|\^/| 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, > array_const_0D1, > array_const_0D2, > #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, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > 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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, 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, > array_const_0D1, > array_const_0D2, > #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, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > 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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, 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, > array_const_0D1, > array_const_0D2, > #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, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > 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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, 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, > array_const_0D1, > array_const_0D2, > #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, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > 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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, 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, > array_const_0D1, > array_const_0D2, > #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, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > 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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, 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, > array_const_0D1, > array_const_0D2, > #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, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > 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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, 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, > array_const_0D1, > array_const_0D2, > #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, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > 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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, 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, > array_const_0D1, > array_const_0D2, > #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, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > 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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, 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, > array_const_0D1, > array_const_0D2, > #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, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > 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 mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D1[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp3[1] := sqrt(array_tmp2[1]); > #emit pre arccos FULL $eq_no = 1 > array_tmp4[1] := arccos(array_tmp3[1]); > array_tmp4_a1[1] := sin(array_tmp4[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[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 mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D1[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/2.0; > #emit pre arccos FULL $eq_no = 1 > temp := att(1,array_tmp4_a1,array_tmp4,2); > array_tmp4[2] := - (array_tmp3[2] + temp) / array_tmp4_a1[1]; > temp2 := att(1,array_tmp3,array_tmp4,1); > array_tmp4_a1[2] := temp2; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp4[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[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 sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := 0.0; > array_tmp3[3] := -ats(3,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre arccos FULL $eq_no = 1 > temp := att(2,array_tmp4_a1,array_tmp4,2); > array_tmp4[3] := - (array_tmp3[3] + temp) / array_tmp4_a1[1]; > temp2 := att(2,array_tmp3,array_tmp4,1); > array_tmp4_a1[3] := temp2; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp4[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[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 sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := 0.0; > array_tmp3[4] := -ats(4,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre arccos FULL $eq_no = 1 > temp := att(3,array_tmp4_a1,array_tmp4,2); > array_tmp4[4] := - (array_tmp3[4] + temp) / array_tmp4_a1[1]; > temp2 := att(3,array_tmp3,array_tmp4,1); > array_tmp4_a1[4] := temp2; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp4[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[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 sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := 0.0; > array_tmp3[5] := -ats(5,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre arccos FULL $eq_no = 1 > temp := att(4,array_tmp4_a1,array_tmp4,2); > array_tmp4[5] := - (array_tmp3[5] + temp) / array_tmp4_a1[1]; > temp2 := att(4,array_tmp3,array_tmp4,1); > array_tmp4_a1[5] := temp2; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp4[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[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 sqrt LINEAR $eq_no = 1 > array_tmp3[kkk] := 0.0; > array_tmp3[kkk] := -ats(kkk,array_tmp3,array_tmp3,2) /array_tmp3[1] / 2.0; > #emit arcsin $eq_no = 1 > temp := att(kkk-1,array_tmp4_a1,array_tmp4,2); > array_tmp4[kkk] := - (array_tmp3[kkk] + temp) / array_tmp4_a1[1]; > temp2 := att(kkk-1,array_tmp3,array_tmp4,1); > array_tmp4_a1[kkk] := temp2; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[kkk] := array_tmp4[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp5[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; Warning, `temp` is implicitly declared local to procedure `atomall` Warning, `temp2` is implicitly declared local to procedure `atomall` atomall := proc() local kkk, order_d, adj2, adj3, temporary, term, temp, temp2; 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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, 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] := array_const_0D1[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; array_tmp3[1] := sqrt(array_tmp2[1]); array_tmp4[1] := arccos(array_tmp3[1]); array_tmp4_a1[1] := sin(array_tmp4[1]); array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[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_const_0D1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*2.0); temp := att(1, array_tmp4_a1, array_tmp4, 2); array_tmp4[2] := -(array_tmp3[2] + temp)/array_tmp4_a1[1]; temp2 := att(1, array_tmp3, array_tmp4, 1); array_tmp4_a1[2] := temp2; array_tmp5[2] := array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[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_tmp3[3] := 0.; array_tmp3[3] := -ats(3, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; temp := att(2, array_tmp4_a1, array_tmp4, 2); array_tmp4[3] := -(array_tmp3[3] + temp)/array_tmp4_a1[1]; temp2 := att(2, array_tmp3, array_tmp4, 1); array_tmp4_a1[3] := temp2; array_tmp5[3] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[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_tmp3[4] := 0.; array_tmp3[4] := -ats(4, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; temp := att(3, array_tmp4_a1, array_tmp4, 2); array_tmp4[4] := -(array_tmp3[4] + temp)/array_tmp4_a1[1]; temp2 := att(3, array_tmp3, array_tmp4, 1); array_tmp4_a1[4] := temp2; array_tmp5[4] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[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_tmp3[5] := 0.; array_tmp3[5] := -ats(5, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; temp := att(4, array_tmp4_a1, array_tmp4, 2); array_tmp4[5] := -(array_tmp3[5] + temp)/array_tmp4_a1[1]; temp2 := att(4, array_tmp3, array_tmp4, 1); array_tmp4_a1[5] := temp2; array_tmp5[5] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[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_tmp3[kkk] := 0.; array_tmp3[kkk] := -ats(kkk, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0); temp := att(kkk - 1, array_tmp4_a1, array_tmp4, 2); array_tmp4[kkk] := -(array_tmp3[kkk] + temp)/array_tmp4_a1[1]; temp2 := att(kkk - 1, array_tmp3, array_tmp4, 1); array_tmp4_a1[kkk] := temp2; array_tmp5[kkk] := array_tmp4[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_tmp5[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(10.0 * (0.1 * x + 0.2) * arccos(sqrt ( 0.1 * x + 0.2)) - 5.0 * sqrt( 0.1 * x + > 0.2) * sqrt( 0.8 - 0.1 * x) + 5.0 * arcsin(sqrt( 0.1 * x + 0.2))); > end; exact_soln_y := proc(x) return 10.0*(0.1*x + 0.2)*arccos(sqrt(0.1*x + 0.2)) - 5.0*sqrt(0.1*x + 0.2)*sqrt(0.8 - 0.1*x) + 5.0*arcsin(sqrt(0.1*x + 0.2)) 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, > array_const_0D1, > array_const_0D2, > #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, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > 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/arccos_sqrtpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = arccos(sqrt(0.1 * x + 0.2));"); > 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 := 0.0;"); > omniout_str(ALWAYS,"x_end := 0.5 ;"); > 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 := 1000000;"); > 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(10.0 * (0.1 * x + 0.2) * arccos(sqrt ( 0.1 * x + 0.2)) - 5.0 * sqrt( 0.1 * x +"); > omniout_str(ALWAYS,"0.2) * sqrt( 0.8 - 0.1 * x) + 5.0 * arcsin(sqrt( 0.1 * x + 0.2)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > 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:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4_a1:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= 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[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_a1[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_tmp5[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 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_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_a1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4_a1[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_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp5[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_const_0D1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D1[1] := 0.1; > array_const_0D2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D2[1] := 0.2; > 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 := 0.0; > x_end := 0.5 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.05; > glob_look_poles := true; > glob_max_iter := 1000000; > 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 ) = arccos(sqrt(0.1 * x + 0.2));"); > 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,"2013-01-12T20:51:11-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"arccos_sqrt") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = arccos(sqrt(0.1 * x + 0.2));") > ; > 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,"arccos_sqrt diffeq.mxt") > ; > logitem_str(html_log_file,"arccos_sqrt 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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, 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/arccos_sqrtpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = arccos(sqrt(0.1 * x + 0.2));") ; 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 := 0.0;"); omniout_str(ALWAYS, "x_end := 0.5 ;"); 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 := 1000000;"); 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(10.0 * (0.1 * x + 0.2) * arccos(sqrt ( 0.\ 1 * x + 0.2)) - 5.0 * sqrt( 0.1 * x +"); omniout_str(ALWAYS, "0.2) * sqrt( 0.8 - 0.1 * x) + 5.0 * arcsin(sqrt(\ 0.1 * x + 0.2)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 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 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4_a1 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := 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[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_a1[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_tmp5[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 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_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_a1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_a1[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_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[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_const_0D1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D1[term] := 0.; term := term + 1 end do; array_const_0D1[1] := 0.1; array_const_0D2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D2[term] := 0.; term := term + 1 end do; array_const_0D2[1] := 0.2; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.; x_end := 0.5; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.05; glob_look_poles := true; glob_max_iter := 1000000; 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 ) = arccos(sqrt(0.1 * x + 0.2));"); 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, "2013-01-12T20:51:11-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "arccos_sqrt"); logitem_str(html_log_file, "diff ( y , x , 1 ) = arccos(sqrt(0.1 * x + 0.2));"); 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, "arccos_sqrt diffeq.mxt"); logitem_str(html_log_file, "arccos_sqrt 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/arccos_sqrtpostode.ode################# diff ( y , x , 1 ) = arccos(sqrt(0.1 * x + 0.2)); ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 0.5 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.05; glob_look_poles := true; glob_max_iter := 1000000; 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(10.0 * (0.1 * x + 0.2) * arccos(sqrt ( 0.1 * x + 0.2)) - 5.0 * sqrt( 0.1 * x + 0.2) * sqrt( 0.8 - 0.1 * x) + 5.0 * arcsin(sqrt( 0.1 * x + 0.2))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 0.5 estimated_steps = 500 step_error = 2.0000000000000000000000000000000e-13 est_needed_step_err = 2.0000000000000000000000000000000e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 1.1718309454379427110227424203722e-90 max_value3 = 1.1718309454379427110227424203722e-90 value3 = 1.1718309454379427110227424203722e-90 best_h = 0.001 START of Soultion x[1] = 0 y[1] (analytic) = 2.5325354805922115871054120776631 y[1] (numeric) = 2.5325354805922115871054120776631 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 2.5325354805922115871054120776631 y[1] (numeric) = 2.5325354805922115871054120776631 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.001 y[1] (analytic) = 2.5336425668139110529839867211056 y[1] (numeric) = 2.5336425668139110529839867211056 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE memory used=3.8MB, alloc=2.8MB, time=0.12 TOP MAIN SOLVE Loop x[1] = 0.002 y[1] (analytic) = 2.5347495280590357775231090564521 y[1] (numeric) = 2.534749528059035777523109056452 absolute error = 1e-31 relative error = 3.9451629793407714705211031505065e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.003 y[1] (analytic) = 2.5358563643509917984772048963088 y[1] (numeric) = 2.5358563643509917984772048963088 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.004 y[1] (analytic) = 2.5369630757131642084953181281344 y[1] (numeric) = 2.5369630757131642084953181281342 absolute error = 2e-31 relative error = 7.8834415019532011442619847215881e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.005 y[1] (analytic) = 2.5380696621689171805513234614831 y[1] (numeric) = 2.538069662168917180551323461483 absolute error = 1e-31 relative error = 3.9400021792366650732682972133140e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.006 y[1] (analytic) = 2.5391761237415939933291082161395 y[1] (numeric) = 2.5391761237415939933291082161395 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 memory used=7.6MB, alloc=3.9MB, time=0.26 NO POLE TOP MAIN SOLVE Loop x[1] = 0.007 y[1] (analytic) = 2.5402824604545170565628242197235 y[1] (numeric) = 2.5402824604545170565628242197234 absolute error = 1e-31 relative error = 3.9365701081173318582474925334588e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.008 y[1] (analytic) = 2.5413886723309879363323106056772 y[1] (numeric) = 2.541388672330987936332310605677 absolute error = 2e-31 relative error = 7.8697132074865956850880630603678e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.009 y[1] (analytic) = 2.5424947593942873803137880257652 y[1] (numeric) = 2.542494759394287380313788025765 absolute error = 2e-31 relative error = 7.8662895670096527006583623516599e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (analytic) = 2.5436007216676753429859245153375 y[1] (numeric) = 2.5436007216676753429859245153376 absolute error = 1e-31 relative error = 3.9314346449169283849359089256712e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.011 y[1] (analytic) = 2.544706559174391010791372974621 y[1] (numeric) = 2.5447065591743910107913729746211 absolute error = 1e-31 relative error = 3.9297261854995246539848335574659e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.1MB, time=0.41 x[1] = 0.012 y[1] (analytic) = 2.545812271937652827253879955202 y[1] (numeric) = 2.5458122719376528272538799552022 absolute error = 2e-31 relative error = 7.8560388055548668548920216159499e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.013 y[1] (analytic) = 2.5469178599806585180510651676621 y[1] (numeric) = 2.5469178599806585180510651676621 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.014 y[1] (analytic) = 2.5480233233265851160429708539898 y[1] (numeric) = 2.5480233233265851160429708539896 absolute error = 2e-31 relative error = 7.8492217150857535597729348035020e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.015 y[1] (analytic) = 2.549128661998588986256479896954 y[1] (numeric) = 2.5491286619985889862564798969541 absolute error = 1e-31 relative error = 3.9229090901044269371761970674042e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.016 y[1] (analytic) = 2.5502338760198058508257012680502 y[1] (numeric) = 2.55023387601980585082570126805 absolute error = 2e-31 relative error = 7.8424179790185934458172651617407e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.1MB, time=0.56 x[1] = 0.017 y[1] (analytic) = 2.5513389654133508138884211459273 y[1] (numeric) = 2.5513389654133508138884211459271 absolute error = 2e-31 relative error = 7.8390211066132226948107275930168e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.018 y[1] (analytic) = 2.5524439302023183864387177683937 y[1] (numeric) = 2.5524439302023183864387177683934 absolute error = 3e-31 relative error = 1.1753441337150964453728662897209e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.019 y[1] (analytic) = 2.5535487704097825111358378131185 y[1] (numeric) = 2.5535487704097825111358378131183 absolute error = 2e-31 relative error = 7.8322373285983827595644897793374e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.02 y[1] (analytic) = 2.5546534860587965870694318350684 y[1] (numeric) = 2.5546534860587965870694318350681 absolute error = 3e-31 relative error = 1.1743275619850360978677611601425e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.021 y[1] (analytic) = 2.5557580771723934944812460224697 y[1] (numeric) = 2.5557580771723934944812460224694 absolute error = 3e-31 relative error = 1.1738200210714392529240336026311e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.022 y[1] (analytic) = 2.5568625437735856194433672677183 y[1] (numeric) = 2.5568625437735856194433672677183 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.2MB, time=0.71 x[1] = 0.023 y[1] (analytic) = 2.5579668858853648784931182851296 y[1] (numeric) = 2.5579668858853648784931182851295 absolute error = 1e-31 relative error = 3.9093547516893654412121329557898e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.024 y[1] (analytic) = 2.5590711035307027432246992437472 y[1] (numeric) = 2.559071103530702743224699243747 absolute error = 2e-31 relative error = 7.8153357960262895648924294796360e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.025 y[1] (analytic) = 2.5601751967325502648376721206112 y[1] (numeric) = 2.560175196732550264837672120611 absolute error = 2e-31 relative error = 7.8119653785901856276757061300004e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.026 y[1] (analytic) = 2.5612791655138380986423837178978 y[1] (numeric) = 2.5612791655138380986423837178976 absolute error = 2e-31 relative error = 7.8085982462546774842024081060741e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.027 y[1] (analytic) = 2.5623830098974765285224230262083 y[1] (numeric) = 2.5623830098974765285224230262081 absolute error = 2e-31 relative error = 7.8052343942134629302708913747694e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.3MB, time=0.86 x[1] = 0.028 y[1] (analytic) = 2.5634867299063554913542083559833 y[1] (numeric) = 2.5634867299063554913542083559832 absolute error = 1e-31 relative error = 3.9009369088348279922970659497680e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.029 y[1] (analytic) = 2.5645903255633446013837993995546 y[1] (numeric) = 2.5645903255633446013837993995544 absolute error = 2e-31 relative error = 7.7985165118357637975784315224942e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.03 y[1] (analytic) = 2.5656937968912931745610291277108 y[1] (numeric) = 2.5656937968912931745610291277107 absolute error = 1e-31 relative error = 3.8975812359668318140508232778741e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.031 y[1] (analytic) = 2.566797143913030252831050166856 y[1] (numeric) = 2.5667971439130302528310501668558 absolute error = 2e-31 relative error = 7.7918116931945798880572540952190e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.032 y[1] (analytic) = 2.5679003666513646283833900458526 y[1] (numeric) = 2.5679003666513646283833900458525 absolute error = 1e-31 relative error = 3.8942320854295306272157444542362e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.033 y[1] (analytic) = 2.5690034651290848678586094454983 y[1] (numeric) = 2.5690034651290848678586094454982 absolute error = 1e-31 relative error = 3.8925599500884789243408487654589e-30 % Correct digits = 31 h = 0.001 memory used=26.7MB, alloc=4.3MB, time=1.01 NO POLE TOP MAIN SOLVE Loop x[1] = 0.034 y[1] (analytic) = 2.5701064393689593365126573282399 y[1] (numeric) = 2.5701064393689593365126573282398 absolute error = 1e-31 relative error = 3.8908894382036992415924829762321e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.035 y[1] (analytic) = 2.5712092893937362223390165712191 y[1] (numeric) = 2.5712092893937362223390165712189 absolute error = 2e-31 relative error = 7.7784410948187679745269830088965e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.036 y[1] (analytic) = 2.5723120152261435601487334720356 y[1] (numeric) = 2.5723120152261435601487334720353 absolute error = 3e-31 relative error = 1.1662659826033026785103004993018e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.037 y[1] (analytic) = 2.5734146168888892556084242437244 y[1] (numeric) = 2.5734146168888892556084242437241 absolute error = 3e-31 relative error = 1.1657662858955965741343507169160e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.038 y[1] (analytic) = 2.5745170944046611092363513633575 y[1] (numeric) = 2.5745170944046611092363513633573 absolute error = 2e-31 relative error = 7.7684471559606632609233624952491e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.3MB, time=1.16 x[1] = 0.039 y[1] (analytic) = 2.5756194477961268403566623874014 y[1] (numeric) = 2.5756194477961268403566623874011 absolute error = 3e-31 relative error = 1.1647683443945889177896377147908e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.04 y[1] (analytic) = 2.5767216770859341110118835964832 y[1] (numeric) = 2.576721677085934111011883596483 absolute error = 2e-31 relative error = 7.7618006546280925942988753458298e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.041 y[1] (analytic) = 2.5778237822967105498337605825441 y[1] (numeric) = 2.577823782296710549833760582544 absolute error = 1e-31 relative error = 3.8792411136383054116127510701795e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.042 y[1] (analytic) = 2.5789257634510637758725376424703 y[1] (numeric) = 2.5789257634510637758725376424702 absolute error = 1e-31 relative error = 3.8775835046210139950990818472191e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.043 y[1] (analytic) = 2.5800276205715814223847675942074 y[1] (numeric) = 2.5800276205715814223847675942072 absolute error = 2e-31 relative error = 7.7518549958659681694967525947913e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.3MB, time=1.32 x[1] = 0.044 y[1] (analytic) = 2.5811293536808311605797433840643 y[1] (numeric) = 2.5811293536808311605797433840643 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.045 y[1] (analytic) = 2.5822309628013607233246426074027 y[1] (numeric) = 2.5822309628013607233246426074025 absolute error = 2e-31 relative error = 7.7452405645011658019566347941499e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.046 y[1] (analytic) = 2.5833324479556979288084758191746 y[1] (numeric) = 2.5833324479556979288084758191745 absolute error = 1e-31 relative error = 3.8709690686204286577591155942135e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.047 y[1] (analytic) = 2.5844338091663507041649292658398 y[1] (numeric) = 2.5844338091663507041649292658396 absolute error = 2e-31 relative error = 7.7386388960958960935634226574198e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.048 y[1] (analytic) = 2.5855350464558071090541924260106 y[1] (numeric) = 2.5855350464558071090541924260105 absolute error = 1e-31 relative error = 3.8676714182264802579228545599939e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.049 y[1] (analytic) = 2.5866361598465353592038605037978 y[1] (numeric) = 2.5866361598465353592038605037977 absolute error = 1e-31 relative error = 3.8660249768538371219482904097018e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.3MB, time=1.47 x[1] = 0.05 y[1] (analytic) = 2.5877371493609838499090017762012 y[1] (numeric) = 2.587737149360983849909001776201 absolute error = 2e-31 relative error = 7.7287602432645845099172076573468e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.051 y[1] (analytic) = 2.5888380150215811794914794540495 y[1] (numeric) = 2.5888380150215811794914794540494 absolute error = 1e-31 relative error = 3.8627368502685702344748680575091e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.052 y[1] (analytic) = 2.5899387568507361727186174749126 y[1] (numeric) = 2.5899387568507361727186174749125 absolute error = 1e-31 relative error = 3.8610951604738358070564788153358e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.053 y[1] (analytic) = 2.5910393748708379041812994060901 y[1] (numeric) = 2.59103937487083790418129940609 absolute error = 1e-31 relative error = 3.8594550499636831273439745114710e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.054 y[1] (analytic) = 2.5921398691042557216315893962337 y[1] (numeric) = 2.5921398691042557216315893962336 absolute error = 1e-31 relative error = 3.8578165164581250284200593052349e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.3MB, time=1.62 x[1] = 0.055 y[1] (analytic) = 2.5932402395733392692799638753609 y[1] (numeric) = 2.5932402395733392692799638753609 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.056 y[1] (analytic) = 2.594340486300418511052242464984 y[1] (numeric) = 2.5943404863004185110522424649839 absolute error = 1e-31 relative error = 3.8545441713628731380226650490207e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.057 y[1] (analytic) = 2.5954406093078037538063063227887 y[1] (numeric) = 2.5954406093078037538063063227888 absolute error = 1e-31 relative error = 3.8529103552352022745049896696091e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.058 y[1] (analytic) = 2.5965406086177856705086919097713 y[1] (numeric) = 2.5965406086177856705086919097714 absolute error = 1e-31 relative error = 3.8512781070361506059408511158395e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.059 y[1] (analytic) = 2.5976404842526353233711479319465 y[1] (numeric) = 2.5976404842526353233711479319464 absolute error = 1e-31 relative error = 3.8496474245076645017535072348736e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.06 y[1] (analytic) = 2.5987402362346041869472429737081 y[1] (numeric) = 2.598740236234604186947242973708 absolute error = 1e-31 relative error = 3.8480183053960452837289479232526e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.3MB, time=1.78 x[1] = 0.061 y[1] (analytic) = 2.5998398645859241711891111056218 y[1] (numeric) = 2.5998398645859241711891111056219 absolute error = 1e-31 relative error = 3.8463907474519387126490176937083e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.062 y[1] (analytic) = 2.600939369328807644464422515871 y[1] (numeric) = 2.600939369328807644464422515871 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.063 y[1] (analytic) = 2.6020387504854474565336659817557 y[1] (numeric) = 2.6020387504854474565336659817555 absolute error = 2e-31 relative error = 7.6862806121810117649526544284739e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.064 y[1] (analytic) = 2.6031380080780169614878297655622 y[1] (numeric) = 2.6031380080780169614878297655622 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.065 y[1] (analytic) = 2.6042371421286700406465672877644 y[1] (numeric) = 2.6042371421286700406465672877644 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.3MB, time=1.93 x[1] = 0.066 y[1] (analytic) = 2.6053361526595411254169336998856 y[1] (numeric) = 2.6053361526595411254169336998856 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.067 y[1] (analytic) = 2.6064350396927452201127792494646 y[1] (numeric) = 2.6064350396927452201127792494646 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.068 y[1] (analytic) = 2.6075338032503779247348851003823 y[1] (numeric) = 2.6075338032503779247348851003823 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.069 y[1] (analytic) = 2.6086324433545154577119270433577 y[1] (numeric) = 2.6086324433545154577119270433577 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.07 y[1] (analytic) = 2.6097309600272146786023523036853 y[1] (numeric) = 2.6097309600272146786023523036853 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.071 y[1] (analytic) = 2.6108293532905131107572544262662 y[1] (numeric) = 2.6108293532905131107572544262662 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.4MB, time=2.08 x[1] = 0.072 y[1] (analytic) = 2.6119276231664289639443309916814 y[1] (numeric) = 2.6119276231664289639443309916812 absolute error = 2e-31 relative error = 7.6571800162494868117409401747469e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.073 y[1] (analytic) = 2.6130257696769611569330086914573 y[1] (numeric) = 2.6130257696769611569330086914571 absolute error = 2e-31 relative error = 7.6539620206166305952729610566958e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.074 y[1] (analytic) = 2.6141237928440893400408200657923 y[1] (numeric) = 2.6141237928440893400408200657922 absolute error = 1e-31 relative error = 3.8253735448084101172332915586409e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.075 y[1] (analytic) = 2.6152216926897739176411159828258 y[1] (numeric) = 2.6152216926897739176411159828256 absolute error = 2e-31 relative error = 7.6475352188708175000030042722625e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.076 y[1] (analytic) = 2.6163194692359560706321977150565 y[1] (numeric) = 2.6163194692359560706321977150565 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.4MB, time=2.23 x[1] = 0.077 y[1] (analytic) = 2.617417122504557778867952245744 y[1] (numeric) = 2.6174171225045577788679522457439 absolute error = 1e-31 relative error = 3.8205603203325826531144545502481e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.078 y[1] (analytic) = 2.6185146525174818435500742160356 y[1] (numeric) = 2.6185146525174818435500742160355 absolute error = 1e-31 relative error = 3.8189589622444312661328096455066e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.079 y[1] (analytic) = 2.6196120592966119095819577021938 y[1] (numeric) = 2.6196120592966119095819577021937 absolute error = 1e-31 relative error = 3.8173591255665103884779471852485e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.08 y[1] (analytic) = 2.620709342863812487884340791593 y[1] (numeric) = 2.620709342863812487884340791593 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.081 y[1] (analytic) = 2.6218065032409289776727857061663 y[1] (numeric) = 2.6218065032409289776727857061662 absolute error = 1e-31 relative error = 3.8141640077704305568012907967444e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.082 y[1] (analytic) = 2.6229035404497876886970770026613 y[1] (numeric) = 2.6229035404497876886970770026612 absolute error = 1e-31 relative error = 3.8125687223271479996499238947245e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.4MB, time=2.39 x[1] = 0.083 y[1] (analytic) = 2.6240004545121958634426201604468 y[1] (numeric) = 2.6240004545121958634426201604465 absolute error = 3e-31 relative error = 1.1432924848931486955195073064610e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.084 y[1] (analytic) = 2.6250972454499416992939226496591 y[1] (numeric) = 2.6250972454499416992939226496589 absolute error = 2e-31 relative error = 7.6187653751364169979879813835094e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.085 y[1] (analytic) = 2.6261939132847943706602393552228 y[1] (numeric) = 2.6261939132847943706602393552227 absolute error = 1e-31 relative error = 3.8077919339521225569777526001476e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.086 y[1] (analytic) = 2.6272904580385040510634640156885 y[1] (numeric) = 2.6272904580385040510634640156883 absolute error = 2e-31 relative error = 7.6124053733029968454255138763087e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.087 y[1] (analytic) = 2.6283868797328019351883481199248 y[1] (numeric) = 2.6283868797328019351883481199247 absolute error = 1e-31 relative error = 3.8046149435263448546295176873006e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.4MB, time=2.54 x[1] = 0.088 y[1] (analytic) = 2.6294831783894002608951284894697 y[1] (numeric) = 2.6294831783894002608951284894695 absolute error = 2e-31 relative error = 7.6060574048814847607881619577000e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.089 y[1] (analytic) = 2.6305793540299923311946445597706 y[1] (numeric) = 2.6305793540299923311946445597705 absolute error = 1e-31 relative error = 3.8014439612628335992391140504485e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.09 y[1] (analytic) = 2.6316754066762525361860261596604 y[1] (numeric) = 2.6316754066762525361860261596602 absolute error = 2e-31 relative error = 7.5997214357296270240633664687846e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.091 y[1] (analytic) = 2.6327713363498363749570323751726 y[1] (numeric) = 2.6327713363498363749570323751724 absolute error = 2e-31 relative error = 7.5965579402458397579702815716909e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.092 y[1] (analytic) = 2.6338671430723804774471218712441 y[1] (numeric) = 2.6338671430723804774471218712439 absolute error = 2e-31 relative error = 7.5933974318348472098457870868041e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.093 y[1] (analytic) = 2.6349628268655026262733348329386 y[1] (numeric) = 2.6349628268655026262733348329385 absolute error = 1e-31 relative error = 3.7951199531326191520021780828390e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.4MB, time=2.70 x[1] = 0.094 y[1] (analytic) = 2.6360583877508017785190664765854 y[1] (numeric) = 2.6360583877508017785190664765851 absolute error = 3e-31 relative error = 1.1380628038970444939418951554701e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.095 y[1] (analytic) = 2.6371538257498580874858118706304 y[1] (numeric) = 2.6371538257498580874858118706302 absolute error = 2e-31 relative error = 7.5839337867646480254285621934620e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.096 y[1] (analytic) = 2.6382491408842329244079615960716 y[1] (numeric) = 2.6382491408842329244079615960714 absolute error = 2e-31 relative error = 7.5807851844109082689134484624809e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.097 y[1] (analytic) = 2.6393443331754689001307275670524 y[1] (numeric) = 2.6393443331754689001307275670521 absolute error = 3e-31 relative error = 1.1366459322079496129304040879179e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.098 y[1] (analytic) = 2.6404394026450898867512781235661 y[1] (numeric) = 2.6404394026450898867512781235658 absolute error = 3e-31 relative error = 1.1361745310249181399132329052602e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.4MB, time=2.85 x[1] = 0.099 y[1] (analytic) = 2.6415343493146010392231613002299 y[1] (numeric) = 2.6415343493146010392231613002295 absolute error = 4e-31 relative error = 1.5142714313133501615666009736553e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 2.6426291732054888169240949677441 y[1] (numeric) = 2.6426291732054888169240949677438 absolute error = 3e-31 relative error = 1.1352330589618910188958243474302e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.101 y[1] (analytic) = 2.6437238743392210051872023369588 y[1] (numeric) = 2.6437238743392210051872023369586 absolute error = 2e-31 relative error = 7.5650865788693043085889766950486e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.102 y[1] (analytic) = 2.6448184527372467367957711094022 y[1] (numeric) = 2.6448184527372467367957711094018 absolute error = 4e-31 relative error = 1.5123911419554004857776722579383e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.103 y[1] (analytic) = 2.6459129084209965134416143527097 y[1] (numeric) = 2.6459129084209965134416143527093 absolute error = 4e-31 relative error = 1.5117655563300770486448358631658e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.104 y[1] (analytic) = 2.6470072414118822271471109746073 y[1] (numeric) = 2.6470072414118822271471109746069 absolute error = 4e-31 relative error = 1.5111405580690619884141777336924e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.4MB, time=3.00 x[1] = 0.105 y[1] (analytic) = 2.648101451731297181651003464944 y[1] (numeric) = 2.6481014517312971816510034649436 absolute error = 4e-31 relative error = 1.5105161463450909907527935794894e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.106 y[1] (analytic) = 2.6491955394006161137580303717548 y[1] (numeric) = 2.6491955394006161137580303717542 absolute error = 6e-31 relative error = 2.2648384804986904402502740205995e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.107 y[1] (analytic) = 2.6502895044411952146524707744374 y[1] (numeric) = 2.6502895044411952146524707744371 absolute error = 3e-31 relative error = 1.1319518094052672513142890327127e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.108 y[1] (analytic) = 2.6513833468743721511756778148674 y[1] (numeric) = 2.6513833468743721511756778148671 absolute error = 3e-31 relative error = 1.1314848166096390600465107498627e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.109 y[1] (analytic) = 2.6524770667214660870676781456237 y[1] (numeric) = 2.6524770667214660870676781456234 absolute error = 3e-31 relative error = 1.1310182612466775162896999811360e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.4MB, time=3.16 x[1] = 0.11 y[1] (analytic) = 2.6535706640037777041729139534923 y[1] (numeric) = 2.653570664003777704172913953492 absolute error = 3e-31 relative error = 1.1305521427017588963113509736881e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.111 y[1] (analytic) = 2.6546641387425892236102040160056 y[1] (numeric) = 2.6546641387425892236102040160052 absolute error = 4e-31 relative error = 1.5067819471485548669121634777635e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.112 y[1] (analytic) = 2.6557574909591644269070000489987 y[1] (numeric) = 2.6557574909591644269070000489984 absolute error = 3e-31 relative error = 1.1296212136133361770251750372438e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.113 y[1] (analytic) = 2.6568507206747486770980144039991 y[1] (numeric) = 2.6568507206747486770980144039989 absolute error = 2e-31 relative error = 7.5277093456423807196248662210541e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.114 y[1] (analytic) = 2.6579438279105689397882949757116 y[1] (numeric) = 2.6579438279105689397882949757114 absolute error = 2e-31 relative error = 7.5246134963364373111427064320796e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.115 y[1] (analytic) = 2.659036812687833804180822981922 y[1] (numeric) = 2.6590368126878338041808229819218 absolute error = 2e-31 relative error = 7.5215205387786274523331809342222e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.4MB, time=3.31 x[1] = 0.116 y[1] (analytic) = 2.6601296750277335040687090808107 y[1] (numeric) = 2.6601296750277335040687090808104 absolute error = 3e-31 relative error = 1.1277645703376182729512972766179e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.117 y[1] (analytic) = 2.6612224149514399387920630939418 y[1] (numeric) = 2.6612224149514399387920630939415 absolute error = 3e-31 relative error = 1.1273014924063541038042290713962e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.118 y[1] (analytic) = 2.6623150324801066941596124070758 y[1] (numeric) = 2.6623150324801066941596124070754 absolute error = 4e-31 relative error = 1.5024517952234072182713480699263e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.119 y[1] (analytic) = 2.6634075276348690633351439254322 y[1] (numeric) = 2.6634075276348690633351439254319 absolute error = 3e-31 relative error = 1.1263766317669110960755900995637e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 2.6644999004368440676888442651182 y[1] (numeric) = 2.6644999004368440676888442651179 absolute error = 3e-31 relative error = 1.1259148478512424706765412309277e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.4MB, time=3.47 x[1] = 0.121 y[1] (analytic) = 2.6655921509071304776136126681135 y[1] (numeric) = 2.6655921509071304776136126681132 absolute error = 3e-31 relative error = 1.1254534940685006272972899601134e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.122 y[1] (analytic) = 2.6666842790668088333064209344859 y[1] (numeric) = 2.6666842790668088333064209344854 absolute error = 5e-31 relative error = 1.8749876163629396282524095689663e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.123 y[1] (analytic) = 2.6677762849369414655147944723789 y[1] (numeric) = 2.6677762849369414655147944723785 absolute error = 4e-31 relative error = 1.4993760993323128140281971193327e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.124 y[1] (analytic) = 2.6688681685385725162484883737823 y[1] (numeric) = 2.6688681685385725162484883737819 absolute error = 4e-31 relative error = 1.4987626766856502197818898486038e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.125 y[1] (analytic) = 2.6699599298927279594564322321427 y[1] (numeric) = 2.6699599298927279594564322321422 absolute error = 5e-31 relative error = 1.8726872804420278269393357044340e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.126 y[1] (analytic) = 2.6710515690204156216690172265206 y[1] (numeric) = 2.6710515690204156216690172265202 absolute error = 4e-31 relative error = 1.4975375415409760814381151559486e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.4MB, time=3.62 x[1] = 0.127 y[1] (analytic) = 2.6721430859426252026057988062245 y[1] (numeric) = 2.672143085942625202605798806224 absolute error = 5e-31 relative error = 1.8711572843174301745009160318009e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.128 y[1] (analytic) = 2.6732344806803282957486881196609 y[1] (numeric) = 2.6732344806803282957486881196606 absolute error = 3e-31 relative error = 1.1222360109751805562621088726823e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.129 y[1] (analytic) = 2.6743257532544784088807051415407 y[1] (numeric) = 2.6743257532544784088807051415404 absolute error = 3e-31 relative error = 1.1217780767167939319918192080808e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 2.6754169036860109845903662635426 y[1] (numeric) = 2.6754169036860109845903662635422 absolute error = 4e-31 relative error = 1.4950940896310652603800775240966e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.131 y[1] (analytic) = 2.676507931995843420741778925096 y[1] (numeric) = 2.6765079319958434207417789250958 absolute error = 2e-31 relative error = 7.4724232126919994942628569997022e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.4MB, time=3.77 x[1] = 0.132 y[1] (analytic) = 2.6775988382048750909105156730654 y[1] (numeric) = 2.6775988382048750909105156730651 absolute error = 3e-31 relative error = 1.1204068201685022358308986983868e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.133 y[1] (analytic) = 2.6786896223339873647853398518146 y[1] (numeric) = 2.6786896223339873647853398518142 absolute error = 4e-31 relative error = 1.4932674419049462917426502120947e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.134 y[1] (analytic) = 2.6797802844040436285358549384082 y[1] (numeric) = 2.679780284404043628535854938408 absolute error = 2e-31 relative error = 7.4632984339788141451559526941395e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.135 y[1] (analytic) = 2.6808708244358893051461493515406 y[1] (numeric) = 2.6808708244358893051461493515404 absolute error = 2e-31 relative error = 7.4602624705755503330036344537268e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.136 y[1] (analytic) = 2.6819612424503518747145083771903 y[1] (numeric) = 2.68196124245035187471450837719 absolute error = 3e-31 relative error = 1.1185843973118249184766634905496e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.137 y[1] (analytic) = 2.6830515384682408947192646689757 y[1] (numeric) = 2.6830515384682408947192646689754 absolute error = 3e-31 relative error = 1.1181298446889714129339708498195e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.4MB, time=3.93 x[1] = 0.138 y[1] (analytic) = 2.6841417125103480202508585967206 y[1] (numeric) = 2.6841417125103480202508585967204 absolute error = 2e-31 relative error = 7.4511714142301997131654527737107e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.139 y[1] (analytic) = 2.6852317645974470242101795328347 y[1] (numeric) = 2.6852317645974470242101795328344 absolute error = 3e-31 relative error = 1.1172219990663416870245492085888e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 2.6863216947502938174732589827746 y[1] (numeric) = 2.6863216947502938174732589827743 absolute error = 3e-31 relative error = 1.1167687049033284340380323310392e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.141 y[1] (analytic) = 2.687411502989626469022386283066 y[1] (numeric) = 2.6874115029896264690223862830657 absolute error = 3e-31 relative error = 1.1163158290654902122868569866380e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.142 y[1] (analytic) = 2.688501189336165226043717408135 y[1] (numeric) = 2.6885011893361652260437174081347 absolute error = 3e-31 relative error = 1.1158633709739027151542961431238e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=103.0MB, alloc=4.4MB, time=4.09 x[1] = 0.143 y[1] (analytic) = 2.6895907538106125339914472455231 y[1] (numeric) = 2.6895907538106125339914472455229 absolute error = 2e-31 relative error = 7.4360755336714321194347134991683e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.144 y[1] (analytic) = 2.6906801964336530566186155179376 y[1] (numeric) = 2.6906801964336530566186155179375 absolute error = 1e-31 relative error = 3.7165323523971536249271152024857e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.145 y[1] (analytic) = 2.691769517225953695974616350011 y[1] (numeric) = 2.6917695172259536959746163500109 absolute error = 1e-31 relative error = 3.7150283246782809968898817039836e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.146 y[1] (analytic) = 2.6928587162081636123694812976206 y[1] (numeric) = 2.6928587162081636123694812976203 absolute error = 3e-31 relative error = 1.1140577045290829598195577393755e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.147 y[1] (analytic) = 2.6939477934009142443050054781357 y[1] (numeric) = 2.6939477934009142443050054781355 absolute error = 2e-31 relative error = 7.4240488434823922618725398632143e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.148 y[1] (analytic) = 2.6950367488248193283727862610285 y[1] (numeric) = 2.6950367488248193283727862610284 absolute error = 1e-31 relative error = 3.7105245427026316892274433118532e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.4MB, time=4.24 x[1] = 0.149 y[1] (analytic) = 2.6961255825004749191192437998819 y[1] (numeric) = 2.6961255825004749191192437998817 absolute error = 2e-31 relative error = 7.4180520854860725039083213111188e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 2.6972142944484594088776925089822 y[1] (numeric) = 2.697214294448459408877692508982 absolute error = 2e-31 relative error = 7.4150578399220983604629511441332e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.151 y[1] (analytic) = 2.6983028846893335475675324103651 y[1] (numeric) = 2.6983028846893335475675324103648 absolute error = 3e-31 relative error = 1.1118099517376464034301499896088e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.152 y[1] (analytic) = 2.6993913532436404624606291004024 y[1] (numeric) = 2.6993913532436404624606291004022 absolute error = 2e-31 relative error = 7.4090775966840140159318426952714e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.153 y[1] (analytic) = 2.7004797001319056779149509087771 y[1] (numeric) = 2.7004797001319056779149509087768 absolute error = 3e-31 relative error = 1.1109137387159267185713867949807e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.4MB, time=4.40 x[1] = 0.154 y[1] (analytic) = 2.701567925374637135075531646976 y[1] (numeric) = 2.7015679253746371350755316469757 absolute error = 3e-31 relative error = 1.1104662488114112866317142018873e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.155 y[1] (analytic) = 2.7026560289923252115428271682568 y[1] (numeric) = 2.7026560289923252115428271682565 absolute error = 3e-31 relative error = 1.1100191692238905931107669239106e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.156 y[1] (analytic) = 2.7037440110054427410085337863847 y[1] (numeric) = 2.7037440110054427410085337863845 absolute error = 2e-31 relative error = 7.3971499959282717865152529279768e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.157 y[1] (analytic) = 2.7048318714344450328589364263175 y[1] (numeric) = 2.7048318714344450328589364263173 absolute error = 2e-31 relative error = 7.3941749249625125523226790792987e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.158 y[1] (analytic) = 2.7059196102997698917458542064128 y[1] (numeric) = 2.7059196102997698917458542064125 absolute error = 3e-31 relative error = 1.1086803867272505558618647669772e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.159 y[1] (analytic) = 2.707007227621837637125250978658 y[1] (numeric) = 2.7070072276218376371252509786578 absolute error = 2e-31 relative error = 7.3882329518456504211960800005590e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.4MB, time=4.55 x[1] = 0.16 y[1] (analytic) = 2.7080947234210511227635781808703 y[1] (numeric) = 2.7080947234210511227635781808701 absolute error = 2e-31 relative error = 7.3852660422212363806651902847533e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.161 y[1] (analytic) = 2.7091820977177957562119171827749 y[1] (numeric) = 2.7091820977177957562119171827748 absolute error = 1e-31 relative error = 3.6911509227910373025334854206550e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.162 y[1] (analytic) = 2.7102693505324395182479881363604 y[1] (numeric) = 2.7102693505324395182479881363602 absolute error = 2e-31 relative error = 7.3793403582086583293603072154756e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.163 y[1] (analytic) = 2.7113564818853329822860921699031 y[1] (numeric) = 2.711356481885332982286092169903 absolute error = 1e-31 relative error = 3.6881907881941559606554646189915e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.164 y[1] (analytic) = 2.7124434917968093337550535945746 y[1] (numeric) = 2.7124434917968093337550535945745 absolute error = 1e-31 relative error = 3.6867127482075875885424849484307e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.4MB, time=4.71 x[1] = 0.165 y[1] (analytic) = 2.7135303802871843894442286225649 y[1] (numeric) = 2.7135303802871843894442286225648 absolute error = 1e-31 relative error = 3.6852360572950938301003477794659e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.166 y[1] (analytic) = 2.7146171473767566168176469262003 y[1] (numeric) = 2.7146171473767566168176469262 absolute error = 3e-31 relative error = 1.1051282140831609625548055398997e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.167 y[1] (analytic) = 2.7157037930858071532963521985763 y[1] (numeric) = 2.7157037930858071532963521985763 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.168 y[1] (analytic) = 2.7167903174345998255090077077872 y[1] (numeric) = 2.7167903174345998255090077077871 absolute error = 1e-31 relative error = 3.6808140605575924730265328684348e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.169 y[1] (analytic) = 2.7178767204433811685108326688821 y[1] (numeric) = 2.7178767204433811685108326688819 absolute error = 2e-31 relative error = 7.3586854950276396004123873619982e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 2.7189630021323804449709350902595 y[1] (numeric) = 2.7189630021323804449709350902594 absolute error = 1e-31 relative error = 3.6778727743471963454048613065741e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.4MB, time=4.86 x[1] = 0.171 y[1] (analytic) = 2.7200491625218096643281065842627 y[1] (numeric) = 2.7200491625218096643281065842625 absolute error = 2e-31 relative error = 7.3528082784568559133820187799822e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.172 y[1] (analytic) = 2.7211352016318636019151444653119 y[1] (numeric) = 2.7211352016318636019151444653117 absolute error = 2e-31 relative error = 7.3498736806631323066386927876824e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.173 y[1] (analytic) = 2.7222211194827198180517662929772 y[1] (numeric) = 2.722221119482719818051766292977 absolute error = 2e-31 relative error = 7.3469417516680009322923401559051e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.174 y[1] (analytic) = 2.7233069160945386771061818519524 y[1] (numeric) = 2.7233069160945386771061818519522 absolute error = 2e-31 relative error = 7.3440124878329015982086236655063e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.175 y[1] (analytic) = 2.7243925914874633665253873959525 y[1] (numeric) = 2.7243925914874633665253873959526 absolute error = 1e-31 relative error = 3.6705429427629598116700961442493e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.4MB, time=5.02 x[1] = 0.176 y[1] (analytic) = 2.7254781456816199158342468181083 y[1] (numeric) = 2.7254781456816199158342468181081 absolute error = 2e-31 relative error = 7.3381619411217706445099765929311e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.177 y[1] (analytic) = 2.7265635786971172156034242464672 y[1] (numeric) = 2.7265635786971172156034242464672 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.178 y[1] (analytic) = 2.7276488905540470363862323997609 y[1] (numeric) = 2.7276488905540470363862323997608 absolute error = 1e-31 relative error = 3.6661610057769474720899702060956e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.179 y[1] (analytic) = 2.7287340812724840476244608755951 y[1] (numeric) = 2.7287340812724840476244608755948 absolute error = 3e-31 relative error = 1.0994109028758922394907830701144e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 2.7298191508724858365232483807511 y[1] (numeric) = 2.729819150872485836523248380751 absolute error = 1e-31 relative error = 3.6632463351295156153123919168602e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.181 y[1] (analytic) = 2.7309040993740929268950627512678 y[1] (numeric) = 2.7309040993740929268950627512676 absolute error = 2e-31 relative error = 7.3235819612207846295268359500818e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.4MB, time=5.17 x[1] = 0.182 y[1] (analytic) = 2.731988926797328797972852448448 y[1] (numeric) = 2.7319889267973287979728524484478 absolute error = 2e-31 relative error = 7.3206738884720559398612027729224e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.183 y[1] (analytic) = 2.733073633162199903192433055904 y[1] (numeric) = 2.7330736331621999031924330559039 absolute error = 1e-31 relative error = 3.6588842242167755503862484052912e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.184 y[1] (analytic) = 2.7341582184886956889441721421835 y[1] (numeric) = 2.7341582184886956889441721421833 absolute error = 2e-31 relative error = 7.3148656375324863141230295179632e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.185 y[1] (analytic) = 2.735242682796788613294035693438 y[1] (numeric) = 2.7352426827967886132940356934379 absolute error = 1e-31 relative error = 3.6559827261012866109709264648213e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.186 y[1] (analytic) = 2.7363270261064341646740591609954 y[1] (numeric) = 2.7363270261064341646740591609954 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.4MB, time=5.32 x[1] = 0.187 y[1] (analytic) = 2.7374112484375708805423060095573 y[1] (numeric) = 2.7374112484375708805423060095572 absolute error = 1e-31 relative error = 3.6530864720117186191033895270683e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.188 y[1] (analytic) = 2.7384953498101203660123764930915 y[1] (numeric) = 2.7384953498101203660123764930915 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.189 y[1] (analytic) = 2.7395793302439873124525292273052 y[1] (numeric) = 2.739579330243987312452529227305 absolute error = 2e-31 relative error = 7.3003908954951843813025180047979e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 2.7406631897590595160544779698599 y[1] (numeric) = 2.74066318975905951605447796986 absolute error = 1e-31 relative error = 3.6487518923765061575283662302936e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.191 y[1] (analytic) = 2.741746928375207896371925862258 y[1] (numeric) = 2.7417469283752078963719258622579 absolute error = 1e-31 relative error = 3.6473096391599205332906488540471e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.192 y[1] (analytic) = 2.7428305461122865148288992305313 y[1] (numeric) = 2.7428305461122865148288992305313 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.4MB, time=5.48 x[1] = 0.193 y[1] (analytic) = 2.7439140429901325931979428855708 y[1] (numeric) = 2.7439140429901325931979428855707 absolute error = 1e-31 relative error = 3.6444290321509758255286063875565e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.194 y[1] (analytic) = 2.7449974190285665320482387080641 y[1] (numeric) = 2.7449974190285665320482387080641 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.195 y[1] (analytic) = 2.7460806742473919291637091476374 y[1] (numeric) = 2.7460806742473919291637091476372 absolute error = 2e-31 relative error = 7.2831072253481137361571123202505e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.196 y[1] (analytic) = 2.7471638086663955979311671108572 y[1] (numeric) = 2.7471638086663955979311671108572 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.197 y[1] (analytic) = 2.7482468223053475856985735582934 y[1] (numeric) = 2.7482468223053475856985735582933 absolute error = 1e-31 relative error = 3.6386833667332579995052723629302e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.4MB, time=5.63 x[1] = 0.198 y[1] (analytic) = 2.7493297151840011921034639768167 y[1] (numeric) = 2.7493297151840011921034639768165 absolute error = 2e-31 relative error = 7.2745003589580317986686604209560e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.199 y[1] (analytic) = 2.7504124873220929873716047397683 y[1] (numeric) = 2.7504124873220929873716047397682 absolute error = 1e-31 relative error = 3.6358182803832392681145763186286e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 2.7514951387393428305859402145249 y[1] (numeric) = 2.7514951387393428305859402145248 absolute error = 1e-31 relative error = 3.6343876677106240026756659088492e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.201 y[1] (analytic) = 2.7525776694554538879258913243396 y[1] (numeric) = 2.7525776694554538879258913243395 absolute error = 1e-31 relative error = 3.6329583397289978521211481910030e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.202 y[1] (analytic) = 2.7536600794901126508770661191469 y[1] (numeric) = 2.7536600794901126508770661191469 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.203 y[1] (analytic) = 2.7547423688629889544114427582683 y[1] (numeric) = 2.7547423688629889544114427582682 absolute error = 1e-31 relative error = 3.6301035309256407201855599636037e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.4MB, time=5.79 x[1] = 0.204 y[1] (analytic) = 2.7558245375937359951380851566583 y[1] (numeric) = 2.7558245375937359951380851566582 absolute error = 1e-31 relative error = 3.6286780466551609156143728156912e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.205 y[1] (analytic) = 2.7569065857019903494244513954846 y[1] (numeric) = 2.7569065857019903494244513954845 absolute error = 1e-31 relative error = 3.6272538401781585244688845055627e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.206 y[1] (analytic) = 2.7579885132073719914883548474212 y[1] (numeric) = 2.7579885132073719914883548474212 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.207 y[1] (analytic) = 2.7590703201294843114606378170801 y[1] (numeric) = 2.7590703201294843114606378170799 absolute error = 2e-31 relative error = 7.2488185074824014368200347179377e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.208 y[1] (analytic) = 2.7601520064879141334186173474786 y[1] (numeric) = 2.7601520064879141334186173474784 absolute error = 2e-31 relative error = 7.2459777407145398534506198877812e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.209 y[1] (analytic) = 2.7612335723022317333903626943693 y[1] (numeric) = 2.7612335723022317333903626943692 absolute error = 1e-31 relative error = 3.6215697579188518914871679645498e-30 % Correct digits = 31 h = 0.001 memory used=148.7MB, alloc=4.4MB, time=5.94 NO POLE TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 2.7623150175919908573298638216103 y[1] (numeric) = 2.7623150175919908573298638216102 absolute error = 1e-31 relative error = 3.6201519147216449297316278377958e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.211 y[1] (analytic) = 2.7633963423767287390631501225559 y[1] (numeric) = 2.7633963423767287390631501225557 absolute error = 2e-31 relative error = 7.2374706781288186265616791204890e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.212 y[1] (analytic) = 2.7644775466759661182054184246812 y[1] (numeric) = 2.7644775466759661182054184246812 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.213 y[1] (analytic) = 2.7655586305092072580492291873235 y[1] (numeric) = 2.7655586305092072580492291873233 absolute error = 2e-31 relative error = 7.2318119671603233584220521371644e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.214 y[1] (analytic) = 2.7666395938959399634238296555175 y[1] (numeric) = 2.7666395938959399634238296555174 absolute error = 1e-31 relative error = 3.6144932003659180967517073865406e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.4MB, time=6.10 x[1] = 0.215 y[1] (analytic) = 2.7677204368556355985256625864496 y[1] (numeric) = 2.7677204368556355985256625864495 absolute error = 1e-31 relative error = 3.6130816779171690503763140206284e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.216 y[1] (analytic) = 2.7688011594077491047201190190026 y[1] (numeric) = 2.7688011594077491047201190190024 absolute error = 2e-31 relative error = 7.2233428290957633293701286045458e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.217 y[1] (analytic) = 2.7698817615717190183145934112687 y[1] (numeric) = 2.7698817615717190183145934112685 absolute error = 2e-31 relative error = 7.2205248171500879599541839863914e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.218 y[1] (analytic) = 2.7709622433669674883028993257231 y[1] (numeric) = 2.770962243366967488302899325723 absolute error = 1e-31 relative error = 3.6088546583186581768182483541278e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.219 y[1] (analytic) = 2.7720426048129002940811036969951 y[1] (numeric) = 2.7720426048129002940811036969948 absolute error = 3e-31 relative error = 1.0822344486305201456577429505562e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 2.7731228459289068631348375728457 y[1] (numeric) = 2.7731228459289068631348375728455 absolute error = 2e-31 relative error = 7.2120858365005622276921063314776e-30 % Correct digits = 31 h = 0.001 NO POLE memory used=156.4MB, alloc=4.4MB, time=6.25 TOP MAIN SOLVE Loop x[1] = 0.221 y[1] (analytic) = 2.7742029667343602886981410750586 y[1] (numeric) = 2.7742029667343602886981410750584 absolute error = 2e-31 relative error = 7.2092778501866083855350648570858e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.222 y[1] (analytic) = 2.7752829672486173473839001834558 y[1] (numeric) = 2.7752829672486173473839001834556 absolute error = 2e-31 relative error = 7.2064723619255888141595293536057e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.223 y[1] (analytic) = 2.7763628474910185167859328031975 y[1] (numeric) = 2.7763628474910185167859328031974 absolute error = 1e-31 relative error = 3.6018346841937236439539017969827e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.224 y[1] (analytic) = 2.7774426074808879930527814328706 y[1] (numeric) = 2.7774426074808879930527814328705 absolute error = 1e-31 relative error = 3.6004344331240376594888366388249e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.225 y[1] (analytic) = 2.7785222472375337084332696086453 y[1] (numeric) = 2.7785222472375337084332696086452 absolute error = 1e-31 relative error = 3.5990354260946494298330609304663e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.4MB, time=6.41 x[1] = 0.226 y[1] (analytic) = 2.7796017667802473487938791579681 y[1] (numeric) = 2.779601766780247348793879157968 absolute error = 1e-31 relative error = 3.5976376614494325201594611746605e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.227 y[1] (analytic) = 2.7806811661283043711080051548594 y[1] (numeric) = 2.7806811661283043711080051548594 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.228 y[1] (analytic) = 2.7817604453009640209171453279006 y[1] (numeric) = 2.7817604453009640209171453279004 absolute error = 2e-31 relative error = 7.1896917054035404098885670219353e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.229 y[1] (analytic) = 2.7828396043174693497640805314207 y[1] (numeric) = 2.7828396043174693497640805314206 absolute error = 1e-31 relative error = 3.5934518053018154444672303640599e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = 2.7839186431970472325981027502363 y[1] (numeric) = 2.7839186431970472325981027502363 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.231 y[1] (analytic) = 2.7849975619589083851523469685351 y[1] (numeric) = 2.784997561958908385152346968535 absolute error = 1e-31 relative error = 3.5906674162279020057948813405819e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.4MB, time=6.56 x[1] = 0.232 y[1] (analytic) = 2.7860763606222473812932830941565 y[1] (numeric) = 2.7860763606222473812932830941564 absolute error = 1e-31 relative error = 3.5892770712740198339946851060846e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.233 y[1] (analytic) = 2.7871550392062426703424239905805 y[1] (numeric) = 2.7871550392062426703424239905803 absolute error = 2e-31 relative error = 7.1757759143875342966300862776764e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.234 y[1] (analytic) = 2.7882335977300565943703055303978 y[1] (numeric) = 2.7882335977300565943703055303976 absolute error = 2e-31 relative error = 7.1730001447089312663985121957997e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.235 y[1] (analytic) = 2.7893120362128354054627944459098 y[1] (numeric) = 2.7893120362128354054627944459096 absolute error = 2e-31 relative error = 7.1702268302526773542101347065022e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.236 y[1] (analytic) = 2.7903903546737092829597796147723 y[1] (numeric) = 2.7903903546737092829597796147719 absolute error = 4e-31 relative error = 1.4334911935530019667858443258095e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.4MB, time=6.71 x[1] = 0.237 y[1] (analytic) = 2.791468553131792350666302281271 y[1] (numeric) = 2.7914685531317923506663022812706 absolute error = 4e-31 relative error = 1.4329375107995887199571122272997e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.238 y[1] (analytic) = 2.7925466316061826940361805768912 y[1] (numeric) = 2.7925466316061826940361805768909 absolute error = 3e-31 relative error = 1.0742882378563887486270710424720e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.239 y[1] (analytic) = 2.7936245901159623773281835673074 y[1] (numeric) = 2.7936245901159623773281835673071 absolute error = 3e-31 relative error = 1.0738737089493728474662362731092e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 2.7947024286801974607348099167907 y[1] (numeric) = 2.7947024286801974607348099167905 absolute error = 2e-31 relative error = 7.1563969726268964157528202019885e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.241 y[1] (analytic) = 2.795780147317938017483726125292 y[1] (numeric) = 2.7957801473179380174837261252918 absolute error = 2e-31 relative error = 7.1536383213774879181533980024791e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.242 y[1] (analytic) = 2.7968577460482181509119191581127 y[1] (numeric) = 2.7968577460482181509119191581124 absolute error = 3e-31 relative error = 1.0726323154042456806249154200304e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.4MB, time=6.87 x[1] = 0.243 y[1] (analytic) = 2.7979352248900560115126181531282 y[1] (numeric) = 2.7979352248900560115126181531278 absolute error = 4e-31 relative error = 1.4296256626731516800565683689276e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.244 y[1] (analytic) = 2.7990125838624538139550397559652 y[1] (numeric) = 2.799012583862453813955039755965 absolute error = 2e-31 relative error = 7.1453769501819500742019876285593e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.245 y[1] (analytic) = 2.8000898229843978540770114993696 y[1] (numeric) = 2.8000898229843978540770114993693 absolute error = 3e-31 relative error = 1.0713942014911983945568982631862e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.246 y[1] (analytic) = 2.8011669422748585258505275092128 y[1] (numeric) = 2.8011669422748585258505275092125 absolute error = 3e-31 relative error = 1.0709822234170973608682035905293e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.247 y[1] (analytic) = 2.8022439417527903383202906862051 y[1] (numeric) = 2.8022439417527903383202906862046 absolute error = 5e-31 relative error = 1.7842843463772549497792160675984e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.4MB, time=7.02 x[1] = 0.248 y[1] (analytic) = 2.8033208214371319325152953793621 y[1] (numeric) = 2.8033208214371319325152953793617 absolute error = 4e-31 relative error = 1.4268791389882326866605586750236e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.249 y[1] (analytic) = 2.8043975813468060983335044346645 y[1] (numeric) = 2.804397581346806098333504434664 absolute error = 5e-31 relative error = 1.7829141036410252544902900052033e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = 2.8054742215007197913996743700984 y[1] (numeric) = 2.8054742215007197913996743700981 absolute error = 3e-31 relative error = 1.0693379311805700367415729049663e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.251 y[1] (analytic) = 2.8065507419177641498963822964238 y[1] (numeric) = 2.8065507419177641498963822964236 absolute error = 2e-31 relative error = 7.1261850716918297169224270120872e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.252 y[1] (analytic) = 2.8076271426168145113683080715296 y[1] (numeric) = 2.8076271426168145113683080715294 absolute error = 2e-31 relative error = 7.1234530028653465755612446686600e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.253 y[1] (analytic) = 2.808703423616730429499825045152 y[1] (numeric) = 2.8087034236167304294998250451517 absolute error = 3e-31 relative error = 1.0681084997350626243766218610184e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.4MB, time=7.17 x[1] = 0.254 y[1] (analytic) = 2.8097795849363556908659526200088 y[1] (numeric) = 2.8097795849363556908659526200084 absolute error = 4e-31 relative error = 1.4235992109290679426241740316456e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.255 y[1] (analytic) = 2.8108556265945183316567237250694 y[1] (numeric) = 2.8108556265945183316567237250689 absolute error = 5e-31 relative error = 1.7788177922384905206928176875847e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.256 y[1] (analytic) = 2.8119315486100306543750201667143 y[1] (numeric) = 2.8119315486100306543750201667139 absolute error = 4e-31 relative error = 1.4225097342704679011439969859751e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.257 y[1] (analytic) = 2.813007351001689244507928693955 y[1] (numeric) = 2.8130073510016892445079286939545 absolute error = 5e-31 relative error = 1.7774571396763468465919138956529e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.258 y[1] (analytic) = 2.8140830337882749871716704846656 y[1] (numeric) = 2.8140830337882749871716704846651 absolute error = 5e-31 relative error = 1.7767777069708840307096284216910e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.4MB, time=7.33 x[1] = 0.259 y[1] (analytic) = 2.8151585969885530837301566309443 y[1] (numeric) = 2.8151585969885530837301566309439 absolute error = 4e-31 relative error = 1.4208790951525437925555644913587e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = 2.8162340406212730683872220732457 y[1] (numeric) = 2.8162340406212730683872220732453 absolute error = 4e-31 relative error = 1.4203364998448719782532737292767e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.261 y[1] (analytic) = 2.8173093647051688247525903048278 y[1] (numeric) = 2.8173093647051688247525903048272 absolute error = 6e-31 relative error = 2.1296915685466084652258613273919e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.262 y[1] (analytic) = 2.8183845692589586023816210403267 y[1] (numeric) = 2.8183845692589586023816210403262 absolute error = 5e-31 relative error = 1.7740659151120232982263815726869e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.263 y[1] (analytic) = 2.8194596543013450332888929149087 y[1] (numeric) = 2.8194596543013450332888929149084 absolute error = 3e-31 relative error = 1.0640336688000567993426388733348e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.264 y[1] (analytic) = 2.8205346198510151484356731534474 y[1] (numeric) = 2.8205346198510151484356731534469 absolute error = 5e-31 relative error = 1.7727135716788711029338985000175e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.4MB, time=7.48 x[1] = 0.265 y[1] (analytic) = 2.821609465926640394191326022544 y[1] (numeric) = 2.8216094659266403941913260225437 absolute error = 3e-31 relative error = 1.0632229712253161324118609639429e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.266 y[1] (analytic) = 2.8226841925468766487687117519457 y[1] (numeric) = 2.8226841925468766487687117519452 absolute error = 5e-31 relative error = 1.7713635883185909793302902380911e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.267 y[1] (analytic) = 2.8237587997303642386336274859944 y[1] (numeric) = 2.8237587997303642386336274859941 absolute error = 3e-31 relative error = 1.0624136878427664301949373113878e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.268 y[1] (analytic) = 2.8248332874957279548883417002154 y[1] (numeric) = 2.8248332874957279548883417002151 absolute error = 3e-31 relative error = 1.0620095753188893108492071916726e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.269 y[1] (analytic) = 2.8259076558615770696292733929492 y[1] (numeric) = 2.8259076558615770696292733929488 absolute error = 4e-31 relative error = 1.4154744199454244718156671870229e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.4MB, time=7.63 x[1] = 0.27 y[1] (analytic) = 2.8269819048465053522788672371205 y[1] (numeric) = 2.8269819048465053522788672371201 absolute error = 4e-31 relative error = 1.4149365417382058503207376458432e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.271 y[1] (analytic) = 2.8280560344690910858917157527628 y[1] (numeric) = 2.8280560344690910858917157527625 absolute error = 3e-31 relative error = 1.0607993488938021804111754369455e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.272 y[1] (analytic) = 2.8291300447478970834349794368055 y[1] (numeric) = 2.8291300447478970834349794368051 absolute error = 4e-31 relative error = 1.4138621896952915720928584488225e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.273 y[1] (analytic) = 2.830203935701470704043155662878 y[1] (numeric) = 2.8302039357014707040431556628775 absolute error = 5e-31 relative error = 1.7666571432990187577727211270303e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.274 y[1] (analytic) = 2.8312777073483438692472470404825 y[1] (numeric) = 2.831277707348343869247247040482 absolute error = 5e-31 relative error = 1.7659871326019765849795448367421e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.275 y[1] (analytic) = 2.8323513597070330791783797998391 y[1] (numeric) = 2.8323513597070330791783797998387 absolute error = 4e-31 relative error = 1.4122541634148609845048197174525e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.4MB, time=7.79 x[1] = 0.276 y[1] (analytic) = 2.8334248927960394287459226460088 y[1] (numeric) = 2.8334248927960394287459226460085 absolute error = 3e-31 relative error = 1.0587893145244387719961058141446e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.277 y[1] (analytic) = 2.8344983066338486237901564035574 y[1] (numeric) = 2.834498306633848623790156403557 absolute error = 4e-31 relative error = 1.4111844733293422062345588746598e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.278 y[1] (analytic) = 2.8355716012389309972095446510249 y[1] (numeric) = 2.8355716012389309972095446510245 absolute error = 4e-31 relative error = 1.4106503247007769391203165069552e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.279 y[1] (analytic) = 2.8366447766297415250626554228209 y[1] (numeric) = 2.8366447766297415250626554228203 absolute error = 6e-31 relative error = 2.1151749593153804519041379528892e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 2.83771783282471984264478393486 y[1] (numeric) = 2.8377178328247198426447839348596 absolute error = 4e-31 relative error = 1.4095834172555210506660162761298e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.4MB, time=7.95 x[1] = 0.281 y[1] (analytic) = 2.8387907698422902605393261693082 y[1] (numeric) = 2.8387907698422902605393261693077 absolute error = 5e-31 relative error = 1.7613133215442208391601023489260e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.282 y[1] (analytic) = 2.839863587700861780643953033187 y[1] (numeric) = 2.8398635877008617806439530331867 absolute error = 3e-31 relative error = 1.0563887691622483154831453475310e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.283 y[1] (analytic) = 2.8409362864188281121716346853363 y[1] (numeric) = 2.840936286418828112171634685336 absolute error = 3e-31 relative error = 1.0559898911994542870211354866134e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.284 y[1] (analytic) = 2.8420088660145676876265645062951 y[1] (numeric) = 2.8420088660145676876265645062947 absolute error = 4e-31 relative error = 1.4074551447861305275401468542105e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.285 y[1] (analytic) = 2.8430813265064436787550320660951 y[1] (numeric) = 2.8430813265064436787550320660946 absolute error = 5e-31 relative error = 1.7586552848081772205695139058787e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.286 y[1] (analytic) = 2.8441536679128040124712943257123 y[1] (numeric) = 2.844153667912804012471294325712 absolute error = 3e-31 relative error = 1.0547953276383848048234549952162e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.4MB, time=8.10 x[1] = 0.287 y[1] (analytic) = 2.8452258902519813867584941890265 y[1] (numeric) = 2.8452258902519813867584941890261 absolute error = 4e-31 relative error = 1.4058637712050864605826484737880e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.288 y[1] (analytic) = 2.8462979935422932865446754035703 y[1] (numeric) = 2.8462979935422932865446754035701 absolute error = 2e-31 relative error = 7.0266711515716841556110152481359e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.289 y[1] (analytic) = 2.8473699778020419995539426901359 y[1] (numeric) = 2.8473699778020419995539426901354 absolute error = 5e-31 relative error = 1.7560064336492121019250313368200e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = 2.8484418430495146321328158634018 y[1] (numeric) = 2.8484418430495146321328158634013 absolute error = 5e-31 relative error = 1.7553456505353985933030690237388e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.291 y[1] (analytic) = 2.8495135893029831250518265882078 y[1] (numeric) = 2.8495135893029831250518265882074 absolute error = 4e-31 relative error = 1.4037483502503444064308354599384e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=206.0MB, alloc=4.4MB, time=8.26 x[1] = 0.292 y[1] (analytic) = 2.8505852165807042692824062988684 y[1] (numeric) = 2.850585216580704269282406298868 absolute error = 4e-31 relative error = 1.4032206357956301791359269426519e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.293 y[1] (analytic) = 2.8516567249009197217491136920384 y[1] (numeric) = 2.8516567249009197217491136920379 absolute error = 5e-31 relative error = 1.7533667205942272250711803545316e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.294 y[1] (analytic) = 2.8527281142818560210572500870868 y[1] (numeric) = 2.8527281142818560210572500870863 absolute error = 5e-31 relative error = 1.7527082146272803327344352976215e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.295 y[1] (analytic) = 2.8537993847417246031959108317084 y[1] (numeric) = 2.8537993847417246031959108317081 absolute error = 3e-31 relative error = 1.0512301656661499659584001472643e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.296 y[1] (analytic) = 2.8548705362987218172165208146087 y[1] (numeric) = 2.8548705362987218172165208146082 absolute error = 5e-31 relative error = 1.7513929043109577733104288630359e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.297 y[1] (analytic) = 2.8559415689710289408869020315276 y[1] (numeric) = 2.8559415689710289408869020315273 absolute error = 3e-31 relative error = 1.0504416590990949673034506627146e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.4MB, time=8.41 x[1] = 0.298 y[1] (analytic) = 2.8570124827768121963209210356377 y[1] (numeric) = 2.8570124827768121963209210356374 absolute error = 3e-31 relative error = 1.0500479147659215487769371220601e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.299 y[1] (analytic) = 2.8580832777342227655837639884228 y[1] (numeric) = 2.8580832777342227655837639884226 absolute error = 2e-31 relative error = 6.9976967276668096035663623186390e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 2.8591539538613968062728869125735 y[1] (numeric) = 2.8591539538613968062728869125733 absolute error = 2e-31 relative error = 6.9950762787674426546818741773224e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.301 y[1] (analytic) = 2.8602245111764554670746886341569 y[1] (numeric) = 2.8602245111764554670746886341565 absolute error = 4e-31 relative error = 1.3984916164342416925123887866177e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.302 y[1] (analytic) = 2.8612949496975049032969537873872 y[1] (numeric) = 2.8612949496975049032969537873868 absolute error = 4e-31 relative error = 1.3979684269959231551825641653571e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.4MB, time=8.57 x[1] = 0.303 y[1] (analytic) = 2.8623652694426362923771131417021 y[1] (numeric) = 2.8623652694426362923771131417018 absolute error = 3e-31 relative error = 1.0480842651448758431597225210694e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.304 y[1] (analytic) = 2.8634354704299258493663683975491 y[1] (numeric) = 2.8634354704299258493663683975488 absolute error = 3e-31 relative error = 1.0476925465862060764491793703585e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.305 y[1] (analytic) = 2.8645055526774348423897284843142 y[1] (numeric) = 2.8645055526774348423897284843138 absolute error = 4e-31 relative error = 1.3964015521845387348661332903139e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.306 y[1] (analytic) = 2.8655755162032096080820042811621 y[1] (numeric) = 2.8655755162032096080820042811618 absolute error = 3e-31 relative error = 1.0469101173696857498388191337673e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.307 y[1] (analytic) = 2.8666453610252815669998085692204 y[1] (numeric) = 2.8666453610252815669998085692201 absolute error = 3e-31 relative error = 1.0465194058490105464860912678522e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.308 y[1] (analytic) = 2.867715087161667239009607911511 y[1] (numeric) = 2.8677150871616672390096079115107 absolute error = 3e-31 relative error = 1.0461290291460796043195457330153e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.4MB, time=8.72 x[1] = 0.309 y[1] (analytic) = 2.8687846946303682586518730453296 y[1] (numeric) = 2.8687846946303682586518730453293 absolute error = 3e-31 relative error = 1.0457389868313342778406352629182e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = 2.8698541834493713904813742603777 y[1] (numeric) = 2.8698541834493713904813742603773 absolute error = 4e-31 relative error = 1.3937990379679393586307326799675e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.311 y[1] (analytic) = 2.8709235536366485443836681248718 y[1] (numeric) = 2.8709235536366485443836681248716 absolute error = 2e-31 relative error = 6.9663993576790485822240607471003e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.312 y[1] (analytic) = 2.8719928052101567908678218110916 y[1] (numeric) = 2.8719928052101567908678218110913 absolute error = 3e-31 relative error = 1.0445708619316949646126987458671e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.313 y[1] (analytic) = 2.8730619381878383763354211613662 y[1] (numeric) = 2.8730619381878383763354211613659 absolute error = 3e-31 relative error = 1.0441821528888537730518405581163e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.4MB, time=8.87 x[1] = 0.314 y[1] (analytic) = 2.8741309525876207383259085253647 y[1] (numeric) = 2.8741309525876207383259085253644 absolute error = 3e-31 relative error = 1.0437937760974521980060521226853e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.315 y[1] (analytic) = 2.8751998484274165207382962897108 y[1] (numeric) = 2.8751998484274165207382962897105 absolute error = 3e-31 relative error = 1.0434057311323394145786756622018e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.316 y[1] (analytic) = 2.8762686257251235890293019114243 y[1] (numeric) = 2.8762686257251235890293019114239 absolute error = 4e-31 relative error = 1.3906906900921249577552102646798e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.317 y[1] (analytic) = 2.87733728449862504538795015747 y[1] (numeric) = 2.8773372844986250453879501574696 absolute error = 4e-31 relative error = 1.3901741799786946132697340766060e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.318 y[1] (analytic) = 2.8784058247657892438866881437847 y[1] (numeric) = 2.8784058247657892438866881437843 absolute error = 4e-31 relative error = 1.3896581106055373122460656678614e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.319 y[1] (analytic) = 2.8794742465444698056090586585462 y[1] (numeric) = 2.8794742465444698056090586585456 absolute error = 6e-31 relative error = 2.0837137221144921449578383865064e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.4MB, time=9.03 x[1] = 0.32 y[1] (analytic) = 2.880542549852505633753977146148 y[1] (numeric) = 2.8805425498525056337539771461474 absolute error = 6e-31 relative error = 2.0829409377435587797654239638689e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.321 y[1] (analytic) = 2.8816107347077209287166576203482 y[1] (numeric) = 2.8816107347077209287166576203479 absolute error = 3e-31 relative error = 1.0410844059769534358382080814413e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.322 y[1] (analytic) = 2.8826788011279252031462326673634 y[1] (numeric) = 2.8826788011279252031462326673631 absolute error = 3e-31 relative error = 1.0406986719526884989835667004132e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.323 y[1] (analytic) = 2.8837467491309132969801125922855 y[1] (numeric) = 2.8837467491309132969801125922849 absolute error = 6e-31 relative error = 2.0806265327592462318584088802422e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.324 y[1] (analytic) = 2.8848145787344653924551286551129 y[1] (numeric) = 2.8848145787344653924551286551125 absolute error = 4e-31 relative error = 1.3865709184521500453302872301209e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.4MB, time=9.19 x[1] = 0.325 y[1] (analytic) = 2.8858822899563470290955052358926 y[1] (numeric) = 2.8858822899563470290955052358924 absolute error = 2e-31 relative error = 6.9302895927548478527695771822579e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.326 y[1] (analytic) = 2.8869498828143091186777056619708 y[1] (numeric) = 2.8869498828143091186777056619704 absolute error = 4e-31 relative error = 1.3855453549130014939250701044236e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.327 y[1] (analytic) = 2.8880173573260879601721963241646 y[1] (numeric) = 2.8880173573260879601721963241642 absolute error = 4e-31 relative error = 1.3850332269829074092515674370014e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.328 y[1] (analytic) = 2.8890847135094052546621736027654 y[1] (numeric) = 2.889084713509405254662173602765 absolute error = 4e-31 relative error = 1.3845215342062963784345005090658e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.329 y[1] (analytic) = 2.8901519513819681202392980186773 y[1] (numeric) = 2.8901519513819681202392980186769 absolute error = 4e-31 relative error = 1.3840102760297229079749014067797e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 2.8912190709614691068764799196937 y[1] (numeric) = 2.8912190709614691068764799196935 absolute error = 2e-31 relative error = 6.9174972595034246533538341845921e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.4MB, time=9.34 x[1] = 0.331 y[1] (analytic) = 2.8922860722655862112777609068999 y[1] (numeric) = 2.8922860722655862112777609068996 absolute error = 3e-31 relative error = 1.0372417959507163443666816099947e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.332 y[1] (analytic) = 2.8933529553119828917053351014659 y[1] (numeric) = 2.8933529553119828917053351014655 absolute error = 4e-31 relative error = 1.3824791035799122445961451977803e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.333 y[1] (analytic) = 2.8944197201183080827837542476727 y[1] (numeric) = 2.8944197201183080827837542476724 absolute error = 3e-31 relative error = 1.0364771837159043304007983784818e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.334 y[1] (analytic) = 2.8954863667021962102813605438736 y[1] (numeric) = 2.8954863667021962102813605438733 absolute error = 3e-31 relative error = 1.0360953636320654538932391052356e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.335 y[1] (analytic) = 2.8965528950812672058689909892458 y[1] (numeric) = 2.8965528950812672058689909892452 absolute error = 6e-31 relative error = 2.0714277340451125633231767108155e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.4MB, time=9.50 x[1] = 0.336 y[1] (analytic) = 2.8976193052731265218559969306341 y[1] (numeric) = 2.8976193052731265218559969306337 absolute error = 4e-31 relative error = 1.3804435913029521465343161585952e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.337 y[1] (analytic) = 2.8986855972953651459036223905205 y[1] (numeric) = 2.8986855972953651459036223905201 absolute error = 4e-31 relative error = 1.3799357901154310886152049460591e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.338 y[1] (analytic) = 2.8997517711655596157157846541642 y[1] (numeric) = 2.8997517711655596157157846541638 absolute error = 4e-31 relative error = 1.3794284185891518371318368565017e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.339 y[1] (analytic) = 2.900817826901272033707300491275 y[1] (numeric) = 2.9008178269012720337073004912746 absolute error = 4e-31 relative error = 1.3789214761800131866814329910771e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = 2.9018837645200500816496012851651 y[1] (numeric) = 2.9018837645200500816496012851645 absolute error = 6e-31 relative error = 2.0676224435172561858092062432888e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.341 y[1] (analytic) = 2.9029495840394270352939802402023 y[1] (numeric) = 2.9029495840394270352939802402018 absolute error = 5e-31 relative error = 1.7223860956767106647126302630991e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.4MB, time=9.65 x[1] = 0.342 y[1] (analytic) = 2.9040152854769217789724147365534 y[1] (numeric) = 2.9040152854769217789724147365528 absolute error = 6e-31 relative error = 2.0661048273424048490159260588188e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.343 y[1] (analytic) = 2.9050808688500388201760067996379 y[1] (numeric) = 2.9050808688500388201760067996376 absolute error = 3e-31 relative error = 1.0326734901488420269362495223264e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.344 y[1] (analytic) = 2.9061463341762683041110845504524 y[1] (numeric) = 2.9061463341762683041110845504521 absolute error = 3e-31 relative error = 1.0322948864343178429313319544066e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.345 y[1] (analytic) = 2.9072116814730860282330074019152 y[1] (numeric) = 2.907211681473086028233007401915 absolute error = 2e-31 relative error = 6.8794440141579188828564331207375e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.346 y[1] (analytic) = 2.9082769107579534567577176656842 y[1] (numeric) = 2.9082769107579534567577176656839 absolute error = 3e-31 relative error = 1.0315386368136938254782337383765e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.347 y[1] (analytic) = 2.9093420220483177351510811334512 y[1] (numeric) = 2.9093420220483177351510811334508 memory used=244.1MB, alloc=4.4MB, time=9.81 absolute error = 4e-31 relative error = 1.3748813201356800972606703773823e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.348 y[1] (analytic) = 2.910407015361611704596059096572 y[1] (numeric) = 2.9104070153616117045960590965717 absolute error = 3e-31 relative error = 1.0307836615859918008973470620436e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.349 y[1] (analytic) = 2.9114718907152539164377541680067 y[1] (numeric) = 2.9114718907152539164377541680063 absolute error = 4e-31 relative error = 1.3738755344868983582253418758033e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (analytic) = 2.9125366481266486466063721709416 y[1] (numeric) = 2.9125366481266486466063721709414 absolute error = 2e-31 relative error = 6.8668663835917922039796102246567e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.351 y[1] (analytic) = 2.9136012876131859100181422591483 y[1] (numeric) = 2.9136012876131859100181422591478 absolute error = 5e-31 relative error = 1.7160893020115275023468449412257e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.352 y[1] (analytic) = 2.914665809192241474954237335067 y[1] (numeric) = 2.9146658091922414749542373350667 absolute error = 3e-31 relative error = 1.0292775214704315252545931096956e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.4MB, time=9.96 x[1] = 0.353 y[1] (analytic) = 2.9157302128811768774177367328472 y[1] (numeric) = 2.9157302128811768774177367328467 absolute error = 5e-31 relative error = 1.7148362965513374139713775807644e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.354 y[1] (analytic) = 2.9167944986973394354686730350483 y[1] (numeric) = 2.9167944986973394354686730350481 absolute error = 2e-31 relative error = 6.8568423346012679695103613487592e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.355 y[1] (analytic) = 2.9178586666580622635372047934991 y[1] (numeric) = 2.9178586666580622635372047934986 absolute error = 5e-31 relative error = 1.7135853964190444155214559821994e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.356 y[1] (analytic) = 2.9189227167806642867149568268265 y[1] (numeric) = 2.918922716780664286714956826826 absolute error = 5e-31 relative error = 1.7129607341966887246176795460700e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.357 y[1] (analytic) = 2.9199866490824502550245696695023 y[1] (numeric) = 2.9199866490824502550245696695018 absolute error = 5e-31 relative error = 1.7123365963235325090505991343934e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.358 y[1] (analytic) = 2.9210504635807107576674996498126 y[1] (numeric) = 2.9210504635807107576674996498122 absolute error = 4e-31 relative error = 1.3693703857127756460074883057947e-29 % Correct digits = 30 h = 0.001 NO POLE memory used=251.7MB, alloc=4.4MB, time=10.12 TOP MAIN SOLVE Loop x[1] = 0.359 y[1] (analytic) = 2.9221141602927222372501109770189 y[1] (numeric) = 2.9221141602927222372501109770186 absolute error = 3e-31 relative error = 1.0266539345949015090443117125979e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 2.9231777392357470039881011210899 y[1] (numeric) = 2.9231777392357470039881011210895 absolute error = 4e-31 relative error = 1.3683738577749924369870502567121e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.361 y[1] (analytic) = 2.924241200427033249889300671768 y[1] (numeric) = 2.9242412004270332498893006717678 absolute error = 2e-31 relative error = 6.8393811006695880152942252325269e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.362 y[1] (analytic) = 2.9253045438838150629148887673878 y[1] (numeric) = 2.9253045438838150629148887673875 absolute error = 3e-31 relative error = 1.0255342495099722623129193389823e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.363 y[1] (analytic) = 2.9263677696233124411190650877713 y[1] (numeric) = 2.9263677696233124411190650877709 absolute error = 4e-31 relative error = 1.3668821948906604849844888844846e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.4MB, time=10.27 x[1] = 0.364 y[1] (analytic) = 2.9274308776627313067672193097162 y[1] (numeric) = 2.9274308776627313067672193097159 absolute error = 3e-31 relative error = 1.0247893546833147007930501686205e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.365 y[1] (analytic) = 2.9284938680192635204326388280275 y[1] (numeric) = 2.9284938680192635204326388280271 absolute error = 4e-31 relative error = 1.3658898328871925619123215223426e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.366 y[1] (analytic) = 2.9295567407100868950717954497526 y[1] (numeric) = 2.9295567407100868950717954497523 absolute error = 3e-31 relative error = 1.0240457057243542463050528747743e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.367 y[1] (analytic) = 2.9306194957523652100782516742534 y[1] (numeric) = 2.9306194957523652100782516742531 absolute error = 3e-31 relative error = 1.0236743474709680911725757463446e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.368 y[1] (analytic) = 2.9316821331632482253152270769698 y[1] (numeric) = 2.9316821331632482253152270769696 absolute error = 2e-31 relative error = 6.8220219967777512856181773271609e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.369 y[1] (analytic) = 2.9327446529598716951268652202287 y[1] (numeric) = 2.9327446529598716951268652202284 absolute error = 3e-31 relative error = 1.0229325614735162385415713668517e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.4MB, time=10.43 x[1] = 0.37 y[1] (analytic) = 2.9338070551593573823282414201945 y[1] (numeric) = 2.933807055159357382328241420194 absolute error = 5e-31 relative error = 1.7042702215904283312548573126744e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.371 y[1] (analytic) = 2.9348693397788130721741516050729 y[1] (numeric) = 2.9348693397788130721741516050727 absolute error = 2e-31 relative error = 6.8146134238150797566798812466882e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.372 y[1] (analytic) = 2.935931506835332586306722405943 y[1] (numeric) = 2.9359315068353325863067224059425 absolute error = 5e-31 relative error = 1.7030370049025924701251062313688e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.373 y[1] (analytic) = 2.9369935563459957966818825281096 y[1] (numeric) = 2.9369935563459957966818825281093 absolute error = 3e-31 relative error = 1.0214527006768079061650032983203e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.374 y[1] (analytic) = 2.9380554883278686394747353576674 y[1] (numeric) = 2.938055488327868639474735357667 absolute error = 4e-31 relative error = 1.3614446751911123152433011556124e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.4MB, time=10.58 x[1] = 0.375 y[1] (analytic) = 2.9391173027980031289638726649772 y[1] (numeric) = 2.9391173027980031289638726649769 absolute error = 3e-31 relative error = 1.0207146197070927724730091780128e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.376 y[1] (analytic) = 2.9401789997734373713946691740699 y[1] (numeric) = 2.9401789997734373713946691740695 absolute error = 4e-31 relative error = 1.3604613869795783549063330734101e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.377 y[1] (analytic) = 2.9412405792711955788215976745182 y[1] (numeric) = 2.941240579271195578821597674518 absolute error = 2e-31 relative error = 6.7998517839556538566133637289320e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.378 y[1] (analytic) = 2.9423020413082880829296042601295 y[1] (numeric) = 2.9423020413082880829296042601292 absolute error = 3e-31 relative error = 1.0196098014009658395196218107558e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.379 y[1] (analytic) = 2.9433633859017113488345831868461 y[1] (numeric) = 2.9433633859017113488345831868458 absolute error = 3e-31 relative error = 1.0192421412760551120333106781418e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = 2.9444246130684479888629907505572 y[1] (numeric) = 2.9444246130684479888629907505568 absolute error = 4e-31 relative error = 1.3584997157836940777480389876821e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.4MB, time=10.74 x[1] = 0.381 y[1] (analytic) = 2.9454857228254667763106374940632 y[1] (numeric) = 2.9454857228254667763106374940627 absolute error = 5e-31 relative error = 1.6975128961765035172176766581120e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.382 y[1] (analytic) = 2.9465467151897226591806979612449 y[1] (numeric) = 2.9465467151897226591806979612443 absolute error = 6e-31 relative error = 2.0362819870017472865975834574779e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.383 y[1] (analytic) = 2.947607590178156773900977125535 y[1] (numeric) = 2.9476075901781567739009771255345 absolute error = 5e-31 relative error = 1.6962909230729027541782863578633e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.384 y[1] (analytic) = 2.9486683478076964590204725290909 y[1] (numeric) = 2.9486683478076964590204725290906 absolute error = 3e-31 relative error = 1.0174084183561939335038016181986e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.385 y[1] (analytic) = 2.9497289880952552688852710786126 y[1] (numeric) = 2.9497289880952552688852710786122 absolute error = 4e-31 relative error = 1.3560567822140643541000804024815e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.4MB, time=10.89 x[1] = 0.386 y[1] (analytic) = 2.9507895110577329872938193535416 y[1] (numeric) = 2.9507895110577329872938193535413 absolute error = 3e-31 relative error = 1.0166770583797510985210507591208e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.387 y[1] (analytic) = 2.9518499167120156411316061924223 y[1] (numeric) = 2.9518499167120156411316061924218 absolute error = 5e-31 relative error = 1.6938530552289604045365095739098e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.388 y[1] (analytic) = 2.9529102050749755139852962334796 y[1] (numeric) = 2.9529102050749755139852962334791 absolute error = 5e-31 relative error = 1.6932448509293726041353207989802e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.389 y[1] (analytic) = 2.9539703761634711597363529960094 y[1] (numeric) = 2.9539703761634711597363529960088 absolute error = 6e-31 relative error = 2.0311645805306353452764802137066e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = 2.9550304299943474161341899999376 y[1] (numeric) = 2.9550304299943474161341899999372 absolute error = 4e-31 relative error = 1.3536239625145421845861951078029e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.391 y[1] (analytic) = 2.9560903665844354183488883319307 y[1] (numeric) = 2.9560903665844354183488883319302 absolute error = 5e-31 relative error = 1.6914232584091011311007523936519e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.4MB, time=11.05 x[1] = 0.392 y[1] (analytic) = 2.9571501859505526125035189776857 y[1] (numeric) = 2.9571501859505526125035189776853 absolute error = 4e-31 relative error = 1.3526536524942278292873328101464e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.393 y[1] (analytic) = 2.9582098881095027691861081515411 y[1] (numeric) = 2.9582098881095027691861081515406 absolute error = 5e-31 relative error = 1.6902113741480797775025651370462e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.394 y[1] (analytic) = 2.9592694730780759969412837662728 y[1] (numeric) = 2.9592694730780759969412837662724 absolute error = 4e-31 relative error = 1.3516849467038941236141922151246e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.395 y[1] (analytic) = 2.960328940873048755741641097935 y[1] (numeric) = 2.9603289408730487557416410979348 absolute error = 2e-31 relative error = 6.7560059707762331957038232173885e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.396 y[1] (analytic) = 2.9613882915111838704388656128107 y[1] (numeric) = 2.9613882915111838704388656128104 absolute error = 3e-31 relative error = 1.0130383808835526727477102108826e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.4MB, time=11.20 x[1] = 0.397 y[1] (analytic) = 2.9624475250092305441946508360007 y[1] (numeric) = 2.9624475250092305441946508360003 absolute error = 4e-31 relative error = 1.3502348872787330122243479283436e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.398 y[1] (analytic) = 2.9635066413839243718914490538741 y[1] (numeric) = 2.9635066413839243718914490538738 absolute error = 3e-31 relative error = 1.0123142489733154904734211712755e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.399 y[1] (analytic) = 2.9645656406519873535230925555315 y[1] (numeric) = 2.9645656406519873535230925555313 absolute error = 2e-31 relative error = 6.7463508737156734191616397786302e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 2.9656245228301279075653230316005 y[1] (numeric) = 2.9656245228301279075653230316001 absolute error = 4e-31 relative error = 1.3487884151236907985093273569488e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.401 y[1] (analytic) = 2.9666832879350408843262666620853 y[1] (numeric) = 2.9666832879350408843262666620851 absolute error = 2e-31 relative error = 6.7415352630785858827317040422339e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.402 y[1] (analytic) = 2.9677419359834075792768923386359 y[1] (numeric) = 2.9677419359834075792768923386356 absolute error = 3e-31 relative error = 1.0108695650472395970211638530958e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.4MB, time=11.35 x[1] = 0.403 y[1] (analytic) = 2.9688004669918957463614903804589 y[1] (numeric) = 2.9688004669918957463614903804587 absolute error = 2e-31 relative error = 6.7367275848837287821140194130836e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.404 y[1] (analytic) = 2.9698588809771596112882090172157 y[1] (numeric) = 2.9698588809771596112882090172155 absolute error = 2e-31 relative error = 6.7343267143452580230083477456652e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.405 y[1] (analytic) = 2.9709171779558398847996858265725 y[1] (numeric) = 2.9709171779558398847996858265722 absolute error = 3e-31 relative error = 1.0097891729395737487654196559733e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.406 y[1] (analytic) = 2.9719753579445637759238112286489 y[1] (numeric) = 2.9719753579445637759238112286486 absolute error = 3e-31 relative error = 1.0094296347311635305356061989579e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.407 y[1] (analytic) = 2.9730334209599450052046610544038 y[1] (numeric) = 2.9730334209599450052046610544037 absolute error = 1e-31 relative error = 3.3635679738746965460659447234270e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.4MB, time=11.50 x[1] = 0.408 y[1] (analytic) = 2.9740913670185838179136351200306 y[1] (numeric) = 2.9740913670185838179136351200306 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.409 y[1] (analytic) = 2.9751491961370669972408386546906 y[1] (numeric) = 2.9751491961370669972408386546904 absolute error = 2e-31 relative error = 6.7223519499351478586576041876872e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 2.9762069083319678774667433444046 y[1] (numeric) = 2.9762069083319678774667433444044 absolute error = 2e-31 relative error = 6.7199628977439320492903986065195e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.411 y[1] (analytic) = 2.9772645036198463571141646706398 y[1] (numeric) = 2.9772645036198463571141646706396 absolute error = 2e-31 relative error = 6.7175758068130687371140412692539e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.412 y[1] (analytic) = 2.9783219820172489120805921380678 y[1] (numeric) = 2.9783219820172489120805921380676 absolute error = 2e-31 relative error = 6.7151906747348347195750196220986e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.413 y[1] (analytic) = 2.9793793435407086087509089021463 y[1] (numeric) = 2.979379343540708608750908902146 absolute error = 3e-31 relative error = 1.0069211248658204446213420645945e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.4MB, time=11.66 x[1] = 0.414 y[1] (analytic) = 2.9804365882067451170905372235699 y[1] (numeric) = 2.9804365882067451170905372235698 absolute error = 1e-31 relative error = 3.3552131387625838885194965525893e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.415 y[1] (analytic) = 2.981493716031864723719046093261 y[1] (numeric) = 2.9814937160318647237190460932608 absolute error = 2e-31 relative error = 6.7080470075980699921785492068232e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.416 y[1] (analytic) = 2.9825507270325603449642572884106 y[1] (numeric) = 2.9825507270325603449642572884107 absolute error = 1e-31 relative error = 3.3528348434661277567898885540872e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.417 y[1] (analytic) = 2.983607621225311539896886037164 y[1] (numeric) = 2.9836076212253115398968860371638 absolute error = 2e-31 relative error = 6.7032943131397338778698767660343e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.418 y[1] (analytic) = 2.9846643986265845233457523868186 y[1] (numeric) = 2.9846643986265845233457523868185 absolute error = 1e-31 relative error = 3.3504604419182184184085524152646e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.4MB, time=11.81 x[1] = 0.419 y[1] (analytic) = 2.9857210592528321788935992879435 y[1] (numeric) = 2.9857210592528321788935992879434 absolute error = 1e-31 relative error = 3.3492746983211051465843824350623e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = 2.9867776031204940718535533245423 y[1] (numeric) = 2.9867776031204940718535533245421 absolute error = 2e-31 relative error = 6.6961798491808062564035813372551e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.421 y[1] (analytic) = 2.9878340302459964622262639383601 y[1] (numeric) = 2.9878340302459964622262639383599 absolute error = 2e-31 relative error = 6.6938122390798748183410590378168e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.422 y[1] (analytic) = 2.9888903406457523176377569136049 y[1] (numeric) = 2.9888903406457523176377569136047 absolute error = 2e-31 relative error = 6.6914465639709561485506189692385e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.423 y[1] (analytic) = 2.9899465343361613262580378067553 y[1] (numeric) = 2.989946534336161326258037806755 absolute error = 3e-31 relative error = 1.0033624232234208764255234688606e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.424 y[1] (analytic) = 2.9910026113336099097004809247452 y[1] (numeric) = 2.9910026113336099097004809247451 absolute error = 1e-31 relative error = 3.3433605046373601457052609526278e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.4MB, time=11.97 x[1] = 0.425 y[1] (analytic) = 2.9920585716544712359020393736564 y[1] (numeric) = 2.9920585716544712359020393736563 absolute error = 1e-31 relative error = 3.3421805624849310333446390466688e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.426 y[1] (analytic) = 2.9931144153151052319843116190954 y[1] (numeric) = 2.9931144153151052319843116190952 absolute error = 2e-31 relative error = 6.6820031662219186640039410477302e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.427 y[1] (analytic) = 2.9941701423318585970954999187152 y[1] (numeric) = 2.994170142331858597095499918715 absolute error = 2e-31 relative error = 6.6796471306817612618217636665407e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.428 y[1] (analytic) = 2.995225752721064815233295906821 y[1] (numeric) = 2.9952257527210648152332959068208 absolute error = 2e-31 relative error = 6.6772930160041035014299729953118e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.429 y[1] (analytic) = 2.9962812464990441680487285307063 y[1] (numeric) = 2.9962812464990441680487285307063 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.5MB, time=12.12 x[1] = 0.43 y[1] (analytic) = 2.9973366236821037476310094582867 y[1] (numeric) = 2.9973366236821037476310094582863 absolute error = 4e-31 relative error = 1.3345181079748613198287748554802e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.431 y[1] (analytic) = 2.9983918842865374692734109967245 y[1] (numeric) = 2.9983918842865374692734109967244 absolute error = 1e-31 relative error = 3.3351210868753681712027820127400e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.432 y[1] (analytic) = 2.9994470283286260842202114821012 y[1] (numeric) = 2.9994470283286260842202114821008 absolute error = 4e-31 relative error = 1.3335791438293575718269414348773e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.433 y[1] (analytic) = 3.0005020558246371923947430207271 y[1] (numeric) = 3.0005020558246371923947430207268 absolute error = 3e-31 relative error = 9.9983267606044042157771353957533e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.434 y[1] (analytic) = 3.0015569667908252551085763834839 y[1] (numeric) = 3.0015569667908252551085763834836 absolute error = 3e-31 relative error = 9.9948128027951776063233438325431e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.435 y[1] (analytic) = 3.0026117612434316077518777755488 y[1] (numeric) = 3.0026117612434316077518777755484 absolute error = 4e-31 relative error = 1.3321735602419452617423356129352e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.5MB, time=12.27 x[1] = 0.436 y[1] (analytic) = 3.0036664391986844724649721250661 y[1] (numeric) = 3.0036664391986844724649721250658 absolute error = 3e-31 relative error = 9.9877934541903973800284816385907e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.437 y[1] (analytic) = 3.0047210006727989707911474557286 y[1] (numeric) = 3.0047210006727989707911474557282 absolute error = 4e-31 relative error = 1.3312384075274689961357053562076e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.438 y[1] (analytic) = 3.0057754456819771363107348298454 y[1] (numeric) = 3.0057754456819771363107348298449 absolute error = 5e-31 relative error = 1.6634642508584188044174716189853e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.439 y[1] (analytic) = 3.0068297742424079272564982703046 y[1] (numeric) = 3.0068297742424079272564982703042 absolute error = 4e-31 relative error = 1.3303047729091442665020210438372e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 3.0078839863702672391103689918661 y[1] (numeric) = 3.0078839863702672391103689918657 absolute error = 4e-31 relative error = 1.3298385237347396686974911263344e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.441 y[1] (analytic) = 3.008938082081717917181558194463 y[1] (numeric) = 3.0089380820817179171815581944624 absolute error = 6e-31 relative error = 1.9940589790564688839929146104425e-29 % Correct digits = 30 h = 0.001 memory used=309.0MB, alloc=4.5MB, time=12.43 NO POLE TOP MAIN SOLVE Loop x[1] = 0.442 y[1] (analytic) = 3.0099920613929097691660825936395 y[1] (numeric) = 3.0099920613929097691660825936391 absolute error = 4e-31 relative error = 1.3289071593594011790893368562321e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.443 y[1] (analytic) = 3.0110459243199795776877367859102 y[1] (numeric) = 3.0110459243199795776877367859096 absolute error = 6e-31 relative error = 1.9926630648634333197340657205973e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.444 y[1] (analytic) = 3.0120996708790511128205464696766 y[1] (numeric) = 3.012099670879051112820546469676 absolute error = 6e-31 relative error = 1.9919659558440043618525692525961e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.445 y[1] (analytic) = 3.0131533010862351445927364654197 y[1] (numeric) = 3.0131533010862351445927364654192 absolute error = 5e-31 relative error = 1.6593911760803909266463161850277e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.446 y[1] (analytic) = 3.0142068149576294554722474021423 y[1] (numeric) = 3.0142068149576294554722474021417 absolute error = 6e-31 relative error = 1.9905734305375929156919361299636e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.5MB, time=12.58 x[1] = 0.447 y[1] (analytic) = 3.015260212509318852833834860518 y[1] (numeric) = 3.0152602125093188528338348605174 absolute error = 6e-31 relative error = 1.9898780128852499888981434324712e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.448 y[1] (analytic) = 3.0163134937573751814077846868835 y[1] (numeric) = 3.0163134937573751814077846868829 absolute error = 6e-31 relative error = 1.9891831576584211650161998936733e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.449 y[1] (analytic) = 3.0173666587178573357102781160859 y[1] (numeric) = 3.0173666587178573357102781160855 absolute error = 4e-31 relative error = 1.3256592427847944318057758365818e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = 3.018419707406811272455440265287 y[1] (numeric) = 3.0184197074068112724554402652866 absolute error = 4e-31 relative error = 1.3251967545084991793835308909853e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.451 y[1] (analytic) = 3.0194726398402700229491054851046 y[1] (numeric) = 3.0194726398402700229491054851042 absolute error = 4e-31 relative error = 1.3247346398249198355437853731363e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.452 y[1] (analytic) = 3.0205254560342537054643329789651 y[1] (numeric) = 3.0205254560342537054643329789646 absolute error = 5e-31 relative error = 1.6553411228537245715352018823036e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.5MB, time=12.74 x[1] = 0.453 y[1] (analytic) = 3.0215781560047695375987060262198 y[1] (numeric) = 3.0215781560047695375987060262193 absolute error = 5e-31 relative error = 1.6547644117904152398568521266988e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.454 y[1] (analytic) = 3.0226307397678118486134480694696 y[1] (numeric) = 3.0226307397678118486134480694692 absolute error = 4e-31 relative error = 1.3233505328233597974500399688944e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.455 y[1] (analytic) = 3.0236832073393620917543888516246 y[1] (numeric) = 3.0236832073393620917543888516242 absolute error = 4e-31 relative error = 1.3228899080071721659225774217319e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.456 y[1] (analytic) = 3.0247355587353888565548137135093 y[1] (numeric) = 3.0247355587353888565548137135087 absolute error = 6e-31 relative error = 1.9836444818034072758155892797900e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.457 y[1] (analytic) = 3.0257877939718478811202290883064 y[1] (numeric) = 3.0257877939718478811202290883058 absolute error = 6e-31 relative error = 1.9829546579418266948245788876736e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.5MB, time=12.89 x[1] = 0.458 y[1] (analytic) = 3.0268399130646820643950771548133 y[1] (numeric) = 3.0268399130646820643950771548125 absolute error = 8e-31 relative error = 2.6430205196745877510003939309393e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.459 y[1] (analytic) = 3.0278919160298214784114325373528 y[1] (numeric) = 3.0278919160298214784114325373523 absolute error = 5e-31 relative error = 1.6513138971472967789599671297110e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = 3.0289438028831833805197138662651 y[1] (numeric) = 3.0289438028831833805197138662645 absolute error = 6e-31 relative error = 1.9808885177363591714709922267001e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.461 y[1] (analytic) = 3.0299955736406722256014429391568 y[1] (numeric) = 3.0299955736406722256014429391562 absolute error = 6e-31 relative error = 1.9802009125679142615061193851770e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.462 y[1] (analytic) = 3.0310472283181796782640841495659 y[1] (numeric) = 3.0310472283181796782640841495653 absolute error = 6e-31 relative error = 1.9795138604056613916861184172341e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.463 y[1] (analytic) = 3.0320987669315846250179967763391 y[1] (numeric) = 3.0320987669315846250179967763385 absolute error = 6e-31 relative error = 1.9788273605849140256251634823424e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.5MB, time=13.04 x[1] = 0.464 y[1] (analytic) = 3.0331501894967531864355326538795 y[1] (numeric) = 3.0331501894967531864355326538788 absolute error = 7e-31 relative error = 2.3078316478490664265534693452627e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.465 y[1] (analytic) = 3.0342014960295387292923116704615 y[1] (numeric) = 3.0342014960295387292923116704609 absolute error = 6e-31 relative error = 1.9774560153145440483548460957243e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.466 y[1] (analytic) = 3.0352526865457818786907074690477 y[1] (numeric) = 3.0352526865457818786907074690472 absolute error = 5e-31 relative error = 1.6473093071174135620472589600223e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.467 y[1] (analytic) = 3.0363037610613105301655756524657 y[1] (numeric) = 3.036303761061310530165575652465 absolute error = 7e-31 relative error = 2.3054346833708159337554597313733e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.468 y[1] (analytic) = 3.037354719591939861772256722427 y[1] (numeric) = 3.0373547195919398617722567224263 absolute error = 7e-31 relative error = 2.3046369773170354246700424651000e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.5MB, time=13.20 x[1] = 0.469 y[1] (analytic) = 3.0384055621534723461568859096791 y[1] (numeric) = 3.0384055621534723461568859096785 absolute error = 6e-31 relative error = 1.9747199237443125442449455067445e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = 3.0394562887616977626090419805772 y[1] (numeric) = 3.0394562887616977626090419805767 absolute error = 5e-31 relative error = 1.6450310598271658783951778512419e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.471 y[1] (analytic) = 3.0405068994323932090967670335568 y[1] (numeric) = 3.0405068994323932090967670335561 absolute error = 7e-31 relative error = 2.3022476947204992121098848747137e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.472 y[1] (analytic) = 3.0415573941813231142839892273641 y[1] (numeric) = 3.0415573941813231142839892273634 absolute error = 7e-31 relative error = 2.3014525431581231103665841242667e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.473 y[1] (analytic) = 3.042607773024239249530380311472 y[1] (numeric) = 3.0426077730242392495303803114714 absolute error = 6e-31 relative error = 1.9719925956924190042161405735752e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.474 y[1] (analytic) = 3.0436580359768807408736797578573 y[1] (numeric) = 3.0436580359768807408736797578568 absolute error = 5e-31 relative error = 1.6427601067198139720942148818048e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.5MB, time=13.35 x[1] = 0.475 y[1] (analytic) = 3.044708183054974080994517222265 y[1] (numeric) = 3.0447081830549740809945172222642 absolute error = 8e-31 relative error = 2.6275096065111324575429056571910e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.476 y[1] (analytic) = 3.0457582142742331411637649922075 y[1] (numeric) = 3.0457582142742331411637649922067 absolute error = 8e-31 relative error = 2.6266037673336135007765669705627e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.477 y[1] (analytic) = 3.0468081296503591831724520082709 y[1] (numeric) = 3.04680812965035918317245200827 absolute error = 9e-31 relative error = 2.9539109838967141817510881818136e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.478 y[1] (analytic) = 3.0478579291990408712442709747888 y[1] (numeric) = 3.047857929199040871244270974788 absolute error = 8e-31 relative error = 2.6247942607030744783487242166561e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.479 y[1] (analytic) = 3.0489076129359542839307100056423 y[1] (numeric) = 3.0489076129359542839307100056417 absolute error = 6e-31 relative error = 1.9679179436408972992603715006778e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=335.7MB, alloc=4.5MB, time=13.51 x[1] = 0.48 y[1] (analytic) = 3.0499571808767629259888401808076 y[1] (numeric) = 3.0499571808767629259888401808069 absolute error = 7e-31 relative error = 2.2951141884515667097512175635342e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.481 y[1] (analytic) = 3.0510066330371177402417903193282 y[1] (numeric) = 3.0510066330371177402417903193276 absolute error = 6e-31 relative error = 1.9665640628343417914643632587544e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.482 y[1] (analytic) = 3.0520559694326571194219402046315 y[1] (numeric) = 3.0520559694326571194219402046309 absolute error = 6e-31 relative error = 1.9658879326237691907689412213486e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.483 y[1] (analytic) = 3.0531051900790069179968634285209 y[1] (numeric) = 3.0531051900790069179968634285204 absolute error = 5e-31 relative error = 1.6376769514025857037029184759721e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.484 y[1] (analytic) = 3.0541542949917804639780509507877 y[1] (numeric) = 3.054154294991780463978050950787 absolute error = 7e-31 relative error = 2.2919601709313244926238549849621e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.485 y[1] (analytic) = 3.0552032841865785707124464021609 y[1] (numeric) = 3.0552032841865785707124464021602 absolute error = 7e-31 relative error = 2.2911732375489670271261417305031e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.5MB, time=13.66 x[1] = 0.486 y[1] (analytic) = 3.0562521576789895486568240892913 y[1] (numeric) = 3.0562521576789895486568240892907 absolute error = 6e-31 relative error = 1.9631887980593138356278544222111e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.487 y[1] (analytic) = 3.0573009154845892171350405915994 y[1] (numeric) = 3.0573009154845892171350405915987 absolute error = 7e-31 relative error = 2.2896012507458671016521939214468e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.488 y[1] (analytic) = 3.0583495576189409160781907711516 y[1] (numeric) = 3.058349557618940916078190771151 absolute error = 6e-31 relative error = 1.9618424535720052861782985527750e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.489 y[1] (analytic) = 3.0593980840975955177476989482358 y[1] (numeric) = 3.0593980840975955177476989482351 absolute error = 7e-31 relative error = 2.2880317655898415458424787520145e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = 3.0604464949360914384413759269838 y[1] (numeric) = 3.0604464949360914384413759269833 absolute error = 5e-31 relative error = 1.6337485423362745373822358390190e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.5MB, time=13.82 x[1] = 0.491 y[1] (analytic) = 3.0614947901499546501824724872636 y[1] (numeric) = 3.0614947901499546501824724872629 absolute error = 7e-31 relative error = 2.2864647761354295737148931718195e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.492 y[1] (analytic) = 3.0625429697546986923917598910927 y[1] (numeric) = 3.0625429697546986923917598910919 absolute error = 8e-31 relative error = 2.6122082462212042362112845843357e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.493 y[1] (analytic) = 3.0635910337658246835426678840556 y[1] (numeric) = 3.063591033765824683542667884055 absolute error = 6e-31 relative error = 1.9584859512480963434660456966729e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.494 y[1] (analytic) = 3.0646389821988213327995106045944 y[1] (numeric) = 3.0646389821988213327995106045937 absolute error = 7e-31 relative error = 2.2841189584352381067543557058539e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.495 y[1] (analytic) = 3.0656868150691649516388307466147 y[1] (numeric) = 3.0656868150691649516388307466141 absolute error = 6e-31 relative error = 1.9571470805522037699808315359843e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.496 y[1] (analytic) = 3.0667345323923194654538922536043 y[1] (numeric) = 3.0667345323923194654538922536036 absolute error = 7e-31 relative error = 2.2825581823475902980551775561574e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=347.1MB, alloc=4.5MB, time=13.97 x[1] = 0.497 y[1] (analytic) = 3.0677821341837364251423517553725 y[1] (numeric) = 3.0677821341837364251423517553719 absolute error = 6e-31 relative error = 1.9558103338379525229362800115709e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.498 y[1] (analytic) = 3.0688296204588550186771388916292 y[1] (numeric) = 3.0688296204588550186771388916286 absolute error = 6e-31 relative error = 1.9551427554009573638219840022390e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.499 y[1] (analytic) = 3.0698769912331020826605755998817 y[1] (numeric) = 3.069876991233102082660575599881 absolute error = 7e-31 relative error = 2.2802216570860886271926469834152e-29 % Correct digits = 30 h = 0.001 NO POLE Finished! diff ( y , x , 1 ) = arccos(sqrt(0.1 * x + 0.2)); Iterations = 500 Total Elapsed Time = 14 Seconds Elapsed Time(since restart) = 13 Seconds Time to Timeout = 2 Minutes 45 Seconds Percent Done = 100.2 % > quit memory used=349.0MB, alloc=4.5MB, time=14.04