69e-28 TOP MAIN SOLVE Loop x[1] = -4.855 y[1] (analytic) = 3.9510264489868069324202161763207 y[1] (numeric) = 3.9510264489868069324202161763204 absolute error = 3e-31 relative error = 7.5929635975211297508256530444570e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1426 Order of pole = 9e-30 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.1MB, time=2.01 x[1] = -4.854 y[1] (analytic) = 3.9580157957708169269400075257417 y[1] (numeric) = 3.9580157957708169269400075257415 absolute error = 2e-31 relative error = 5.0530369336499915607561527681398e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.853 y[1] (analytic) = 3.9650553446297584438367691949279 y[1] (numeric) = 3.9650553446297584438367691949277 absolute error = 2e-31 relative error = 5.0440657851315623352734861315451e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.852 y[1] (analytic) = 3.9721458073806560270670559192939 y[1] (numeric) = 3.9721458073806560270670559192936 absolute error = 3e-31 relative error = 7.5525928439628047153310456926741e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.851 y[1] (analytic) = 3.979287911192036756358782299909 y[1] (numeric) = 3.9792879111920367563587822999087 absolute error = 3e-31 relative error = 7.5390373025341587881785908867418e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1386 Order of pole = 7.3e-29 TOP MAIN SOLVE Loop x[1] = -4.85 y[1] (analytic) = 3.9864823990285492517577304021098 y[1] (numeric) = 3.9864823990285492517577304021095 absolute error = 3e-31 relative error = 7.5254314448523806371119935634478e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.849 y[1] (analytic) = 3.9937300301117969352240453954106 y[1] (numeric) = 3.9937300301117969352240453954103 absolute error = 3e-31 relative error = 7.5117746502159552872962173131768e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.848 y[1] (analytic) = 4.0010315803981003226950019230733 y[1] (numeric) = 4.0010315803981003226950019230731 absolute error = 2e-31 relative error = 4.9987108569660456403552824816817e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1356 Order of pole = 5.6e-29 TOP MAIN SOLVE Loop x[1] = -4.847 y[1] (analytic) = 4.0083878430739401532204133483018 y[1] (numeric) = 4.0083878430739401532204133483015 absolute error = 3e-31 relative error = 7.4843057045581926961892927671431e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1346 Order of pole = 3.0e-29 TOP MAIN SOLVE Loop x[1] = -4.846 y[1] (analytic) = 4.0157996290698724041630935165322 y[1] (numeric) = 4.0157996290698724041630935165319 absolute error = 3e-31 relative error = 7.4704922483765732591346317090085e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.845 y[1] (analytic) = 4.0232677675937478424153430227217 y[1] (numeric) = 4.0232677675937478424153430227214 absolute error = 3e-31 relative error = 7.4566252441960930137511251261509e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.844 y[1] (analytic) = 4.0307931066841128817975660629393 y[1] (numeric) = 4.0307931066841128817975660629391 absolute error = 2e-31 relative error = 4.9618026702573126005389698224637e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1316 Order of pole = 9e-30 TOP MAIN SOLVE Loop x[1] = -4.843 y[1] (analytic) = 4.0383765137847153292170779578661 y[1] (numeric) = 4.0383765137847153292170779578659 absolute error = 2e-31 relative error = 4.9524852206651363638274618059035e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1306 Order of pole = 5.1e-29 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.1MB, time=2.17 x[1] = -4.842 y[1] (analytic) = 4.0460188763410882930066238854408 y[1] (numeric) = 4.0460188763410882930066238854406 absolute error = 2e-31 relative error = 4.9431306702371291649851731874659e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1296 Order of pole = 3.8e-29 TOP MAIN SOLVE Loop x[1] = -4.841 y[1] (analytic) = 4.0537211024202382967907754171883 y[1] (numeric) = 4.0537211024202382967907754171882 absolute error = 1e-31 relative error = 2.4668692658776126777806337429842e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1286 Order of pole = 1e-30 TOP MAIN SOLVE Loop x[1] = -4.84 y[1] (analytic) = 4.0614841213545197075655208706915 y[1] (numeric) = 4.0614841213545197075655208706914 absolute error = 1e-31 relative error = 2.4621541538035026653283694417966e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1276 Order of pole = 2.7e-29 TOP MAIN SOLVE Loop x[1] = -4.839 y[1] (analytic) = 4.0693088844108371807625632356911 y[1] (numeric) = 4.069308884410837180762563235691 absolute error = 1e-31 relative error = 2.4574197447407142072630304639960e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1266 Order of pole = 1.08e-28 TOP MAIN SOLVE Loop x[1] = -4.838 y[1] (analytic) = 4.0771963654863811997494447284817 y[1] (numeric) = 4.0771963654863811997494447284816 absolute error = 1e-31 relative error = 2.4526657790265810451865849781195e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1256 Order of pole = 1.6e-29 TOP MAIN SOLVE Loop x[1] = -4.837 y[1] (analytic) = 4.0851475618321692144647937066179 y[1] (numeric) = 4.0851475618321692144647937066178 absolute error = 1e-31 relative error = 2.4478919913274926238294433189968e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1246 Order of pole = 4.1e-29 TOP MAIN SOLVE Loop x[1] = -4.836 y[1] (analytic) = 4.0931634948057366575950169062117 y[1] (numeric) = 4.0931634948057366575950169062116 absolute error = 1e-31 relative error = 2.4430981104688573904040886240698e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1236 Order of pole = 4.4e-29 TOP MAIN SOLVE Loop x[1] = -4.835 y[1] (analytic) = 4.1012452106543985546282769842906 y[1] (numeric) = 4.1012452106543985546282769842904 absolute error = 2e-31 relative error = 4.8765677185170747528786536510280e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1226 Order of pole = 3.3e-29 TOP MAIN SOLVE Loop x[1] = -4.834 y[1] (analytic) = 4.109393781330583890061298632229 y[1] (numeric) = 4.1093937813305838900612986322288 absolute error = 2e-31 relative error = 4.8668979086068953090775930881535e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1216 Order of pole = 2.2e-29 TOP MAIN SOLVE Loop x[1] = -4.833 y[1] (analytic) = 4.1176103053408317181599987244319 y[1] (numeric) = 4.1176103053408317181599987244317 absolute error = 2e-31 relative error = 4.8571862116379944502942386043114e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.832 y[1] (analytic) = 4.1258959086301306161495541590161 y[1] (numeric) = 4.1258959086301306161495541590159 absolute error = 2e-31 relative error = 4.8474320348620595071806846335858e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1196 Order of pole = 1.53e-28 TOP MAIN SOLVE Loop x[1] = -4.831 y[1] (analytic) = 4.1342517455033819075465233669056 y[1] (numeric) = 4.1342517455033819075465233669054 absolute error = 2e-31 relative error = 4.8376347719398065297273157845483e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.1MB, time=2.32 x[1] = -4.83 y[1] (analytic) = 4.1426789995858726075607830777096 y[1] (numeric) = 4.1426789995858726075607830777093 absolute error = 3e-31 relative error = 7.2416907037689819771223322347131e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1176 Order of pole = 4.1e-29 TOP MAIN SOLVE Loop x[1] = -4.829 y[1] (analytic) = 4.1511788848247567755824467144763 y[1] (numeric) = 4.1511788848247567755824467144761 absolute error = 2e-31 relative error = 4.8179084917571086120621917400656e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1166 Order of pole = 3.3e-29 TOP MAIN SOLVE Loop x[1] = -4.828 y[1] (analytic) = 4.1597526465336644605361338304908 y[1] (numeric) = 4.1597526465336644605361338304905 absolute error = 3e-31 relative error = 7.2119672848814937371421463686129e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.827 y[1] (analytic) = 4.1684015624826863006878160714432 y[1] (numeric) = 4.168401562482686300687816071443 absolute error = 2e-31 relative error = 4.7980022318406544278185234205555e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1146 Order of pole = 5.2e-29 TOP MAIN SOLVE Loop x[1] = -4.826 y[1] (analytic) = 4.1771269440361197509124168695575 y[1] (numeric) = 4.1771269440361197509124168695573 absolute error = 2e-31 relative error = 4.7879799364381154314572360085391e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1136 Order of pole = 1.1e-29 TOP MAIN SOLVE Loop x[1] = -4.825 y[1] (analytic) = 4.1859301373405105764632642795663 y[1] (numeric) = 4.185930137340510576463264279566 absolute error = 3e-31 relative error = 7.1668659092958976342778692605535e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.824 y[1] (analytic) = 4.1948125245656814560536984382819 y[1] (numeric) = 4.1948125245656814560536984382817 absolute error = 2e-31 relative error = 4.7677935266179127140651640988084e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.823 y[1] (analytic) = 4.2037755252016091321793637214162 y[1] (numeric) = 4.203775525201609132179363721416 absolute error = 2e-31 relative error = 4.7576279656466239963214288090083e-30 % Correct digits = 31 h = 0.001 Complex estimate of poles used Radius of convergence = 0.101 Order of pole = 6.746e-27 TOP MAIN SOLVE Loop x[1] = -4.822 y[1] (analytic) = 4.212820597414193464218245217077 y[1] (numeric) = 4.2128205974141934642182452170768 absolute error = 2e-31 relative error = 4.7474131730831101640109491761396e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1096 Order of pole = 2.1e-29 TOP MAIN SOLVE Loop x[1] = -4.821 y[1] (analytic) = 4.2219492394631569964307864206525 y[1] (numeric) = 4.2219492394631569964307864206523 absolute error = 2e-31 relative error = 4.7371483799608886260914017189456e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1086 Order of pole = 1.18e-28 TOP MAIN SOLVE Loop x[1] = -4.82 y[1] (analytic) = 4.2311629911855233590604142329946 y[1] (numeric) = 4.2311629911855233590604142329944 absolute error = 2e-31 relative error = 4.7268327979008507312821923019595e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.819 y[1] (analytic) = 4.2404634355483481905083477818901 y[1] (numeric) = 4.2404634355483481905083477818899 absolute error = 2e-31 relative error = 4.7164656184362864604056247105977e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.1MB, time=2.48 x[1] = -4.818 y[1] (analytic) = 4.249852200274618630665024343906 y[1] (numeric) = 4.2498522002746186306650243439058 absolute error = 2e-31 relative error = 4.7060460123078238081440637219806e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1056 Order of pole = 1.9e-29 TOP MAIN SOLVE Loop x[1] = -4.817 y[1] (analytic) = 4.2593309595464982449766332201665 y[1] (numeric) = 4.2593309595464982449766332201663 absolute error = 2e-31 relative error = 4.6955731287266417669309485591255e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1046 Order of pole = 6.3e-29 TOP MAIN SOLVE Loop x[1] = -4.816 y[1] (analytic) = 4.2689014357903750905329176478337 y[1] (numeric) = 4.2689014357903750905329176478335 absolute error = 2e-31 relative error = 4.6850460946042096352187868095990e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1036 Order of pole = 2e-30 TOP MAIN SOLVE Loop x[1] = -4.815 y[1] (analytic) = 4.2785654015484732788886754163041 y[1] (numeric) = 4.2785654015484732788886754163038 absolute error = 3e-31 relative error = 7.0116960206200368171022497674615e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.814 y[1] (analytic) = 4.2883246814421147463315404798321 y[1] (numeric) = 4.2883246814421147463315404798319 absolute error = 2e-31 relative error = 4.6638259660120296208751875969713e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = -4.813 y[1] (analytic) = 4.2981811542320701217290547323145 y[1] (numeric) = 4.2981811542320701217290547323143 absolute error = 2e-31 relative error = 4.6531310064275963090124118036447e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.1006 Order of pole = 2.5e-29 TOP MAIN SOLVE Loop x[1] = -4.812 y[1] (analytic) = 4.3081367549818179066440727412812 y[1] (numeric) = 4.308136754981817906644072741281 absolute error = 2e-31 relative error = 4.6423781642661452963036697437596e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used Radius of convergence = 0.09961 Order of pole = 1.02e-28 TOP MAIN SOLVE Loop x[1] = -4.8100177407096553281681099049909 y[1] (analytic) = 4.3281722209962260474135195837425 y[1] (numeric) = 4.3281722209962260474135195837424 absolute error = 1e-31 relative error = 2.3104441065190043200251194049523e-30 % Correct digits = 31 h = 0.00098614909419157040882974575830146 NO POLE TOP MAIN SOLVE Loop x[1] = -4.8090315916154637577592801592326 y[1] (analytic) = 4.3382926422673920384013497356244 y[1] (numeric) = 4.3382926422673920384013497356242 absolute error = 2e-31 relative error = 4.6101085494193578833539806030009e-30 % Correct digits = 31 h = 0.00098614909419157040882974575830146 Real estimate of pole used Radius of convergence = 0.09664 Order of pole = 9.4e-29 TOP MAIN SOLVE Loop x[1] = -4.8080651655031560187586270083895 y[1] (analytic) = 4.3483119820236176554993442478215 y[1] (numeric) = 4.3483119820236176554993442478217 absolute error = 2e-31 relative error = 4.5994859804637106474848484030941e-30 % Correct digits = 31 h = 0.00096642611230773900065315084313707 Complex estimate of poles used Radius of convergence = 0.07202 Order of pole = 2.276e-26 TOP MAIN SOLVE Loop x[1] = -4.8073449452700603778660445085668 y[1] (analytic) = 4.3558452468344652990582098043686 y[1] (numeric) = 4.3558452468344652990582098043683 absolute error = 3e-31 relative error = 6.8872970227310021450252542526072e-30 % memory used=64.8MB, alloc=4.1MB, time=2.64 Correct digits = 31 h = 0.00072022023309564089258249982265019 NO POLE TOP MAIN SOLVE Loop x[1] = -4.8066247250369647369734620087441 y[1] (analytic) = 4.3634362154265243455866010897742 y[1] (numeric) = 4.3634362154265243455866010897733 absolute error = 9e-31 relative error = 2.0625946056416120169223690339441e-29 % Correct digits = 30 h = 0.00072022023309564089258249982265019 Real estimate of pole used Radius of convergence = 0.09424 Order of pole = 2.0e-29 TOP MAIN SOLVE Loop x[1] = -4.8059045048038690960808795089214 y[1] (analytic) = 4.3710857705647245781490446520257 y[1] (numeric) = 4.3710857705647245781490446520243 absolute error = 1.4e-30 relative error = 3.2028655429909953716982998712875e-29 % Correct digits = 30 h = 0.00072022023309564089258249982265019 NO POLE TOP MAIN SOLVE Loop x[1] = -4.804464064337677814295714509276 y[1] (analytic) = 4.3865642745550917392230461510637 y[1] (numeric) = 4.3865642745550917392230461510612 absolute error = 2.5e-30 relative error = 5.6992211752181906831513399322558e-29 % Correct digits = 30 h = 0.00072022023309564089258249982265019 Real estimate of pole used Radius of convergence = 0.09208 Order of pole = 1.51e-28 TOP MAIN SOLVE Loop x[1] = -4.8037438441045821734031320094533 y[1] (analytic) = 4.3943950938924958630762805122239 y[1] (numeric) = 4.3943950938924958630762805122209 absolute error = 3.0e-30 relative error = 6.8268781843706285657650366809089e-29 % Correct digits = 30 h = 0.00072022023309564089258249982265019 NO POLE TOP MAIN SOLVE Loop x[1] = -4.8023034036383908916179670098079 y[1] (analytic) = 4.4102447109560673922180281121712 y[1] (numeric) = 4.4102447109560673922180281121671 absolute error = 4.1e-30 relative error = 9.2965362892781259734790540185254e-29 % Correct digits = 30 h = 0.00072022023309564089258249982265019 NO POLE TOP MAIN SOLVE Loop x[1] = -4.8015831834052952507253845099852 y[1] (analytic) = 4.4182655161730775180190217415206 y[1] (numeric) = 4.418265516173077518019021741516 absolute error = 4.6e-30 relative error = 1.0411325401702733168240153457710e-28 % Correct digits = 29 h = 0.00072022023309564089258249982265019 NO POLE TOP MAIN SOLVE Loop x[1] = -4.8008629631721996098328020101625 y[1] (analytic) = 4.4263516981654598829552375265903 y[1] (numeric) = 4.4263516981654598829552375265851 absolute error = 5.2e-30 relative error = 1.1747823839111531539806229111732e-28 % Correct digits = 29 h = 0.00072022023309564089258249982265019 Real estimate of pole used Radius of convergence = 0.08847 Order of pole = 1.6e-29 TOP MAIN SOLVE Loop x[1] = -4.7994225227060083280476370105171 y[1] (analytic) = 4.4427244825431142699629190090371 y[1] (numeric) = 4.4427244825431142699629190090307 absolute error = 6.4e-30 relative error = 1.4405574833973268824607343700015e-28 % Correct digits = 29 h = 0.00072022023309564089258249982265019 NO POLE TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.1MB, time=2.79 x[1] = -4.7987023024729126871550545106944 y[1] (analytic) = 4.4510132967227909570166428750898 y[1] (numeric) = 4.4510132967227909570166428750828 absolute error = 7.0e-30 relative error = 1.5726755984202488662125773147254e-28 % Correct digits = 29 h = 0.00072022023309564089258249982265019 Complex estimate of poles used Radius of convergence = 0.05723 Order of pole = 8.027e-27 TOP MAIN SOLVE Loop x[1] = -4.7975577185377326939196005824156 y[1] (analytic) = 4.4643300803402403068998651101427 y[1] (numeric) = 4.4643300803402403068998651101359 absolute error = 6.8e-30 relative error = 1.5231848625946025735815626680252e-28 % Correct digits = 29 h = 0.00057229196758999661772696413940686 Real estimate of pole used Radius of convergence = 0.08517 Order of pole = 4e-30 TOP MAIN SOLVE Loop x[1] = -4.7969854265701426973018736182762 y[1] (analytic) = 4.4710560649655134047805013600758 y[1] (numeric) = 4.471056064965513404780501360069 absolute error = 6.8e-30 relative error = 1.5208934759918852499736006820465e-28 % Correct digits = 29 h = 0.00057229196758999661772696413940686 Real estimate of pole used Radius of convergence = 0.0846 Order of pole = 2.7e-29 TOP MAIN SOLVE Loop x[1] = -4.7958408426349627040664196899974 y[1] (analytic) = 4.4846462851460490989602165415548 y[1] (numeric) = 4.4846462851460490989602165415482 absolute error = 6.6e-30 relative error = 1.4716879727751062306189456907632e-28 % Correct digits = 29 h = 0.00057229196758999661772696413940686 Real estimate of pole used Radius of convergence = 0.08345 Order of pole = 2.0e-29 TOP MAIN SOLVE Loop x[1] = -4.794961242262060980216720291203 y[1] (analytic) = 4.495218088923505727149289989791 y[1] (numeric) = 4.4952180889235057271492899897846 absolute error = 6.4e-30 relative error = 1.4237351499741456893370471657437e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 Real estimate of pole used Radius of convergence = 0.08257 Order of pole = 6.8e-29 memory used=72.4MB, alloc=4.1MB, time=2.95 TOP MAIN SOLVE Loop x[1] = -4.7938856628434699349048167699105 y[1] (analytic) = 4.5083001623047747482426821655753 y[1] (numeric) = 4.5083001623047747482426821655696 absolute error = 5.7e-30 relative error = 1.2643346260879828996265331901978e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 Real estimate of pole used Radius of convergence = 0.0815 Order of pole = 1e-30 TOP MAIN SOLVE Loop x[1] = -4.7929637376275347532088994659455 y[1] (analytic) = 4.519652146941565767851680111687 y[1] (numeric) = 4.519652146941565767851680111682 absolute error = 5.0e-30 relative error = 1.1062798280578924854797544001052e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 NO POLE memory used=76.2MB, alloc=4.1MB, time=3.10 TOP MAIN SOLVE Loop x[1] = -4.791888158208943707896995944653 y[1] (analytic) = 4.5330621744207562347530152453577 y[1] (numeric) = 4.5330621744207562347530152453533 absolute error = 4.4e-30 relative error = 9.7064629398387654236184226492700e-29 % Correct digits = 30 h = 0.00015365420265586361598621732750778 Real estimate of pole used Radius of convergence = 0.0795 Order of pole = 7e-30 TOP MAIN SOLVE Loop x[1] = -4.790966232993008526201078640688 y[1] (analytic) = 4.5447023044343475512083567875725 y[1] (numeric) = 4.5447023044343475512083567875686 absolute error = 3.9e-30 relative error = 8.5814201651771559392694799703666e-29 % Correct digits = 30 h = 0.00015365420265586361598621732750778 NO POLE memory used=80.1MB, alloc=4.1MB, time=3.25 TOP MAIN SOLVE Loop x[1] = -4.7898906535744174808891751193955 y[1] (analytic) = 4.5584570387128803276098184854954 y[1] (numeric) = 4.5584570387128803276098184854922 absolute error = 3.2e-30 relative error = 7.0199191805996434433742002600378e-29 % Correct digits = 30 h = 0.00015365420265586361598621732750778 NO POLE memory used=83.9MB, alloc=4.1MB, time=3.40 TOP MAIN SOLVE Loop x[1] = -4.7889687283584822991932578154305 y[1] (analytic) = 4.5704002247274259619539787660055 y[1] (numeric) = 4.570400224727425961953978766003 absolute error = 2.5e-30 relative error = 5.4699804767078083772344352024394e-29 % Correct digits = 30 h = 0.00015365420265586361598621732750778 Real estimate of pole used Radius of convergence = 0.07658 Order of pole = 2.6e-29 TOP MAIN SOLVE Loop x[1] = -4.787893148939891253881354294138 y[1] (analytic) = 4.5845177387989343265773483577121 y[1] (numeric) = 4.5845177387989343265773483577103 absolute error = 1.8e-30 relative error = 3.9262581203831689946496237855233e-29 % Correct digits = 30 h = 0.00015365420265586361598621732750778 NO POLE memory used=87.7MB, alloc=4.1MB, time=3.55 TOP MAIN SOLVE Loop x[1] = -4.786971223723956072185436990173 y[1] (analytic) = 4.5967800821760374463695756832689 y[1] (numeric) = 4.5967800821760374463695756832677 absolute error = 1.2e-30 relative error = 2.6105229716187345336628879162501e-29 % Correct digits = 30 h = 0.00015365420265586361598621732750778 Real estimate of pole used Radius of convergence = 0.07458 Order of pole = 1.9e-29 TOP MAIN SOLVE Loop x[1] = -4.7858956443053650268735334688805 y[1] (analytic) = 4.6112799118087641220484589797257 y[1] (numeric) = 4.6112799118087641220484589797253 absolute error = 4e-31 relative error = 8.6743812488082273921614468572938e-30 % Correct digits = 31 h = 0.00015365420265586361598621732750778 NO POLE memory used=91.5MB, alloc=4.1MB, time=3.70 TOP MAIN SOLVE Loop x[1] = -4.7849737190894298451776161649155 y[1] (analytic) = 4.6238788349029990145305040915283 y[1] (numeric) = 4.6238788349029990145305040915286 absolute error = 3e-31 relative error = 6.4880592833763880718712693206159e-30 % Correct digits = 31 h = 0.00015365420265586361598621732750778 Real estimate of pole used Radius of convergence = 0.07258 Order of pole = 7.1e-29 TOP MAIN SOLVE Loop x[1] = -4.783898139670838799865712643623 y[1] (analytic) = 4.6387821408759074348877635630163 y[1] (numeric) = 4.6387821408759074348877635630174 absolute error = 1.1e-30 relative error = 2.3713120525903702265045651238455e-29 % Correct digits = 30 h = 0.00015365420265586361598621732750778 NO POLE memory used=95.3MB, alloc=4.1MB, time=3.84 TOP MAIN SOLVE Loop x[1] = -4.782976214454903618169795339658 y[1] (analytic) = 4.651736535602313482244745729079 y[1] (numeric) = 4.6517365356023134822447457290805 absolute error = 1.5e-30 relative error = 3.2246022286938868094732319357852e-29 % Correct digits = 30 h = 0.00015365420265586361598621732750778 NO POLE TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.1MB, time=3.99 x[1] = -4.7819006350363125728578918183655 y[1] (analytic) = 4.6670662890750813198870590811469 y[1] (numeric) = 4.6670662890750813198870590811492 absolute error = 2.3e-30 relative error = 4.9281494145132739162080725183310e-29 % Correct digits = 30 h = 0.00015365420265586361598621732750778 NO POLE TOP MAIN SOLVE Loop x[1] = -4.7809787098203773911619745144005 y[1] (analytic) = 4.6803966869673162047928232317271 y[1] (numeric) = 4.6803966869673162047928232317301 absolute error = 3.0e-30 relative error = 6.4097131090481634106397457300672e-29 % Correct digits = 30 h = 0.00015365420265586361598621732750778 NO POLE memory used=103.0MB, alloc=4.1MB, time=4.14 TOP MAIN SOLVE Loop x[1] = -4.779903130401786345850070993108 y[1] (analytic) = 4.6961778820590026412520743132157 y[1] (numeric) = 4.6961778820590026412520743132194 absolute error = 3.7e-30 relative error = 7.8787475536973565356469895258282e-29 % Correct digits = 30 h = 0.00015365420265586361598621732750778 NO POLE TOP MAIN SOLVE Loop x[1] = -4.778981205185851164154153689143 y[1] (analytic) = 4.7099066496597663401430595695024 y[1] (numeric) = 4.7099066496597663401430595695069 absolute error = 4.5e-30 relative error = 9.5543294904264619533397528903149e-29 % Correct digits = 30 h = 0.00015365420265586361598621732750778 NO POLE memory used=106.8MB, alloc=4.1MB, time=4.29 TOP MAIN SOLVE Loop x[1] = -4.7779056257672601188422501678505 y[1] (analytic) = 4.7261665481736428343592140050461 y[1] (numeric) = 4.7261665481736428343592140050514 absolute error = 5.3e-30 relative error = 1.1214162569129322402908129444059e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 Real estimate of pole used Radius of convergence = 0.06552 Order of pole = 1.4e-29 TOP MAIN SOLVE Loop x[1] = -4.7769837005513249371463328638855 y[1] (analytic) = 4.7403181124247685163417845221343 y[1] (numeric) = 4.7403181124247685163417845221403 absolute error = 6.0e-30 relative error = 1.2657378381998246822280358293586e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 NO POLE memory used=110.6MB, alloc=4.1MB, time=4.44 TOP MAIN SOLVE Loop x[1] = -4.775908121132733891834429342593 y[1] (analytic) = 4.7570865267347558082565267077322 y[1] (numeric) = 4.757086526734755808256526707739 absolute error = 6.8e-30 relative error = 1.4294463558281104907243745180796e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 Real estimate of pole used Radius of convergence = 0.06352 Order of pole = 2.1e-29 TOP MAIN SOLVE Loop x[1] = -4.774986195916798710138512038628 y[1] (analytic) = 4.7716876360694463950898520782736 y[1] (numeric) = 4.7716876360694463950898520782812 absolute error = 7.6e-30 relative error = 1.5927278941209786242165174345174e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 Real estimate of pole used Radius of convergence = 0.0626 Order of pole = 1.07e-28 memory used=114.4MB, alloc=4.1MB, time=4.59 TOP MAIN SOLVE Loop x[1] = -4.7739106164982076648266085173355 y[1] (analytic) = 4.7889972575391774491316466823414 y[1] (numeric) = 4.7889972575391774491316466823498 absolute error = 8.4e-30 relative error = 1.7540206327694440000175373626988e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 Real estimate of pole used Radius of convergence = 0.06152 Order of pole = 8e-30 TOP MAIN SOLVE Loop x[1] = -4.7729886912822724831306912133705 y[1] (analytic) = 4.8040772856848793186039033978405 y[1] (numeric) = 4.8040772856848793186039033978497 absolute error = 9.2e-30 relative error = 1.9150399656171286455998174770926e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 NO POLE memory used=118.2MB, alloc=4.1MB, time=4.74 TOP MAIN SOLVE Loop x[1] = -4.771913111863681437818787692078 y[1] (analytic) = 4.8219640677067258405100205882703 y[1] (numeric) = 4.8219640677067258405100205882804 absolute error = 1.01e-29 relative error = 2.0945821781711142414481019377711e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 NO POLE TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.1MB, time=4.89 x[1] = -4.770991186647746256122870388113 y[1] (analytic) = 4.8375553688665538234642295736055 y[1] (numeric) = 4.8375553688665538234642295736164 absolute error = 1.09e-29 relative error = 2.2532041845246901366017663958258e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 Real estimate of pole used Radius of convergence = 0.0586 Order of pole = 1.4e-29 TOP MAIN SOLVE Loop x[1] = -4.7699156072291552108109668668205 y[1] (analytic) = 4.856058975796731093128233709115 y[1] (numeric) = 4.8560589757967310931282337091267 absolute error = 1.17e-29 relative error = 2.4093611832793663776921275509065e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 NO POLE memory used=125.8MB, alloc=4.1MB, time=5.04 TOP MAIN SOLVE Loop x[1] = -4.7689936820132200291150495628555 y[1] (analytic) = 4.8721973020015482371701087895749 y[1] (numeric) = 4.8721973020015482371701087895873 absolute error = 1.24e-29 relative error = 2.5450529261009101175475993547027e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 Real estimate of pole used Radius of convergence = 0.0566 Order of pole = 6.0e-29 TOP MAIN SOLVE Loop x[1] = -4.767918102594628983803146041563 y[1] (analytic) = 4.891361638080181036440286495562 y[1] (numeric) = 4.8913616380801810364402864955753 absolute error = 1.33e-29 relative error = 2.7190792634216553109614016423876e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 NO POLE memory used=129.7MB, alloc=4.1MB, time=5.19 TOP MAIN SOLVE Loop x[1] = -4.766996177378693802107228737598 y[1] (analytic) = 4.9080866322441509388530250552786 y[1] (numeric) = 4.9080866322441509388530250552929 absolute error = 1.43e-29 relative error = 2.9135590040434012929540154357922e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 NO POLE TOP MAIN SOLVE Loop x[1] = -4.7659205979601027567953252163055 y[1] (analytic) = 4.9279604682334722623325897184727 y[1] (numeric) = 4.927960468233472262332589718488 absolute error = 1.53e-29 relative error = 3.1047326979643155353875915635130e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 Real estimate of pole used Radius of convergence = 0.05353 Order of pole = 5.9e-29 memory used=133.5MB, alloc=4.1MB, time=5.35 TOP MAIN SOLVE Loop x[1] = -4.7649986727441675750994079123405 y[1] (analytic) = 4.9453162500120325995488547110567 y[1] (numeric) = 4.9453162500120325995488547110728 absolute error = 1.61e-29 relative error = 3.2556057461362206309389803951693e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 Real estimate of pole used Radius of convergence = 0.05261 Order of pole = 3.8e-29 TOP MAIN SOLVE Loop x[1] = -4.763923093325576529787504391048 y[1] (analytic) = 4.9659539700488625019477143263376 y[1] (numeric) = 4.9659539700488625019477143263547 absolute error = 1.71e-29 relative error = 3.4434471408988401391426870385160e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 Real estimate of pole used Radius of convergence = 0.05153 Order of pole = 5.9e-29 memory used=137.3MB, alloc=4.1MB, time=5.51 TOP MAIN SOLVE Loop x[1] = -4.7628475139069854844756008697555 y[1] (analytic) = 4.9870277783271329188389425545407 y[1] (numeric) = 4.9870277783271329188389425545588 absolute error = 1.81e-29 relative error = 3.6294163186056146419188555386432e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 Real estimate of pole used Radius of convergence = 0.05046 Order of pole = 1.8e-29 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.1MB, time=5.67 x[1] = -4.7619255886910503027796835657905 y[1] (analytic) = 5.0054523337223003295175783028361 y[1] (numeric) = 5.0054523337223003295175783028552 absolute error = 1.91e-29 relative error = 3.8158389545178829826578475650559e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 NO POLE TOP MAIN SOLVE Loop x[1] = -4.760850009272459257467780044498 y[1] (analytic) = 5.0273867746596936348448975729025 y[1] (numeric) = 5.0273867746596936348448975729225 absolute error = 2.00e-29 relative error = 3.9782099322075354271610568142163e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 NO POLE memory used=144.9MB, alloc=4.1MB, time=5.84 TOP MAIN SOLVE Loop x[1] = -4.759928084056524075771862740533 y[1] (analytic) = 5.0465793608590378847447778017528 y[1] (numeric) = 5.0465793608590378847447778017738 absolute error = 2.10e-29 relative error = 4.1612344715857875544439851774037e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 Real estimate of pole used Radius of convergence = 0.04754 Order of pole = 7.4e-29 TOP MAIN SOLVE Loop x[1] = -4.7588525046379330304599592192405 y[1] (analytic) = 5.0694475346161212193705678724383 y[1] (numeric) = 5.0694475346161212193705678724603 absolute error = 2.20e-29 relative error = 4.3397233820402734910968272640414e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 NO POLE memory used=148.7MB, alloc=4.1MB, time=6.00 TOP MAIN SOLVE Loop x[1] = -4.7579305794219978487640419152755 y[1] (analytic) = 5.0894748029291953893833009872726 y[1] (numeric) = 5.0894748029291953893833009872957 absolute error = 2.31e-29 relative error = 4.5387787334569433884468674502488e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 NO POLE TOP MAIN SOLVE Loop x[1] = -4.756855000003406803452138393983 y[1] (analytic) = 5.1133595451163619503778768506837 y[1] (numeric) = 5.1133595451163619503778768507079 absolute error = 2.42e-29 relative error = 4.7327006416188349068629014625307e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 NO POLE memory used=152.5MB, alloc=4.1MB, time=6.17 TOP MAIN SOLVE Loop x[1] = -4.755933074787471621756221090018 y[1] (analytic) = 5.1342972245349575811589439739614 y[1] (numeric) = 5.1342972245349575811589439739868 absolute error = 2.54e-29 relative error = 4.9471230217492175000325444393842e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 Real estimate of pole used Radius of convergence = 0.04354 Order of pole = 5.1e-29 TOP MAIN SOLVE Loop x[1] = -4.7548574953688805764443175687255 y[1] (analytic) = 5.1592929153665852837673034022733 y[1] (numeric) = 5.1592929153665852837673034022999 absolute error = 2.66e-29 relative error = 5.1557452612883832862121316847486e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 Complex estimate of poles used Radius of convergence = 0.01859 Order of pole = 1.047e-27 memory used=156.4MB, alloc=4.1MB, time=6.33 TOP MAIN SOLVE Loop x[1] = -4.7539355701529453947484002647605 y[1] (analytic) = 5.181227539496708573742333811126 y[1] (numeric) = 5.1812275394967085737423338111538 absolute error = 2.78e-29 relative error = 5.3655238624591310956701581264298e-28 % Correct digits = 29 h = 0.00015365420265586361598621732750778 NO POLE memory used=160.2MB, alloc=4.1MB, time=6.49 TOP MAIN SOLVE Loop x[1] = -4.7528778758806310998951774124243 y[1] (analytic) = 5.2070007677923958894632571778411 y[1] (numeric) = 5.2070007677923958894632571778639 absolute error = 2.28e-29 relative error = 4.3787203069045217268929134874788e-28 % Correct digits = 29 h = 0.00012506431116709460354173628016476 NO POLE memory used=164.0MB, alloc=4.1MB, time=6.65 TOP MAIN SOLVE Loop x[1] = -4.7519998035981998459448059890454 y[1] (analytic) = 5.228914401156607225601958107418 y[1] (numeric) = 5.228914401156607225601958107442 absolute error = 2.40e-29 relative error = 4.5898628584723688445480768573945e-28 % Correct digits = 29 h = 5.7923690097243026679206699906218e-05 NO POLE memory used=167.8MB, alloc=4.2MB, time=6.81 memory used=171.6MB, alloc=4.2MB, time=6.97 memory used=175.4MB, alloc=4.2MB, time=7.13 TOP MAIN SOLVE Loop x[1] = -4.7509904472741993525784786915359 y[1] (analytic) = 5.2547133587917951954281968140459 y[1] (numeric) = 5.2547133587917951954281968140933 absolute error = 4.74e-29 relative error = 9.0204730046204801594910808852072e-28 % Correct digits = 29 h = 2.0563939243265092369464686024901e-05 NO POLE memory used=179.2MB, alloc=4.2MB, time=7.30 memory used=183.1MB, alloc=4.2MB, time=7.46 memory used=186.9MB, alloc=4.2MB, time=7.62 memory used=190.7MB, alloc=4.2MB, time=7.78 TOP MAIN SOLVE Loop x[1] = -4.7499828142512793630523749219219 y[1] (analytic) = 5.2811507954329464180551764969405 y[1] (numeric) = 5.2811507954329464180551764970198 absolute error = 7.93e-29 relative error = 1.5015666674122873800411528792550e-27 % Correct digits = 28 h = 2.0563939243265092369464686024901e-05 Real estimate of pole used Radius of convergence = 0.03759 Order of pole = 2.0e-29 memory used=194.5MB, alloc=4.2MB, time=7.94 memory used=198.3MB, alloc=4.2MB, time=8.10 memory used=202.1MB, alloc=4.2MB, time=8.27 memory used=206.0MB, alloc=4.2MB, time=8.43 TOP MAIN SOLVE Loop x[1] = -4.7489957451676026386186406169939 y[1] (analytic) = 5.3077455780347776596628328871988 y[1] (numeric) = 5.3077455780347776596628328873106 absolute error = 1.118e-28 relative error = 2.1063556712790776271332759675444e-27 % Correct digits = 28 h = 2.0563939243265092369464686024901e-05 Real estimate of pole used Radius of convergence = 0.03661 Order of pole = 4e-30 memory used=209.8MB, alloc=4.2MB, time=8.59 memory used=213.6MB, alloc=4.2MB, time=8.75 memory used=217.4MB, alloc=4.2MB, time=8.91 memory used=221.2MB, alloc=4.2MB, time=9.07 TOP MAIN SOLVE Loop x[1] = -4.7479881121446826490925368473799 y[1] (analytic) = 5.3356452554726764699216053230618 y[1] (numeric) = 5.3356452554726764699216053232076 absolute error = 1.458e-28 relative error = 2.7325654727599353114239547034911e-27 % Correct digits = 28 h = 2.0563939243265092369464686024901e-05 Real estimate of pole used Radius of convergence = 0.0356 Order of pole = 2.6e-29 memory used=225.0MB, alloc=4.2MB, time=9.24 memory used=228.8MB, alloc=4.2MB, time=9.40 memory used=232.7MB, alloc=4.2MB, time=9.56 memory used=236.5MB, alloc=4.2MB, time=9.72 TOP MAIN SOLVE Loop x[1] = -4.7469804791217626595664330777659 y[1] (analytic) = 5.3643467649343968896465389040623 y[1] (numeric) = 5.3643467649343968896465389042429 absolute error = 1.806e-28 relative error = 3.3666727360084940748651162249502e-27 % Correct digits = 28 h = 2.0563939243265092369464686024901e-05 Real estimate of pole used Radius of convergence = 0.03459 Order of pole = 5.7e-29 memory used=240.3MB, alloc=4.2MB, time=9.88 memory used=244.1MB, alloc=4.2MB, time=10.05 memory used=247.9MB, alloc=4.2MB, time=10.21 memory used=251.7MB, alloc=4.2MB, time=10.37 TOP MAIN SOLVE Loop x[1] = -4.7459934100380859351326987728379 y[1] (analytic) = 5.3932856024804040899027184390921 y[1] (numeric) = 5.3932856024804040899027184393077 absolute error = 2.156e-28 relative error = 3.9975631904389465139377520371870e-27 % Correct digits = 28 h = 2.0563939243265092369464686024901e-05 Real estimate of pole used Radius of convergence = 0.0336 Order of pole = 3.6e-29 memory used=255.5MB, alloc=4.2MB, time=10.53 memory used=259.4MB, alloc=4.2MB, time=10.70 memory used=263.2MB, alloc=4.2MB, time=10.86 memory used=267.0MB, alloc=4.2MB, time=11.02 TOP MAIN SOLVE Loop x[1] = -4.7449857770151659456065950032239 y[1] (analytic) = 5.423718356437575285547755968679 y[1] (numeric) = 5.4237183564375752855477559689313 absolute error = 2.523e-28 relative error = 4.6517902187995713777989764295740e-27 % Correct digits = 28 h = 2.0563939243265092369464686024901e-05 Real estimate of pole used Radius of convergence = 0.0326 Order of pole = 5.4e-29 memory used=270.8MB, alloc=4.2MB, time=11.18 memory used=274.6MB, alloc=4.2MB, time=11.35 memory used=278.4MB, alloc=4.2MB, time=11.51 memory used=282.2MB, alloc=4.2MB, time=11.67 TOP MAIN SOLVE Loop x[1] = -4.7439987079314892211728606982959 y[1] (analytic) = 5.4544569066935611240873186553881 y[1] (numeric) = 5.4544569066935611240873186556777 absolute error = 2.896e-28 relative error = 5.3094195252438562443050151976523e-27 % Correct digits = 28 h = 2.0563939243265092369464686024901e-05 NO POLE memory used=286.1MB, alloc=4.2MB, time=11.83 memory used=289.9MB, alloc=4.2MB, time=11.99 memory used=293.7MB, alloc=4.2MB, time=12.15 memory used=297.5MB, alloc=4.2MB, time=12.31 TOP MAIN SOLVE Loop x[1] = -4.7429910749085692316467569286819 y[1] (analytic) = 5.4868429101109461125327110253927 y[1] (numeric) = 5.4868429101109461125327110257214 absolute error = 3.287e-28 relative error = 5.9906945648887468744124757122408e-27 % Correct digits = 28 h = 2.0563939243265092369464686024901e-05 NO POLE memory used=301.3MB, alloc=4.2MB, time=12.48 memory used=305.1MB, alloc=4.2MB, time=12.64 memory used=309.0MB, alloc=4.2MB, time=12.80 memory used=312.8MB, alloc=4.2MB, time=12.95 TOP MAIN SOLVE Loop x[1] = -4.7419834418856492421206531590679 y[1] (analytic) = 5.5203140229007879978565110750553 y[1] (numeric) = 5.5203140229007879978565110754246 absolute error = 3.693e-28 relative error = 6.6898368184848661289236791065232e-27 % Correct digits = 28 h = 2.0563939243265092369464686024901e-05 NO POLE memory used=316.6MB, alloc=4.2MB, time=13.11 memory used=320.4MB, alloc=4.2MB, time=13.26 memory used=324.2MB, alloc=4.2MB, time=13.41 memory used=328.0MB, alloc=4.2MB, time=13.56 TOP MAIN SOLVE Loop x[1] = -4.7409963728019725176869188541399 y[1] (analytic) = 5.5542265192979478388311910936777 y[1] (numeric) = 5.5542265192979478388311910940881 absolute error = 4.104e-28 relative error = 7.3889676370612699999144528657984e-27 % Correct digits = 28 h = 2.0563939243265092369464686024901e-05 NO POLE memory used=331.8MB, alloc=4.2MB, time=13.71 memory used=335.7MB, alloc=4.3MB, time=13.86 memory used=339.5MB, alloc=4.3MB, time=14.01 memory used=343.3MB, alloc=4.3MB, time=14.17 TOP MAIN SOLVE Loop x[1] = -4.7399887397790525281608150845259 y[1] (analytic) = 5.5900751849028362230011165539594 y[1] (numeric) = 5.5900751849028362230011165544134 absolute error = 4.540e-28 relative error = 8.1215365622652388650161273546676e-27 % Correct digits = 28 h = 2.0563939243265092369464686024901e-05 NO POLE memory used=347.1MB, alloc=4.3MB, time=14.33 memory used=350.9MB, alloc=4.3MB, time=14.49 memory used=354.7MB, alloc=4.3MB, time=14.65 memory used=358.5MB, alloc=4.3MB, time=14.82 TOP MAIN SOLVE Loop x[1] = -4.7389811067561325386347113149119 y[1] (analytic) = 5.627257967727363608885718768677 y[1] (numeric) = 5.6272579677273636088857187691761 absolute error = 4.991e-28 relative error = 8.8693285941815030967715440615482e-27 % Correct digits = 28 h = 2.0563939243265092369464686024901e-05 NO POLE memory used=362.4MB, alloc=4.3MB, time=14.98 memory used=366.2MB, alloc=4.3MB, time=15.14 memory used=370.0MB, alloc=4.3MB, time=15.31 memory used=373.8MB, alloc=4.3MB, time=15.47 TOP MAIN SOLVE Loop x[1] = -4.7379940376724558142009770099839 y[1] (analytic) = 5.6650746689182843019395709374785 y[1] (numeric) = 5.6650746689182843019395709380234 absolute error = 5.449e-28 relative error = 9.6185846055943643830194747678311e-27 % Correct digits = 28 h = 2.0563939243265092369464686024901e-05 NO POLE memory used=377.6MB, alloc=4.3MB, time=15.63 memory used=381.4MB, alloc=4.3MB, time=15.79 memory used=385.3MB, alloc=4.3MB, time=15.95 memory used=389.1MB, alloc=4.3MB, time=16.11 TOP MAIN SOLVE Loop x[1] = -4.7369864046495358246748732403699 y[1] (analytic) = 5.7052143871206475071043558071628 y[1] (numeric) = 5.7052143871206475071043558077563 absolute error = 5.935e-28 relative error = 1.0402764203564526352977085859454e-26 % Correct digits = 27 h = 2.0563939243265092369464686024901e-05 Real estimate of pole used Radius of convergence = 0.0246 Order of pole = 5.6e-29 memory used=392.9MB, alloc=4.3MB, time=16.28 memory used=396.7MB, alloc=4.3MB, time=16.44 memory used=400.5MB, alloc=4.3MB, time=16.61 memory used=404.3MB, alloc=4.3MB, time=16.77 TOP MAIN SOLVE Loop x[1] = -4.7359993355658591002411389354419 y[1] (analytic) = 5.7461627941945075009211355938863 y[1] (numeric) = 5.7461627941945075009211355945294 absolute error = 6.431e-28 relative error = 1.1191816574527614702195102719582e-26 % Correct digits = 27 h = 2.0563939243265092369464686024901e-05 Real estimate of pole used Radius of convergence = 0.02361 Order of pole = 1.35e-28 memory used=408.1MB, alloc=4.3MB, time=16.94 memory used=412.0MB, alloc=4.3MB, time=17.10 memory used=415.8MB, alloc=4.3MB, time=17.26 memory used=419.6MB, alloc=4.3MB, time=17.43 TOP MAIN SOLVE Loop x[1] = -4.7349917025429391107150351658279 y[1] (analytic) = 5.7897700791021800738911329868594 y[1] (numeric) = 5.789770079102180073891132987555 absolute error = 6.956e-28 relative error = 1.2014294013344770430557650936059e-26 % Correct digits = 27 h = 2.0563939243265092369464686024901e-05 Real estimate of pole used Radius of convergence = 0.0226 Order of pole = 2e-30 memory used=423.4MB, alloc=4.3MB, time=17.59 memory used=427.2MB, alloc=4.3MB, time=17.75 memory used=431.0MB, alloc=4.3MB, time=17.91 memory used=434.8MB, alloc=4.3MB, time=18.08 TOP MAIN SOLVE Loop x[1] = -4.7339840695200191211889313962139 y[1] (analytic) = 5.8353670708409698347827569813318 y[1] (numeric) = 5.8353670708409698347827569820825 absolute error = 7.507e-28 relative error = 1.2864657713671680113860739013686e-26 % Correct digits = 27 h = 2.0563939243265092369464686024901e-05 Real estimate of pole used Radius of convergence = 0.0216 Order of pole = 8.9e-29 memory used=438.7MB, alloc=4.3MB, time=18.24 memory used=442.5MB, alloc=4.3MB, time=18.40 memory used=446.3MB, alloc=4.3MB, time=18.57 memory used=450.1MB, alloc=4.3MB, time=18.73 TOP MAIN SOLVE Loop x[1] = -4.7329970004363423967551970912859 y[1] (analytic) = 5.8821457388077878823653036617356 y[1] (numeric) = 5.882145738807787882365303662543 absolute error = 8.074e-28 relative error = 1.3726283500137254592905212165704e-26 % Correct digits = 27 h = 2.0563939243265092369464686024901e-05 NO POLE memory used=453.9MB, alloc=4.3MB, time=18.89 memory used=457.7MB, alloc=4.3MB, time=19.05 memory used=461.5MB, alloc=4.3MB, time=19.22 memory used=465.4MB, alloc=4.3MB, time=19.38 TOP MAIN SOLVE Loop x[1] = -4.7319893674134224072290933216719 y[1] (analytic) = 5.9322699965919637174099961878099 y[1] (numeric) = 5.9322699965919637174099961886781 absolute error = 8.682e-28 relative error = 1.4635207104510974182798893824117e-26 % Correct digits = 27 h = 2.0563939243265092369464686024901e-05 Real estimate of pole used Radius of convergence = 0.0196 Order of pole = 3.6e-29 memory used=469.2MB, alloc=4.3MB, time=19.55 memory used=473.0MB, alloc=4.3MB, time=19.71 memory used=476.8MB, alloc=4.3MB, time=19.87 memory used=480.6MB, alloc=4.3MB, time=20.03 TOP MAIN SOLVE Loop x[1] = -4.7309817343905024177029895520579 y[1] (analytic) = 5.9850409594923944854116762393729 y[1] (numeric) = 5.9850409594923944854116762403054 absolute error = 9.325e-28 relative error = 1.5580511583985676448927492157060e-26 % Correct digits = 27 h = 2.0563939243265092369464686024901e-05 Real estimate of pole used Radius of convergence = 0.01859 Order of pole = 1.14e-28 memory used=484.4MB, alloc=4.3MB, time=20.19 memory used=488.3MB, alloc=4.3MB, time=20.36 memory used=492.1MB, alloc=4.3MB, time=20.52 memory used=495.9MB, alloc=4.3MB, time=20.68 TOP MAIN SOLVE Loop x[1] = -4.7299946653068256932692552471299 y[1] (analytic) = 6.0395850827113639429311901816066 y[1] (numeric) = 6.0395850827113639429311901826052 absolute error = 9.986e-28 relative error = 1.6534248401575565694406998140366e-26 % Correct digits = 27 h = 2.0563939243265092369464686024901e-05 NO POLE memory used=499.7MB, alloc=4.3MB, time=20.85 memory used=503.5MB, alloc=4.3MB, time=21.01 memory used=507.3MB, alloc=4.3MB, time=21.17 memory used=511.1MB, alloc=4.3MB, time=21.33 TOP MAIN SOLVE Loop x[1] = -4.7289870322839057037431514775159 y[1] (analytic) = 6.098515862284725585897474080434 y[1] (numeric) = 6.0985158622847255858974740815042 absolute error = 1.0702e-27 relative error = 1.7548531875082541841591855786389e-26 % Correct digits = 27 h = 2.0563939243265092369464686024901e-05 NO POLE memory used=515.0MB, alloc=4.3MB, time=21.49 memory used=518.8MB, alloc=4.3MB, time=21.66 memory used=522.6MB, alloc=4.3MB, time=21.83 memory used=526.4MB, alloc=4.3MB, time=22.00 TOP MAIN SOLVE Loop x[1] = -4.7279999632002289793094171725879 y[1] (analytic) = 6.1598212032607189024628147020642 y[1] (numeric) = 6.1598212032607189024628147032086 absolute error = 1.1444e-27 relative error = 1.8578461326023693670777355112909e-26 % Correct digits = 27 h = 2.0563939243265092369464686024901e-05 Real estimate of pole used Radius of convergence = 0.01561 Order of pole = 5.6e-29 memory used=530.2MB, alloc=4.3MB, time=22.17 memory used=534.0MB, alloc=4.3MB, time=22.34 memory used=537.8MB, alloc=4.3MB, time=22.50 memory used=541.7MB, alloc=4.3MB, time=22.65 TOP MAIN SOLVE Loop x[1] = -4.7269923301773089897833134029739 y[1] (analytic) = 6.2265398819575840610741158724971 y[1] (numeric) = 6.2265398819575840610741158737223 absolute error = 1.2252e-27 relative error = 1.9677060184745897847448675227136e-26 % Correct digits = 27 h = 2.0563939243265092369464686024901e-05 Real estimate of pole used Radius of convergence = 0.0146 Order of pole = 8.0e-29 memory used=545.5MB, alloc=4.3MB, time=22.80 memory used=549.3MB, alloc=4.3MB, time=22.95 memory used=553.1MB, alloc=4.3MB, time=23.12 memory used=556.9MB, alloc=4.3MB, time=23.28 TOP MAIN SOLVE Loop x[1] = -4.7259846971543890002572096333599 y[1] (analytic) = 6.2980312866919282551746713826171 y[1] (numeric) = 6.2980312866919282551746713839291 absolute error = 1.3120e-27 relative error = 2.0831906674905300742336005128833e-26 % Correct digits = 27 h = 2.0563939243265092369464686024901e-05 NO POLE memory used=560.7MB, alloc=4.3MB, time=23.44 memory used=564.6MB, alloc=4.3MB, time=23.60 memory used=568.4MB, alloc=4.3MB, time=23.75 memory used=572.2MB, alloc=4.3MB, time=23.91 TOP MAIN SOLVE Loop x[1] = -4.7249976280707122758234753284319 y[1] (analytic) = 6.3733988726231757652436970460644 y[1] (numeric) = 6.3733988726231757652436970474679 absolute error = 1.4035e-27 relative error = 2.2021217062511337389503328570622e-26 % Correct digits = 27 h = 2.0563939243265092369464686024901e-05 Real estimate of pole used Radius of convergence = 0.01261 Order of pole = 3.0e-29 memory used=576.0MB, alloc=4.3MB, time=24.06 memory used=579.8MB, alloc=4.3MB, time=24.21 memory used=583.6MB, alloc=4.3MB, time=24.36 memory used=587.4MB, alloc=4.3MB, time=24.52 TOP MAIN SOLVE Loop x[1] = -4.7239899950477922862973715588179 y[1] (analytic) = 6.4566851444289026622570463558368 y[1] (numeric) = 6.4566851444289026622570463573414 absolute error = 1.5046e-27 relative error = 2.3302979258609685452777527228259e-26 % Correct digits = 27 h = 2.0563939243265092369464686024901e-05 NO POLE memory used=591.3MB, alloc=4.3MB, time=24.67 memory used=595.1MB, alloc=4.3MB, time=24.83 memory used=598.9MB, alloc=4.3MB, time=24.98 memory used=602.7MB, alloc=4.3MB, time=25.13 TOP MAIN SOLVE Loop x[1] = -4.7229823620248722967712677892039 y[1] (analytic) = 6.5475445497932186657148687954159 y[1] (numeric) = 6.5475445497932186657148687970306 absolute error = 1.6147e-27 relative error = 2.4661153318170162918271616354146e-26 % Correct digits = 27 h = 2.0563939243265092369464686024901e-05 Real estimate of pole used Radius of convergence = 0.01059 Order of pole = 3.6e-29 memory used=606.5MB, alloc=4.3MB, time=25.28 memory used=610.3MB, alloc=4.3MB, time=25.44 memory used=614.1MB, alloc=4.3MB, time=25.59 memory used=618.0MB, alloc=4.3MB, time=25.74 memory used=621.8MB, alloc=4.3MB, time=25.90 memory used=625.6MB, alloc=4.3MB, time=26.05 TOP MAIN SOLVE Loop x[1] = -4.7219983527079654239304007305329 y[1] (analytic) = 6.6450317631422121351175673466982 y[1] (numeric) = 6.6450317631422121351175673486503 absolute error = 1.9521e-27 relative error = 2.9376834747843515704127000795213e-26 % Correct digits = 27 h = 1.0532029228395596177621177743989e-05 Real estimate of pole used Radius of convergence = 0.009609 Order of pole = 5.2e-29 memory used=629.4MB, alloc=4.3MB, time=26.21 memory used=633.2MB, alloc=4.3MB, time=26.36 memory used=637.0MB, alloc=4.3MB, time=26.52 memory used=640.8MB, alloc=4.3MB, time=26.68 memory used=644.7MB, alloc=4.3MB, time=26.83 memory used=648.5MB, alloc=4.3MB, time=26.98 memory used=652.3MB, alloc=4.3MB, time=27.14 memory used=656.1MB, alloc=4.3MB, time=27.30 TOP MAIN SOLVE Loop x[1] = -4.7209978099312678422935267186514 y[1] (analytic) = 6.7549792629688737657774623842806 y[1] (numeric) = 6.7549792629688737657774623866922 absolute error = 2.4116e-27 relative error = 3.5701071848147765353745556156964e-26 % Correct digits = 27 h = 1.0532029228395596177621177743989e-05 Real estimate of pole used Radius of convergence = 0.008609 Order of pole = 6.3e-29 memory used=659.9MB, alloc=4.3MB, time=27.45 memory used=663.7MB, alloc=4.3MB, time=27.60 memory used=667.6MB, alloc=4.3MB, time=27.75 memory used=671.4MB, alloc=4.3MB, time=27.91 memory used=675.2MB, alloc=4.3MB, time=28.06 memory used=679.0MB, alloc=4.3MB, time=28.21 memory used=682.8MB, alloc=4.3MB, time=28.36 memory used=686.6MB, alloc=4.3MB, time=28.51 TOP MAIN SOLVE Loop x[1] = -4.7199972671545702606566527067699 y[1] (analytic) = 6.8785269089373507493130593665037 y[1] (numeric) = 6.8785269089373507493130593694313 absolute error = 2.9276e-27 relative error = 4.2561438499224811599866162790539e-26 % Correct digits = 27 h = 1.0532029228395596177621177743989e-05 NO POLE memory used=690.4MB, alloc=4.3MB, time=28.67 memory used=694.3MB, alloc=4.3MB, time=28.81 memory used=698.1MB, alloc=4.3MB, time=28.97 memory used=701.9MB, alloc=4.3MB, time=29.12 memory used=705.7MB, alloc=4.3MB, time=29.27 memory used=709.5MB, alloc=4.3MB, time=29.42 memory used=713.3MB, alloc=4.3MB, time=29.58 TOP MAIN SOLVE Loop x[1] = -4.7189967243778726790197786948884 y[1] (analytic) = 7.0195202625230721464405960516087 y[1] (numeric) = 7.0195202625230721464405960551258 absolute error = 3.5171e-27 relative error = 5.0104563680479009112258662424031e-26 % Correct digits = 27 h = 1.0532029228395596177621177743989e-05 NO POLE memory used=717.1MB, alloc=4.3MB, time=29.73 memory used=721.0MB, alloc=4.3MB, time=29.88 memory used=724.8MB, alloc=4.3MB, time=30.03 memory used=728.6MB, alloc=4.3MB, time=30.18 memory used=732.4MB, alloc=4.3MB, time=30.34 memory used=736.2MB, alloc=4.3MB, time=30.49 memory used=740.0MB, alloc=4.3MB, time=30.64 memory used=743.8MB, alloc=4.3MB, time=30.79 TOP MAIN SOLVE Loop x[1] = -4.7179961816011750973829046830069 y[1] (analytic) = 7.1837088159506841331017260919221 y[1] (numeric) = 7.1837088159506841331017260961253 absolute error = 4.2032e-27 relative error = 5.8510166651900312713176226897866e-26 % Correct digits = 27 h = 1.0532029228395596177621177743989e-05 NO POLE memory used=747.7MB, alloc=4.3MB, time=30.95 memory used=751.5MB, alloc=4.3MB, time=31.10 memory used=755.3MB, alloc=4.3MB, time=31.25 memory used=759.1MB, alloc=4.3MB, time=31.40 memory used=762.9MB, alloc=4.3MB, time=31.55 memory used=766.7MB, alloc=4.3MB, time=31.70 memory used=770.5MB, alloc=4.3MB, time=31.86 TOP MAIN SOLVE Loop memory used=774.4MB, alloc=4.3MB, time=32.01 x[1] = -4.7169956388244775157460306711254 y[1] (analytic) = 7.380256072062233013473160369383 y[1] (numeric) = 7.3802560720622330134731603744079 absolute error = 5.0249e-27 relative error = 6.8085713435088356494964773945238e-26 % Correct digits = 27 h = 1.0532029228395596177621177743989e-05 NO POLE memory used=778.2MB, alloc=4.3MB, time=32.16 memory used=782.0MB, alloc=4.3MB, time=32.31 memory used=785.8MB, alloc=4.3MB, time=32.46 memory used=789.6MB, alloc=4.3MB, time=32.62 memory used=793.4MB, alloc=4.3MB, time=32.77 memory used=797.3MB, alloc=4.3MB, time=32.92 memory used=801.1MB, alloc=4.3MB, time=33.06 TOP MAIN SOLVE Loop x[1] = -4.7159950960477799341091566592439 y[1] (analytic) = 7.6251262468838746063779444906131 y[1] (numeric) = 7.6251262468838746063779444966623 absolute error = 6.0492e-27 relative error = 7.9332456986821678363038840209603e-26 % Correct digits = 27 h = 1.0532029228395596177621177743989e-05 Real estimate of pole used Radius of convergence = 0.003606 Order of pole = 8.4e-29 memory used=804.9MB, alloc=4.3MB, time=33.21 memory used=808.7MB, alloc=4.3MB, time=33.36 memory used=812.5MB, alloc=4.3MB, time=33.51 memory used=816.3MB, alloc=4.3MB, time=33.66 memory used=820.1MB, alloc=4.3MB, time=33.81 memory used=824.0MB, alloc=4.3MB, time=33.96 memory used=827.8MB, alloc=4.3MB, time=34.11 memory used=831.6MB, alloc=4.3MB, time=34.27 memory used=835.4MB, alloc=4.3MB, time=34.42 TOP MAIN SOLVE Loop x[1] = -4.7149918403816523018695670193582 y[1] (analytic) = 7.9511455688253556809234777466726 y[1] (numeric) = 7.9511455688253556809234777529867 absolute error = 6.3141e-27 relative error = 7.9411198617167301255523730796187e-26 % Correct digits = 27 h = 8.3997626540732418428655547814105e-06 Complex estimate of poles used Radius of convergence = 0.002595 Order of pole = 8.248e-27 memory used=839.2MB, alloc=4.3MB, time=34.57 memory used=843.0MB, alloc=4.3MB, time=34.73 memory used=846.8MB, alloc=4.3MB, time=34.88 memory used=850.7MB, alloc=4.3MB, time=35.03 memory used=854.5MB, alloc=4.3MB, time=35.18 memory used=858.3MB, alloc=4.3MB, time=35.34 memory used=862.1MB, alloc=4.3MB, time=35.49 memory used=865.9MB, alloc=4.3MB, time=35.64 memory used=869.7MB, alloc=4.3MB, time=35.80 TOP MAIN SOLVE Loop x[1] = -4.713992268625817586090266018337 y[1] (analytic) = 8.4356990363870589695801617753357 y[1] (numeric) = 8.4356990363870589695801617805754 absolute error = 5.2397e-27 relative error = 6.2113406101838843392931606754870e-26 % Correct digits = 27 h = 8.3997626540732418428655547814105e-06 NO POLE memory used=873.6MB, alloc=4.3MB, time=35.95 memory used=877.4MB, alloc=4.3MB, time=36.11 memory used=881.2MB, alloc=4.3MB, time=36.26 memory used=885.0MB, alloc=4.3MB, time=36.41 memory used=888.8MB, alloc=4.3MB, time=36.57 memory used=892.6MB, alloc=4.3MB, time=36.72 memory used=896.4MB, alloc=4.3MB, time=36.88 memory used=900.3MB, alloc=4.3MB, time=37.03 memory used=904.1MB, alloc=4.3MB, time=37.18 memory used=907.9MB, alloc=4.3MB, time=37.33 memory used=911.7MB, alloc=4.3MB, time=37.49 memory used=915.5MB, alloc=4.3MB, time=37.64 memory used=919.3MB, alloc=4.3MB, time=37.79 memory used=923.1MB, alloc=4.3MB, time=37.95 memory used=927.0MB, alloc=4.3MB, time=38.10 memory used=930.8MB, alloc=4.3MB, time=38.26 memory used=934.6MB, alloc=4.3MB, time=38.41 memory used=938.4MB, alloc=4.3MB, time=38.56 memory used=942.2MB, alloc=4.3MB, time=38.72 memory used=946.0MB, alloc=4.3MB, time=38.87 memory used=949.8MB, alloc=4.3MB, time=39.02 memory used=953.7MB, alloc=4.3MB, time=39.18 memory used=957.5MB, alloc=4.3MB, time=39.33 memory used=961.3MB, alloc=4.3MB, time=39.48 memory used=965.1MB, alloc=4.3MB, time=39.63 memory used=968.9MB, alloc=4.3MB, time=39.79 memory used=972.7MB, alloc=4.3MB, time=39.94 memory used=976.6MB, alloc=4.3MB, time=40.09 memory used=980.4MB, alloc=4.3MB, time=40.24 TOP MAIN SOLVE Loop x[1] = -4.7129993869802025224804615262555 y[1] (analytic) = 9.4013853349213254506159215891454 y[1] (numeric) = 9.4013853349213254506159215896224 absolute error = 4.770e-28 relative error = 5.0737203402161339727138561487564e-27 % Correct digits = 28 h = 1.2343788689472157317867957536685e-06 Real estimate of pole used Radius of convergence = 0.0006104 Order of pole = 2.2e-29 memory used=984.2MB, alloc=4.3MB, time=40.39 memory used=988.0MB, alloc=4.3MB, time=40.55 memory used=991.8MB, alloc=4.3MB, time=40.70 memory used=995.6MB, alloc=4.3MB, time=40.85 memory used=999.4MB, alloc=4.3MB, time=41.00 memory used=1003.3MB, alloc=4.3MB, time=41.15 memory used=1007.1MB, alloc=4.3MB, time=41.31 memory used=1010.9MB, alloc=4.3MB, time=41.46 memory used=1014.7MB, alloc=4.3MB, time=41.61 memory used=1018.5MB, alloc=4.3MB, time=41.76 memory used=1022.3MB, alloc=4.3MB, time=41.91 memory used=1026.1MB, alloc=4.3MB, time=42.06 memory used=1030.0MB, alloc=4.3MB, time=42.22 memory used=1033.8MB, alloc=4.3MB, time=42.36 memory used=1037.6MB, alloc=4.3MB, time=42.52 memory used=1041.4MB, alloc=4.3MB, time=42.67 memory used=1045.2MB, alloc=4.3MB, time=42.82 memory used=1049.0MB, alloc=4.3MB, time=42.97 memory used=1052.9MB, alloc=4.3MB, time=43.12 memory used=1056.7MB, alloc=4.3MB, time=43.27 memory used=1060.5MB, alloc=4.3MB, time=43.42 memory used=1064.3MB, alloc=4.3MB, time=43.58 memory used=1068.1MB, alloc=4.3MB, time=43.73 memory used=1071.9MB, alloc=4.3MB, time=43.88 memory used=1075.7MB, alloc=4.3MB, time=44.03 memory used=1079.6MB, alloc=4.3MB, time=44.19 memory used=1083.4MB, alloc=4.3MB, time=44.34 memory used=1087.2MB, alloc=4.3MB, time=44.50 memory used=1091.0MB, alloc=4.3MB, time=44.65 memory used=1094.8MB, alloc=4.3MB, time=44.81 memory used=1098.6MB, alloc=4.3MB, time=44.96 memory used=1102.4MB, alloc=4.3MB, time=45.12 memory used=1106.3MB, alloc=4.3MB, time=45.27 memory used=1110.1MB, alloc=4.3MB, time=45.42 memory used=1113.9MB, alloc=4.3MB, time=45.58 memory used=1117.7MB, alloc=4.3MB, time=45.73 memory used=1121.5MB, alloc=4.3MB, time=45.89 memory used=1125.3MB, alloc=4.3MB, time=46.04 memory used=1129.1MB, alloc=4.3MB, time=46.19 memory used=1133.0MB, alloc=4.3MB, time=46.35 memory used=1136.8MB, alloc=4.3MB, time=46.50 memory used=1140.6MB, alloc=4.3MB, time=46.66 memory used=1144.4MB, alloc=4.3MB, time=46.81 memory used=1148.2MB, alloc=4.3MB, time=46.97 memory used=1152.0MB, alloc=4.3MB, time=47.12 memory used=1155.8MB, alloc=4.3MB, time=47.27 memory used=1159.7MB, alloc=4.3MB, time=47.43 memory used=1163.5MB, alloc=4.3MB, time=47.58 memory used=1167.3MB, alloc=4.3MB, time=47.73 memory used=1171.1MB, alloc=4.3MB, time=47.89 memory used=1174.9MB, alloc=4.3MB, time=48.04 memory used=1178.7MB, alloc=4.3MB, time=48.20 memory used=1182.6MB, alloc=4.3MB, time=48.35 memory used=1186.4MB, alloc=4.3MB, time=48.51 memory used=1190.2MB, alloc=4.3MB, time=48.66 memory used=1194.0MB, alloc=4.3MB, time=48.82 memory used=1197.8MB, alloc=4.3MB, time=48.97 memory used=1201.6MB, alloc=4.3MB, time=49.12 memory used=1205.4MB, alloc=4.3MB, time=49.28 memory used=1209.3MB, alloc=4.3MB, time=49.44 memory used=1213.1MB, alloc=4.3MB, time=49.59 memory used=1216.9MB, alloc=4.3MB, time=49.75 memory used=1220.7MB, alloc=4.3MB, time=49.90 memory used=1224.5MB, alloc=4.3MB, time=50.06 memory used=1228.3MB, alloc=4.3MB, time=50.22 memory used=1232.1MB, alloc=4.3MB, time=50.37 memory used=1236.0MB, alloc=4.3MB, time=50.53 memory used=1239.8MB, alloc=4.3MB, time=50.69 memory used=1243.6MB, alloc=4.3MB, time=50.84 memory used=1247.4MB, alloc=4.3MB, time=51.01 memory used=1251.2MB, alloc=4.3MB, time=51.17 memory used=1255.0MB, alloc=4.3MB, time=51.32 memory used=1258.8MB, alloc=4.3MB, time=51.48 memory used=1262.7MB, alloc=4.3MB, time=51.64 memory used=1266.5MB, alloc=4.3MB, time=51.79 memory used=1270.3MB, alloc=4.3MB, time=51.95 memory used=1274.1MB, alloc=4.3MB, time=52.10 memory used=1277.9MB, alloc=4.3MB, time=52.26 memory used=1281.7MB, alloc=4.3MB, time=52.41 memory used=1285.6MB, alloc=4.3MB, time=52.57 memory used=1289.4MB, alloc=4.3MB, time=52.72 memory used=1293.2MB, alloc=4.3MB, time=52.87 memory used=1297.0MB, alloc=4.3MB, time=53.03 memory used=1300.8MB, alloc=4.3MB, time=53.18 memory used=1304.6MB, alloc=4.3MB, time=53.33 memory used=1308.4MB, alloc=4.3MB, time=53.48 memory used=1312.3MB, alloc=4.3MB, time=53.63 memory used=1316.1MB, alloc=4.3MB, time=53.79 memory used=1319.9MB, alloc=4.3MB, time=53.94 memory used=1323.7MB, alloc=4.3MB, time=54.09 memory used=1327.5MB, alloc=4.3MB, time=54.25 memory used=1331.3MB, alloc=4.3MB, time=54.40 memory used=1335.1MB, alloc=4.3MB, time=54.55 memory used=1339.0MB, alloc=4.3MB, time=54.70 memory used=1342.8MB, alloc=4.3MB, time=54.86 memory used=1346.6MB, alloc=4.3MB, time=55.01 memory used=1350.4MB, alloc=4.3MB, time=55.16 memory used=1354.2MB, alloc=4.3MB, time=55.32 memory used=1358.0MB, alloc=4.3MB, time=55.47 memory used=1361.9MB, alloc=4.3MB, time=55.63 memory used=1365.7MB, alloc=4.3MB, time=55.78 memory used=1369.5MB, alloc=4.3MB, time=55.93 memory used=1373.3MB, alloc=4.3MB, time=56.09 memory used=1377.1MB, alloc=4.3MB, time=56.24 memory used=1380.9MB, alloc=4.3MB, time=56.39 memory used=1384.7MB, alloc=4.3MB, time=56.55 memory used=1388.6MB, alloc=4.3MB, time=56.70 memory used=1392.4MB, alloc=4.3MB, time=56.86 memory used=1396.2MB, alloc=4.3MB, time=57.01 memory used=1400.0MB, alloc=4.3MB, time=57.16 memory used=1403.8MB, alloc=4.3MB, time=57.31 memory used=1407.6MB, alloc=4.3MB, time=57.47 memory used=1411.4MB, alloc=4.3MB, time=57.62 memory used=1415.3MB, alloc=4.3MB, time=57.77 memory used=1419.1MB, alloc=4.3MB, time=57.92 memory used=1422.9MB, alloc=4.3MB, time=58.08 memory used=1426.7MB, alloc=4.3MB, time=58.23 memory used=1430.5MB, alloc=4.3MB, time=58.38 memory used=1434.3MB, alloc=4.3MB, time=58.53 memory used=1438.2MB, alloc=4.3MB, time=58.68 memory used=1442.0MB, alloc=4.3MB, time=58.83 memory used=1445.8MB, alloc=4.3MB, time=58.98 memory used=1449.6MB, alloc=4.3MB, time=59.14 memory used=1453.4MB, alloc=4.3MB, time=59.29 memory used=1457.2MB, alloc=4.3MB, time=59.44 memory used=1461.0MB, alloc=4.3MB, time=59.59 memory used=1464.9MB, alloc=4.3MB, time=59.74 memory used=1468.7MB, alloc=4.3MB, time=59.89 memory used=1472.5MB, alloc=4.3MB, time=60.04 memory used=1476.3MB, alloc=4.3MB, time=60.19 memory used=1480.1MB, alloc=4.3MB, time=60.34 memory used=1483.9MB, alloc=4.3MB, time=60.49 memory used=1487.7MB, alloc=4.3MB, time=60.65 memory used=1491.6MB, alloc=4.3MB, time=60.79 memory used=1495.4MB, alloc=4.3MB, time=60.94 memory used=1499.2MB, alloc=4.3MB, time=61.10 memory used=1503.0MB, alloc=4.3MB, time=61.25 memory used=1506.8MB, alloc=4.3MB, time=61.40 memory used=1510.6MB, alloc=4.3MB, time=61.55 memory used=1514.4MB, alloc=4.3MB, time=61.70 memory used=1518.3MB, alloc=4.3MB, time=61.85 memory used=1522.1MB, alloc=4.3MB, time=62.00 memory used=1525.9MB, alloc=4.3MB, time=62.16 memory used=1529.7MB, alloc=4.3MB, time=62.31 memory used=1533.5MB, alloc=4.3MB, time=62.46 memory used=1537.3MB, alloc=4.3MB, time=62.62 memory used=1541.2MB, alloc=4.3MB, time=62.77 memory used=1545.0MB, alloc=4.3MB, time=62.92 memory used=1548.8MB, alloc=4.3MB, time=63.08 memory used=1552.6MB, alloc=4.3MB, time=63.23 memory used=1556.4MB, alloc=4.3MB, time=63.38 memory used=1560.2MB, alloc=4.3MB, time=63.54 memory used=1564.0MB, alloc=4.3MB, time=63.69 memory used=1567.9MB, alloc=4.3MB, time=63.84 memory used=1571.7MB, alloc=4.3MB, time=64.00 memory used=1575.5MB, alloc=4.3MB, time=64.15 memory used=1579.3MB, alloc=4.3MB, time=64.30 memory used=1583.1MB, alloc=4.3MB, time=64.46 memory used=1586.9MB, alloc=4.3MB, time=64.62 memory used=1590.7MB, alloc=4.3MB, time=64.77 memory used=1594.6MB, alloc=4.3MB, time=64.92 memory used=1598.4MB, alloc=4.3MB, time=65.08 memory used=1602.2MB, alloc=4.3MB, time=65.23 memory used=1606.0MB, alloc=4.3MB, time=65.39 memory used=1609.8MB, alloc=4.3MB, time=65.54 memory used=1613.6MB, alloc=4.3MB, time=65.69 memory used=1617.5MB, alloc=4.3MB, time=65.85 memory used=1621.3MB, alloc=4.3MB, time=66.00 memory used=1625.1MB, alloc=4.3MB, time=66.15 memory used=1628.9MB, alloc=4.3MB, time=66.31 memory used=1632.7MB, alloc=4.3MB, time=66.46 memory used=1636.5MB, alloc=4.3MB, time=66.61 memory used=1640.3MB, alloc=4.3MB, time=66.77 memory used=1644.2MB, alloc=4.3MB, time=66.92 memory used=1648.0MB, alloc=4.3MB, time=67.07 memory used=1651.8MB, alloc=4.3MB, time=67.23 memory used=1655.6MB, alloc=4.3MB, time=67.38 memory used=1659.4MB, alloc=4.3MB, time=67.54 memory used=1663.2MB, alloc=4.3MB, time=67.69 memory used=1667.0MB, alloc=4.3MB, time=67.84 memory used=1670.9MB, alloc=4.3MB, time=68.00 memory used=1674.7MB, alloc=4.3MB, time=68.15 memory used=1678.5MB, alloc=4.3MB, time=68.31 memory used=1682.3MB, alloc=4.3MB, time=68.46 memory used=1686.1MB, alloc=4.3MB, time=68.62 memory used=1689.9MB, alloc=4.3MB, time=68.77 memory used=1693.7MB, alloc=4.3MB, time=68.93 memory used=1697.6MB, alloc=4.3MB, time=69.08 memory used=1701.4MB, alloc=4.3MB, time=69.24 memory used=1705.2MB, alloc=4.3MB, time=69.39 memory used=1709.0MB, alloc=4.3MB, time=69.55 memory used=1712.8MB, alloc=4.3MB, time=69.70 memory used=1716.6MB, alloc=4.3MB, time=69.86 memory used=1720.5MB, alloc=4.3MB, time=70.01 memory used=1724.3MB, alloc=4.3MB, time=70.16 memory used=1728.1MB, alloc=4.3MB, time=70.32 memory used=1731.9MB, alloc=4.3MB, time=70.47 memory used=1735.7MB, alloc=4.3MB, time=70.63 memory used=1739.5MB, alloc=4.3MB, time=70.78 memory used=1743.3MB, alloc=4.3MB, time=70.94 memory used=1747.2MB, alloc=4.3MB, time=71.09 memory used=1751.0MB, alloc=4.3MB, time=71.24 memory used=1754.8MB, alloc=4.3MB, time=71.40 memory used=1758.6MB, alloc=4.3MB, time=71.56 memory used=1762.4MB, alloc=4.3MB, time=71.71 memory used=1766.2MB, alloc=4.3MB, time=71.86 memory used=1770.0MB, alloc=4.3MB, time=72.02 memory used=1773.9MB, alloc=4.3MB, time=72.17 memory used=1777.7MB, alloc=4.3MB, time=72.33 memory used=1781.5MB, alloc=4.3MB, time=72.48 memory used=1785.3MB, alloc=4.3MB, time=72.63 memory used=1789.1MB, alloc=4.3MB, time=72.79 memory used=1792.9MB, alloc=4.3MB, time=72.94 memory used=1796.7MB, alloc=4.3MB, time=73.10 memory used=1800.6MB, alloc=4.3MB, time=73.25 memory used=1804.4MB, alloc=4.3MB, time=73.41 memory used=1808.2MB, alloc=4.3MB, time=73.56 memory used=1812.0MB, alloc=4.3MB, time=73.71 memory used=1815.8MB, alloc=4.3MB, time=73.86 memory used=1819.6MB, alloc=4.3MB, time=74.02 memory used=1823.5MB, alloc=4.3MB, time=74.17 memory used=1827.3MB, alloc=4.3MB, time=74.33 memory used=1831.1MB, alloc=4.3MB, time=74.49 memory used=1834.9MB, alloc=4.3MB, time=74.64 memory used=1838.7MB, alloc=4.3MB, time=74.80 memory used=1842.5MB, alloc=4.3MB, time=74.95 memory used=1846.3MB, alloc=4.3MB, time=75.10 memory used=1850.2MB, alloc=4.3MB, time=75.26 memory used=1854.0MB, alloc=4.3MB, time=75.41 memory used=1857.8MB, alloc=4.3MB, time=75.56 memory used=1861.6MB, alloc=4.3MB, time=75.72 memory used=1865.4MB, alloc=4.3MB, time=75.88 memory used=1869.2MB, alloc=4.3MB, time=76.03 memory used=1873.0MB, alloc=4.3MB, time=76.18 memory used=1876.9MB, alloc=4.3MB, time=76.34 memory used=1880.7MB, alloc=4.3MB, time=76.49 memory used=1884.5MB, alloc=4.3MB, time=76.64 memory used=1888.3MB, alloc=4.3MB, time=76.80 memory used=1892.1MB, alloc=4.3MB, time=76.95 memory used=1895.9MB, alloc=4.3MB, time=77.11 memory used=1899.7MB, alloc=4.3MB, time=77.26 memory used=1903.6MB, alloc=4.3MB, time=77.42 memory used=1907.4MB, alloc=4.3MB, time=77.57 memory used=1911.2MB, alloc=4.3MB, time=77.72 memory used=1915.0MB, alloc=4.3MB, time=77.87 memory used=1918.8MB, alloc=4.3MB, time=78.03 memory used=1922.6MB, alloc=4.3MB, time=78.18 memory used=1926.5MB, alloc=4.3MB, time=78.34 memory used=1930.3MB, alloc=4.3MB, time=78.49 memory used=1934.1MB, alloc=4.3MB, time=78.64 memory used=1937.9MB, alloc=4.3MB, time=78.80 memory used=1941.7MB, alloc=4.3MB, time=78.95 memory used=1945.5MB, alloc=4.3MB, time=79.10 memory used=1949.3MB, alloc=4.3MB, time=79.26 memory used=1953.2MB, alloc=4.3MB, time=79.41 memory used=1957.0MB, alloc=4.3MB, time=79.57 memory used=1960.8MB, alloc=4.3MB, time=79.72 memory used=1964.6MB, alloc=4.3MB, time=79.87 memory used=1968.4MB, alloc=4.3MB, time=80.03 memory used=1972.2MB, alloc=4.3MB, time=80.18 memory used=1976.0MB, alloc=4.3MB, time=80.34 memory used=1979.9MB, alloc=4.3MB, time=80.49 memory used=1983.7MB, alloc=4.3MB, time=80.65 memory used=1987.5MB, alloc=4.3MB, time=80.80 memory used=1991.3MB, alloc=4.3MB, time=80.96 memory used=1995.1MB, alloc=4.3MB, time=81.11 memory used=1998.9MB, alloc=4.3MB, time=81.26 memory used=2002.8MB, alloc=4.3MB, time=81.42 memory used=2006.6MB, alloc=4.3MB, time=81.57 memory used=2010.4MB, alloc=4.3MB, time=81.72 memory used=2014.2MB, alloc=4.3MB, time=81.87 memory used=2018.0MB, alloc=4.3MB, time=82.03 memory used=2021.8MB, alloc=4.3MB, time=82.18 memory used=2025.6MB, alloc=4.3MB, time=82.34 memory used=2029.5MB, alloc=4.3MB, time=82.49 memory used=2033.3MB, alloc=4.3MB, time=82.64 memory used=2037.1MB, alloc=4.3MB, time=82.80 memory used=2040.9MB, alloc=4.3MB, time=82.95 memory used=2044.7MB, alloc=4.3MB, time=83.11 memory used=2048.5MB, alloc=4.3MB, time=83.26 memory used=2052.3MB, alloc=4.3MB, time=83.41 memory used=2056.2MB, alloc=4.3MB, time=83.57 memory used=2060.0MB, alloc=4.3MB, time=83.72 memory used=2063.8MB, alloc=4.3MB, time=83.87 memory used=2067.6MB, alloc=4.3MB, time=84.03 memory used=2071.4MB, alloc=4.3MB, time=84.18 memory used=2075.2MB, alloc=4.3MB, time=84.34 memory used=2079.0MB, alloc=4.3MB, time=84.49 memory used=2082.9MB, alloc=4.3MB, time=84.64 memory used=2086.7MB, alloc=4.3MB, time=84.80 memory used=2090.5MB, alloc=4.3MB, time=84.95 memory used=2094.3MB, alloc=4.3MB, time=85.11 memory used=2098.1MB, alloc=4.3MB, time=85.26 memory used=2101.9MB, alloc=4.3MB, time=85.42 memory used=2105.8MB, alloc=4.3MB, time=85.57 memory used=2109.6MB, alloc=4.3MB, time=85.72 memory used=2113.4MB, alloc=4.3MB, time=85.88 memory used=2117.2MB, alloc=4.3MB, time=86.03 memory used=2121.0MB, alloc=4.3MB, time=86.19 memory used=2124.8MB, alloc=4.3MB, time=86.35 memory used=2128.6MB, alloc=4.3MB, time=86.50 memory used=2132.5MB, alloc=4.3MB, time=86.66 memory used=2136.3MB, alloc=4.3MB, time=86.81 memory used=2140.1MB, alloc=4.3MB, time=86.96 memory used=2143.9MB, alloc=4.3MB, time=87.12 memory used=2147.7MB, alloc=4.3MB, time=87.27 memory used=2151.5MB, alloc=4.3MB, time=87.42 memory used=2155.3MB, alloc=4.3MB, time=87.58 memory used=2159.2MB, alloc=4.3MB, time=87.73 memory used=2163.0MB, alloc=4.3MB, time=87.89 memory used=2166.8MB, alloc=4.3MB, time=88.04 memory used=2170.6MB, alloc=4.3MB, time=88.19 memory used=2174.4MB, alloc=4.3MB, time=88.34 memory used=2178.2MB, alloc=4.3MB, time=88.50 memory used=2182.1MB, alloc=4.3MB, time=88.65 memory used=2185.9MB, alloc=4.3MB, time=88.81 memory used=2189.7MB, alloc=4.3MB, time=88.96 memory used=2193.5MB, alloc=4.3MB, time=89.12 memory used=2197.3MB, alloc=4.3MB, time=89.27 memory used=2201.1MB, alloc=4.3MB, time=89.43 memory used=2204.9MB, alloc=4.3MB, time=89.58 memory used=2208.8MB, alloc=4.3MB, time=89.74 memory used=2212.6MB, alloc=4.3MB, time=89.89 memory used=2216.4MB, alloc=4.3MB, time=90.04 memory used=2220.2MB, alloc=4.3MB, time=90.20 memory used=2224.0MB, alloc=4.3MB, time=90.36 memory used=2227.8MB, alloc=4.3MB, time=90.51 memory used=2231.6MB, alloc=4.3MB, time=90.66 memory used=2235.5MB, alloc=4.3MB, time=90.82 memory used=2239.3MB, alloc=4.3MB, time=90.97 memory used=2243.1MB, alloc=4.3MB, time=91.12 memory used=2246.9MB, alloc=4.3MB, time=91.28 memory used=2250.7MB, alloc=4.3MB, time=91.43 memory used=2254.5MB, alloc=4.3MB, time=91.58 memory used=2258.3MB, alloc=4.3MB, time=91.74 memory used=2262.2MB, alloc=4.3MB, time=91.89 memory used=2266.0MB, alloc=4.3MB, time=92.05 memory used=2269.8MB, alloc=4.3MB, time=92.20 memory used=2273.6MB, alloc=4.3MB, time=92.35 memory used=2277.4MB, alloc=4.3MB, time=92.51 memory used=2281.2MB, alloc=4.3MB, time=92.66 memory used=2285.1MB, alloc=4.3MB, time=92.82 memory used=2288.9MB, alloc=4.3MB, time=92.97 memory used=2292.7MB, alloc=4.3MB, time=93.12 memory used=2296.5MB, alloc=4.3MB, time=93.28 memory used=2300.3MB, alloc=4.3MB, time=93.43 memory used=2304.1MB, alloc=4.3MB, time=93.59 memory used=2307.9MB, alloc=4.3MB, time=93.74 memory used=2311.8MB, alloc=4.3MB, time=93.89 memory used=2315.6MB, alloc=4.3MB, time=94.05 memory used=2319.4MB, alloc=4.3MB, time=94.20 memory used=2323.2MB, alloc=4.3MB, time=94.36 memory used=2327.0MB, alloc=4.3MB, time=94.52 memory used=2330.8MB, alloc=4.3MB, time=94.67 memory used=2334.6MB, alloc=4.3MB, time=94.83 memory used=2338.5MB, alloc=4.3MB, time=94.98 memory used=2342.3MB, alloc=4.3MB, time=95.13 memory used=2346.1MB, alloc=4.3MB, time=95.29 memory used=2349.9MB, alloc=4.3MB, time=95.44 memory used=2353.7MB, alloc=4.3MB, time=95.59 memory used=2357.5MB, alloc=4.3MB, time=95.75 memory used=2361.4MB, alloc=4.3MB, time=95.90 memory used=2365.2MB, alloc=4.3MB, time=96.06 memory used=2369.0MB, alloc=4.3MB, time=96.21 memory used=2372.8MB, alloc=4.3MB, time=96.37 memory used=2376.6MB, alloc=4.3MB, time=96.52 memory used=2380.4MB, alloc=4.3MB, time=96.67 memory used=2384.2MB, alloc=4.3MB, time=96.83 memory used=2388.1MB, alloc=4.3MB, time=96.98 memory used=2391.9MB, alloc=4.3MB, time=97.14 memory used=2395.7MB, alloc=4.3MB, time=97.29 memory used=2399.5MB, alloc=4.3MB, time=97.44 memory used=2403.3MB, alloc=4.3MB, time=97.60 memory used=2407.1MB, alloc=4.3MB, time=97.75 memory used=2410.9MB, alloc=4.3MB, time=97.91 memory used=2414.8MB, alloc=4.3MB, time=98.06 memory used=2418.6MB, alloc=4.3MB, time=98.22 memory used=2422.4MB, alloc=4.3MB, time=98.38 memory used=2426.2MB, alloc=4.3MB, time=98.53 memory used=2430.0MB, alloc=4.3MB, time=98.68 memory used=2433.8MB, alloc=4.3MB, time=98.84 memory used=2437.6MB, alloc=4.3MB, time=98.99 memory used=2441.5MB, alloc=4.3MB, time=99.15 memory used=2445.3MB, alloc=4.3MB, time=99.30 memory used=2449.1MB, alloc=4.3MB, time=99.45 memory used=2452.9MB, alloc=4.3MB, time=99.61 memory used=2456.7MB, alloc=4.3MB, time=99.77 memory used=2460.5MB, alloc=4.3MB, time=99.92 memory used=2464.4MB, alloc=4.3MB, time=100.07 memory used=2468.2MB, alloc=4.3MB, time=100.23 memory used=2472.0MB, alloc=4.3MB, time=100.38 memory used=2475.8MB, alloc=4.3MB, time=100.54 memory used=2479.6MB, alloc=4.3MB, time=100.69 memory used=2483.4MB, alloc=4.3MB, time=100.84 memory used=2487.2MB, alloc=4.3MB, time=101.00 memory used=2491.1MB, alloc=4.3MB, time=101.15 memory used=2494.9MB, alloc=4.3MB, time=101.31 memory used=2498.7MB, alloc=4.3MB, time=101.46 memory used=2502.5MB, alloc=4.3MB, time=101.62 memory used=2506.3MB, alloc=4.3MB, time=101.77 memory used=2510.1MB, alloc=4.3MB, time=101.92 memory used=2513.9MB, alloc=4.3MB, time=102.08 memory used=2517.8MB, alloc=4.3MB, time=102.23 memory used=2521.6MB, alloc=4.3MB, time=102.39 memory used=2525.4MB, alloc=4.3MB, time=102.54 memory used=2529.2MB, alloc=4.3MB, time=102.70 memory used=2533.0MB, alloc=4.3MB, time=102.85 memory used=2536.8MB, alloc=4.3MB, time=103.00 memory used=2540.6MB, alloc=4.3MB, time=103.16 memory used=2544.5MB, alloc=4.3MB, time=103.31 memory used=2548.3MB, alloc=4.3MB, time=103.47 memory used=2552.1MB, alloc=4.3MB, time=103.62 memory used=2555.9MB, alloc=4.3MB, time=103.78 memory used=2559.7MB, alloc=4.3MB, time=103.93 memory used=2563.5MB, alloc=4.3MB, time=104.08 memory used=2567.4MB, alloc=4.3MB, time=104.24 memory used=2571.2MB, alloc=4.3MB, time=104.39 memory used=2575.0MB, alloc=4.3MB, time=104.55 memory used=2578.8MB, alloc=4.3MB, time=104.70 memory used=2582.6MB, alloc=4.3MB, time=104.85 memory used=2586.4MB, alloc=4.3MB, time=105.00 memory used=2590.2MB, alloc=4.3MB, time=105.16 memory used=2594.1MB, alloc=4.3MB, time=105.31 memory used=2597.9MB, alloc=4.3MB, time=105.47 memory used=2601.7MB, alloc=4.3MB, time=105.62 memory used=2605.5MB, alloc=4.3MB, time=105.77 memory used=2609.3MB, alloc=4.3MB, time=105.92 memory used=2613.1MB, alloc=4.3MB, time=106.08 memory used=2616.9MB, alloc=4.3MB, time=106.23 memory used=2620.8MB, alloc=4.3MB, time=106.39 memory used=2624.6MB, alloc=4.3MB, time=106.54 memory used=2628.4MB, alloc=4.3MB, time=106.70 memory used=2632.2MB, alloc=4.3MB, time=106.85 memory used=2636.0MB, alloc=4.3MB, time=107.00 memory used=2639.8MB, alloc=4.3MB, time=107.15 memory used=2643.6MB, alloc=4.3MB, time=107.31 memory used=2647.5MB, alloc=4.3MB, time=107.46 memory used=2651.3MB, alloc=4.3MB, time=107.62 memory used=2655.1MB, alloc=4.3MB, time=107.77 memory used=2658.9MB, alloc=4.3MB, time=107.92 memory used=2662.7MB, alloc=4.3MB, time=108.08 memory used=2666.5MB, alloc=4.3MB, time=108.23 memory used=2670.4MB, alloc=4.3MB, time=108.39 memory used=2674.2MB, alloc=4.3MB, time=108.54 memory used=2678.0MB, alloc=4.3MB, time=108.69 memory used=2681.8MB, alloc=4.3MB, time=108.85 memory used=2685.6MB, alloc=4.3MB, time=109.00 memory used=2689.4MB, alloc=4.3MB, time=109.15 memory used=2693.2MB, alloc=4.3MB, time=109.31 memory used=2697.1MB, alloc=4.3MB, time=109.46 memory used=2700.9MB, alloc=4.3MB, time=109.61 memory used=2704.7MB, alloc=4.3MB, time=109.77 memory used=2708.5MB, alloc=4.3MB, time=109.92 memory used=2712.3MB, alloc=4.3MB, time=110.08 memory used=2716.1MB, alloc=4.3MB, time=110.23 memory used=2719.9MB, alloc=4.3MB, time=110.39 memory used=2723.8MB, alloc=4.3MB, time=110.54 memory used=2727.6MB, alloc=4.3MB, time=110.70 memory used=2731.4MB, alloc=4.3MB, time=110.85 memory used=2735.2MB, alloc=4.3MB, time=111.00 memory used=2739.0MB, alloc=4.3MB, time=111.16 memory 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used=4024.6MB, alloc=4.3MB, time=163.59 memory used=4028.4MB, alloc=4.3MB, time=163.75 memory used=4032.2MB, alloc=4.3MB, time=163.91 memory used=4036.1MB, alloc=4.3MB, time=164.06 memory used=4039.9MB, alloc=4.3MB, time=164.22 memory used=4043.7MB, alloc=4.3MB, time=164.38 memory used=4047.5MB, alloc=4.3MB, time=164.53 memory used=4051.3MB, alloc=4.3MB, time=164.69 memory used=4055.1MB, alloc=4.3MB, time=164.85 memory used=4059.0MB, alloc=4.3MB, time=165.01 memory used=4062.8MB, alloc=4.3MB, time=165.16 memory used=4066.6MB, alloc=4.3MB, time=165.32 memory used=4070.4MB, alloc=4.3MB, time=165.48 memory used=4074.2MB, alloc=4.3MB, time=165.63 memory used=4078.0MB, alloc=4.3MB, time=165.79 memory used=4081.8MB, alloc=4.3MB, time=165.95 memory used=4085.7MB, alloc=4.3MB, time=166.11 memory used=4089.5MB, alloc=4.3MB, time=166.26 memory used=4093.3MB, alloc=4.3MB, time=166.42 memory used=4097.1MB, alloc=4.3MB, time=166.57 memory used=4100.9MB, alloc=4.3MB, time=166.73 memory used=4104.7MB, alloc=4.3MB, time=166.89 memory used=4108.5MB, alloc=4.3MB, time=167.05 memory used=4112.4MB, alloc=4.3MB, time=167.20 memory used=4116.2MB, alloc=4.3MB, time=167.36 memory used=4120.0MB, alloc=4.3MB, time=167.52 memory used=4123.8MB, alloc=4.3MB, time=167.67 memory used=4127.6MB, alloc=4.3MB, time=167.83 memory used=4131.4MB, alloc=4.3MB, time=167.99 memory used=4135.2MB, alloc=4.3MB, time=168.14 memory used=4139.1MB, alloc=4.3MB, time=168.30 memory used=4142.9MB, alloc=4.3MB, time=168.46 memory used=4146.7MB, alloc=4.3MB, time=168.61 memory used=4150.5MB, alloc=4.3MB, time=168.77 memory used=4154.3MB, alloc=4.3MB, time=168.93 memory used=4158.1MB, alloc=4.3MB, time=169.08 memory used=4162.0MB, alloc=4.3MB, time=169.24 memory used=4165.8MB, alloc=4.3MB, time=169.40 memory used=4169.6MB, alloc=4.3MB, time=169.55 memory used=4173.4MB, alloc=4.3MB, time=169.71 memory used=4177.2MB, alloc=4.3MB, time=169.87 memory used=4181.0MB, alloc=4.3MB, time=170.02 memory used=4184.8MB, alloc=4.3MB, time=170.18 memory used=4188.7MB, alloc=4.3MB, time=170.34 memory used=4192.5MB, alloc=4.3MB, time=170.50 memory used=4196.3MB, alloc=4.3MB, time=170.65 memory used=4200.1MB, alloc=4.3MB, time=170.81 memory used=4203.9MB, alloc=4.3MB, time=170.97 memory used=4207.7MB, alloc=4.3MB, time=171.12 memory used=4211.5MB, alloc=4.3MB, time=171.28 memory used=4215.4MB, alloc=4.3MB, time=171.44 memory used=4219.2MB, alloc=4.3MB, time=171.59 memory used=4223.0MB, alloc=4.3MB, time=171.75 memory used=4226.8MB, alloc=4.3MB, time=171.91 memory used=4230.6MB, alloc=4.3MB, time=172.06 memory used=4234.4MB, alloc=4.3MB, time=172.22 memory used=4238.3MB, alloc=4.3MB, time=172.38 memory used=4242.1MB, alloc=4.3MB, time=172.53 memory used=4245.9MB, alloc=4.3MB, time=172.69 memory used=4249.7MB, alloc=4.3MB, time=172.85 memory used=4253.5MB, alloc=4.3MB, time=173.00 memory used=4257.3MB, alloc=4.3MB, time=173.16 memory used=4261.1MB, alloc=4.3MB, time=173.32 memory used=4265.0MB, alloc=4.3MB, time=173.48 memory used=4268.8MB, alloc=4.3MB, time=173.63 memory used=4272.6MB, alloc=4.3MB, time=173.79 memory used=4276.4MB, alloc=4.3MB, time=173.95 memory used=4280.2MB, alloc=4.3MB, time=174.10 memory used=4284.0MB, alloc=4.3MB, time=174.26 memory used=4287.8MB, alloc=4.3MB, time=174.42 memory used=4291.7MB, alloc=4.3MB, time=174.57 memory used=4295.5MB, alloc=4.3MB, time=174.73 memory used=4299.3MB, alloc=4.3MB, time=174.89 memory used=4303.1MB, alloc=4.3MB, time=175.04 memory used=4306.9MB, alloc=4.3MB, time=175.20 memory used=4310.7MB, alloc=4.3MB, time=175.36 memory used=4314.5MB, alloc=4.3MB, time=175.52 memory used=4318.4MB, alloc=4.3MB, time=175.68 memory used=4322.2MB, alloc=4.3MB, time=175.83 memory used=4326.0MB, alloc=4.3MB, time=175.99 memory used=4329.8MB, alloc=4.3MB, time=176.15 memory used=4333.6MB, alloc=4.3MB, time=176.30 memory used=4337.4MB, alloc=4.3MB, time=176.46 memory used=4341.3MB, alloc=4.3MB, time=176.62 memory used=4345.1MB, alloc=4.3MB, time=176.77 memory used=4348.9MB, alloc=4.3MB, time=176.93 memory used=4352.7MB, alloc=4.3MB, time=177.09 memory used=4356.5MB, alloc=4.3MB, time=177.24 memory used=4360.3MB, alloc=4.3MB, time=177.40 memory used=4364.1MB, alloc=4.3MB, time=177.56 memory used=4368.0MB, alloc=4.3MB, time=177.71 memory used=4371.8MB, alloc=4.3MB, time=177.87 memory used=4375.6MB, alloc=4.3MB, time=178.02 memory used=4379.4MB, alloc=4.3MB, time=178.18 memory used=4383.2MB, alloc=4.3MB, time=178.34 memory used=4387.0MB, alloc=4.3MB, time=178.50 memory used=4390.8MB, alloc=4.3MB, time=178.65 memory used=4394.7MB, alloc=4.3MB, time=178.81 memory used=4398.5MB, alloc=4.3MB, time=178.97 memory used=4402.3MB, alloc=4.3MB, time=179.12 memory used=4406.1MB, alloc=4.3MB, time=179.28 memory used=4409.9MB, alloc=4.3MB, time=179.43 memory used=4413.7MB, alloc=4.3MB, time=179.59 memory used=4417.5MB, alloc=4.3MB, time=179.75 memory used=4421.4MB, alloc=4.3MB, time=179.90 memory used=4425.2MB, alloc=4.3MB, time=180.06 Finished! Maximum Time Reached before Solution Completed! diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; Iterations = 15609 Total Elapsed Time = 3 Minutes 0 Seconds Elapsed Time(since restart) = 3 Minutes 0 Seconds Expected Time Remaining = 1 Hours 41 Minutes 19 Seconds Optimized Time Remaining = 1 Hours 41 Minutes 18 Seconds Expected Total Time = 1 Hours 44 Minutes 18 Seconds Time to Timeout Unknown Percent Done = 2.876 % > quit memory used=4425.3MB, alloc=4.3MB, time=180.06