|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 1 > ret := 1.0; > else > ret := -1.0; > fi;# end if 1; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 3 > # Begin Function number 4 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 1 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > if (min_size < 1.0) then # if number 1 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 4 > # Begin Function number 5 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms; > max_value3 := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > value3 := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (value3 > max_value3) then # if number 1 > max_value3 := value3; > omniout_float(ALWAYS,"value3",32,value3,32,""); > fi;# end if 1; > omniout_float(ALWAYS,"max_value3",32,max_value3,32,""); > max_value3; > end; test_suggested_h := proc() local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; max_value3 := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); value3 := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_value3 < value3 then max_value3 := value3; omniout_float(ALWAYS, "value3", 32, value3, 32, "") end if; omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""); max_value3 end proc > # End Function number 5 > # Begin Function number 6 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1 > ret := true; > else > ret := false; > fi;# end if 1; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 6 > # Begin Function number 7 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 1 > if (iter >= 0) then # if number 2 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 3 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 4 > glob_good_digits := -trunc(log10(relerr)) + 2; > else > glob_good_digits := Digits; > fi;# end if 4; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 3; > if (glob_iter = 1) then # if number 3 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 3; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 2; > #BOTTOM DISPLAY ALOT > fi;# end if 1; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 2 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 7 > # Begin Function number 8 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 2 > fi;# end if 1; > if ( not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 8 > # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 1; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 9 > # Begin Function number 10 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) < glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2; > if (m > 10) then # if number 1 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (omniabs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1; > n := n - 1; > od;# end do number 2; > m := n + cnt; > if (m <= 10) then # if number 1 > rad_c := glob_large_float; > ord_no := glob_large_float; > elif > (((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-5]) <= (glob_small_float)))) then # if number 2 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2; > #BOTTOM RADII COMPLEX EQ = 1 > found := false; > #TOP WHICH RADII EQ = 1 > if ( not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if ( not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if ( not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3; > fi;# end if 2; > if ( not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if ( not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if ( not found ) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3; > fi;# end if 2; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if (array_pole[1] > array_poles[1,1]) then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2; > #BOTTOM WHICH RADIUS EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 2 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 2 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 2; > #BOTTOM ADJUST ALL SERIES > if (reached_interval()) then # if number 2 > display_pole(); > fi;# end if 2 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) < glob_small_float or omniabs(array_y_higher[1, m - 1]) < glob_small_float or omniabs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float elif glob_large_float <= omniabs(array_y_higher[1, m]) or glob_large_float <= omniabs(array_y_higher[1, m - 1]) or glob_large_float <= omniabs(array_y_higher[1, m - 2]) or glob_large_float <= omniabs(array_y_higher[1, m - 3]) or glob_large_float <= omniabs(array_y_higher[1, m - 4]) or glob_large_float <= omniabs(array_y_higher[1, m - 5]) or omniabs(array_y_higher[1, m]) <= glob_small_float or omniabs(array_y_higher[1, m - 1]) <= glob_small_float or omniabs(array_y_higher[1, m - 2]) <= glob_small_float or omniabs(array_y_higher[1, m - 3]) <= glob_small_float or omniabs(array_y_higher[1, m - 4]) <= glob_small_float or omniabs(array_y_higher[1, m - 5]) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(dr1) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used") end if end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used") end if end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_pole() end if end proc > # End Function number 10 > # Begin Function number 11 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 2 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 3; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 2; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 11 > # Begin Function number 12 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre sin 1 $eq_no = 1 > array_tmp1[1] := sin(array_x[1]); > array_tmp1_g[1] := cos(array_x[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp1[2] := array_tmp1_g[1] * array_x[2] / 1; > array_tmp1_g[2] := -array_tmp1[1] * array_x[2] / 1; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sin ID_LINEAR iii = 3 $eq_no = 1 > array_tmp1[3] := array_tmp1_g[2] * array_x[2] / 2; > array_tmp1_g[3] := -array_tmp1[2] * array_x[2] / 2; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sin ID_LINEAR iii = 4 $eq_no = 1 > array_tmp1[4] := array_tmp1_g[3] * array_x[2] / 3; > array_tmp1_g[4] := -array_tmp1[3] * array_x[2] / 3; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sin ID_LINEAR iii = 5 $eq_no = 1 > array_tmp1[5] := array_tmp1_g[4] * array_x[2] / 4; > array_tmp1_g[5] := -array_tmp1[4] * array_x[2] / 4; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sin LINEAR $eq_no = 1 > array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp1_g[kkk] := -array_tmp1[kkk - 1] * array_x[2] / (kkk - 1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp2[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 2 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; array_tmp1[1] := sin(array_x[1]); array_tmp1_g[1] := cos(array_x[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_tmp1_g[1]*array_x[2]; array_tmp1_g[2] := -array_tmp1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := 1/2*array_tmp1_g[2]*array_x[2]; array_tmp1_g[3] := -1/2*array_tmp1[2]*array_x[2]; array_tmp2[3] := array_tmp1[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := 1/3*array_tmp1_g[3]*array_x[2]; array_tmp1_g[4] := -1/3*array_tmp1[3]*array_x[2]; array_tmp2[4] := array_tmp1[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := 1/4*array_tmp1_g[4]*array_x[2]; array_tmp1_g[5] := -1/4*array_tmp1[4]*array_x[2]; array_tmp2[5] := array_tmp1[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp1_g[kkk] := -array_tmp1[kkk - 1]*array_x[2]/(kkk - 1); array_tmp2[kkk] := array_tmp1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 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 > ## Comment 5 > exact_soln_y := proc(x) > ## Comment 6 > return(2.0 - cos(x)); > ## Comment 7 > end; exact_soln_y := proc(x) return 2.0 - cos(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_value3 := 0.0; > glob_ratio_of_radius := 0.01; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_log10normmin := 0.1; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_hmax := 1.0; > glob_hmin := 0.00000000001; > glob_hmin_init := 0.001; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_log10_abserr := 0.1e-10; > glob_log10_relerr := 0.1e-10; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.1e-50; > glob_smallish_float := 0.1e-100; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_log10abserr := 0.0; > glob_log10relerr := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/sinpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin(x);"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"## Comment 1"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=20;"); > omniout_str(ALWAYS,"## Comment 2"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"## Comment 3"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 1.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.0005;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"## Comment 4"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.001;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"## Comment 5"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"## Comment 6"); > omniout_str(ALWAYS,"return(2.0 - cos(x));"); > omniout_str(ALWAYS,"## Comment 7"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > ## Comment 1 > Digits:=32; > max_terms:=20; > ## Comment 2 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1_g:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp1_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3; > iiif := iiif + 1; > od;# end do number 2; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > ## Comment 3 > x_start := 0.1; > x_end := 1.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.0005; > glob_look_poles := true; > glob_max_iter := 1000000; > ## Comment 4 > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.001; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > 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; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > if (glob_display_interval < glob_h) then # if number 2 > glob_h := glob_display_interval; > fi;# end if 2; > found_h := -1.0; > best_h := 0.0; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 3 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 3; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 3 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 4 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 4; > r_order := r_order + 1; > od;# end do number 3 > ; > atomall(); > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > value3 := test_suggested_h(); > omniout_float(ALWAYS,"value3",32,value3,32,""); > if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2 > best_h := glob_h; > found_h := 1.0; > fi;# end if 2; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > glob_h := glob_h * 0.5; > od;# end do number 2; > if (found_h > 0.0) then # if number 2 > glob_h := best_h ; > else > omniout_str(ALWAYS,"No increment to obtain desired accuracy found"); > fi;# end if 2; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2; > #BEGIN SOLUTION CODE > if (found_h > 0.0) then # if number 2 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_log10normmin := -glob_large_float ; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_y_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > if (reached_interval()) then # if number 3 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 3; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 3 > #left paren 0004C > check_for_pole(); > fi;# end if 3;#was right paren 0004C > if (reached_interval()) then # if number 3 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 3; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4; > term_no := term_no - 1; > od;# end do number 3; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 2;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 3 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 3; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 3; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = sin(x);"); > 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,"2013-01-13T02:09:29-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sin") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sin(x);") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 4 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 4; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 4 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 4; > log_revs(html_log_file," 156 ") > ; > logitem_str(html_log_file,"sin diffeq.mxt") > ; > logitem_str(html_log_file,"sin maple results") > ; > logitem_str(html_log_file,"Languages compared - single equations") > ; > logend(html_log_file) > ; > ; > fi;# end if 3; > if (glob_html_log) then # if number 3 > fclose(html_log_file); > fi;# end if 3 > ; > ;; > fi;# end if 2 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_value3 := 0.; glob_ratio_of_radius := 0.01; glob_percent_done := 0.; glob_subiter_method := 3; glob_log10normmin := 0.1; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_hmax := 1.0; glob_hmin := 0.1*10^(-10); glob_hmin_init := 0.001; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_log10_abserr := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.1*10^(-50); glob_smallish_float := 0.1*10^(-100); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_log10abserr := 0.; glob_log10relerr := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/sinpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x);"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "## Comment 1"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=20;"); omniout_str(ALWAYS, "## Comment 2"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "## Comment 3"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 1.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.0005;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "## Comment 4"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.001;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "## Comment 5"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "## Comment 6"); omniout_str(ALWAYS, "return(2.0 - cos(x));"); omniout_str(ALWAYS, "## Comment 7"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 20; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1_g := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 1.0; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.0005; glob_look_poles := true; glob_max_iter := 1000000; glob_desired_digits_correct := 10; glob_display_interval := 0.001; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_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; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); if glob_display_interval < glob_h then glob_h := glob_display_interval end if; found_h := -1.0; best_h := 0.; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; while opt_iter <= 20 and found_h < 0. do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer) ; omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); value3 := test_suggested_h(); omniout_float(ALWAYS, "value3", 32, value3, 32, ""); if value3 < est_needed_step_err and found_h < 0. then best_h := glob_h; found_h := 1.0 end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1; glob_h := glob_h*0.5 end do; if 0. < found_h then glob_h := best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found") end if; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; if 0. < found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_log10normmin := -glob_large_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = sin(x);"); 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, "2013-01-13T02:09:29-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sin"); logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(x);"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 156 "); logitem_str(html_log_file, "sin diffeq.mxt"); logitem_str(html_log_file, "sin 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/sinpostode.ode################# diff ( y , x , 1 ) = sin(x); ! #BEGIN FIRST INPUT BLOCK ## Comment 1 Digits:=32; max_terms:=20; ## Comment 2 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK ## Comment 3 x_start := 0.1; x_end := 1.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.0005; glob_look_poles := true; glob_max_iter := 1000000; ## Comment 4 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.001; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK ## Comment 5 exact_soln_y := proc(x) ## Comment 6 return(2.0 - cos(x)); ## Comment 7 end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 0.9 estimated_steps = 900 step_error = 1.1111111111111111111111111111111e-13 est_needed_step_err = 1.1111111111111111111111111111111e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 4.7555858158228887220692803267041e-62 max_value3 = 4.7555858158228887220692803267041e-62 value3 = 4.7555858158228887220692803267041e-62 best_h = 0.001 START of Soultion x[1] = 0.1 y[1] (analytic) = 1.0049958347219742339044380121961 y[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 1.0049958347219742339044380121961 y[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.101 y[1] (analytic) = 1.005096165624023340621597000171 y[1] (numeric) = 1.005096165624023340621597000171 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.102 y[1] (analytic) = 1.0051974914298239146653143235401 y[1] (numeric) = 1.0051974914298239146653143235401 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.103 y[1] (analytic) = 1.0052998120380501586788328071734 y[1] (numeric) = 1.0052998120380501586788328071733 absolute error = 1e-31 relative error = 9.9472812789320449697981767287103e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.104 y[1] (analytic) = 1.0054031273463814729626255055154 y[1] (numeric) = 1.0054031273463814729626255055153 absolute error = 1e-31 relative error = 9.9462590954869788504619490995116e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.105 y[1] (analytic) = 1.0055074372515025577949868753959 y[1] (numeric) = 1.0055074372515025577949868753959 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.106 y[1] (analytic) = 1.0056127416491035167473238881278 y[1] (numeric) = 1.0056127416491035167473238881277 absolute error = 1e-31 relative error = 9.9441858538914375101877095183376e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.107 y[1] (analytic) = 1.0057190404338799609940437656082 y[1] (numeric) = 1.0057190404338799609940437656081 absolute error = 1e-31 relative error = 9.9431348099821924983009246296662e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.108 y[1] (analytic) = 1.0058263334995331146169340305467 y[1] (numeric) = 1.0058263334995331146169340305466 absolute error = 1e-31 relative error = 9.9420741602652042805188552925067e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.109 y[1] (analytic) = 1.0059346207387699209039295664461 y[1] (numeric) = 1.005934620738769920903929566446 absolute error = 1e-31 relative error = 9.9410039120195359477852278641993e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 1.0060439020433031496421603885802 y[1] (numeric) = 1.0060439020433031496421603885801 absolute error = 1e-31 relative error = 9.9399240725874107832453568516521e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.111 y[1] (analytic) = 1.006154177303851505405172832928 y[1] (numeric) = 1.006154177303851505405172832928 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.112 y[1] (analytic) = 1.0062654464101397368342158758533 y[1] (numeric) = 1.0062654464101397368342158758533 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.113 y[1] (analytic) = 1.0063777092508987469134833032516 y[1] (numeric) = 1.0063777092508987469134833032515 absolute error = 1e-31 relative error = 9.9366270815393355624247019446757e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.114 y[1] (analytic) = 1.0064909657138657042392014539315 y[1] (numeric) = 1.0064909657138657042392014539314 absolute error = 1e-31 relative error = 9.9355089520424864469352688007190e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.115 y[1] (analytic) = 1.0066052156857841552824512681535 y[1] (numeric) = 1.0066052156857841552824512681534 absolute error = 1e-31 relative error = 9.9343812690133527007168064857172e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.116 y[1] (analytic) = 1.006720459052404137645612378511 y[1] (numeric) = 1.0067204590524041376456123785109 absolute error = 1e-31 relative error = 9.9332440401704967357293435859319e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.117 y[1] (analytic) = 1.006836695698482294312315986721 y[1] (numeric) = 1.0068366956984822943123159867209 absolute error = 1e-31 relative error = 9.9320972732947580036462414903544e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.118 y[1] (analytic) = 1.00695392550778198889079227638 y[1] (numeric) = 1.0069539255077819888907922763799 absolute error = 1e-31 relative error = 9.9309409762291229358218249095572e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.119 y[1] (analytic) = 1.0070721483630734218504971183478 y[1] (numeric) = 1.0070721483630734218504971183478 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 1.0071913641461337477519018321424 y[1] (numeric) = 1.0071913641461337477519018321423 absolute error = 1e-31 relative error = 9.9285998232100573272046486262470e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.121 y[1] (analytic) = 1.0073115727377471934693287735644 y[1] (numeric) = 1.0073115727377471934693287735643 absolute error = 1e-31 relative error = 9.9274149832521505646917778195947e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.122 y[1] (analytic) = 1.007432774017705177406714525728 y[1] (numeric) = 1.0074327740177051774067145257279 absolute error = 1e-31 relative error = 9.9262206450951282060438490869793e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.123 y[1] (analytic) = 1.0075549678648064297061814777427 y[1] (numeric) = 1.0075549678648064297061814777425 absolute error = 2e-31 relative error = 1.9850033633781454311089551351548e-29 % Correct digits = 30 h = 0.001 NO POLE memory used=3.8MB, alloc=2.9MB, time=0.15 TOP MAIN SOLVE Loop x[1] = 0.124 y[1] (analytic) = 1.007678154156857113449297582485 y[1] (numeric) = 1.0076781541568571134492975824848 absolute error = 2e-31 relative error = 1.9847607013704061758348239022002e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.125 y[1] (analytic) = 1.0078023327706709468509030922118 y[1] (numeric) = 1.0078023327706709468509030922116 absolute error = 2e-31 relative error = 1.9845161446506665393994812214058e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.126 y[1] (analytic) = 1.0079275035820693264453820781963 y[1] (numeric) = 1.0079275035820693264453820781961 absolute error = 2e-31 relative error = 1.9842696948859996284987992722659e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.127 y[1] (analytic) = 1.0080536664658814512652555481279 y[1] (numeric) = 1.0080536664658814512652555481277 absolute error = 2e-31 relative error = 1.9840213537556652786093371430120e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.128 y[1] (analytic) = 1.0081808212959444480119719826911 y[1] (numeric) = 1.0081808212959444480119719826909 absolute error = 2e-31 relative error = 1.9837711229510821551684250766351e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.129 y[1] (analytic) = 1.0083089679451034972187701205446 y[1] (numeric) = 1.0083089679451034972187701205444 absolute error = 2e-31 relative error = 1.9835190041757996706911755916302e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 1.0084381062852119604054878288482 y[1] (numeric) = 1.008438106285211960405487828848 absolute error = 2e-31 relative error = 1.9832649991454697186840859402028e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.131 y[1] (analytic) = 1.0085682361871315082251899045384 y[1] (numeric) = 1.0085682361871315082251899045382 absolute error = 2e-31 relative error = 1.9830091095878182252197566580888e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.132 y[1] (analytic) = 1.008699357520732249602486659737 y[1] (numeric) = 1.0086993575207322496024866597367 absolute error = 3e-31 relative error = 2.9741270058639247785631040277301e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.133 y[1] (analytic) = 1.0088314701548928618634141529829 y[1] (numeric) = 1.0088314701548928618634141529827 absolute error = 2e-31 relative error = 1.9824916838616525210759431749345e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.134 y[1] (analytic) = 1.0089645739575007218567459364203 y[1] (numeric) = 1.0089645739575007218567459364201 absolute error = 2e-31 relative error = 1.9822301512087017542205234809191e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.135 y[1] (analytic) = 1.0090986687954520380666051976395 y[1] (numeric) = 1.0090986687954520380666051976393 absolute error = 2e-31 relative error = 1.9819667410594981743093477272186e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.136 y[1] (analytic) = 1.009233754534651983716245183572 y[1] (numeric) = 1.0092337545346519837162451835718 absolute error = 2e-31 relative error = 1.9817014552017048231256826639682e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.137 y[1] (analytic) = 1.0093698310400148308628648026684 y[1] (numeric) = 1.0093698310400148308628648026682 absolute error = 2e-31 relative error = 1.9814342954348843043658329987874e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.138 y[1] (analytic) = 1.0095068981754640854833253105562 y[1] (numeric) = 1.0095068981754640854833253105559 absolute error = 3e-31 relative error = 2.9717478953557036251716773702130e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.139 y[1] (analytic) = 1.0096449558039326235506329934705 y[1] (numeric) = 1.0096449558039326235506329934703 absolute error = 2e-31 relative error = 1.9808943614317316120670678512873e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 1.0097840037873628281010517729886 y[1] (numeric) = 1.0097840037873628281010517729884 absolute error = 2e-31 relative error = 1.9806215908537542784061947291135e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.141 y[1] (analytic) = 1.0099240419867067272917086649643 y[1] (numeric) = 1.0099240419867067272917086649641 absolute error = 2e-31 relative error = 1.9803469536833991839084739948141e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.142 y[1] (analytic) = 1.0100650702619261334485540350706 y[1] (numeric) = 1.0100650702619261334485540350704 absolute error = 2e-31 relative error = 1.9800704517792777475313765866455e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.143 y[1] (analytic) = 1.0102070884719927831045376030009 y[1] (numeric) = 1.0102070884719927831045376030007 absolute error = 2e-31 relative error = 1.9797920870117201383989867026587e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.144 y[1] (analytic) = 1.0103500964748884780278601571639 y[1] (numeric) = 1.0103500964748884780278601571638 absolute error = 1e-31 relative error = 9.8975593063137226888868359982296e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.145 y[1] (analytic) = 1.010494094127605227240159951634 y[1] (numeric) = 1.0104940941276052272401599516339 absolute error = 1e-31 relative error = 9.8961488821301311565046413159335e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.146 y[1] (analytic) = 1.0106390812861453900244917671803 y[1] (numeric) = 1.0106390812861453900244917671802 absolute error = 1e-31 relative error = 9.8947291720343326619105078758322e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.147 y[1] (analytic) = 1.0107850578055218199229556284092 y[1] (numeric) = 1.010785057805521819922955628409 absolute error = 2e-31 relative error = 1.9786600371221615377407914083725e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.148 y[1] (analytic) = 1.0109320235397580097238311794022 y[1] (numeric) = 1.010932023539758009723831179402 absolute error = 2e-31 relative error = 1.9783723865003707159941987580660e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.149 y[1] (analytic) = 1.0110799783418882374380727307282 y[1] (numeric) = 1.011079978341888237438072730728 absolute error = 2e-31 relative error = 1.9780828844814853302516946394199e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 1.0112289220639577132650190013457 y[1] (numeric) = 1.0112289220639577132650190013455 absolute error = 2e-31 relative error = 1.9777915330169966956634539021488e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.151 y[1] (analytic) = 1.0113788545570227275471705896988 y[1] (numeric) = 1.0113788545570227275471705896986 absolute error = 2e-31 relative error = 1.9774983340698642728755512072646e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.152 y[1] (analytic) = 1.0115297756711507997138872192414 y[1] (numeric) = 1.0115297756711507997138872192412 absolute error = 2e-31 relative error = 1.9772032896144835983481660465194e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.153 y[1] (analytic) = 1.0116816852554208282138558147042 y[1] (numeric) = 1.011681685255420828213855814704 absolute error = 2e-31 relative error = 1.9769064016366540524974437366093e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.154 y[1] (analytic) = 1.0118345831579232414361794766499 y[1] (numeric) = 1.0118345831579232414361794766497 absolute error = 2e-31 relative error = 1.9766076721335464666254140645369e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.155 y[1] (analytic) = 1.0119884692257601496199364332395 y[1] (numeric) = 1.0119884692257601496199364332394 absolute error = 1e-31 relative error = 9.8815355155683528480308928884575e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.156 y[1] (analytic) = 1.0121433433050454977520570596639 y[1] (numeric) = 1.0121433433050454977520570596638 absolute error = 1e-31 relative error = 9.8800234829842113765017064262592e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.157 y[1] (analytic) = 1.0122992052409052194533660673757 y[1] (numeric) = 1.0122992052409052194533660673755 absolute error = 2e-31 relative error = 1.9757004546141508116733756526007e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.158 y[1] (analytic) = 1.0124560548774773918526359770927 y[1] (numeric) = 1.0124560548774773918526359770926 absolute error = 1e-31 relative error = 9.8769718960396284629864655838113e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.159 y[1] (analytic) = 1.0126138920579123914484970015328 y[1] (numeric) = 1.0126138920579123914484970015327 absolute error = 1e-31 relative error = 9.8754323621585176665930241036470e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 1.0127727166243730509590474759817 y[1] (numeric) = 1.0127727166243730509590474759815 absolute error = 2e-31 relative error = 1.9747767363501947105791487532903e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.161 y[1] (analytic) = 1.0129325284180348171590079870976 y[1] (numeric) = 1.0129325284180348171590079870975 absolute error = 1e-31 relative error = 9.8723258651962493418994444351344e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.162 y[1] (analytic) = 1.0130933272790859097042613628125 y[1] (numeric) = 1.0130933272790859097042613628124 absolute error = 1e-31 relative error = 9.8707589229291313519064056603120e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.163 y[1] (analytic) = 1.0132551130467274809436196988004 y[1] (numeric) = 1.0132551130467274809436196988003 memory used=7.6MB, alloc=3.9MB, time=0.33 absolute error = 1e-31 relative error = 9.8691828654397699996862143573932e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.164 y[1] (analytic) = 1.0134178855591737767176586097624 y[1] (numeric) = 1.0134178855591737767176586097623 absolute error = 1e-31 relative error = 9.8675977032735100438157921187662e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.165 y[1] (analytic) = 1.0135816446536522981444579067051 y[1] (numeric) = 1.0135816446536522981444579067049 absolute error = 2e-31 relative error = 1.9732006894061440152417018988730e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.166 y[1] (analytic) = 1.0137463901664039643920869144861 y[1] (numeric) = 1.0137463901664039643920869144859 absolute error = 2e-31 relative error = 1.9728800214733242533735614917559e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.167 y[1] (analytic) = 1.0139121219326832764376716571557 y[1] (numeric) = 1.0139121219326832764376716571555 absolute error = 2e-31 relative error = 1.9725575389982230733834052061891e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.168 y[1] (analytic) = 1.014078839786758481812880152039 y[1] (numeric) = 1.0140788397867584818128801520388 absolute error = 2e-31 relative error = 1.9722332441337223949946372446596e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.169 y[1] (analytic) = 1.0142465435619117403356610670895 y[1] (numeric) = 1.0142465435619117403356610670894 absolute error = 1e-31 relative error = 9.8595356952178550719482837862528e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 1.0144152330904392908280700097875 y[1] (numeric) = 1.0144152330904392908280700097874 absolute error = 1e-31 relative error = 9.8578961295117488293772312119487e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.171 y[1] (analytic) = 1.0145849082036516188200167297711 y[1] (numeric) = 1.014584908203651618820016729771 absolute error = 1e-31 relative error = 9.8562475344771826963869278141901e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.172 y[1] (analytic) = 1.0147555687318736252387655314679 y[1] (numeric) = 1.0147555687318736252387655314678 absolute error = 1e-31 relative error = 9.8545899210948557704360460710775e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.173 y[1] (analytic) = 1.0149272145044447960840202072392 y[1] (numeric) = 1.0149272145044447960840202072391 absolute error = 1e-31 relative error = 9.8529233003991004569699954796845e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.174 y[1] (analytic) = 1.0150998453497193730884238159675 y[1] (numeric) = 1.0150998453497193730884238159674 absolute error = 1e-31 relative error = 9.8512476834777054231501626204298e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.175 y[1] (analytic) = 1.0152734610950665253633026466005 y[1] (numeric) = 1.0152734610950665253633026466004 absolute error = 1e-31 relative error = 9.8495630814717378508309276700903e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.176 y[1] (analytic) = 1.0154480615668705220294827209227 y[1] (numeric) = 1.0154480615668705220294827209226 absolute error = 1e-31 relative error = 9.8478695055753649939721229594336e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.177 y[1] (analytic) = 1.0156236465905309058330062047525 y[1] (numeric) = 1.0156236465905309058330062047524 absolute error = 1e-31 relative error = 9.8461669670356750456885280823934e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.178 y[1] (analytic) = 1.0158002159904626677455741118622 y[1] (numeric) = 1.0158002159904626677455741118621 absolute error = 1e-31 relative error = 9.8444554771524973201516882819593e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.179 y[1] (analytic) = 1.0159777695900964225495407001936 y[1] (numeric) = 1.0159777695900964225495407001935 absolute error = 1e-31 relative error = 9.8427350472782217545727981321633e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 1.0161563072118785854072839753885 y[1] (numeric) = 1.0161563072118785854072839753884 absolute error = 1e-31 relative error = 9.8410056888176177365086106897088e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.181 y[1] (analytic) = 1.0163358286772715494147757322793 y[1] (numeric) = 1.0163358286772715494147757322792 absolute error = 1e-31 relative error = 9.8392674132276522617453131020006e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.182 y[1] (analytic) = 1.016516333806753864139173580784 y[1] (numeric) = 1.0165163338067538641391735807839 absolute error = 1e-31 relative error = 9.8375202320173074280280529450554e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.183 y[1] (analytic) = 1.0166978224198204151402564186277 y[1] (numeric) = 1.0166978224198204151402564186276 absolute error = 1e-31 relative error = 9.8357641567473972699163051545140e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.184 y[1] (analytic) = 1.0168802943349826044755238294719 y[1] (numeric) = 1.0168802943349826044755238294718 absolute error = 1e-31 relative error = 9.8339991990303839400575371504772e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.185 y[1] (analytic) = 1.0170637493697685321887789013652 y[1] (numeric) = 1.0170637493697685321887789013651 absolute error = 1e-31 relative error = 9.8322253705301932421836595020925e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.186 y[1] (analytic) = 1.0172481873407231787820129769491 y[1] (numeric) = 1.017248187340723178782012976949 absolute error = 1e-31 relative error = 9.8304426829620295211465411056019e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.187 y[1] (analytic) = 1.0174336080634085886704098635492 y[1] (numeric) = 1.017433608063408588670409863549 absolute error = 2e-31 relative error = 1.9657302296184379830640842500215e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.188 y[1] (analytic) = 1.0176200113524040546202860481617 y[1] (numeric) = 1.0176200113524040546202860481615 absolute error = 2e-31 relative error = 1.9653701555475755953420732047401e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.189 y[1] (analytic) = 1.0178073970213063031697824794125 y[1] (numeric) = 1.0178073970213063031697824794123 absolute error = 2e-31 relative error = 1.9650083167534033328233986377926e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 1.0179957648827296810321224958101 y[1] (numeric) = 1.0179957648827296810321224958099 absolute error = 2e-31 relative error = 1.9646447156196121429437055732874e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.191 y[1] (analytic) = 1.0181851147483063424812494970519 y[1] (numeric) = 1.0181851147483063424812494970517 absolute error = 2e-31 relative error = 1.9642793545399616798883702114906e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.192 y[1] (analytic) = 1.0183754464286864377196569727608 y[1] (numeric) = 1.0183754464286864377196569727606 absolute error = 2e-31 relative error = 1.9639122359182425335009128357783e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.193 y[1] (analytic) = 1.0185667597335383022282225208382 y[1] (numeric) = 1.018566759733538302228222520838 absolute error = 2e-31 relative error = 1.9635433621682383371040430703671e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.194 y[1] (analytic) = 1.0187590544715486470978565056148 y[1] (numeric) = 1.0187590544715486470978565056146 absolute error = 2e-31 relative error = 1.9631727357136877553137434357135e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.195 y[1] (analytic) = 1.0189523304504227503427750241667 y[1] (numeric) = 1.0189523304504227503427750241664 absolute error = 3e-31 relative error = 2.9442005384823695293930893502394e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.196 y[1] (analytic) = 1.0191465874768846491952058675394 y[1] (numeric) = 1.0191465874768846491952058675391 absolute error = 3e-31 relative error = 2.9436393516531725189692202542718e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.197 y[1] (analytic) = 1.019341825356677333381335182191 y[1] (numeric) = 1.0193418253566773333813351821907 absolute error = 3e-31 relative error = 2.9430755467630023540344351978921e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.198 y[1] (analytic) = 1.0195380438945629393783015557216 y[1] (numeric) = 1.0195380438945629393783015557213 absolute error = 3e-31 relative error = 2.9425091275066234931560992916623e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.199 y[1] (analytic) = 1.0197352428943229456520432699139 y[1] (numeric) = 1.0197352428943229456520432699136 absolute error = 3e-31 relative error = 2.9419400975934452072103343354548e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 1.0199334221587583688758034832518 y[1] (numeric) = 1.0199334221587583688758034832515 absolute error = 3e-31 relative error = 2.9413684607474635152303106787816e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.201 y[1] (analytic) = 1.020132581489689961129097124429 y[1] (numeric) = 1.0201325814896899611290971244287 absolute error = 3e-31 relative error = 2.9407942207072029516653740880267e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.202 y[1] (analytic) = 1.0203327206879584080769422978976 y[1] (numeric) = 1.0203327206879584080769422978972 absolute error = 4e-31 relative error = 3.9202898416342108889236836878855e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.203 y[1] (analytic) = 1.0205338395534245281291580222406 y[1] (numeric) = 1.0205338395534245281291580222403 absolute error = 3e-31 relative error = 2.9396379460702353612259913677853e-29 % Correct digits = 30 h = 0.001 NO POLE memory used=11.4MB, alloc=4.0MB, time=0.51 TOP MAIN SOLVE Loop x[1] = 0.204 y[1] (analytic) = 1.020735937884969472579529142089 y[1] (numeric) = 1.0207359378849694725795291420887 absolute error = 3e-31 relative error = 2.9390559190226935582662292122478e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.205 y[1] (analytic) = 1.0209390154804949267246382744327 y[1] (numeric) = 1.0209390154804949267246382744324 absolute error = 3e-31 relative error = 2.9384713038790857122451789371906e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.206 y[1] (analytic) = 1.0211430721369233119621636705127 y[1] (numeric) = 1.0211430721369233119621636705124 absolute error = 3e-31 relative error = 2.9378841044496996580100696569104e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.207 y[1] (analytic) = 1.0213481076501979888684408950116 y[1] (numeric) = 1.0213481076501979888684408950113 absolute error = 3e-31 relative error = 2.9372943245589989011034152874538e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.208 y[1] (analytic) = 1.0215541218152834612550852449989 y[1] (numeric) = 1.0215541218152834612550852449986 absolute error = 3e-31 relative error = 2.9367019680455632509921541846818e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.209 y[1] (analytic) = 1.0217611144261655812044708520248 y[1] (numeric) = 1.0217611144261655812044708520244 absolute error = 4e-31 relative error = 3.9148093850160390652035741957096e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 1.0219690852758517550838614319006 y[1] (numeric) = 1.0219690852758517550838614319003 absolute error = 3e-31 relative error = 2.9355095405750307419201022379575e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.211 y[1] (analytic) = 1.0221780341563711505379866680538 y[1] (numeric) = 1.0221780341563711505379866680534 absolute error = 4e-31 relative error = 3.9132126364868514066824124866377e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.212 y[1] (analytic) = 1.022387960858774904459857235895 y[1] (numeric) = 1.0223879608587749044598572358946 absolute error = 4e-31 relative error = 3.9124091373690680168495002128739e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.213 y[1] (analytic) = 1.0225988651731363319396104974034 y[1] (numeric) = 1.022598865173136331939610497403 absolute error = 4e-31 relative error = 3.9116022286243780821418860913943e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.214 y[1] (analytic) = 1.0228107468885511361911779170994 y[1] (numeric) = 1.0228107468885511361911779170991 absolute error = 3e-31 relative error = 2.9330939366116085468545717112037e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.215 y[1] (analytic) = 1.0230236057931376194565642727558 y[1] (numeric) = 1.0230236057931376194565642727554 absolute error = 4e-31 relative error = 3.9099782031899930557270321717783e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.216 y[1] (analytic) = 1.0232374416740368948875277565849 y[1] (numeric) = 1.0232374416740368948875277565845 absolute error = 4e-31 relative error = 3.9091610970137293798983887991401e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.217 y[1] (analytic) = 1.0234522543174130994044490852411 y[1] (numeric) = 1.0234522543174130994044490852407 absolute error = 4e-31 relative error = 3.9083406022372602991166211196817e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.218 y[1] (analytic) = 1.023668043508453607532176759785 y[1] (numeric) = 1.0236680435084536075321767597845 absolute error = 5e-31 relative error = 4.8843959052031394530737262558293e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.219 y[1] (analytic) = 1.0238848090313692462126346397834 y[1] (numeric) = 1.0238848090313692462126346397829 absolute error = 5e-31 relative error = 4.8833618351366834472179516910616e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 1.0241025506693945105939770189553 y[1] (numeric) = 1.0241025506693945105939770189548 absolute error = 5e-31 relative error = 4.8823235492693572701048247021677e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.221 y[1] (analytic) = 1.0243212682047877807960754132258 y[1] (numeric) = 1.0243212682047877807960754132253 absolute error = 5e-31 relative error = 4.8812810542955291693200411856723e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.222 y[1] (analytic) = 1.0245409614188315396521202957203 y[1] (numeric) = 1.0245409614188315396521202957198 absolute error = 5e-31 relative error = 4.8802343569316834082372308863116e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.223 y[1] (analytic) = 1.024761630091832591426120037115 y[1] (numeric) = 1.0247616300918325914261200371145 absolute error = 5e-31 relative error = 4.8791834639163177279238018475873e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.224 y[1] (analytic) = 1.0249832740031222815060783338625 y[1] (numeric) = 1.024983274003122281506078333862 absolute error = 5e-31 relative error = 4.8781283820098405917681100120785e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.225 y[1] (analytic) = 1.0252058929310567170726304311345 y[1] (numeric) = 1.025205892931056717072630431134 absolute error = 5e-31 relative error = 4.8770691179944682156233268763619e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.226 y[1] (analytic) = 1.0254294866530169887429174718627 y[1] (numeric) = 1.0254294866530169887429174718622 absolute error = 5e-31 relative error = 4.8760056786741213862645447735900e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.227 y[1] (analytic) = 1.0256540549454093931894773280223 y[1] (numeric) = 1.0256540549454093931894773280218 absolute error = 5e-31 relative error = 4.8749380708743220709567106646145e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.228 y[1] (analytic) = 1.0258795975836656567339292952864 y[1] (numeric) = 1.0258795975836656567339292952859 absolute error = 5e-31 relative error = 4.8738663014420898209319155011105e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.229 y[1] (analytic) = 1.0261061143422431599152290573844 y[1] (numeric) = 1.0261061143422431599152290573838 absolute error = 6e-31 relative error = 5.8473484526950055658904650275272e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = 1.0263336049946251630322693519284 y[1] (numeric) = 1.0263336049946251630322693519278 absolute error = 6e-31 relative error = 5.8460523662103235705442934178423e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.231 y[1] (analytic) = 1.0265620693133210326606007951267 y[1] (numeric) = 1.0265620693133210326606007951261 absolute error = 6e-31 relative error = 5.8447513105695282451819827948332e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.232 y[1] (analytic) = 1.0267915070698664691430463486806 y[1] (numeric) = 1.02679150706986646914304634868 absolute error = 6e-31 relative error = 5.8434452940909834674658181676567e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.233 y[1] (analytic) = 1.0270219180348237350539819382704 y[1] (numeric) = 1.0270219180348237350539819382698 absolute error = 6e-31 relative error = 5.8421343251182250446502246438608e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.234 y[1] (analytic) = 1.027253301977781884637054759369 y[1] (numeric) = 1.0272533019777818846370547593684 absolute error = 6e-31 relative error = 5.8408184120198349844703359444626e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.235 y[1] (analytic) = 1.0274856586673569942161098326828 y[1] (numeric) = 1.0274856586673569942161098326822 absolute error = 6e-31 relative error = 5.8394975631893155422493308276178e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.236 y[1] (analytic) = 1.0277189878711923935790943983139 y[1] (numeric) = 1.0277189878711923935790943983133 absolute error = 6e-31 relative error = 5.8381717870449630475868202147989e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.237 y[1] (analytic) = 1.0279532893559588983347087647578 y[1] (numeric) = 1.0279532893559588983347087647572 absolute error = 6e-31 relative error = 5.8368410920297415139904618326040e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.238 y[1] (analytic) = 1.0281885628873550432415712561047 y[1] (numeric) = 1.0281885628873550432415712561041 absolute error = 6e-31 relative error = 5.8355054866111560348127382903551e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.239 y[1] (analytic) = 1.0284248082301073165096639283 y[1] (numeric) = 1.0284248082301073165096639282993 absolute error = 7e-31 relative error = 6.8065258091613136303302022519064e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 1.0286620251479703950738247530366 y[1] (numeric) = 1.0286620251479703950738247530359 absolute error = 7e-31 relative error = 6.8049561749818342388287101983891e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.241 y[1] (analytic) = 1.0289002134037273808390509958078 y[1] (numeric) = 1.0289002134037273808390509958071 absolute error = 7e-31 relative error = 6.8033808418050049250864402537854e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.242 y[1] (analytic) = 1.0291393727591900378973775428355 y[1] (numeric) = 1.0291393727591900378973775428348 absolute error = 7e-31 relative error = 6.8017998196226247742568377440358e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.243 y[1] (analytic) = 1.0293795029751990307160929600163 y[1] (numeric) = 1.0293795029751990307160929600156 absolute error = 7e-31 relative error = 6.8002131184543820051901779840895e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.244 y[1] (analytic) = 1.0296206038116241632970550956892 y[1] (numeric) = 1.0296206038116241632970550956885 absolute error = 7e-31 relative error = 6.7986207483477048521612533033574e-29 % Correct digits = 30 h = 0.001 NO POLE memory used=15.2MB, alloc=4.1MB, time=0.69 TOP MAIN SOLVE Loop x[1] = 0.245 y[1] (analytic) = 1.0298626750273646193068670679285 y[1] (numeric) = 1.0298626750273646193068670679278 absolute error = 7e-31 relative error = 6.7970227193776122247212282858993e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.246 y[1] (analytic) = 1.0301057163803492031776735062069 y[1] (numeric) = 1.0301057163803492031776735062062 absolute error = 7e-31 relative error = 6.7954190416465641495880599411617e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.247 y[1] (analytic) = 1.0303497276275365821783359466519 y[1] (numeric) = 1.0303497276275365821783359466511 absolute error = 8e-31 relative error = 7.7643539717534994268436594708259e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.248 y[1] (analytic) = 1.0305947085249155294557453097401 y[1] (numeric) = 1.0305947085249155294557453097393 absolute error = 8e-31 relative error = 7.7625083205117125781262657933861e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.249 y[1] (analytic) = 1.0308406588275051680460284191387 y[1] (numeric) = 1.0308406588275051680460284191379 absolute error = 8e-31 relative error = 7.7606562483665800918069266501057e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = 1.0310875782893552158554045505058 y[1] (numeric) = 1.031087578289355215855404550505 absolute error = 8e-31 relative error = 7.7587977669875016158471270529634e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.251 y[1] (analytic) = 1.0313354666635462316104470294153 y[1] (numeric) = 1.0313354666635462316104470294145 absolute error = 8e-31 relative error = 7.7569328880743798771515375637775e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.252 y[1] (analytic) = 1.0315843237021898617775039281638 y[1] (numeric) = 1.031584323702189861777503928163 absolute error = 8e-31 relative error = 7.7550616233574483572474841781761e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.253 y[1] (analytic) = 1.0318341491564290884510309420608 y[1] (numeric) = 1.03183414915642908845103094206 absolute error = 8e-31 relative error = 7.7531839845970987501173930603548e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.254 y[1] (analytic) = 1.0320849427764384782105885568886 y[1] (numeric) = 1.0320849427764384782105885568877 absolute error = 9e-31 relative error = 8.7202124815316717324673153975729e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.255 y[1] (analytic) = 1.0323367043114244319462546505563 y[1] (numeric) = 1.0323367043114244319462546505555 absolute error = 8e-31 relative error = 7.7494096321374663700737267580891e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.256 y[1] (analytic) = 1.0325894335096254356522027035565 y[1] (numeric) = 1.0325894335096254356522027035557 absolute error = 8e-31 relative error = 7.7475129421082022070789763219158e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.257 y[1] (analytic) = 1.032843130118312312188194824666 y[1] (numeric) = 1.0328431301183123121881948246651 absolute error = 9e-31 relative error = 8.7138111660471119684686832525291e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.258 y[1] (analytic) = 1.0330977938837884740087378304194 y[1] (numeric) = 1.0330977938837884740087378304185 absolute error = 9e-31 relative error = 8.7116631680779638473259711851025e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.259 y[1] (analytic) = 1.0333534245513901768596496492213 y[1] (numeric) = 1.0333534245513901768596496492204 absolute error = 9e-31 relative error = 8.7095080793942023070533545270306e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = 1.0336100218654867744417823535499 y[1] (numeric) = 1.033610021865486774441782353549 absolute error = 9e-31 relative error = 8.7073459134583093127849356624638e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.261 y[1] (analytic) = 1.0338675855694809740416471565521 y[1] (numeric) = 1.0338675855694809740416471565511 absolute error = 1.0e-30 relative error = 9.6724185375168152408187164376675e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.262 y[1] (analytic) = 1.0341261154058090931286857424248 y[1] (numeric) = 1.0341261154058090931286857424239 absolute error = 9e-31 relative error = 8.7030004038416951675361335403351e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.263 y[1] (analytic) = 1.0343856111159413169189313333344 y[1] (numeric) = 1.0343856111159413169189313333335 absolute error = 9e-31 relative error = 8.7008170872469878243828780092364e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.264 y[1] (analytic) = 1.0346460724403819569048019292326 y[1] (numeric) = 1.0346460724403819569048019292316 absolute error = 1.0e-30 relative error = 9.6651408306353154233444158876844e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.265 y[1] (analytic) = 1.0349074991186697103507671907983 y[1] (numeric) = 1.0349074991186697103507671907973 absolute error = 1.0e-30 relative error = 9.6626993315982632271105829200894e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.266 y[1] (analytic) = 1.0351698908893779207546294698607 y[1] (numeric) = 1.0351698908893779207546294698596 absolute error = 1.1e-30 relative error = 1.0626275065389726102810931923574e-28 % Correct digits = 29 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.267 y[1] (analytic) = 1.0354332474901148392741585260421 y[1] (numeric) = 1.0354332474901148392741585260411 absolute error = 1.0e-30 relative error = 9.6577930293816152898377436888564e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.268 y[1] (analytic) = 1.0356975686575238871188185030108 y[1] (numeric) = 1.0356975686575238871188185030098 absolute error = 1.0e-30 relative error = 9.6553282566473990535440138605606e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.269 y[1] (analytic) = 1.0359628541272839189063247726353 y[1] (numeric) = 1.0359628541272839189063247726342 absolute error = 1.1e-30 relative error = 1.0618141332168345641995759244107e-28 % Correct digits = 29 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 1.0362291036341094869837672905078 y[1] (numeric) = 1.0362291036341094869837672905067 absolute error = 1.1e-30 relative error = 1.0615413098727324439801275166044e-28 % Correct digits = 29 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.271 y[1] (analytic) = 1.0364963169117511067130361417346 y[1] (numeric) = 1.0364963169117511067130361417335 absolute error = 1.1e-30 relative error = 1.0612676398865155781361576241779e-28 % Correct digits = 29 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.272 y[1] (analytic) = 1.0367644936929955227202839915894 y[1] (numeric) = 1.0367644936929955227202839915883 absolute error = 1.1e-30 relative error = 1.0609931249494831173515173232049e-28 % Correct digits = 29 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.273 y[1] (analytic) = 1.0370336337096659761091591915901 y[1] (numeric) = 1.0370336337096659761091591915891 absolute error = 1.0e-30 relative error = 9.6428887886963738573922608101810e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.274 y[1] (analytic) = 1.0373037366926224726375423277883 y[1] (numeric) = 1.0373037366926224726375423277873 absolute error = 1.0e-30 relative error = 9.6403778818770760064957740214658e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.275 y[1] (analytic) = 1.0375748023717620518575180345561 y[1] (numeric) = 1.0375748023717620518575180345551 absolute error = 1.0e-30 relative error = 9.6378593400122005239704344416125e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.276 y[1] (analytic) = 1.0378468304760190572183129339225 y[1] (numeric) = 1.0378468304760190572183129339215 absolute error = 1.0e-30 relative error = 9.6353331786092151809473763700876e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.277 y[1] (analytic) = 1.0381198207333654071319295975428 y[1] (numeric) = 1.0381198207333654071319295975418 absolute error = 1.0e-30 relative error = 9.6327994132080419546488109498390e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.278 y[1] (analytic) = 1.0383937728708108670012054656899 y[1] (numeric) = 1.0383937728708108670012054656889 absolute error = 1.0e-30 relative error = 9.6302580593808363383223637818245e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.279 y[1] (analytic) = 1.0386686866144033222100246952314 y[1] (numeric) = 1.0386686866144033222100246952304 absolute error = 1.0e-30 relative error = 9.6277091327317665217239513830360e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 1.0389445616892290520754099464035 y[1] (numeric) = 1.0389445616892290520754099464025 absolute error = 1.0e-30 relative error = 9.6251526488967924475421000352693e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.281 y[1] (analytic) = 1.0392213978194130047612201563121 y[1] (numeric) = 1.0392213978194130047612201563111 absolute error = 1.0e-30 relative error = 9.6225886235434447491472622146679e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.282 y[1] (analytic) = 1.0394991947281190731531793854871 y[1] (numeric) = 1.0394991947281190731531793854861 absolute error = 1.0e-30 relative error = 9.6200170723706035750401494866095e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.283 y[1] (analytic) = 1.0397779521375503716949608624835 y[1] (numeric) = 1.0397779521375503716949608624826 absolute error = 9e-31 relative error = 8.6556942099974495748270397912375e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.284 y[1] (analytic) = 1.0400576697689495141850493904688 y[1] (numeric) = 1.0400576697689495141850493904678 absolute error = 1.0e-30 relative error = 9.6148514555173811658308100343329e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.285 y[1] (analytic) = 1.040338347342598892534104318956 y[1] (numeric) = 1.0403383473425988925341043189551 absolute error = 9e-31 relative error = 8.6510316792505641699770045501150e-29 % Correct digits = 30 h = 0.001 memory used=19.0MB, alloc=4.1MB, time=0.87 NO POLE TOP MAIN SOLVE Loop x[1] = 0.286 y[1] (analytic) = 1.0406199845778209564825443233454 y[1] (numeric) = 1.0406199845778209564825443233444 absolute error = 1.0e-30 relative error = 9.6096559245467454161540018832242e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.287 y[1] (analytic) = 1.0409025811929784942780742747098 y[1] (numeric) = 1.0409025811929784942780742747088 absolute error = 1.0e-30 relative error = 9.6070469808413766813193363134257e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.288 y[1] (analytic) = 1.0411861369054749143128735223236 y[1] (numeric) = 1.0411861369054749143128735223226 absolute error = 1.0e-30 relative error = 9.6044306061557364223943091945524e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.289 y[1] (analytic) = 1.0414706514317545277201639517677 y[1] (numeric) = 1.0414706514317545277201639517667 absolute error = 1.0e-30 relative error = 9.6018068164019500850284882950109e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = 1.0417561244873028319298752220681 y[1] (numeric) = 1.0417561244873028319298752220671 absolute error = 1.0e-30 relative error = 9.5991756275217197883411999648011e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.291 y[1] (analytic) = 1.0420425557866467951831236262249 y[1] (numeric) = 1.0420425557866467951831236262239 absolute error = 1.0e-30 relative error = 9.5965370554861023698266984297313e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.292 y[1] (analytic) = 1.0423299450433551420052200606774 y[1] (numeric) = 1.0423299450433551420052200606764 absolute error = 1.0e-30 relative error = 9.5938911162952873701334548230576e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.293 y[1] (analytic) = 1.0426182919700386396369216307212 y[1] (numeric) = 1.0426182919700386396369216307202 absolute error = 1.0e-30 relative error = 9.5912378259783749629745863251189e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.294 y[1] (analytic) = 1.0429075962783503854236404606493 y[1] (numeric) = 1.0429075962783503854236404606483 absolute error = 1.0e-30 relative error = 9.5885772005931538354147380659383e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.295 y[1] (analytic) = 1.043197857678986095162322319432 y[1] (numeric) = 1.0431978576789860951623223194309 absolute error = 1.1e-30 relative error = 1.0544500181848466926143533894656e-28 % Correct digits = 29 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.296 y[1] (analytic) = 1.0434890758816843924057067150814 y[1] (numeric) = 1.0434890758816843924057067150804 absolute error = 1.0e-30 relative error = 9.5832340089910497103201788797554e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.297 y[1] (analytic) = 1.0437812505952270987236791534653 y[1] (numeric) = 1.0437812505952270987236791534643 absolute error = 1.0e-30 relative error = 9.5805514750311869861087481017520e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.298 y[1] (analytic) = 1.0440743815274395249214253002402 y[1] (numeric) = 1.0440743815274395249214253002393 absolute error = 9e-31 relative error = 8.6200755034649504264252515334243e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.299 y[1] (analytic) = 1.0443684683851907632140958277764 y[1] (numeric) = 1.0443684683851907632140958277755 absolute error = 9e-31 relative error = 8.6176481504806994343358498007157e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 1.044663510874393980357689772432 y[1] (numeric) = 1.044663510874393980357689772431 absolute error = 1.0e-30 relative error = 9.5724603146422701446362589810738e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.301 y[1] (analytic) = 1.0449595087000067117358632713184 y[1] (numeric) = 1.0449595087000067117358632713175 absolute error = 9e-31 relative error = 8.6127739161841287844500232540184e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.302 y[1] (analytic) = 1.0452564615660311564023695917739 y[1] (numeric) = 1.0452564615660311564023695917729 absolute error = 1.0e-30 relative error = 9.5670300712781366920612528090345e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.303 y[1] (analytic) = 1.0455543691755144730788354111266 y[1] (numeric) = 1.0455543691755144730788354111256 absolute error = 1.0e-30 relative error = 9.5643041575022352524168739167245e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.304 y[1] (analytic) = 1.0458532312305490771075773489994 y[1] (numeric) = 1.0458532312305490771075773489984 absolute error = 1.0e-30 relative error = 9.5615710707648888201758060356737e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.305 y[1] (analytic) = 1.0461530474322729383591617993617 y[1] (numeric) = 1.0461530474322729383591617993606 absolute error = 1.1e-30 relative error = 1.0514713910167269934879846109229e-28 % Correct digits = 29 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.306 y[1] (analytic) = 1.0464538174808698800944101547946 y[1] (numeric) = 1.0464538174808698800944101547935 absolute error = 1.1e-30 relative error = 1.0511691788253321484318528162387e-28 % Correct digits = 29 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.307 y[1] (analytic) = 1.0467555410755698787805505609892 y[1] (numeric) = 1.0467555410755698787805505609882 absolute error = 1.0e-30 relative error = 9.5533289365009973138684284503944e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.308 y[1] (analytic) = 1.0470582179146493648612163853508 y[1] (numeric) = 1.0470582179146493648612163853497 absolute error = 1.1e-30 relative error = 1.0505624053940295500868784502905e-28 % Correct digits = 29 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.309 y[1] (analytic) = 1.0473618476954315244799906297348 y[1] (numeric) = 1.0473618476954315244799906297338 absolute error = 1.0e-30 relative error = 9.5477986161168231412251670940696e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = 1.0476664301142866021571945637978 y[1] (numeric) = 1.0476664301142866021571945637968 absolute error = 1.0e-30 relative error = 9.5450228360463280020869203157647e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.311 y[1] (analytic) = 1.0479719648666322044196179021966 y[1] (numeric) = 1.0479719648666322044196179021956 absolute error = 1.0e-30 relative error = 9.5422399980639057586246905449760e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.312 y[1] (analytic) = 1.0482784516469336043828868959338 y[1] (numeric) = 1.0482784516469336043828868959328 absolute error = 1.0e-30 relative error = 9.5394501187057303640737947357185e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.313 y[1] (analytic) = 1.0485858901487040472861657555049 y[1] (numeric) = 1.0485858901487040472861657555039 absolute error = 1.0e-30 relative error = 9.5366532145324414668925243395728e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.314 y[1] (analytic) = 1.0488942800645050569788858711721 y[1] (numeric) = 1.0488942800645050569788858711711 absolute error = 1.0e-30 relative error = 9.5338493021289223805644764912666e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.315 y[1] (analytic) = 1.0492036210859467433591963436608 y[1] (numeric) = 1.0492036210859467433591963436598 absolute error = 1.0e-30 relative error = 9.5310383981040781109270523261552e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.316 y[1] (analytic) = 1.0495139129036881107638283868539 y[1] (numeric) = 1.0495139129036881107638283868529 absolute error = 1.0e-30 relative error = 9.5282205190906134459719856553781e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.317 y[1] (analytic) = 1.0498251552074373673090652126448 y[1] (numeric) = 1.0498251552074373673090652126438 absolute error = 1.0e-30 relative error = 9.5253956817448111130483608719517e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.318 y[1] (analytic) = 1.0501373476859522351825080570062 y[1] (numeric) = 1.0501373476859522351825080570052 absolute error = 1.0e-30 relative error = 9.5225639027463100083830285641095e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.319 y[1] (analytic) = 1.0504504900270402618853280555329 y[1] (numeric) = 1.0504504900270402618853280555319 absolute error = 1.0e-30 relative error = 9.5197251987978835038176321326195e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = 1.0507645819175591324246927262339 y[1] (numeric) = 1.0507645819175591324246927262329 absolute error = 1.0e-30 relative error = 9.5168795866252178356456200121295e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.321 y[1] (analytic) = 1.0510796230434169824560548671731 y[1] (numeric) = 1.0510796230434169824560548671721 absolute error = 1.0e-30 relative error = 9.5140270829766905804166371523713e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.322 y[1] (analytic) = 1.0513956130895727123749907266948 y[1] (numeric) = 1.0513956130895727123749907266939 absolute error = 9e-31 relative error = 8.5600509341608343003036107467511e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.323 y[1] (analytic) = 1.051712551740036302358273354424 y[1] (numeric) = 1.0517125517400363023582733544231 absolute error = 9e-31 relative error = 8.5574713215219208367933138189333e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.324 y[1] (analytic) = 1.0520304386778691283538660919921 y[1] (numeric) = 1.0520304386778691283538660919912 absolute error = 9e-31 relative error = 8.5548855518958921868848521841012e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.325 y[1] (analytic) = 1.0523492735851842790195202135225 y[1] (numeric) = 1.0523492735851842790195202135216 absolute error = 9e-31 relative error = 8.5522936404359849945544080566286e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.326 memory used=22.8MB, alloc=4.1MB, time=1.06 y[1] (analytic) = 1.0526690561431468736096597773046 y[1] (numeric) = 1.0526690561431468736096597773037 absolute error = 9e-31 relative error = 8.5496956023148625774883329938773e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.327 y[1] (analytic) = 1.0529897860319743808102358017967 y[1] (numeric) = 1.0529897860319743808102358017958 absolute error = 9e-31 relative error = 8.5470914527244161161034072818610e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.328 y[1] (analytic) = 1.0533114629309369385212309311322 y[1] (numeric) = 1.0533114629309369385212309311313 absolute error = 9e-31 relative error = 8.5444812068755659510890883963197e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.329 y[1] (analytic) = 1.0536340865183576745864948076487 y[1] (numeric) = 1.0536340865183576745864948076478 absolute error = 9e-31 relative error = 8.5418648799980629937328693657197e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 1.0539576564716130284705894216338 y[1] (numeric) = 1.0539576564716130284705894216329 absolute error = 9e-31 relative error = 8.5392424873402902532743847386086e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.331 y[1] (analytic) = 1.0542821724671330738823227614669 y[1] (numeric) = 1.054282172467133073882322761466 absolute error = 9e-31 relative error = 8.5366140441690644855183023035282e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.332 y[1] (analytic) = 1.0546076341804018423446481406519 y[1] (numeric) = 1.054607634180401842344648140651 absolute error = 9e-31 relative error = 8.5339795657694379669203238991148e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.333 y[1] (analytic) = 1.0549340412859576477106056318672 y[1] (numeric) = 1.0549340412859576477106056318662 absolute error = 1.0e-30 relative error = 9.4792656304938893314942108460157e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.334 y[1] (analytic) = 1.0552613934573934116249810921192 y[1] (numeric) = 1.0552613934573934116249810921182 absolute error = 1.0e-30 relative error = 9.4763250716835343807515989590220e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.335 y[1] (analytic) = 1.0555896903673569899313573173679 y[1] (numeric) = 1.0555896903673569899313573173669 absolute error = 1.0e-30 relative error = 9.4733778581333893338364730955202e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.336 y[1] (analytic) = 1.0559189316875515000242309195995 y[1] (numeric) = 1.0559189316875515000242309195985 absolute error = 1.0e-30 relative error = 9.4704240069056928085196944615425e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.337 y[1] (analytic) = 1.056249117088735649145867574257 y[1] (numeric) = 1.056249117088735649145867574256 absolute error = 1.0e-30 relative error = 9.4674635350818461109773237112162e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.338 y[1] (analytic) = 1.0565802462407240636275673412012 y[1] (numeric) = 1.0565802462407240636275673412002 absolute error = 1.0e-30 relative error = 9.4644964597621939186030549610132e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.339 y[1] (analytic) = 1.0569123188123876190750108179637 y[1] (numeric) = 1.0569123188123876190750108179627 absolute error = 1.0e-30 relative error = 9.4615227980658051345138984340886e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = 1.0572453344716537714973559399734 y[1] (numeric) = 1.0572453344716537714973559399725 absolute error = 9e-31 relative error = 8.5126883104172285264587977702050e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.341 y[1] (analytic) = 1.0575792928855068893797542986879 y[1] (numeric) = 1.057579292885506889379754298687 absolute error = 9e-31 relative error = 8.5100002057002608077062205050530e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.342 y[1] (analytic) = 1.0579141937199885866989549051396 y[1] (numeric) = 1.0579141937199885866989549051388 absolute error = 8e-31 relative error = 7.5620499729465396513792217752284e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.343 y[1] (analytic) = 1.0582500366401980568816623833228 y[1] (numeric) = 1.0582500366401980568816623833219 absolute error = 9e-31 relative error = 8.5046063674836175757933779054006e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.344 y[1] (analytic) = 1.0585868213102924077053156350886 y[1] (numeric) = 1.0585868213102924077053156350878 absolute error = 8e-31 relative error = 7.5572450355066759727907003350981e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.345 y[1] (analytic) = 1.0589245473934869971409520758003 y[1] (numeric) = 1.0589245473934869971409520757995 absolute error = 8e-31 relative error = 7.5548347799583786100844370842273e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.346 y[1] (analytic) = 1.0592632145520557701378215979091 y[1] (numeric) = 1.0592632145520557701378215979083 absolute error = 8e-31 relative error = 7.5524193515802044254315084957218e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.347 y[1] (analytic) = 1.0596028224473315963494134778678 y[1] (numeric) = 1.059602822447331596349413477867 absolute error = 8e-31 relative error = 7.5499987641809498695189740972415e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.348 y[1] (analytic) = 1.0599433707397066088005585003816 y[1] (numeric) = 1.0599433707397066088005585003807 absolute error = 9e-31 relative error = 8.4910196605306721637873795537017e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.349 y[1] (analytic) = 1.0602848590886325434952676329222 y[1] (numeric) = 1.0602848590886325434952676329213 absolute error = 9e-31 relative error = 8.4882849385739098967757897439703e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (analytic) = 1.0606272871526210799649676426963 y[1] (numeric) = 1.0606272871526210799649676426955 absolute error = 8e-31 relative error = 7.5427061861447508053902688946191e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.351 y[1] (analytic) = 1.0609706545892441827567931078597 y[1] (numeric) = 1.0609706545892441827567931078589 absolute error = 8e-31 relative error = 7.5402651010147003111954356517683e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.352 y[1] (analytic) = 1.0613149610551344438615933347137 y[1] (numeric) = 1.0613149610551344438615933347129 absolute error = 8e-31 relative error = 7.5378189261052040757765185869925e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.353 y[1] (analytic) = 1.0616602062059854260813117529063 y[1] (numeric) = 1.0616602062059854260813117529055 absolute error = 8e-31 relative error = 7.5353676753029057950047977180240e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.354 y[1] (analytic) = 1.0620063896965520073353944212866 y[1] (numeric) = 1.0620063896965520073353944212858 absolute error = 8e-31 relative error = 7.5329113625068177149791846708154e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.355 y[1] (analytic) = 1.062353511180650725905883338033 y[1] (numeric) = 1.0623535111806507259058833380322 absolute error = 8e-31 relative error = 7.5304500016281479967810024958902e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.356 y[1] (analytic) = 1.0627015703111601266208493099901 y[1] (numeric) = 1.0627015703111601266208493099893 absolute error = 8e-31 relative error = 7.5279836065901282782274781308757e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.357 y[1] (analytic) = 1.0630505667400211079758181978111 y[1] (numeric) = 1.0630505667400211079758181978103 absolute error = 8e-31 relative error = 7.5255121913278414359905841360239e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.358 y[1] (analytic) = 1.0634005001182372701928434155077 y[1] (numeric) = 1.0634005001182372701928434155069 absolute error = 8e-31 relative error = 7.5230357697880495514316051474317e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.359 y[1] (analytic) = 1.0637513700958752642168766253644 y[1] (numeric) = 1.0637513700958752642168766253636 absolute error = 8e-31 relative error = 7.5205543559290220834854695349540e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 1.0641031763220651416490876318753 y[1] (numeric) = 1.0641031763220651416490876318745 absolute error = 8e-31 relative error = 7.5180679637203642519124790882004e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.361 y[1] (analytic) = 1.064455918445000705616783541413 y[1] (numeric) = 1.0644559184450007056167835414123 absolute error = 7e-31 relative error = 6.5761295312499899299412664723033e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.362 y[1] (analytic) = 1.0648095961119398625795763177395 y[1] (numeric) = 1.0648095961119398625795763177388 absolute error = 7e-31 relative error = 6.5739452626647003570877442593972e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.363 y[1] (analytic) = 1.0651642089692049750714469272204 y[1] (numeric) = 1.0651642089692049750714469272197 absolute error = 7e-31 relative error = 6.5717566747517118373467278358136e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.364 y[1] (analytic) = 1.0655197566621832153783533317088 y[1] (numeric) = 1.0655197566621832153783533317081 absolute error = 7e-31 relative error = 6.5695637797726062365726865878842e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.365 y[1] (analytic) = 1.0658762388353269201510286515192 y[1] (numeric) = 1.0658762388353269201510286515185 absolute error = 7e-31 relative error = 6.5673665899981362497304246317692e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.366 y[1] (analytic) = 1.0662336551321539459526148857234 y[1] (numeric) = 1.0662336551321539459526148857227 absolute error = 7e-31 relative error = 6.5651651177080764008189315004408e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.367 y[1] (analytic) = 1.0665920051952480257407766421643 memory used=26.7MB, alloc=4.1MB, time=1.24 y[1] (numeric) = 1.0665920051952480257407766421636 absolute error = 7e-31 relative error = 6.5629593751910742467800719611367e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.368 y[1] (analytic) = 1.0669512886662591262839383951033 y[1] (numeric) = 1.0669512886662591262839383951026 absolute error = 7e-31 relative error = 6.5607493747445017881780120379433e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.369 y[1] (analytic) = 1.0673115051859038065112878542941 y[1] (numeric) = 1.0673115051859038065112878542934 absolute error = 7e-31 relative error = 6.5585351286743070894203911204083e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = 1.0676726543939655767961870955091 y[1] (numeric) = 1.0676726543939655767961870955084 absolute error = 7e-31 relative error = 6.5563166492948661112773085676387e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.371 y[1] (analytic) = 1.0680347359292952591726321691378 y[1] (numeric) = 1.0680347359292952591726321691371 absolute error = 7e-31 relative error = 6.5540939489288347584391983987782e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.372 y[1] (analytic) = 1.0683977494298113484844009704265 y[1] (numeric) = 1.0683977494298113484844009704258 absolute error = 7e-31 relative error = 6.5518670399070011448396184247882e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.373 y[1] (analytic) = 1.0687616945325003744665282222431 y[1] (numeric) = 1.0687616945325003744665282222424 absolute error = 7e-31 relative error = 6.5496359345681380794538814518118e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.374 y[1] (analytic) = 1.0691265708734172647587454889206 y[1] (numeric) = 1.0691265708734172647587454889199 absolute error = 7e-31 relative error = 6.5474006452588557752693069009104e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.375 y[1] (analytic) = 1.0694923780876857088505232077704 y[1] (numeric) = 1.0694923780876857088505232077698 absolute error = 6e-31 relative error = 5.6101381580001041006637190879375e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.376 y[1] (analytic) = 1.0698591158094985229573507932542 y[1] (numeric) = 1.0698591158094985229573507932536 absolute error = 6e-31 relative error = 5.6082150549889535656844539111283e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.377 y[1] (analytic) = 1.070226783672118015827889937563 y[1] (numeric) = 1.0702267836721180158278899375624 absolute error = 6e-31 relative error = 5.6062883975049170173029340737589e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.378 y[1] (analytic) = 1.0705953813078763554816353004824 y[1] (numeric) = 1.0705953813078763554816353004818 absolute error = 6e-31 relative error = 5.6043581961564157203791737397083e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.379 y[1] (analytic) = 1.070964908348175936876715850913 y[1] (numeric) = 1.0709649083481759368767158509124 absolute error = 6e-31 relative error = 5.6024244615579604166787757948474e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = 1.0713353644234897505074691922754 y[1] (numeric) = 1.0713353644234897505074691922749 absolute error = 5e-31 relative error = 4.6670726702750218924585065309607e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.381 y[1] (analytic) = 1.0717067491633617519314202742562 y[1] (numeric) = 1.0717067491633617519314202742557 absolute error = 5e-31 relative error = 4.6654553625824400200830432608577e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.382 y[1] (analytic) = 1.0720790621964072322252949639468 y[1] (numeric) = 1.0720790621964072322252949639463 absolute error = 5e-31 relative error = 4.6638351370805794630572910653883e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.383 y[1] (analytic) = 1.072452303150313189369698020393 y[1] (numeric) = 1.0724523031503131893696980203925 absolute error = 5e-31 relative error = 4.6622120026341237148393516165312e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.384 y[1] (analytic) = 1.0728264716518387005620840879077 y[1] (numeric) = 1.0728264716518387005620840879072 absolute error = 5e-31 relative error = 4.6605859681123115190991481346414e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.385 y[1] (analytic) = 1.0732015673268152954576493952072 y[1] (numeric) = 1.0732015673268152954576493952067 absolute error = 5e-31 relative error = 4.6589570423888335392890802491772e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.386 y[1] (analytic) = 1.0735775898001473303377709195101 y[1] (numeric) = 1.0735775898001473303377709195096 absolute error = 5e-31 relative error = 4.6573252343417292098733741714458e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.387 y[1] (analytic) = 1.0739545386958123632056188471909 y[1] (numeric) = 1.0739545386958123632056188471904 absolute error = 5e-31 relative error = 4.6556905528532837709980257121806e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.388 y[1] (analytic) = 1.0743324136368615298085672354074 y[1] (numeric) = 1.0743324136368615298085672354069 absolute error = 5e-31 relative error = 4.6540530068099254883719762329684e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.389 y[1] (analytic) = 1.0747112142454199205870268523226 y[1] (numeric) = 1.0747112142454199205870268523221 absolute error = 5e-31 relative error = 4.6524126051021230601188778881360e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = 1.0750909401426869585493232471189 y[1] (numeric) = 1.0750909401426869585493232471184 absolute error = 5e-31 relative error = 4.6507693566242832123474951383348e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.391 y[1] (analytic) = 1.0754715909489367780722421749589 y[1] (numeric) = 1.0754715909489367780722421749584 absolute error = 5e-31 relative error = 4.6491232702746484851774551429075e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.392 y[1] (analytic) = 1.0758531662835186046268635763786 y[1] (numeric) = 1.0758531662835186046268635763781 absolute error = 5e-31 relative error = 4.6474743549551952109457009080086e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.393 y[1] (analytic) = 1.0762356657648571354293043853106 y[1] (numeric) = 1.0762356657648571354293043853102 absolute error = 4e-31 relative error = 3.7166580956572253490460948981034e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.394 y[1] (analytic) = 1.0766190890104529210159895150267 y[1] (numeric) = 1.0766190890104529210159895150262 absolute error = 5e-31 relative error = 4.6441680730327965399354050949478e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.395 y[1] (analytic) = 1.0770034356368827477430694467592 y[1] (numeric) = 1.0770034356368827477430694467587 absolute error = 5e-31 relative error = 4.6425107242515572975048132449958e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.396 y[1] (analytic) = 1.0773887052598000212096019216175 y[1] (numeric) = 1.077388705259800021209601921617 absolute error = 5e-31 relative error = 4.6408505821437091456499638530972e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.397 y[1] (analytic) = 1.0777748974939351506041143126486 y[1] (numeric) = 1.0777748974939351506041143126481 absolute error = 5e-31 relative error = 4.6391876556283738965544408419465e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.398 y[1] (analytic) = 1.0781620119530959339741623305114 y[1] (numeric) = 1.0781620119530959339741623305109 absolute error = 5e-31 relative error = 4.6375219536277991548353959168032e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.399 y[1] (analytic) = 1.0785500482501679444184997932385 y[1] (numeric) = 1.078550048250167944418499793238 absolute error = 5e-31 relative error = 4.6358534850672576883658770347565e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 1.0789390059971149172014732679482 y[1] (numeric) = 1.0789390059971149172014732679477 absolute error = 5e-31 relative error = 4.6341822588749470046690645502216e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.401 y[1] (analytic) = 1.0793288848049791377892544701431 y[1] (numeric) = 1.0793288848049791377892544701426 absolute error = 5e-31 relative error = 4.6325082839818891345065496178898e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.402 y[1] (analytic) = 1.0797196842838818308075223843972 y[1] (numeric) = 1.0797196842838818308075223843966 absolute error = 6e-31 relative error = 5.5569978831861967491254665830446e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.403 y[1] (analytic) = 1.0801114040430235499202061487794 y[1] (numeric) = 1.0801114040430235499202061487788 absolute error = 6e-31 relative error = 5.5549825485973712865405011663045e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.404 y[1] (analytic) = 1.0805040436906845686288988243055 y[1] (numeric) = 1.0805040436906845686288988243049 absolute error = 6e-31 relative error = 5.5529639477384662512960447683373e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.405 y[1] (analytic) = 1.0808976028342252719925512500355 y[1] (numeric) = 1.0808976028342252719925512500349 absolute error = 6e-31 relative error = 5.5509420913390682349184863278144e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.406 y[1] (analytic) = 1.0812920810800865492670542641556 y[1] (numeric) = 1.081292081080086549267054264155 absolute error = 6e-31 relative error = 5.5489169901315557549995917337352e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.407 y[1] (analytic) = 1.0816874780337901874643166514964 y[1] (numeric) = 1.0816874780337901874643166514958 absolute error = 6e-31 relative error = 5.5468886548509805273985931677782e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.408 y[1] (analytic) = 1.0820837932999392658304452584406 y[1] (numeric) = 1.08208379329993926583044525844 absolute error = 6e-31 relative error = 5.5448570962349490003132824347130e-29 % memory used=30.5MB, alloc=4.1MB, time=1.42 Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.409 y[1] (analytic) = 1.0824810264822185512426327970737 y[1] (numeric) = 1.082481026482218551242632797073 absolute error = 7e-31 relative error = 6.4666260458607548440642613962938e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 1.082879177183394894524357941723 y[1] (numeric) = 1.0828791771833948945243579417223 absolute error = 7e-31 relative error = 6.4642484106188421467405398069793e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.411 y[1] (analytic) = 1.0832782450053176276785014027179 y[1] (numeric) = 1.0832782450053176276785014027172 absolute error = 7e-31 relative error = 6.4618670524170253201265672529558e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.412 y[1] (analytic) = 1.0836782295489189620379807442877 y[1] (numeric) = 1.083678229548918962037980744287 absolute error = 7e-31 relative error = 6.4594819837930580537235078263134e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.413 y[1] (analytic) = 1.084079130414214387333505795996 y[1] (numeric) = 1.0840791304142143873335057959953 absolute error = 7e-31 relative error = 6.4570932172869881639047274910276e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.414 y[1] (analytic) = 1.0844809472003030716780555899898 y[1] (numeric) = 1.0844809472003030716780555899891 absolute error = 7e-31 relative error = 6.4547007654410212611319088820288e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.415 y[1] (analytic) = 1.0848836795053682624676768396186 y[1] (numeric) = 1.0848836795053682624676768396179 absolute error = 7e-31 relative error = 6.4523046407993847373263758002968e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.416 y[1] (analytic) = 1.0852873269266776881982030586595 y[1] (numeric) = 1.0852873269266776881982030586588 absolute error = 7e-31 relative error = 6.4499048559081920754215391591007e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.417 y[1] (analytic) = 1.0856918890605839611974925044623 y[1] (numeric) = 1.0856918890605839611974925044616 absolute error = 7e-31 relative error = 6.4475014233153074831059069624547e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.418 y[1] (analytic) = 1.0860973655025249812727822128099 y[1] (numeric) = 1.0860973655025249812727822128092 absolute error = 7e-31 relative error = 6.4450943555702108527496201475224e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.419 y[1] (analytic) = 1.0865037558470243402727544771743 y[1] (numeric) = 1.0865037558470243402727544771736 absolute error = 7e-31 relative error = 6.4426836652238630494909846248502e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = 1.0869110596876917275639112103343 y[1] (numeric) = 1.0869110596876917275639112103336 absolute error = 7e-31 relative error = 6.4402693648285715294429684274424e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.421 y[1] (analytic) = 1.087319276617223336420850712016 y[1] (numeric) = 1.0873192766172233364208507120153 absolute error = 7e-31 relative error = 6.4378514669378562899631223518439e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.422 y[1] (analytic) = 1.0877284062274022713300404523114 y[1] (numeric) = 1.0877284062274022713300404523107 absolute error = 7e-31 relative error = 6.4354299841063161539138636583361e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.423 y[1] (analytic) = 1.0881384481090989562066785671374 y[1] (numeric) = 1.0881384481090989562066785671368 absolute error = 6e-31 relative error = 5.5140042247624246198487452339175e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.424 y[1] (analytic) = 1.088549401852271543524235848908 y[1] (numeric) = 1.0885494018522715435242358489073 absolute error = 7e-31 relative error = 6.4305763138437506698421266439618e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.425 y[1] (analytic) = 1.0889612670459663243562691029099 y[1] (numeric) = 1.0889612670459663243562691029092 absolute error = 7e-31 relative error = 6.4281441515261183673689802581596e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.426 y[1] (analytic) = 1.0893740432783181393300958276049 y[1] (numeric) = 1.0893740432783181393300958276042 absolute error = 7e-31 relative error = 6.4257084544941821962133106145516e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.427 y[1] (analytic) = 1.089787730136550790491919265217 y[1] (numeric) = 1.0897877301365507904919192652163 absolute error = 7e-31 relative error = 6.4232692353059411931317559942262e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.428 y[1] (analytic) = 1.0902023272069774540829919575135 y[1] (numeric) = 1.0902023272069774540829919575128 absolute error = 7e-31 relative error = 6.4208265065196780455706784384780e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.429 y[1] (analytic) = 1.0906178340750010942264050306518 y[1] (numeric) = 1.0906178340750010942264050306511 absolute error = 7e-31 relative error = 6.4183802806938277664243497546595e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = 1.0910342503251148775240895223366 y[1] (numeric) = 1.0910342503251148775240895223358 absolute error = 8e-31 relative error = 7.3324920804421105344041278777554e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.431 y[1] (analytic) = 1.09145157554090258856361515432 y[1] (numeric) = 1.0914515755409025885636151543193 absolute error = 7e-31 relative error = 6.4134773881570819841930419646587e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.432 y[1] (analytic) = 1.0918698093050390463343710434825 y[1] (numeric) = 1.0918698093050390463343710434818 absolute error = 7e-31 relative error = 6.4110207465626411009580946133728e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.433 y[1] (analytic) = 1.0922889511992905215527119353457 y[1] (numeric) = 1.0922889511992905215527119353451 absolute error = 6e-31 relative error = 5.4930519927096532568118320212465e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.434 y[1] (analytic) = 1.0927090008045151548956526349088 y[1] (numeric) = 1.0927090008045151548956526349082 absolute error = 6e-31 relative error = 5.4909404018658720959286331350262e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.435 y[1] (analytic) = 1.0931299577006633761426924011461 y[1] (numeric) = 1.0931299577006633761426924011454 absolute error = 7e-31 relative error = 6.4036301911660178302920145866264e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.436 y[1] (analytic) = 1.0935518214667783242253501633781 y[1] (numeric) = 1.0935518214667783242253501633774 absolute error = 7e-31 relative error = 6.4011598376846169943572889204310e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.437 y[1] (analytic) = 1.0939745916809962681839905100158 y[1] (numeric) = 1.093974591680996268183990510015 absolute error = 8e-31 relative error = 7.3127841001382282724065986886702e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.438 y[1] (analytic) = 1.0943982679205470290315194928856 y[1] (numeric) = 1.0943982679205470290315194928849 absolute error = 7e-31 relative error = 6.3962089535289705011604352961960e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.439 y[1] (analytic) = 1.0948228497617544025235283834771 y[1] (numeric) = 1.0948228497617544025235283834763 absolute error = 8e-31 relative error = 7.3071182262417054481847639681454e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 1.0952483367800365828344626110016 y[1] (numeric) = 1.0952483367800365828344626110009 absolute error = 7e-31 relative error = 6.3912445834700591730008770364225e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.441 y[1] (analytic) = 1.0956747285499065871393922061318 y[1] (numeric) = 1.095674728549906587139392206131 absolute error = 8e-31 relative error = 7.3014369972626508363000263752152e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.442 y[1] (analytic) = 1.0961020246449726811009591686834 y[1] (numeric) = 1.0961020246449726811009591686826 absolute error = 8e-31 relative error = 7.2985906604735987728236533428131e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.443 y[1] (analytic) = 1.0965302246379388052610762723304 y[1] (numeric) = 1.0965302246379388052610762723296 absolute error = 8e-31 relative error = 7.2957405279380279116797063489264e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.444 y[1] (analytic) = 1.0969593281006050023369509146883 y[1] (numeric) = 1.0969593281006050023369509146875 absolute error = 8e-31 relative error = 7.2928866139933121797165526130335e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.445 y[1] (analytic) = 1.0973893346038678454210067167782 y[1] (numeric) = 1.0973893346038678454210067167774 absolute error = 8e-31 relative error = 7.2900289329746537660332274055022e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.446 y[1] (analytic) = 1.0978202437177208670842746719854 y[1] (numeric) = 1.0978202437177208670842746719846 absolute error = 8e-31 relative error = 7.2871674992149400763737854835065e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.447 y[1] (analytic) = 1.0982520550112549893828247411573 y[1] (numeric) = 1.0982520550112549893828247411565 absolute error = 8e-31 relative error = 7.2843023270446011181356974187894e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.448 y[1] (analytic) = 1.0986847680526589547668078874449 y[1] (numeric) = 1.0986847680526589547668078874441 absolute error = 8e-31 relative error = 7.2814334307914673177032971774928e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.449 y[1] (analytic) = 1.0991183824092197578916776418816 y[1] (numeric) = 1.0991183824092197578916776418808 absolute error = 8e-31 relative error = 7.2785608247806277717984903762486e-29 % Correct digits = 30 h = 0.001 memory used=34.3MB, alloc=4.1MB, time=1.60 NO POLE TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = 1.0995528976473230783311593885136 y[1] (numeric) = 1.0995528976473230783311593885127 absolute error = 9e-31 relative error = 8.1851450887510750513374194488374e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.451 y[1] (analytic) = 1.0999883133324537141915346561489 y[1] (numeric) = 1.0999883133324537141915346561481 absolute error = 8e-31 relative error = 7.2728045407716337417408650411322e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.452 y[1] (analytic) = 1.1004246290291960166268068024775 y[1] (numeric) = 1.1004246290291960166268068024767 absolute error = 8e-31 relative error = 7.2699208914086811744549403516517e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.453 y[1] (analytic) = 1.100861844301234325254313575431 y[1] (numeric) = 1.1008618443012343252543135754301 absolute error = 9e-31 relative error = 8.1754127882529145456104543675741e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.454 y[1] (analytic) = 1.101299958711353404470351136208 y[1] (numeric) = 1.1012999587113534044703511362072 absolute error = 8e-31 relative error = 7.2641426495293005320345751979181e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.455 y[1] (analytic) = 1.1017389718214388806653732283767 y[1] (numeric) = 1.1017389718214388806653732283759 absolute error = 8e-31 relative error = 7.2612480856278328928316440309588e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.456 y[1] (analytic) = 1.1021788831924776803383282778904 y[1] (numeric) = 1.1021788831924776803383282778896 absolute error = 8e-31 relative error = 7.2583499121557109762049033255194e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.457 y[1] (analytic) = 1.1026196923845584691096963097179 y[1] (numeric) = 1.1026196923845584691096963097172 absolute error = 7e-31 relative error = 6.3485171254846625513622047532051e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.458 y[1] (analytic) = 1.1030613989568720916327866680871 y[1] (numeric) = 1.1030613989568720916327866680864 absolute error = 7e-31 relative error = 6.3459749444769471313047311952913e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.459 y[1] (analytic) = 1.1035040024677120124028566290802 y[1] (numeric) = 1.1035040024677120124028566290794 absolute error = 8e-31 relative error = 7.2496338772763772451412835499067e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = 1.1039475024744747574636100964996 y[1] (numeric) = 1.1039475024744747574636100964988 absolute error = 8e-31 relative error = 7.2467214084620607414659585637532e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.461 y[1] (analytic) = 1.104391898533660357010634674543 y[1] (numeric) = 1.1043918985336603570106346745422 absolute error = 8e-31 relative error = 7.2438054015262870239798859960492e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.462 y[1] (analytic) = 1.1048371902008727888913345138855 y[1] (numeric) = 1.1048371902008727888913345138847 absolute error = 8e-31 relative error = 7.2408858707458092183694777465704e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.463 y[1] (analytic) = 1.1052833770308204230009154312754 y[1] (numeric) = 1.1052833770308204230009154312746 absolute error = 8e-31 relative error = 7.2379628303927011144241553521489e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.464 y[1] (analytic) = 1.1057304585773164665739779066934 y[1] (numeric) = 1.1057304585773164665739779066926 absolute error = 8e-31 relative error = 7.2350362947342221179816261245519e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.465 y[1] (analytic) = 1.1061784343932794103712726665209 y[1] (numeric) = 1.1061784343932794103712726665201 absolute error = 8e-31 relative error = 7.2321062780326826614239771192196e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.466 y[1] (analytic) = 1.1066273040307334757611726659979 y[1] (numeric) = 1.106627304030733475761172665997 absolute error = 9e-31 relative error = 8.1328193938634738333626927692566e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.467 y[1] (analytic) = 1.1070770670408090626954143895363 y[1] (numeric) = 1.1070770670408090626954143895354 absolute error = 9e-31 relative error = 8.1295153408396292782861362340454e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.468 y[1] (analytic) = 1.107527722973743198578660493185 y[1] (numeric) = 1.1075277229737431985786604931841 absolute error = 9e-31 relative error = 8.1262074197427274825235236962250e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.469 y[1] (analytic) = 1.1079792713788799880314349197206 y[1] (numeric) = 1.1079792713788799880314349197197 absolute error = 9e-31 relative error = 8.1228956465940935411578065757024e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = 1.1084317118046710635459807234666 y[1] (numeric) = 1.1084317118046710635459807234657 absolute error = 9e-31 relative error = 8.1195800374087356796593838265721e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.471 y[1] (analytic) = 1.1088850437986760370345899490213 y[1] (numeric) = 1.1088850437986760370345899490204 absolute error = 9e-31 relative error = 8.1162606081951969676866759963436e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.472 y[1] (analytic) = 1.109339266907562952269954015601 y[1] (numeric) = 1.1093392669075629522699540156001 absolute error = 9e-31 relative error = 8.1129373749554075591553246476008e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.473 y[1] (analytic) = 1.1097943806771087382170821666872 y[1] (numeric) = 1.1097943806771087382170821666863 absolute error = 9e-31 relative error = 8.1096103536845374599792777863886e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.474 y[1] (analytic) = 1.1102503846521996632563346530956 y[1] (numeric) = 1.1102503846521996632563346530947 absolute error = 9e-31 relative error = 8.1062795603708498248665530118788e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.475 y[1] (analytic) = 1.1107072783768317902971164264731 y[1] (numeric) = 1.1107072783768317902971164264722 absolute error = 9e-31 relative error = 8.1029450109955547845320388212372e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.476 y[1] (analytic) = 1.1111650613941114327817762295659 y[1] (numeric) = 1.1111650613941114327817762295651 absolute error = 8e-31 relative error = 7.1996504191401456041504903369094e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.477 y[1] (analytic) = 1.1116237332462556115792550793985 y[1] (numeric) = 1.1116237332462556115792550793976 absolute error = 9e-31 relative error = 8.0962647079488445780030123425456e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.478 y[1] (analytic) = 1.1120832934745925127680272497516 y[1] (numeric) = 1.1120832934745925127680272497507 absolute error = 9e-31 relative error = 8.0929189862032764507232925179684e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.479 y[1] (analytic) = 1.1125437416195619463078759700387 y[1] (numeric) = 1.1125437416195619463078759700378 absolute error = 9e-31 relative error = 8.0895695722475063845830069448650e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = 1.1130050772207158056000451688413 y[1] (numeric) = 1.1130050772207158056000451688404 absolute error = 9e-31 relative error = 8.0862164820253054559187977016585e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.481 y[1] (analytic) = 1.1134672998167185279353077019906 y[1] (numeric) = 1.1134672998167185279353077019898 absolute error = 8e-31 relative error = 7.1847642057533563491879689037528e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.482 y[1] (analytic) = 1.1139304089453475558294896171662 y[1] (numeric) = 1.1139304089453475558294896171653 absolute error = 9e-31 relative error = 8.0794993365169586517811533797007e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.483 y[1] (analytic) = 1.1143944041434937992459891195241 y[1] (numeric) = 1.1143944041434937992459891195232 absolute error = 9e-31 relative error = 8.0761353130781915346926979882929e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.484 y[1] (analytic) = 1.1148592849471620987048280158762 y[1] (numeric) = 1.1148592849471620987048280158754 absolute error = 8e-31 relative error = 7.1757934907266380870457133284104e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.485 y[1] (analytic) = 1.1153250508914716892777725284065 y[1] (numeric) = 1.1153250508914716892777725284057 absolute error = 8e-31 relative error = 7.1727968394555960925330709617309e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.486 y[1] (analytic) = 1.115791701510656665469059482842 y[1] (numeric) = 1.1157917015106566654690594828412 absolute error = 8e-31 relative error = 7.1697970052733842382262394298523e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.487 y[1] (analytic) = 1.1162592363380664469812629903921 y[1] (numeric) = 1.1162592363380664469812629903913 absolute error = 8e-31 relative error = 7.1667940023003289312946856184802e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.488 y[1] (analytic) = 1.1167276549061662453658358576272 y[1] (numeric) = 1.1167276549061662453658358576264 absolute error = 8e-31 relative error = 7.1637878446488415394942350451994e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.489 y[1] (analytic) = 1.117196956746537531557859073795 y[1] (numeric) = 1.1171969567465375315578590737942 absolute error = 8e-31 relative error = 7.1607785464232951776147509031169e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = 1.1176671413898785042945318408633 y[1] (numeric) = 1.1176671413898785042945318408625 absolute error = 8e-31 relative error = 7.1577661217199019814198623525233e-29 % Correct digits = 30 h = 0.001 NO POLE memory used=38.1MB, alloc=4.1MB, time=1.78 TOP MAIN SOLVE Loop x[1] = 0.491 y[1] (analytic) = 1.1181382083660045594169337278386 y[1] (numeric) = 1.1181382083660045594169337278378 absolute error = 8e-31 relative error = 7.1547505846265908700042343924150e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.492 y[1] (analytic) = 1.1186101572038487600545896476376 y[1] (numeric) = 1.1186101572038487600545896476368 absolute error = 8e-31 relative error = 7.1517319492228857974763778579352e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.493 y[1] (analytic) = 1.1190829874314623076923674719854 y[1] (numeric) = 1.1190829874314623076923674719846 absolute error = 8e-31 relative error = 7.1487102295797844948575490332922e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.494 y[1] (analytic) = 1.1195566985760150141192372174827 y[1] (numeric) = 1.1195566985760150141192372174818 absolute error = 9e-31 relative error = 8.0388961197295924159536201920532e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.495 y[1] (analytic) = 1.1200312901637957742584198541208 y[1] (numeric) = 1.1200312901637957742584198541199 absolute error = 9e-31 relative error = 8.0354897930430325101032548604898e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.496 y[1] (analytic) = 1.1205067617202130398784529061372 y[1] (numeric) = 1.1205067617202130398784529061364 absolute error = 8e-31 relative error = 7.1396267057936545075634464215004e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.497 y[1] (analytic) = 1.1209831127697952941846991341835 y[1] (numeric) = 1.1209831127697952941846991341827 absolute error = 8e-31 relative error = 7.1365927897282046243304814674481e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.498 y[1] (analytic) = 1.1214603428361915272908237073372 y[1] (numeric) = 1.1214603428361915272908237073364 absolute error = 8e-31 relative error = 7.1335558596462442099517436281008e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.499 y[1] (analytic) = 1.1219384514421717125697643935207 y[1] (numeric) = 1.12193845144217171256976439352 absolute error = 7e-31 relative error = 6.2392014383694579471440536869640e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 1.1224174381096272838837184173962 y[1] (numeric) = 1.1224174381096272838837184173954 absolute error = 8e-31 relative error = 7.1274730134927166844108599443208e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.501 y[1] (analytic) = 1.1228973023595716136926687557886 y[1] (numeric) = 1.1228973023595716136926687557878 absolute error = 8e-31 relative error = 7.1244271254275916337308819082705e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.502 y[1] (analytic) = 1.1233780437121404920409717621522 y[1] (numeric) = 1.1233780437121404920409717621514 absolute error = 8e-31 relative error = 7.1213782793586060575403941918520e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.503 y[1] (analytic) = 1.1238596616865926064215271335312 y[1] (numeric) = 1.1238596616865926064215271335305 absolute error = 7e-31 relative error = 6.2285356781068178712565838599998e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.504 y[1] (analytic) = 1.1243421558013100225170503558855 y[1] (numeric) = 1.1243421558013100225170503558848 absolute error = 7e-31 relative error = 6.2258627979764342653908919104168e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.505 y[1] (analytic) = 1.1248255255737986658179668865485 y[1] (numeric) = 1.1248255255737986658179668865477 absolute error = 8e-31 relative error = 7.1122141328709810524142780313895e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.506 y[1] (analytic) = 1.1253097705206888041164464559634 y[1] (numeric) = 1.1253097705206888041164464559626 absolute error = 8e-31 relative error = 7.1091535944794501487446948572178e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.507 y[1] (analytic) = 1.1257948901577355308760949947039 y[1] (numeric) = 1.1257948901577355308760949947032 absolute error = 7e-31 relative error = 6.2178288968954437677821339624381e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.508 y[1] (analytic) = 1.1262808839998192494768208161278 y[1] (numeric) = 1.126280883999819249476820816127 absolute error = 8e-31 relative error = 7.1030238670030413792232267252906e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.509 y[1] (analytic) = 1.126767751560946158334390809836 y[1] (numeric) = 1.1267677515609461583343908098352 absolute error = 8e-31 relative error = 7.0999547057655430568429878409082e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (analytic) = 1.1272554923542487368941915264245 y[1] (numeric) = 1.1272554923542487368941915264237 absolute error = 8e-31 relative error = 7.0968826980759906276157120870085e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.511 y[1] (analytic) = 1.1277441058919862324987091598053 y[1] (numeric) = 1.1277441058919862324987091598045 absolute error = 8e-31 relative error = 7.0938078578317383931906511930281e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.512 y[1] (analytic) = 1.1282335916855451481282415596589 y[1] (numeric) = 1.1282335916855451481282415596581 absolute error = 8e-31 relative error = 7.0907301989194047276371165464530e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.513 y[1] (analytic) = 1.1287239492454397310143545333464 y[1] (numeric) = 1.1287239492454397310143545333457 absolute error = 7e-31 relative error = 6.2016935183129156862000914129098e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.514 y[1] (analytic) = 1.1292151780813124621255938238659 y[1] (numeric) = 1.1292151780813124621255938238652 absolute error = 7e-31 relative error = 6.1989956705097922437993942968066e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.515 y[1] (analytic) = 1.1297072777019345465249632781811 y[1] (numeric) = 1.1297072777019345465249632781804 absolute error = 7e-31 relative error = 6.1962953927671355553667744305923e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.516 y[1] (analytic) = 1.1302002476152064045986788484863 y[1] (numeric) = 1.1302002476152064045986788484855 absolute error = 8e-31 relative error = 7.0783916539396474934928001904649e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.517 y[1] (analytic) = 1.1306940873281581641557071976931 y[1] (numeric) = 1.1306940873281581641557071976923 absolute error = 8e-31 relative error = 7.0753001096026625857663270184233e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.518 y[1] (analytic) = 1.1311887963469501533975968096429 y[1] (numeric) = 1.1311887963469501533975968096421 absolute error = 8e-31 relative error = 7.0722058296856549687141558213228e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.519 y[1] (analytic) = 1.1316843741768733947581086342535 y[1] (numeric) = 1.1316843741768733947581086342527 absolute error = 8e-31 relative error = 7.0691088279970036271594356286940e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (analytic) = 1.1321808203223500996121524280115 y[1] (numeric) = 1.1321808203223500996121524280107 absolute error = 8e-31 relative error = 7.0660091183334754397666150525655e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.521 y[1] (analytic) = 1.1326781342869341638535340809147 y[1] (numeric) = 1.1326781342869341638535340809139 absolute error = 8e-31 relative error = 7.0629067144801179392283878836105e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.522 y[1] (analytic) = 1.1331763155733116643410183521593 y[1] (numeric) = 1.1331763155733116643410183521585 absolute error = 8e-31 relative error = 7.0598016302101525811248383138996e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.523 y[1] (analytic) = 1.133675363683301356212210568549 y[1] (numeric) = 1.1336753636833013562122105685483 absolute error = 7e-31 relative error = 6.1746071443742599566146375781074e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.524 y[1] (analytic) = 1.134175278117855171064759971788 y[1] (numeric) = 1.1341752781178551710647599717873 absolute error = 7e-31 relative error = 6.1718855410218272927041827975469e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.525 y[1] (analytic) = 1.1346760583770587160043865334936 y[1] (numeric) = 1.1346760583770587160043865334929 absolute error = 7e-31 relative error = 6.1691616283965549553996710976545e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.526 y[1] (analytic) = 1.135177703960131773559232189945 y[1] (numeric) = 1.1351777039601317735592321899443 absolute error = 7e-31 relative error = 6.1664354185076954643899838441283e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.527 y[1] (analytic) = 1.1356802143654288024600365822581 y[1] (numeric) = 1.1356802143654288024600365822574 absolute error = 7e-31 relative error = 6.1637069233536932609483882249937e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.528 y[1] (analytic) = 1.1361835890904394392856365218521 y[1] (numeric) = 1.1361835890904394392856365218513 absolute error = 8e-31 relative error = 7.0411156056252502804649358025984e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.529 y[1] (analytic) = 1.1366878276317890009732875357502 y[1] (numeric) = 1.1366878276317890009732875357495 absolute error = 7e-31 relative error = 6.1582431251894542618216484212527e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (analytic) = 1.1371929294852389881933049814358 y[1] (numeric) = 1.1371929294852389881933049814351 absolute error = 7e-31 relative error = 6.1555078461212517800769527393182e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.531 y[1] (analytic) = 1.1376988941456875895875213566629 y[1] (numeric) = 1.1376988941456875895875213566622 absolute error = 7e-31 relative error = 6.1527703296717960256578195323429e-29 % Correct digits = 30 h = 0.001 NO POLE memory used=41.9MB, alloc=4.1MB, time=1.96 TOP MAIN SOLVE Loop x[1] = 0.532 y[1] (analytic) = 1.138205721107170186871055565808 y[1] (numeric) = 1.1382057211071701868710555658073 absolute error = 7e-31 relative error = 6.1500305877841393073128527081147e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.533 y[1] (analytic) = 1.1387134098628598607968890410339 y[1] (numeric) = 1.1387134098628598607968890410332 absolute error = 7e-31 relative error = 6.1472886323899882928116782130902e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.534 y[1] (analytic) = 1.1392219599050678979827427537335 y[1] (numeric) = 1.1392219599050678979827427537328 absolute error = 7e-31 relative error = 6.1445444754096159829899698154393e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.535 y[1] (analytic) = 1.1397313707252442985997482894172 y[1] (numeric) = 1.1397313707252442985997482894165 absolute error = 7e-31 relative error = 6.1417981287517741342612803840597e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.536 y[1] (analytic) = 1.1402416418139782849224052974161 y[1] (numeric) = 1.1402416418139782849224052974154 absolute error = 7e-31 relative error = 6.1390496043136061297617879301126e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.537 y[1] (analytic) = 1.1407527726609988107393167654858 y[1] (numeric) = 1.1407527726609988107393167654851 absolute error = 7e-31 relative error = 6.1362989139805602992809458751891e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.538 y[1] (analytic) = 1.1412647627551750716241927086173 y[1] (numeric) = 1.1412647627551750716241927086167 absolute error = 6e-31 relative error = 5.2573252025368317326725405878347e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.539 y[1] (analytic) = 1.1417776115845170160666120010952 y[1] (numeric) = 1.1417776115845170160666120010946 absolute error = 6e-31 relative error = 5.2549637855251168071351778130157e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (analytic) = 1.1422913186361758574620312210822 y[1] (numeric) = 1.1422913186361758574620312210816 absolute error = 6e-31 relative error = 5.2526005425337762620971303683586e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.541 y[1] (analytic) = 1.1428058833964445869605285177651 y[1] (numeric) = 1.1428058833964445869605285177645 absolute error = 6e-31 relative error = 5.2502354837095046370314098066485e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.542 y[1] (analytic) = 1.1433213053507584871737696523608 y[1] (numeric) = 1.1433213053507584871737696523603 absolute error = 5e-31 relative error = 4.3732238493238386898938446529760e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.543 y[1] (analytic) = 1.1438375839836956467396825060591 y[1] (numeric) = 1.1438375839836956467396825060585 absolute error = 6e-31 relative error = 5.2454999590969240999866439216073e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.544 y[1] (analytic) = 1.1443547187789774757443254902696 y[1] (numeric) = 1.144354718778977475744325490269 absolute error = 6e-31 relative error = 5.2431295135497664864212406470351e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.545 y[1] (analytic) = 1.1448727092194692220004344373497 y[1] (numeric) = 1.1448727092194692220004344373491 absolute error = 6e-31 relative error = 5.2407572926518375714802702233059e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.546 y[1] (analytic) = 1.1453915547871804881821316933069 y[1] (numeric) = 1.1453915547871804881821316933063 absolute error = 6e-31 relative error = 5.2383833064971656596539142487983e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.547 y[1] (analytic) = 1.1459112549632657498152802778119 y[1] (numeric) = 1.1459112549632657498152802778113 absolute error = 6e-31 relative error = 5.2360075651690329299261524494922e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.548 y[1] (analytic) = 1.1464318092280248741229651212096 y[1] (numeric) = 1.146431809228024874122965121209 absolute error = 6e-31 relative error = 5.2336300787399053754702378822324e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.549 y[1] (analytic) = 1.1469532170609036397255825330915 y[1] (numeric) = 1.1469532170609036397255825330909 absolute error = 6e-31 relative error = 5.2312508572713631287322158726843e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (analytic) = 1.1474754779404942571950182023822 y[1] (numeric) = 1.1474754779404942571950182023816 absolute error = 6e-31 relative error = 5.2288699108140311718919433406936e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.551 y[1] (analytic) = 1.1479985913445358904623931748063 y[1] (numeric) = 1.1479985913445358904623931748057 absolute error = 6e-31 relative error = 5.2264872494075104326805218074122e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.552 y[1] (analytic) = 1.1485225567499151790788564000321 y[1] (numeric) = 1.1485225567499151790788564000315 absolute error = 6e-31 relative error = 5.2241028830803092655225657222645e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.553 y[1] (analytic) = 1.1490473736326667613289015877443 y[1] (numeric) = 1.1490473736326667613289015877437 absolute error = 6e-31 relative error = 5.2217168218497753179612879786377e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.554 y[1] (analytic) = 1.1495730414679737981956852593716 y[1] (numeric) = 1.149573041467973798195685259371 absolute error = 6e-31 relative error = 5.2193290757220277823139967863256e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.555 y[1] (analytic) = 1.150099559730168498177822030195 y[1] (numeric) = 1.1500995597301684981778220301944 absolute error = 6e-31 relative error = 5.2169396546918900324952626135123e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.556 y[1] (analytic) = 1.1506269278927326429571323050854 y[1] (numeric) = 1.1506269278927326429571323050848 absolute error = 6e-31 relative error = 5.2145485687428226459347308749160e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.557 y[1] (analytic) = 1.1511551454282981139168167201663 y[1] (numeric) = 1.1511551454282981139168167201657 absolute error = 6e-31 relative error = 5.2121558278468568105063255952322e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.558 y[1] (analytic) = 1.1516842118086474195095308122717 y[1] (numeric) = 1.1516842118086474195095308122711 absolute error = 6e-31 relative error = 5.2097614419645281163754115839608e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.559 y[1] (analytic) = 1.1522141265047142234748325481675 y[1] (numeric) = 1.1522141265047142234748325481669 absolute error = 6e-31 relative error = 5.2073654210448107326603578810569e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (analytic) = 1.1527448889865838739054744961337 y[1] (numeric) = 1.1527448889865838739054744961331 absolute error = 6e-31 relative error = 5.2049677750250519687948735306967e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.561 y[1] (analytic) = 1.153276498723493933162011573659 y[1] (numeric) = 1.1532764987234939331620115736584 absolute error = 6e-31 relative error = 5.2025685138309072204674682671903e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.562 y[1] (analytic) = 1.1538089551838347086351944566842 y[1] (numeric) = 1.1538089551838347086351944566837 absolute error = 5e-31 relative error = 4.3334730394802294166703546693700e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.563 y[1] (analytic) = 1.1543422578351497843556178880455 y[1] (numeric) = 1.154342257835149784355617888045 absolute error = 5e-31 relative error = 4.3314709879693617925439702026494e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.564 y[1] (analytic) = 1.1548764061441365534500922755128 y[1] (numeric) = 1.1548764061441365534500922755122 absolute error = 6e-31 relative error = 5.1953611382819769474098058454359e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.565 y[1] (analytic) = 1.1554113995766467514442061230971 y[1] (numeric) = 1.1554113995766467514442061230965 absolute error = 6e-31 relative error = 5.1929555154107485758361630690039e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.566 y[1] (analytic) = 1.1559472375976869904105459931083 y[1] (numeric) = 1.1559472375976869904105459931077 absolute error = 6e-31 relative error = 5.1905483268157825026792116930072e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.567 y[1] (analytic) = 1.1564839196714192939620398507875 y[1] (numeric) = 1.1564839196714192939620398507869 absolute error = 6e-31 relative error = 5.1881395823512380241244145293626e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.568 y[1] (analytic) = 1.157021445261161633089888798216 y[1] (numeric) = 1.1570214452611616330898887982154 absolute error = 6e-31 relative error = 5.1857292918591378998822229834952e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.569 y[1] (analytic) = 1.1575598138293884628455513596132 y[1] (numeric) = 1.1575598138293884628455513596125 absolute error = 7e-31 relative error = 6.0472037093641907651268103457614e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (analytic) = 1.158099024837731259866243636084 y[1] (numeric) = 1.1580990248377312598662436360833 absolute error = 7e-31 relative error = 6.0443881307825254812398369839999e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.571 y[1] (analytic) = 1.158639077746979060743417804361 y[1] (numeric) = 1.1586390777469790607434178043603 absolute error = 7e-31 relative error = 6.0415707828634482791587962381381e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.572 y[1] (analytic) = 1.1591799720170790012336805911064 y[1] (numeric) = 1.1591799720170790012336805911057 absolute error = 7e-31 relative error = 6.0387516770319632063640246899754e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.2MB, time=2.15 x[1] = 0.573 y[1] (analytic) = 1.1597217071071368563116125119018 y[1] (numeric) = 1.1597217071071368563116125119011 absolute error = 7e-31 relative error = 6.0359308246985579157805983804178e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.574 y[1] (analytic) = 1.1602642824754175810639478221502 y[1] (numeric) = 1.1602642824754175810639478221495 absolute error = 7e-31 relative error = 6.0331082372591335837961135382660e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.575 y[1] (analytic) = 1.1608076975793458524245742857562 y[1] (numeric) = 1.1608076975793458524245742857555 absolute error = 7e-31 relative error = 6.0302839260949352737401095989815e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.576 y[1] (analytic) = 1.1613519518755066117498110266296 y[1] (numeric) = 1.1613519518755066117498110266289 absolute error = 7e-31 relative error = 6.0274579025724827445131170685059e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.577 y[1] (analytic) = 1.1618970448196456082334218877795 y[1] (numeric) = 1.1618970448196456082334218877788 absolute error = 7e-31 relative error = 6.0246301780435017040426391221705e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.578 y[1] (analytic) = 1.162442975866669943160820883031 y[1] (numeric) = 1.1624429758666699431608208830303 absolute error = 7e-31 relative error = 6.0218007638448555072327666657584e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.579 y[1] (analytic) = 1.1629897444706486150019254872046 y[1] (numeric) = 1.1629897444706486150019254872039 absolute error = 7e-31 relative error = 6.0189696712984772980635820284332e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (analytic) = 1.16353735008481306534211267195 y[1] (numeric) = 1.1635373500848130653421126719493 absolute error = 7e-31 relative error = 6.0161369117113025954860266050349e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.581 y[1] (analytic) = 1.1640857921615577256507317563242 y[1] (numeric) = 1.1640857921615577256507317563235 absolute error = 7e-31 relative error = 6.0133024963752023227474927136189e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.582 y[1] (analytic) = 1.1646350701524405648866273036464 y[1] (numeric) = 1.1646350701524405648866273036457 absolute error = 7e-31 relative error = 6.0104664365669162797730497745187e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.583 y[1] (analytic) = 1.165185183508183637940124459152 y[1] (numeric) = 1.1651851835081836379401244591513 absolute error = 7e-31 relative error = 6.0076287435479870582169297370926e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.584 y[1] (analytic) = 1.1657361316786736349109282865074 y[1] (numeric) = 1.1657361316786736349109282865067 absolute error = 7e-31 relative error = 6.0047894285646943987886765630965e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.585 y[1] (analytic) = 1.1662879141129624312213878253303 y[1] (numeric) = 1.1662879141129624312213878253296 absolute error = 7e-31 relative error = 6.0019485028479899904482096008630e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.586 y[1] (analytic) = 1.1668405302592676385645747564984 y[1] (numeric) = 1.1668405302592676385645747564978 absolute error = 6e-31 relative error = 5.1420908379543708951891093665538e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.587 y[1] (analytic) = 1.1673939795649731566866257272142 y[1] (numeric) = 1.1673939795649731566866257272135 absolute error = 7e-31 relative error = 5.9962618640611243090382222703211e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.588 y[1] (analytic) = 1.1679482614766297260027965535271 y[1] (numeric) = 1.1679482614766297260027965535265 absolute error = 6e-31 relative error = 5.1372138628934104505776097184393e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.589 y[1] (analytic) = 1.1685033754399554810466756843086 y[1] (numeric) = 1.168503375439955481046675684308 absolute error = 6e-31 relative error = 5.1347733571937079921315488968371e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (analytic) = 1.1690593208998365047520034775093 y[1] (numeric) = 1.1690593208998365047520034775087 absolute error = 6e-31 relative error = 5.1323315187990124785929213435834e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.591 y[1] (analytic) = 1.1696160973003273835665430069271 y[1] (numeric) = 1.1696160973003273835665430069265 absolute error = 6e-31 relative error = 5.1298883572558714978739495550386e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.592 y[1] (analytic) = 1.1701737040846517633974472856612 y[1] (numeric) = 1.1701737040846517633974472856606 absolute error = 6e-31 relative error = 5.1274438820973136768240090330838e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.593 y[1] (analytic) = 1.1707321406952029063875669609314 y[1] (numeric) = 1.1707321406952029063875669609308 absolute error = 6e-31 relative error = 5.1249981028427958112373352553260e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.594 y[1] (analytic) = 1.1712914065735442485221417040005 y[1] (numeric) = 1.1712914065735442485221417039998 absolute error = 7e-31 relative error = 5.9763095338311754329418237733815e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.595 y[1] (analytic) = 1.1718515011604099580653176885558 y[1] (numeric) = 1.1718515011604099580653176885551 absolute error = 7e-31 relative error = 5.9734531150647889440279138986546e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.596 y[1] (analytic) = 1.172412423895705494825932721079 y[1] (numeric) = 1.1724124238957054948259327210783 absolute error = 7e-31 relative error = 5.9705952080756014513378289800118e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.597 y[1] (analytic) = 1.1729741742185081702520097574644 y[1] (numeric) = 1.1729741742185081702520097574637 absolute error = 7e-31 relative error = 5.9677358239057026029381231833274e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.598 y[1] (analytic) = 1.1735367515670677083533987114403 y[1] (numeric) = 1.1735367515670677083533987114397 absolute error = 6e-31 relative error = 5.1127499773551826217646126660082e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.599 y[1] (analytic) = 1.1741001553788068074520056321979 y[1] (numeric) = 1.1741001553788068074520056321973 absolute error = 6e-31 relative error = 5.1102965726669075094152614763491e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 1.1746643850903217027590475010446 y[1] (numeric) = 1.174664385090321702759047501044 absolute error = 6e-31 relative error = 5.1078419301344962624760199534449e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.601 y[1] (analytic) = 1.1752294401373827297787700698751 y[1] (numeric) = 1.1752294401373827297787700698744 absolute error = 7e-31 relative error = 5.9562837356948014177158104285391e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.602 y[1] (analytic) = 1.1757953199549348885380653377883 y[1] (numeric) = 1.1757953199549348885380653377876 absolute error = 7e-31 relative error = 5.9534171306858845182116821346211e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.603 y[1] (analytic) = 1.1763620239770984086414244362806 y[1] (numeric) = 1.1763620239770984086414244362799 absolute error = 7e-31 relative error = 5.9505491144078934021907045895995e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.604 y[1] (analytic) = 1.1769295516371693151506608681084 y[1] (numeric) = 1.1769295516371693151506608681077 absolute error = 7e-31 relative error = 5.9476796977887430071202766638176e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.605 y[1] (analytic) = 1.177497902367619995288838220145 y[1] (numeric) = 1.1774979023676199952888382201444 absolute error = 6e-31 relative error = 5.0955504786341213855092600908278e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.606 y[1] (analytic) = 1.1780670756000997659678356463513 y[1] (numeric) = 1.1780670756000997659678356463507 absolute error = 6e-31 relative error = 5.0930886061336012802206322675593e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.607 y[1] (analytic) = 1.1786370707654354421389835933405 y[1] (numeric) = 1.1786370707654354421389835933399 absolute error = 6e-31 relative error = 5.0906255613557570972035051588774e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.608 y[1] (analytic) = 1.1792078872936319059662014179512 y[1] (numeric) = 1.1792078872936319059662014179506 absolute error = 6e-31 relative error = 5.0881613536103778483935949200309e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.609 y[1] (analytic) = 1.1797795246138726768210677237362 y[1] (numeric) = 1.1797795246138726768210677237355 absolute error = 7e-31 relative error = 5.9333119908916997662156184936013e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (analytic) = 1.1803519821545204820992534213452 y[1] (numeric) = 1.1803519821545204820992534213445 absolute error = 7e-31 relative error = 5.9304344007816699013542379816472e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.611 y[1] (analytic) = 1.1809252593431178288577466964165 y[1] (numeric) = 1.1809252593431178288577466964158 absolute error = 7e-31 relative error = 5.9275554863596579494337409217164e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.612 y[1] (analytic) = 1.1814993556063875762722982477992 y[1] (numeric) = 1.1814993556063875762722982477985 absolute error = 7e-31 relative error = 5.9246752584197141011951016121514e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.613 y[1] (analytic) = 1.1820742703702335089145143387088 y[1] (numeric) = 1.1820742703702335089145143387081 absolute error = 7e-31 relative error = 5.9217937277389123181839160659857e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.614 y[1] (analytic) = 1.1826500030597409108480243837716 y[1] (numeric) = 1.1826500030597409108480243837709 absolute error = 7e-31 relative error = 5.9189109050772977263522467860761e-29 % Correct digits = 30 h = 0.001 memory used=49.5MB, alloc=4.2MB, time=2.33 NO POLE TOP MAIN SOLVE Loop x[1] = 0.615 y[1] (analytic) = 1.1832265530991771405431489758368 y[1] (numeric) = 1.1832265530991771405431489758361 absolute error = 7e-31 relative error = 5.9160268011778344349601067913698e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.616 y[1] (analytic) = 1.1838039199119922066094934379379 y[1] (numeric) = 1.1838039199119922066094934379372 absolute error = 7e-31 relative error = 5.9131414267663537800885964733047e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.617 y[1] (analytic) = 1.1843821029208193443458911678558 y[1] (numeric) = 1.1843821029208193443458911678551 absolute error = 7e-31 relative error = 5.9102547925515029920686558940489e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.618 y[1] (analytic) = 1.1849611015474755931071202253905 y[1] (numeric) = 1.1849611015474755931071202253898 absolute error = 7e-31 relative error = 5.9073669092246942861214098627879e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.619 y[1] (analytic) = 1.1855409152129623744868157956707 y[1] (numeric) = 1.1855409152129623744868157956701 absolute error = 6e-31 relative error = 5.0609809606800466075698544295062e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (analytic) = 1.1861215433374660713160003456393 y[1] (numeric) = 1.1861215433374660713160003456387 absolute error = 6e-31 relative error = 5.0585035182123209197716445617588e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.621 y[1] (analytic) = 1.1867029853403586074766524752305 y[1] (numeric) = 1.1867029853403586074766524752299 absolute error = 6e-31 relative error = 5.0560250324803374119581369023158e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.622 y[1] (analytic) = 1.1872852406401980285297346497202 y[1] (numeric) = 1.1872852406401980285297346497196 absolute error = 6e-31 relative error = 5.0535455125886430844162295491896e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.623 y[1] (analytic) = 1.1878683086547290831570991852689 y[1] (numeric) = 1.1878683086547290831570991852683 absolute error = 6e-31 relative error = 5.0510649676267993040679411865142e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.624 y[1] (analytic) = 1.1884521888008838054166910457999 y[1] (numeric) = 1.1884521888008838054166910457993 absolute error = 6e-31 relative error = 5.0485834066693403313445680147629e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.625 y[1] (analytic) = 1.1890368804947820978104651960589 y[1] (numeric) = 1.1890368804947820978104651960583 absolute error = 6e-31 relative error = 5.0461008387757322054025735526968e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.626 y[1] (analytic) = 1.189622383151732315164435442986 y[1] (numeric) = 1.1896223831517323151644354429854 absolute error = 6e-31 relative error = 5.0436172729903319870250293655194e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.627 y[1] (analytic) = 1.1902086961862318493202708853993 y[1] (numeric) = 1.1902086961862318493202708853988 absolute error = 5e-31 relative error = 4.2009439319519561321217375794984e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.628 y[1] (analytic) = 1.1907958190119677146378552804441 y[1] (numeric) = 1.1907958190119677146378552804436 absolute error = 5e-31 relative error = 4.1988726532048304834413852704304e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.629 y[1] (analytic) = 1.1913837510418171343082238242947 y[1] (numeric) = 1.1913837510418171343082238242942 absolute error = 5e-31 relative error = 4.1968005654162240014394489379628e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (analytic) = 1.1919724916878481274762910342229 y[1] (numeric) = 1.1919724916878481274762910342225 absolute error = 4e-31 relative error = 3.3557821408579231533561443905488e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.631 y[1] (analytic) = 1.1925620403613200971727826093538 y[1] (numeric) = 1.1925620403613200971727826093534 absolute error = 4e-31 relative error = 3.3541231941175050998369687084415e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.632 y[1] (analytic) = 1.1931523964726844190547833382246 y[1] (numeric) = 1.1931523964726844190547833382242 absolute error = 4e-31 relative error = 3.3524636180803031989933789134888e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.633 y[1] (analytic) = 1.1937435594315850309543123126502 y[1] (numeric) = 1.1937435594315850309543123126497 absolute error = 5e-31 relative error = 4.1885042733807992454438686999071e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.634 y[1] (analytic) = 1.1943355286468590232343358993664 y[1] (numeric) = 1.194335528646859023234335899366 absolute error = 4e-31 relative error = 3.3491426019385541445917069095722e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.635 y[1] (analytic) = 1.1949283035265372299516281134903 y[1] (numeric) = 1.1949283035265372299516281134899 absolute error = 4e-31 relative error = 3.3474811737197813578563813690646e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.636 y[1] (analytic) = 1.1955218834778448208258872309833 y[1] (numeric) = 1.1955218834778448208258872309829 absolute error = 4e-31 relative error = 3.3458191399757235999857279459849e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.637 y[1] (analytic) = 1.1961162679072018940145166710524 y[1] (numeric) = 1.1961162679072018940145166710519 absolute error = 5e-31 relative error = 4.1801956332792843825923999846451e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.638 y[1] (analytic) = 1.1967114562202240696924773737563 y[1] (numeric) = 1.1967114562202240696924773737558 absolute error = 5e-31 relative error = 4.1781165994619492961691804054084e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.639 y[1] (analytic) = 1.1973074478217230844366180930148 y[1] (numeric) = 1.1973074478217230844366180930144 absolute error = 4e-31 relative error = 3.3408294647103813659662718753411e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (analytic) = 1.1979042421157073864138892207397 y[1] (numeric) = 1.1979042421157073864138892207392 absolute error = 5e-31 relative error = 4.1739563349146587473903684267929e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.641 y[1] (analytic) = 1.198501838505382731372844953923 y[1] (numeric) = 1.1985018385053827313728449539225 absolute error = 5e-31 relative error = 4.1718751188862226488057071573710e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.642 y[1] (analytic) = 1.1991002363931527794378378132311 y[1] (numeric) = 1.1991002363931527794378378132306 absolute error = 5e-31 relative error = 4.1697931901338014728052538196133e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.643 y[1] (analytic) = 1.1996994351806196927053087189588 y[1] (numeric) = 1.1996994351806196927053087189584 absolute error = 4e-31 relative error = 3.3341684447803240984905863351428e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.644 y[1] (analytic) = 1.2002994342685847336415750281037 y[1] (numeric) = 1.2002994342685847336415750281033 absolute error = 4e-31 relative error = 3.3325017789727133182456694023846e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.645 y[1] (analytic) = 1.2009002330570488642815181348221 y[1] (numeric) = 1.2009002330570488642815181348217 absolute error = 4e-31 relative error = 3.3308345605175510622228717037482e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.646 y[1] (analytic) = 1.2015018309452133462275714356296 y[1] (numeric) = 1.2015018309452133462275714356292 absolute error = 4e-31 relative error = 3.3291667952376128410255819872027e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.647 y[1] (analytic) = 1.2021042273314803414484086604078 y[1] (numeric) = 1.2021042273314803414484086604074 absolute error = 4e-31 relative error = 3.3274984889450851791368164739087e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.648 y[1] (analytic) = 1.2027074216134535138767317705792 y[1] (numeric) = 1.2027074216134535138767317705788 absolute error = 4e-31 relative error = 3.3258296474415435707381181270203e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.649 y[1] (analytic) = 1.203311413187938631805556826712 y[1] (numeric) = 1.2033114131879386318055568267117 absolute error = 3e-31 relative error = 2.4931202073884479971242730956549e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (analytic) = 1.2039162014509441710823954293201 y[1] (numeric) = 1.2039162014509441710823954293198 absolute error = 3e-31 relative error = 2.4918677864659009988563238366354e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.651 y[1] (analytic) = 1.2045217857976819191007285387257 y[1] (numeric) = 1.2045217857976819191007285387254 absolute error = 3e-31 relative error = 2.4906149771407259896867440652539e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.652 y[1] (analytic) = 1.2051281656225675795881686825627 y[1] (numeric) = 1.2051281656225675795881686825624 absolute error = 3e-31 relative error = 2.4893617837321095715845412331694e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.653 y[1] (analytic) = 1.2057353403192213781907057628076 y[1] (numeric) = 1.2057353403192213781907057628073 absolute error = 3e-31 relative error = 2.4881082105511999573142106258838e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.654 y[1] (analytic) = 1.2063433092804686688524308781435 y[1] (numeric) = 1.2063433092804686688524308781432 absolute error = 3e-31 relative error = 2.4868542619010914541696242539657e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.655 y[1] (analytic) = 1.2069520718983405409901317819836 y[1] (numeric) = 1.2069520718983405409901317819833 absolute error = 3e-31 relative error = 2.4855999420768091157695019005571e-29 % Correct digits = 30 h = 0.001 NO POLE memory used=53.4MB, alloc=4.2MB, time=2.51 TOP MAIN SOLVE Loop x[1] = 0.656 y[1] (analytic) = 1.207561627564074427462152801609 y[1] (numeric) = 1.2075616275640744274621528016087 absolute error = 3e-31 relative error = 2.4843452553652935615032641631607e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.657 y[1] (analytic) = 1.2081719756681147133309112496125 y[1] (numeric) = 1.2081719756681147133309112496122 absolute error = 3e-31 relative error = 2.4830902060453859632137168297007e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.658 y[1] (analytic) = 1.2087831156001133454184615651814 y[1] (numeric) = 1.2087831156001133454184615651811 absolute error = 3e-31 relative error = 2.4818347983878131987006919267213e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.659 y[1] (analytic) = 1.2093950467489304426544976297072 y[1] (numeric) = 1.2093950467489304426544976297068 absolute error = 4e-31 relative error = 3.3074387155402308955032976106020e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (analytic) = 1.2100077685026349072161829087698 y[1] (numeric) = 1.2100077685026349072161829087694 absolute error = 4e-31 relative error = 3.3057639001358937298794168667540e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.661 y[1] (analytic) = 1.2106212802485050364591972807178 y[1] (numeric) = 1.2106212802485050364591972807174 absolute error = 4e-31 relative error = 3.3040886239658015395507994988072e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.662 y[1] (analytic) = 1.2112355813730291356393886208484 y[1] (numeric) = 1.211235581373029135639388620848 absolute error = 4e-31 relative error = 3.3024128926807870690507009995025e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.663 y[1] (analytic) = 1.2118506712619061314244164195866 y[1] (numeric) = 1.2118506712619061314244164195861 absolute error = 5e-31 relative error = 4.1259208899009604304314932453359e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.664 y[1] (analytic) = 1.2124665493000461861947739230711 y[1] (numeric) = 1.2124665493000461861947739230706 absolute error = 5e-31 relative error = 4.1238251091434127503234496926931e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.665 y[1] (analytic) = 1.2130832148715713131335744951767 y[1] (numeric) = 1.2130832148715713131335744951763 absolute error = 4e-31 relative error = 3.2973830244807060263625028056294e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.666 y[1] (analytic) = 1.213700667359815992104487111237 y[1] (numeric) = 1.2137006673598159921044871112365 absolute error = 5e-31 relative error = 4.1196319112821996634337277647635e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.667 y[1] (analytic) = 1.2143189061473277863172051055833 y[1] (numeric) = 1.2143189061473277863172051055829 absolute error = 4e-31 relative error = 3.2940276065459679210988262948356e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.668 y[1] (analytic) = 1.2149379306158679597798315074841 y[1] (numeric) = 1.2149379306158679597798315074836 absolute error = 5e-31 relative error = 4.1154365782830028781219763072688e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.669 y[1] (analytic) = 1.2155577401464120955375635131482 y[1] (numeric) = 1.2155577401464120955375635131477 absolute error = 5e-31 relative error = 4.1133381285513903641831371387316e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (analytic) = 1.2161783341191507146970578551619 y[1] (numeric) = 1.2161783341191507146970578551614 absolute error = 5e-31 relative error = 4.1112391659413848060604802413298e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.671 y[1] (analytic) = 1.2167997119134898962358580450436 y[1] (numeric) = 1.2167997119134898962358580450431 absolute error = 5e-31 relative error = 4.1091396973929281317933259715530e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.672 y[1] (analytic) = 1.2174218729080518975962636795423 y[1] (numeric) = 1.2174218729080518975962636795418 absolute error = 5e-31 relative error = 4.1070397298321208244422740028576e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.673 y[1] (analytic) = 1.2180448164806757760630212168607 y[1] (numeric) = 1.2180448164806757760630212168602 absolute error = 5e-31 relative error = 4.1049392701712012627775806832191e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.674 y[1] (analytic) = 1.2186685420084180109242148451658 y[1] (numeric) = 1.2186685420084180109242148451653 absolute error = 5e-31 relative error = 4.1028383253085253284213071064361e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.675 y[1] (analytic) = 1.219293048867553126414735282546 y[1] (numeric) = 1.2192930488675531264147352825455 absolute error = 5e-31 relative error = 4.1007369021285462786909151181636e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.676 y[1] (analytic) = 1.2199183364335743154417035649992 y[1] (numeric) = 1.2199183364335743154417035649987 absolute error = 5e-31 relative error = 4.0986350075017948843888905423310e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.677 y[1] (analytic) = 1.2205444040811940640912260970796 y[1] (numeric) = 1.2205444040811940640912260970791 absolute error = 5e-31 relative error = 4.0965326482848598317799168866004e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.678 y[1] (analytic) = 1.2211712511843447769158564585004 y[1] (numeric) = 1.2211712511843447769158564584999 absolute error = 5e-31 relative error = 4.0944298313203683879941085350578e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.679 y[1] (analytic) = 1.221798877116179403002138679282 y[1] (numeric) = 1.2217988771161794030021386792815 absolute error = 5e-31 relative error = 4.0923265634369673290918398294936e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (analytic) = 1.2224272812490720628176059159557 y[1] (numeric) = 1.2224272812490720628176059159552 absolute error = 5e-31 relative error = 4.0902228514493041300227753432705e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.681 y[1] (analytic) = 1.2230564629546186758366076818755 y[1] (numeric) = 1.2230564629546186758366076818751 absolute error = 4e-31 relative error = 3.2704949617264067325670535428890e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.682 y[1] (analytic) = 1.223686421603637588944338005864 y[1] (numeric) = 1.2236864216036375889443380058635 absolute error = 5e-31 relative error = 4.0860141223496736724778346327066e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.683 y[1] (analytic) = 1.2243171565661702056184361152149 y[1] (numeric) = 1.2243171565661702056184361152145 absolute error = 4e-31 relative error = 3.2671272950374713752577929542083e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.684 y[1] (analytic) = 1.2249486672114816158875304615069 y[1] (numeric) = 1.2249486672114816158875304615064 absolute error = 5e-31 relative error = 4.0818036982579724364537033962239e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.685 y[1] (analytic) = 1.2255809529080612270660961307334 y[1] (numeric) = 1.225580952908061227066096130733 absolute error = 4e-31 relative error = 3.2637582939819610044980463922126e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.686 y[1] (analytic) = 1.2262140130236233952649949029474 y[1] (numeric) = 1.226214013023623395264994902947 absolute error = 4e-31 relative error = 3.2620733065484375221342519223891e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.687 y[1] (analytic) = 1.2268478469251080576770664509304 y[1] (numeric) = 1.22684784692510805767706645093 absolute error = 4e-31 relative error = 3.2603880016787255202087889249232e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.688 y[1] (analytic) = 1.2274824539786813656371383923497 y[1] (numeric) = 1.2274824539786813656371383923493 absolute error = 4e-31 relative error = 3.2587023847344306598434998897460e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.689 y[1] (analytic) = 1.2281178335497363184558221354451 y[1] (numeric) = 1.2281178335497363184558221354447 absolute error = 4e-31 relative error = 3.2570164610658330547535159701685e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (analytic) = 1.2287539850028933980264606845022 y[1] (numeric) = 1.2287539850028933980264606845019 absolute error = 3e-31 relative error = 2.4414976770089057130827812424009e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.691 y[1] (analytic) = 1.2293909077020012042045937982186 y[1] (numeric) = 1.2293909077020012042045937982183 absolute error = 3e-31 relative error = 2.4402327861751084560165392656387e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.692 y[1] (analytic) = 1.2300286010101370909593051215486 y[1] (numeric) = 1.2300286010101370909593051215483 absolute error = 3e-31 relative error = 2.4389676772851527887428003524982e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.693 y[1] (analytic) = 1.2306670642896078032958151397345 y[1] (numeric) = 1.2306670642896078032958151397342 absolute error = 3e-31 relative error = 2.4377023543176762680284266950833e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.694 y[1] (analytic) = 1.2313062969019501149486830319832 y[1] (numeric) = 1.2313062969019501149486830319829 absolute error = 3e-31 relative error = 2.4364368212427751031453144646550e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.695 y[1] (analytic) = 1.2319462982079314668449797316401 y[1] (numeric) = 1.2319462982079314668449797316398 absolute error = 3e-31 relative error = 2.4351710820219951705205660616905e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.696 y[1] (analytic) = 1.2325870675675506063367937297397 y[1] (numeric) = 1.2325870675675506063367937297394 absolute error = 3e-31 relative error = 2.4339051406083231779370170704378e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.2MB, time=2.70 x[1] = 0.697 y[1] (analytic) = 1.2332286043400382272024303894814 y[1] (numeric) = 1.2332286043400382272024303894811 absolute error = 3e-31 relative error = 2.4326390009461779777975132480580e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.698 y[1] (analytic) = 1.2338709078838576104156647704838 y[1] (numeric) = 1.2338709078838576104156647704835 absolute error = 3e-31 relative error = 2.4313726669714020289650080085344e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.699 y[1] (analytic) = 1.234513977556705265682407193618 y[1] (numeric) = 1.2345139775567052656824071936177 absolute error = 3e-31 relative error = 2.4301061426112530066892492461070e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 1.2351578127155115737441400098081 y[1] (numeric) = 1.2351578127155115737441400098078 absolute error = 3e-31 relative error = 2.4288394317843955601295458894180e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.701 y[1] (analytic) = 1.2358024127164414294474832694162 y[1] (numeric) = 1.2358024127164414294474832694158 absolute error = 4e-31 relative error = 3.2367633845345242893091322568919e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.702 y[1] (analytic) = 1.2364477769148948855792462226979 y[1] (numeric) = 1.2364477769148948855792462226976 absolute error = 3e-31 relative error = 2.4263054663622004347171513602455e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.703 y[1] (analytic) = 1.2370939046655077974663208163335 y[1] (numeric) = 1.2370939046655077974663208163332 absolute error = 3e-31 relative error = 2.4250382195611547979369945722918e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.704 y[1] (analytic) = 1.2377407953221524683397725861917 y[1] (numeric) = 1.2377407953221524683397725861914 absolute error = 3e-31 relative error = 2.4237708018819693613506967360231e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.705 y[1] (analytic) = 1.2383884482379382954624835822915 y[1] (numeric) = 1.2383884482379382954624835822912 absolute error = 3e-31 relative error = 2.4225032172002251378777362360165e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.706 y[1] (analytic) = 1.2390368627652124170197011983717 y[1] (numeric) = 1.2390368627652124170197011983714 absolute error = 3e-31 relative error = 2.4212354693828637313775965007924e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.707 y[1] (analytic) = 1.2396860382555603597718460155734 y[1] (numeric) = 1.2396860382555603597718460155731 absolute error = 3e-31 relative error = 2.4199675622881801135082522466597e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.708 y[1] (analytic) = 1.2403359740598066874689310074817 y[1] (numeric) = 1.2403359740598066874689310074814 absolute error = 3e-31 relative error = 2.4186994997658155442133827066011e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.709 y[1] (analytic) = 1.2409866695280156500259436921618 y[1] (numeric) = 1.2409866695280156500259436921615 absolute error = 3e-31 relative error = 2.4174312856567506353373229050352e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (analytic) = 1.2416381240094918334585420558604 y[1] (numeric) = 1.2416381240094918334585420558602 absolute error = 2e-31 relative error = 1.6107752825288657045771413341951e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.711 y[1] (analytic) = 1.2422903368527808105784143127322 y[1] (numeric) = 1.242290336852780810578414312732 absolute error = 2e-31 relative error = 1.6099296119993989235258451985661e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.712 y[1] (analytic) = 1.2429433074056697924476518052839 y[1] (numeric) = 1.2429433074056697924476518052837 absolute error = 2e-31 relative error = 1.6090838480594057290554057304349e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.713 y[1] (analytic) = 1.2435970350151882805914835912195 y[1] (numeric) = 1.2435970350151882805914835912193 absolute error = 2e-31 relative error = 1.6082379932464004548713717197937e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.714 y[1] (analytic) = 1.2442515190276087199687205040045 y[1] (numeric) = 1.2442515190276087199687205040043 absolute error = 2e-31 relative error = 1.6073920500921019675356004895992e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.715 y[1] (analytic) = 1.2449067587884471526992557167609 y[1] (numeric) = 1.2449067587884471526992557167607 absolute error = 2e-31 relative error = 1.6065460211224296076684178808225e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.716 y[1] (analytic) = 1.2455627536424638725479680820458 y[1] (numeric) = 1.2455627536424638725479680820456 absolute error = 2e-31 relative error = 1.6056999088574992242125047334148e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.717 y[1] (analytic) = 1.2462195029336640801643737636656 y[1] (numeric) = 1.2462195029336640801643737636654 absolute error = 2e-31 relative error = 1.6048537158116193014193154282940e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.718 y[1] (analytic) = 1.2468770060052985390773709209283 y[1] (numeric) = 1.2468770060052985390773709209281 absolute error = 2e-31 relative error = 1.6040074444932871782182487768900e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.719 y[1] (analytic) = 1.2475352621998642324444214506442 y[1] (numeric) = 1.2475352621998642324444214506441 absolute error = 1e-31 relative error = 8.0158054870259267981411023825437e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = 1.248194270859105020554513037748 y[1] (numeric) = 1.2481942708591050205545130377479 absolute error = 1e-31 relative error = 8.0115733852208895993536471220539e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.721 y[1] (analytic) = 1.2488540313240122990842440116342 y[1] (numeric) = 1.248854031324012299084244011634 absolute error = 2e-31 relative error = 1.6014681859013069968429673334363e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.722 y[1] (analytic) = 1.249514542934825658106372752177 y[1] (numeric) = 1.2495145429348256581063727521768 absolute error = 2e-31 relative error = 1.6006216264617893776089922494223e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.723 y[1] (analytic) = 1.2501758050310335418501726369398 y[1] (numeric) = 1.2501758050310335418501726369396 absolute error = 2e-31 relative error = 1.5997750012050131745664716675242e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.724 y[1] (analytic) = 1.2508378169513739092129327692739 y[1] (numeric) = 1.2508378169513739092129327692738 absolute error = 1e-31 relative error = 7.9946415630226729597299995631939e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.725 y[1] (analytic) = 1.2515005780338348950219439758613 y[1] (numeric) = 1.2515005780338348950219439758612 absolute error = 1e-31 relative error = 7.9904078156403739114975360999916e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.726 y[1] (analytic) = 1.2521640876156554720463088117698 y[1] (numeric) = 1.2521640876156554720463088117697 absolute error = 1e-31 relative error = 7.9861737761875839631690222852184e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.727 y[1] (analytic) = 1.2528283450333261137579135612673 y[1] (numeric) = 1.2528283450333261137579135612672 absolute error = 1e-31 relative error = 7.9819394569445129992242379904209e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.728 y[1] (analytic) = 1.2534933496225894578408994734763 y[1] (numeric) = 1.2534933496225894578408994734762 absolute error = 1e-31 relative error = 7.9777048701621511755392991501229e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.729 y[1] (analytic) = 1.2541591007184409704489697234547 y[1] (numeric) = 1.2541591007184409704489697234546 absolute error = 1e-31 relative error = 7.9734700280622549843900823070646e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (analytic) = 1.2548255976551296112098678414497 y[1] (numeric) = 1.2548255976551296112098678414496 absolute error = 1e-31 relative error = 7.9692349428373337607798927945875e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.731 y[1] (analytic) = 1.2554928397661584989763626059028 y[1] (numeric) = 1.2554928397661584989763626059028 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.732 y[1] (analytic) = 1.2561608263842855783230736492765 y[1] (numeric) = 1.2561608263842855783230736492764 absolute error = 1e-31 relative error = 7.9607640916361398832159154700270e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.733 y[1] (analytic) = 1.2568295568415242867884712799312 y[1] (numeric) = 1.2568295568415242867884712799311 absolute error = 1e-31 relative error = 7.9565283498985348137686405797286e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.734 y[1] (analytic) = 1.2574990304691442228613832781104 y[1] (numeric) = 1.2574990304691442228613832781103 absolute error = 1e-31 relative error = 7.9522924135132159550817850781091e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.735 y[1] (analytic) = 1.2581692465976718147113406795812 y[1] (numeric) = 1.2581692465976718147113406795811 absolute error = 1e-31 relative error = 7.9480562945262697758093113543968e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.736 y[1] (analytic) = 1.2588402045568909896620938166407 y[1] (numeric) = 1.2588402045568909896620938166407 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.737 y[1] (analytic) = 1.2595119036758438444076291430284 y[1] (numeric) = 1.2595119036758438444076291430284 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.738 y[1] (analytic) = 1.2601843432828313159700166267826 y[1] (numeric) = 1.2601843432828313159700166267826 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE memory used=61.0MB, alloc=4.2MB, time=2.88 TOP MAIN SOLVE Loop x[1] = 0.739 y[1] (analytic) = 1.2608575227054138533984167532507 y[1] (numeric) = 1.2608575227054138533984167532507 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (analytic) = 1.2615314412704120902085754393012 y[1] (numeric) = 1.2615314412704120902085754393012 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.741 y[1] (analytic) = 1.2622060983039075175621344192991 y[1] (numeric) = 1.2622060983039075175621344192992 absolute error = 1e-31 relative error = 7.9226364168557924634634371286759e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.742 y[1] (analytic) = 1.2628814931312431581850839235906 y[1] (numeric) = 1.2628814931312431581850839235907 absolute error = 1e-31 relative error = 7.9183993544838211204563225277695e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.743 y[1] (analytic) = 1.2635576250770242410246837310994 y[1] (numeric) = 1.2635576250770242410246837310995 absolute error = 1e-31 relative error = 7.9141622048226076454782195269688e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.744 y[1] (analytic) = 1.2642344934651188766441779391716 y[1] (numeric) = 1.2642344934651188766441779391718 absolute error = 2e-31 relative error = 1.5819849959308054695077199984045e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.745 y[1] (analytic) = 1.2649120976186587333546280560096 y[1] (numeric) = 1.2649120976186587333546280560097 absolute error = 1e-31 relative error = 7.9056876907305577511251824482494e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.746 y[1] (analytic) = 1.2655904368600397140831882839174 y[1] (numeric) = 1.2655904368600397140831882839175 absolute error = 1e-31 relative error = 7.9014503497752719271787915695189e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.747 y[1] (analytic) = 1.266269510510922633977146125141 y[1] (numeric) = 1.2662695105109226339771461251411 absolute error = 1e-31 relative error = 7.8972129684818322357495484589859e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.748 y[1] (analytic) = 1.2669493178922338987430507063167 y[1] (numeric) = 1.2669493178922338987430507063169 absolute error = 2e-31 relative error = 1.5785951117028968957158391775702e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.749 y[1] (analytic) = 1.2676298583241661837202504824584 y[1] (numeric) = 1.2676298583241661837202504824586 absolute error = 2e-31 relative error = 1.5777476263016104919706956216424e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (analytic) = 1.2683111311261791136881612469999 y[1] (numeric) = 1.2683111311261791136881612470001 absolute error = 2e-31 relative error = 1.5769001398135865906735341046468e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.751 y[1] (analytic) = 1.2689931356169999434065846406836 y[1] (numeric) = 1.2689931356169999434065846406837 absolute error = 1e-31 relative error = 7.8802632727700910743475900236224e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.752 y[1] (analytic) = 1.2696758711146242388883966190315 y[1] (numeric) = 1.2696758711146242388883966190317 absolute error = 2e-31 relative error = 1.5752051728322112108335423649853e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.753 y[1] (analytic) = 1.270359336936316559403924605769 y[1] (numeric) = 1.2703593369363165594039246057692 absolute error = 2e-31 relative error = 1.5743576969515834832414745612493e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.754 y[1] (analytic) = 1.2710435323986111402163313278786 y[1] (numeric) = 1.2710435323986111402163313278788 absolute error = 2e-31 relative error = 1.5735102292096643102170908596163e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.755 y[1] (analytic) = 1.2717284568173125760473225969591 y[1] (numeric) = 1.2717284568173125760473225969593 absolute error = 2e-31 relative error = 1.5726627718980937379026817271109e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.756 y[1] (analytic) = 1.2724141095074965052724955712377 y[1] (numeric) = 1.2724141095074965052724955712379 absolute error = 2e-31 relative error = 1.5718153273026220542012046446614e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.757 y[1] (analytic) = 1.2731004897835102948456433029448 y[1] (numeric) = 1.273100489783510294845643302945 absolute error = 2e-31 relative error = 1.5709678977031093413377805979465e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.758 y[1] (analytic) = 1.2737875969589737259513306468032 y[1] (numeric) = 1.2737875969589737259513306468034 absolute error = 2e-31 relative error = 1.5701204853735251068882593161607e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.759 y[1] (analytic) = 1.274475430346779680385055877114 y[1] (numeric) = 1.2744754303467796803850558771141 absolute error = 1e-31 relative error = 7.8463654629097399646125930969973e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (analytic) = 1.275163989259094827660311633333 y[1] (numeric) = 1.2751639892590948276603116333331 absolute error = 1e-31 relative error = 7.8421286079528278145505742503394e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.761 y[1] (analytic) = 1.2758532730073603128418580871366 y[1] (numeric) = 1.2758532730073603128418580871367 absolute error = 1e-31 relative error = 7.8378918732783708301793211516232e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.762 y[1] (analytic) = 1.2765432809022924451045204977583 y[1] (numeric) = 1.2765432809022924451045204977584 absolute error = 1e-31 relative error = 7.8336552701383943928645451698169e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.763 y[1] (analytic) = 1.2772340122538833870168225968583 y[1] (numeric) = 1.2772340122538833870168225968583 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.764 y[1] (analytic) = 1.277925466371401844548766519348 y[1] (numeric) = 1.277925466371401844548766519348 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.765 y[1] (analytic) = 1.2786176425633937578030692724491 y[1] (numeric) = 1.2786176425633937578030692724492 absolute error = 1e-31 relative error = 7.8209463620037612773173805316877e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.766 y[1] (analytic) = 1.2793105401376829924691650118068 y[1] (numeric) = 1.2793105401376829924691650118069 absolute error = 1e-31 relative error = 7.8167103969328447190667648922365e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.767 y[1] (analytic) = 1.2800041584013720319992816707128 y[1] (numeric) = 1.2800041584013720319992816707128 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.768 y[1] (analytic) = 1.2806984966608426705058997664195 y[1] (numeric) = 1.2806984966608426705058997664196 absolute error = 1e-31 relative error = 7.8082390399246494163976684910609e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.769 y[1] (analytic) = 1.2813935542217567063799004861449 y[1] (numeric) = 1.2813935542217567063799004861449 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (analytic) = 1.2820893303890566366287094346757 y[1] (numeric) = 1.2820893303890566366287094346757 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.771 y[1] (analytic) = 1.2827858244669663519337417054856 y[1] (numeric) = 1.2827858244669663519337417054856 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.772 y[1] (analytic) = 1.2834830357589918324264532179796 y[1] (numeric) = 1.2834830357589918324264532179796 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.773 y[1] (analytic) = 1.2841809635679218441823025448716 y[1] (numeric) = 1.2841809635679218441823025448716 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.774 y[1] (analytic) = 1.2848796071958286364319267357915 y[1] (numeric) = 1.2848796071958286364319267357915 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.775 y[1] (analytic) = 1.2855789659440686394888339260045 y[1] (numeric) = 1.2855789659440686394888339260045 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.776 y[1] (analytic) = 1.2862790391132831633929148026071 y[1] (numeric) = 1.2862790391132831633929148026071 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.777 y[1] (analytic) = 1.2869798260033990972690742847478 y[1] (numeric) = 1.2869798260033990972690742847478 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.778 y[1] (analytic) = 1.2876813259136296094002840592981 y[1] (numeric) = 1.2876813259136296094002840592981 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.779 y[1] (analytic) = 1.28838353814247484801435589898 y[1] (numeric) = 1.28838353814247484801435589898 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (analytic) = 1.2890864619877226427837349762354 y[1] (numeric) = 1.2890864619877226427837349762354 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.2MB, time=3.06 x[1] = 0.781 y[1] (analytic) = 1.289790096746449207037611673102 y[1] (numeric) = 1.289790096746449207037611673102 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.782 y[1] (analytic) = 1.2904944417150198406856496750424 y[1] (numeric) = 1.2904944417150198406856496750424 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.783 y[1] (analytic) = 1.2911994961890896338526274250576 y[1] (numeric) = 1.2911994961890896338526274250577 absolute error = 1e-31 relative error = 7.7447366030690818914636765036904e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.784 y[1] (analytic) = 1.2919052594636041712232893035015 y[1] (numeric) = 1.2919052594636041712232893035016 absolute error = 1e-31 relative error = 7.7405056808515316052132140084880e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.785 y[1] (analytic) = 1.2926117308328002370967021888034 y[1] (numeric) = 1.2926117308328002370967021888035 absolute error = 1e-31 relative error = 7.7362751408400326279439671408954e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.786 y[1] (analytic) = 1.293318909590206521149412344802 y[1] (numeric) = 1.2933189095902065211494123448022 absolute error = 2e-31 relative error = 1.5464089987161080968882824699771e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.787 y[1] (analytic) = 1.2940267950286443249066968715924 y[1] (numeric) = 1.2940267950286443249066968715925 absolute error = 1e-31 relative error = 7.7278152495896670742214629320924e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.788 y[1] (analytic) = 1.2947353864402282689212032486917 y[1] (numeric) = 1.2947353864402282689212032486918 absolute error = 1e-31 relative error = 7.7235859193546897781770404171349e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.789 y[1] (analytic) = 1.2954446831163670006582697919461 y[1] (numeric) = 1.2954446831163670006582697919463 absolute error = 2e-31 relative error = 1.5438714026667121806154333466459e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (analytic) = 1.296154684347763903087219138915 y[1] (numeric) = 1.2961546843477639030872191389152 absolute error = 2e-31 relative error = 1.5430257083909834924347890232619e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.791 y[1] (analytic) = 1.2968653894244178039779161714986 y[1] (numeric) = 1.2968653894244178039779161714988 absolute error = 2e-31 relative error = 1.5421801031236182580348264960182e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.792 y[1] (analytic) = 1.2975767976356236859018810793109 y[1] (numeric) = 1.2975767976356236859018810793111 absolute error = 2e-31 relative error = 1.5413345889386238981666771715301e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.793 y[1] (analytic) = 1.2982889082699733969372475627432 y[1] (numeric) = 1.2982889082699733969372475627434 absolute error = 2e-31 relative error = 1.5404891679041510430865380406920e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.794 y[1] (analytic) = 1.2990017206153563620768554708199 y[1] (numeric) = 1.2990017206153563620768554708201 absolute error = 2e-31 relative error = 1.5396438420824957540795887910841e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.795 y[1] (analytic) = 1.2997152339589602953387664658126 y[1] (numeric) = 1.2997152339589602953387664658128 absolute error = 2e-31 relative error = 1.5387986135301018104650383893389e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.796 y[1] (analytic) = 1.3004294475872719125784906041565 y[1] (numeric) = 1.3004294475872719125784906041568 absolute error = 3e-31 relative error = 2.3069302264463445926026656525316e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.797 y[1] (analytic) = 1.3011443607860776450022110215024 y[1] (numeric) = 1.3011443607860776450022110215027 absolute error = 3e-31 relative error = 2.3056626846444387667216449696141e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.798 y[1] (analytic) = 1.3018599728404643533802932087375 y[1] (numeric) = 1.3018599728404643533802932087378 absolute error = 3e-31 relative error = 2.3043952979477871956399047537339e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.799 y[1] (analytic) = 1.3025762830348200429603646655274 y[1] (numeric) = 1.3025762830348200429603646655277 absolute error = 3e-31 relative error = 2.3031280694059781078326773965931e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (analytic) = 1.3032932906528345790792500183577 y[1] (numeric) = 1.303293290652834579079250018358 absolute error = 3e-31 relative error = 2.3018610020598399164790633953528e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.801 y[1] (analytic) = 1.3040109949775004034730459911998 y[1] (numeric) = 1.3040109949775004034730459912001 absolute error = 3e-31 relative error = 2.3005940989414452283805121047725e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.802 y[1] (analytic) = 1.3047293952911132512846199187868 y[1] (numeric) = 1.3047293952911132512846199187871 absolute error = 3e-31 relative error = 2.2993273630741149474660243064065e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.803 y[1] (analytic) = 1.3054484908752728687678147950589 y[1] (numeric) = 1.3054484908752728687678147950592 absolute error = 3e-31 relative error = 2.2980607974724224723669185533774e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.804 y[1] (analytic) = 1.3061682810108837316876431526351 y[1] (numeric) = 1.3061682810108837316876431526354 absolute error = 3e-31 relative error = 2.2967944051421979875445714905155e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.805 y[1] (analytic) = 1.3068887649781557644157513731752 y[1] (numeric) = 1.3068887649781557644157513731755 absolute error = 3e-31 relative error = 2.2955281890805328474551227668967e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.806 y[1] (analytic) = 1.3076099420566050597204353332294 y[1] (numeric) = 1.3076099420566050597204353332297 absolute error = 3e-31 relative error = 2.2942621522757840532357276472933e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.807 y[1] (analytic) = 1.3083318115250545992504875956188 y[1] (numeric) = 1.3083318115250545992504875956191 absolute error = 3e-31 relative error = 2.2929962977075788213975448872539e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.808 y[1] (analytic) = 1.3090543726616349747121556625597 y[1] (numeric) = 1.30905437266163497471215566256 absolute error = 3e-31 relative error = 2.2917306283468192440112637601482e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.809 y[1] (analytic) = 1.3097776247437851097384901136346 y[1] (numeric) = 1.3097776247437851097384901136348 absolute error = 2e-31 relative error = 1.5269767647704580265810681403019e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (analytic) = 1.3105015670482529824503607593199 y[1] (numeric) = 1.3105015670482529824503607593201 absolute error = 2e-31 relative error = 1.5261332380584322640852319019757e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.811 y[1] (analytic) = 1.311226198851096348708418249117 y[1] (numeric) = 1.3112261988510963487084182491172 absolute error = 2e-31 relative error = 1.5252898407249725999121098932256e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.812 y[1] (analytic) = 1.3119515194276834660552778823829 y[1] (numeric) = 1.311951519427683466055277882383 absolute error = 1e-31 relative error = 7.6222328736372285304868412467331e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.813 y[1] (analytic) = 1.3126775280526938183472016797382 y[1] (numeric) = 1.3126775280526938183472016797384 absolute error = 2e-31 relative error = 1.5236034420174179419586765042977e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.814 y[1] (analytic) = 1.3134042240001188410745540834314 y[1] (numeric) = 1.3134042240001188410745540834316 absolute error = 2e-31 relative error = 1.5227604445406588196814588090870e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.815 y[1] (analytic) = 1.3141316065432626473703059662622 y[1] (numeric) = 1.3141316065432626473703059662623 absolute error = 1e-31 relative error = 7.6095879211857226425612208664758e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.816 y[1] (analytic) = 1.314859674954742754705860940622 y[1] (numeric) = 1.3148596749547427547058609406221 absolute error = 1e-31 relative error = 7.6053743152053075861019096794619e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.817 y[1] (analytic) = 1.315588428506490812273477271886 y[1] (numeric) = 1.3155884285064908122734772718861 absolute error = 1e-31 relative error = 7.6011614144040506724468383603378e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.818 y[1] (analytic) = 1.316317866469753329054558013794 y[1] (numeric) = 1.3163178664697533290545580137941 absolute error = 1e-31 relative error = 7.5969492283950416344975548666648e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.819 y[1] (analytic) = 1.3170479881150924025730812975917 y[1] (numeric) = 1.3170479881150924025730812975918 absolute error = 1e-31 relative error = 7.5927377667624769708208496578401e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (analytic) = 1.3177787927123864483334420215631 y[1] (numeric) = 1.3177787927123864483334420215631 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.821 y[1] (analytic) = 1.3185102795308309299419755031717 y[1] (numeric) = 1.3185102795308309299419755031717 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.822 y[1] (analytic) = 1.3192424478389390899114329723498 y[1] (numeric) = 1.3192424478389390899114329723498 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE memory used=68.6MB, alloc=4.2MB, time=3.25 TOP MAIN SOLVE Loop x[1] = 0.823 y[1] (analytic) = 1.3199752969045426811476781015192 y[1] (numeric) = 1.3199752969045426811476781015191 absolute error = 1e-31 relative error = 7.5758993546704041388525110206991e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.824 y[1] (analytic) = 1.3207088259947926991178730857087 y[1] (numeric) = 1.3207088259947926991178730857086 absolute error = 1e-31 relative error = 7.5716916576730956719207948331230e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.825 y[1] (analytic) = 1.3214430343761601146994221046441 y[1] (numeric) = 1.3214430343761601146994221046441 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.826 y[1] (analytic) = 1.3221779213144366077089393179268 y[1] (numeric) = 1.3221779213144366077089393179268 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.827 y[1] (analytic) = 1.3229134860747353011105078643946 y[1] (numeric) = 1.3229134860747353011105078643946 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.828 y[1] (analytic) = 1.3236497279214914959024956574681 y[1] (numeric) = 1.3236497279214914959024956574681 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.829 y[1] (analytic) = 1.3243866461184634066821930897261 y[1] (numeric) = 1.3243866461184634066821930897261 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = 1.3251242399287328978875370821356 y[1] (numeric) = 1.3251242399287328978875370821355 absolute error = 1e-31 relative error = 7.5464622098663099641874975272178e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.831 y[1] (analytic) = 1.3258625086147062207151852362717 y[1] (numeric) = 1.3258625086147062207151852362716 absolute error = 1e-31 relative error = 7.5422601778281264669689501790369e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.832 y[1] (analytic) = 1.3266014514381147507142031715169 y[1] (numeric) = 1.3266014514381147507142031715168 absolute error = 1e-31 relative error = 7.5380589921407112676144017566724e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.833 y[1] (analytic) = 1.3273410676600157260546274536119 y[1] (numeric) = 1.3273410676600157260546274536118 absolute error = 1e-31 relative error = 7.5338586619858833955722422128176e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.834 y[1] (analytic) = 1.3280813565407929864701658460576 y[1] (numeric) = 1.3280813565407929864701658460574 absolute error = 2e-31 relative error = 1.5059318393033767000661193207483e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.835 y[1] (analytic) = 1.3288223173401577128742959417292 y[1] (numeric) = 1.328822317340157712874295941729 absolute error = 2e-31 relative error = 1.5050921209716793960686847694940e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.836 y[1] (analytic) = 1.3295639493171491676490225586661 y[1] (numeric) = 1.329563949317149167649022558666 absolute error = 1e-31 relative error = 7.5212628961065773699241014504042e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.837 y[1] (analytic) = 1.3303062517301354356055536113409 y[1] (numeric) = 1.3303062517301354356055536113408 absolute error = 1e-31 relative error = 7.5170660793290699824677727303106e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.838 y[1] (analytic) = 1.3310492238368141656161534967937 y[1] (numeric) = 1.3310492238368141656161534967936 absolute error = 1e-31 relative error = 7.5128701635650358083668179374226e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.839 y[1] (analytic) = 1.3317928648942133129164323638407 y[1] (numeric) = 1.3317928648942133129164323638406 absolute error = 1e-31 relative error = 7.5086751578251756659869248454979e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (analytic) = 1.3325371741586918820773289631291 y[1] (numeric) = 1.332537174158691882077328963129 absolute error = 1e-31 relative error = 7.5044810710917546040743775356377e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.841 y[1] (analytic) = 1.3332821508859406706460441061175 y[1] (numeric) = 1.3332821508859406706460441061173 absolute error = 2e-31 relative error = 1.5000575824637253107936707826411e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.842 y[1] (analytic) = 1.3340277943309830134551810921098 y[1] (numeric) = 1.3340277943309830134551810921096 absolute error = 2e-31 relative error = 1.4992191380862518459990445338116e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.843 y[1] (analytic) = 1.334774103748175527599348794266 y[1] (numeric) = 1.3347741037481755275993487942658 absolute error = 2e-31 relative error = 1.4983808828653518552850117216689e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.844 y[1] (analytic) = 1.3355210783912088580784824280462 y[1] (numeric) = 1.335521078391208858078482428046 absolute error = 2e-31 relative error = 1.4975428185747795318747702424721e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.845 y[1] (analytic) = 1.3362687175131084241071363588314 y[1] (numeric) = 1.3362687175131084241071363588312 absolute error = 2e-31 relative error = 1.4967049469826270604076329322539e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.846 y[1] (analytic) = 1.3370170203662351660890026394896 y[1] (numeric) = 1.3370170203662351660890026394894 absolute error = 2e-31 relative error = 1.4958672698513297923304636038532e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.847 y[1] (analytic) = 1.3377659862022862932559083034306 y[1] (numeric) = 1.3377659862022862932559083034304 absolute error = 2e-31 relative error = 1.4950297889376714693122983122070e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.848 y[1] (analytic) = 1.3385156142722960319705437742155 y[1] (numeric) = 1.3385156142722960319705437742153 absolute error = 2e-31 relative error = 1.4941925059927894943615057985391e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.849 y[1] (analytic) = 1.3392659038266363746921740890535 y[1] (numeric) = 1.3392659038266363746921740890533 absolute error = 2e-31 relative error = 1.4933554227621802503255190572510e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (analytic) = 1.3400168541150178296045839705385 y[1] (numeric) = 1.3400168541150178296045839705383 absolute error = 2e-31 relative error = 1.4925185409857044654538531399221e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.851 y[1] (analytic) = 1.3407684643864901709055071187424 y[1] (numeric) = 1.3407684643864901709055071187421 absolute error = 3e-31 relative error = 2.2375227935963889385587188973445e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.852 y[1] (analytic) = 1.3415207338894431897567894342973 y[1] (numeric) = 1.341520733889443189756789434297 absolute error = 3e-31 relative error = 2.2362680830896756502274779670867e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.853 y[1] (analytic) = 1.3422736618716074458945352223685 y[1] (numeric) = 1.3422736618716074458945352223682 absolute error = 3e-31 relative error = 2.2350136825428964687249766755909e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.854 y[1] (analytic) = 1.3430272475800550198984847674316 y[1] (numeric) = 1.3430272475800550198984847674313 absolute error = 3e-31 relative error = 2.2337595945321104374774054113346e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.855 y[1] (analytic) = 1.3437814902612002661198710095412 y[1] (numeric) = 1.343781490261200266119871009541 absolute error = 2e-31 relative error = 1.4883372144166429346472582727816e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.856 y[1] (analytic) = 1.3445363891608005662670023942965 y[1] (numeric) = 1.3445363891608005662670023942963 absolute error = 2e-31 relative error = 1.4875015775871343144442998077784e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.857 y[1] (analytic) = 1.3452919435239570836478183109831 y[1] (numeric) = 1.3452919435239570836478183109829 absolute error = 2e-31 relative error = 1.4866661542334463661245057972797e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.858 y[1] (analytic) = 1.3460481525951155180686628763995 y[1] (numeric) = 1.3460481525951155180686628763992 absolute error = 3e-31 relative error = 2.2287464190758299263041596243199e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.859 y[1] (analytic) = 1.3468050156180668613885221656564 y[1] (numeric) = 1.3468050156180668613885221656562 absolute error = 2e-31 relative error = 1.4849959547278439641737668517989e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (analytic) = 1.3475625318359481537279693357761 y[1] (numeric) = 1.3475625318359481537279693357759 absolute error = 2e-31 relative error = 1.4841611819491278213010108011191e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.861 y[1] (analytic) = 1.3483207004912432403320614332074 y[1] (numeric) = 1.3483207004912432403320614332072 absolute error = 2e-31 relative error = 1.4833266293926406530036395695712e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.862 y[1] (analytic) = 1.3490795208257835290864310224247 y[1] (numeric) = 1.3490795208257835290864310224245 absolute error = 2e-31 relative error = 1.4824922987310505445301085990428e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.863 y[1] (analytic) = 1.3498389920807487486858151195816 y[1] (numeric) = 1.3498389920807487486858151195814 absolute error = 2e-31 relative error = 1.4816581916314638176089016322089e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.864 y[1] (analytic) = 1.3505991134966677074542632627533 y[1] (numeric) = 1.3505991134966677074542632627531 absolute error = 2e-31 relative error = 1.4808243097554310217670254468088e-29 % Correct digits = 30 h = 0.001 memory used=72.4MB, alloc=4.2MB, time=3.43 NO POLE TOP MAIN SOLVE Loop x[1] = 0.865 y[1] (analytic) = 1.3513598843134190528162658986232 y[1] (numeric) = 1.351359884313419052816265898623 absolute error = 2e-31 relative error = 1.4799906547589529680078351138131e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.866 y[1] (analytic) = 1.3521213037702320314180436145485 y[1] (numeric) = 1.3521213037702320314180436145483 absolute error = 2e-31 relative error = 1.4791572282924868045404909889931e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.867 y[1] (analytic) = 1.3528833711056872498982370947791 y[1] (numeric) = 1.3528833711056872498982370947789 absolute error = 2e-31 relative error = 1.4783240320009521342541107484005e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.868 y[1] (analytic) = 1.3536460855577174363072370302028 y[1] (numeric) = 1.3536460855577174363072370302025 absolute error = 3e-31 relative error = 2.2162366012856057604456690021540e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.869 y[1] (analytic) = 1.3544094463636082021743925623504 y[1] (numeric) = 1.3544094463636082021743925623502 absolute error = 2e-31 relative error = 1.4766583364947049527896833042157e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (analytic) = 1.3551734527599988052223361945172 y[1] (numeric) = 1.3551734527599988052223361945169 absolute error = 3e-31 relative error = 2.2137387608132993345471155421531e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.871 y[1] (analytic) = 1.3559381039828829127276624557362 y[1] (numeric) = 1.355938103982882912727662455736 absolute error = 2e-31 relative error = 1.4749935812890524049002331244283e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.872 y[1] (analytic) = 1.3567033992676093655271969569926 y[1] (numeric) = 1.3567033992676093655271969569923 absolute error = 3e-31 relative error = 2.2112423405288828647094674665260e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.873 y[1] (analytic) = 1.3574693378488829426690918334692 y[1] (numeric) = 1.3574693378488829426690918334689 absolute error = 3e-31 relative error = 2.2099946690169497523478028007281e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.874 y[1] (analytic) = 1.3582359189607651267079829217956 y[1] (numeric) = 1.3582359189607651267079829217953 absolute error = 3e-31 relative error = 2.2087473598072765463332705091521e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.875 y[1] (analytic) = 1.359003141836674869643443377204 y[1] (numeric) = 1.3590031418366748696434433772037 absolute error = 3e-31 relative error = 2.2075004153011298137905334650689e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.876 y[1] (analytic) = 1.3597710057093893595009677922045 y[1] (numeric) = 1.3597710057093893595009677922043 absolute error = 2e-31 relative error = 1.4708358919277034214260009067176e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.877 y[1] (analytic) = 1.3605395098110447875547202358586 y[1] (numeric) = 1.3605395098110447875547202358583 absolute error = 3e-31 relative error = 2.2050076299633868664080138289995e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.878 y[1] (analytic) = 1.3613086533731371161912789909656 y[1] (numeric) = 1.3613086533731371161912789909654 absolute error = 2e-31 relative error = 1.4691745292621720027878448440849e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.879 y[1] (analytic) = 1.3620784356265228474136101254846 y[1] (numeric) = 1.3620784356265228474136101254844 absolute error = 2e-31 relative error = 1.4683442213664066984851710154645e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (analytic) = 1.3628488558014197919845013942779 y[1] (numeric) = 1.3628488558014197919845013942777 absolute error = 2e-31 relative error = 1.4675141645284686419091464888454e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.881 y[1] (analytic) = 1.3636199131274078392086873278103 y[1] (numeric) = 1.3636199131274078392086873278101 absolute error = 2e-31 relative error = 1.4666843603164167894128644487916e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.882 y[1] (analytic) = 1.3643916068334297273528957257406 y[1] (numeric) = 1.3643916068334297273528957257404 absolute error = 2e-31 relative error = 1.4658548102928691171665588541626e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.883 y[1] (analytic) = 1.3651639361477918147030451354242 y[1] (numeric) = 1.365163936147791814703045135424 absolute error = 2e-31 relative error = 1.4650255160150093654406914045141e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.884 y[1] (analytic) = 1.3659369002981648512578222581931 y[1] (numeric) = 1.3659369002981648512578222581929 absolute error = 2e-31 relative error = 1.4641964790345938195361903374083e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.885 y[1] (analytic) = 1.3667104985115847510578675899006 y[1] (numeric) = 1.3667104985115847510578675899004 absolute error = 2e-31 relative error = 1.4633677008979581270692734908410e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.886 y[1] (analytic) = 1.3674847300144533651497969666091 y[1] (numeric) = 1.367484730014453365149796966609 absolute error = 1e-31 relative error = 7.3126959157301207565955955188616e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.887 y[1] (analytic) = 1.3682595940325392551842860514642 y[1] (numeric) = 1.368259594032539255184286051464 absolute error = 2e-31 relative error = 1.4617109273143068603474819623637e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.888 y[1] (analytic) = 1.3690350897909784676474441647341 y[1] (numeric) = 1.3690350897909784676474441647339 absolute error = 2e-31 relative error = 1.4608829349329212516001896785537e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.889 y[1] (analytic) = 1.369811216514275308724703225707 y[1] (numeric) = 1.3698112165142753087247032257068 absolute error = 2e-31 relative error = 1.4600552075265893117012940598747e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (analytic) = 1.3705879734263031197964469426198 y[1] (numeric) = 1.3705879734263031197964469426195 absolute error = 3e-31 relative error = 2.1888416199219705167272434660619e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.891 y[1] (analytic) = 1.3713653597503050535646047550548 y[1] (numeric) = 1.3713653597503050535646047550545 absolute error = 3e-31 relative error = 2.1876008305665770004649582172637e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.892 y[1] (analytic) = 1.3721433747088948508094344022757 y[1] (numeric) = 1.3721433747088948508094344022754 absolute error = 3e-31 relative error = 2.1863604454865810095593856053295e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.893 y[1] (analytic) = 1.3729220175240576177757163607833 y[1] (numeric) = 1.372922017524057617775716360783 absolute error = 3e-31 relative error = 2.1851204669368128965944996185100e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.894 y[1] (analytic) = 1.373701287417150604187582764963 y[1] (numeric) = 1.3737012874171506041875827649626 absolute error = 4e-31 relative error = 2.9118411962187552974892513795863e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.895 y[1] (analytic) = 1.3744811836089039818912027960585 y[1] (numeric) = 1.3744811836089039818912027960582 absolute error = 3e-31 relative error = 2.1826417384071097570216600412951e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.896 y[1] (analytic) = 1.3752617053194216241245458968532 y[1] (numeric) = 1.3752617053194216241245458968528 absolute error = 4e-31 relative error = 2.9085373238622610263004860163221e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.897 y[1] (analytic) = 1.3760428517681818854134435423582 y[1] (numeric) = 1.3760428517681818854134435423578 absolute error = 4e-31 relative error = 2.9068862171407645102721113394391e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.898 y[1] (analytic) = 1.3768246221740383820931696705131 y[1] (numeric) = 1.3768246221740383820931696705127 absolute error = 4e-31 relative error = 2.9052356673313309506301704223573e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.899 y[1] (analytic) = 1.3776070157552207734547592513822 y[1] (numeric) = 1.3776070157552207734547592513817 absolute error = 5e-31 relative error = 3.6294820967204059451414841234870e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (analytic) = 1.3783900317293355435152838485929 y[1] (numeric) = 1.3783900317293355435152838485924 absolute error = 5e-31 relative error = 3.6274203127593523887255078370614e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.901 y[1] (analytic) = 1.3791736693133667834113024028072 y[1] (numeric) = 1.3791736693133667834113024028067 absolute error = 5e-31 relative error = 3.6253592359324058684051087425374e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.902 y[1] (analytic) = 1.3799579277236769744147048438388 y[1] (numeric) = 1.3799579277236769744147048438383 absolute error = 5e-31 relative error = 3.6232988698777205810033886836812e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.903 y[1] (analytic) = 1.380742806176007771570165515639 y[1] (numeric) = 1.3807428061760077715701655156385 absolute error = 5e-31 relative error = 3.6212392182202206273009331573891e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.904 y[1] (analytic) = 1.3815283038854807879534227767624 y[1] (numeric) = 1.3815283038854807879534227767618 absolute error = 6e-31 relative error = 4.3430163414859423751135674680592e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.905 y[1] (analytic) = 1.3823144200665983795496005180982 y[1] (numeric) = 1.3823144200665983795496005180977 absolute error = 5e-31 relative error = 3.6171220725304345239604607954907e-29 % Correct digits = 30 h = 0.001 NO POLE memory used=76.2MB, alloc=4.2MB, time=3.61 TOP MAIN SOLVE Loop x[1] = 0.906 y[1] (analytic) = 1.3831011539332444307507867196122 y[1] (numeric) = 1.3831011539332444307507867196116 absolute error = 6e-31 relative error = 4.3380775028184170202404798636437e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.907 y[1] (analytic) = 1.3838885046986851404720835485838 y[1] (numeric) = 1.3838885046986851404720835485832 absolute error = 6e-31 relative error = 4.3356093931182581325475660664411e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.908 y[1] (analytic) = 1.3846764715755698088853428833566 y[1] (numeric) = 1.384676471575569808885342883356 absolute error = 6e-31 relative error = 4.3331421622069103489702809995156e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.909 y[1] (analytic) = 1.3854650537759316247698005289301 y[1] (numeric) = 1.3854650537759316247698005289295 absolute error = 6e-31 relative error = 4.3306758143394986658160577799750e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (analytic) = 1.3862542505111884534788217738253 y[1] (numeric) = 1.3862542505111884534788217738247 absolute error = 6e-31 relative error = 4.3282103537554303930413468077431e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.911 y[1] (analytic) = 1.3870440609921436255219703215436 y[1] (numeric) = 1.387044060992143625521970321543 absolute error = 6e-31 relative error = 4.3257457846784181420327583877569e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.912 y[1] (analytic) = 1.387834484428986725761612014616 y[1] (numeric) = 1.3878344844289867257616120146155 absolute error = 5e-31 relative error = 3.6027350927637524164364403558332e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.913 y[1] (analytic) = 1.3886255200312943832232641547054 y[1] (numeric) = 1.3886255200312943832232641547049 absolute error = 5e-31 relative error = 3.6006827815517309902015277657393e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.914 y[1] (analytic) = 1.3894171670080310615189006084766 y[1] (numeric) = 1.3894171670080310615189006084761 absolute error = 5e-31 relative error = 3.5986312237432569244038146562055e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.915 y[1] (analytic) = 1.390209424567549849882422275997 y[1] (numeric) = 1.3902094245675498498824222759965 absolute error = 5e-31 relative error = 3.5965804228059680603534838277351e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.916 y[1] (analytic) = 1.3910022919175932548165018862618 y[1] (numeric) = 1.3910022919175932548165018862614 absolute error = 4e-31 relative error = 2.8756243057556161376963976471312e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.917 y[1] (analytic) = 1.3917957682652939923500114730661 y[1] (numeric) = 1.3917957682652939923500114730657 absolute error = 4e-31 relative error = 2.8739848842804852357444762263392e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.918 y[1] (analytic) = 1.3925898528171757809052402738607 y[1] (numeric) = 1.3925898528171757809052402738603 absolute error = 4e-31 relative error = 2.8723460765623820960136023905637e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.919 y[1] (analytic) = 1.3933845447791541347741101844421 y[1] (numeric) = 1.3933845447791541347741101844417 absolute error = 4e-31 relative error = 2.8707078853339685684165276694048e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (analytic) = 1.3941798433565371582025952933256 y[1] (numeric) = 1.3941798433565371582025952933252 absolute error = 4e-31 relative error = 2.8690703133175838232272584725222e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.921 y[1] (analytic) = 1.3949757477540263400825514114488 y[1] (numeric) = 1.3949757477540263400825514114484 absolute error = 4e-31 relative error = 2.8674333632252602279089342213723e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.922 y[1] (analytic) = 1.3957722571757173492501609054418 y[1] (numeric) = 1.3957722571757173492501609054414 absolute error = 4e-31 relative error = 2.8657970377587392762142219961199e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.923 y[1] (analytic) = 1.3965693708251008303901975360864 y[1] (numeric) = 1.396569370825100830390197536086 absolute error = 4e-31 relative error = 2.8641613396094875690397758281360e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.924 y[1] (analytic) = 1.3973670879050632005453153977649 y[1] (numeric) = 1.3973670879050632005453153977645 absolute error = 4e-31 relative error = 2.8625262714587128465181383157311e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.925 y[1] (analytic) = 1.3981654076178874462295654496762 y[1] (numeric) = 1.3981654076178874462295654496758 absolute error = 4e-31 relative error = 2.8608918359773800708322944464474e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.926 y[1] (analytic) = 1.3989643291652539211453425253694 y[1] (numeric) = 1.3989643291652539211453425253689 absolute error = 5e-31 relative error = 3.5740725447827844490499028635236e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.927 y[1] (analytic) = 1.3997638517482411445029651037137 y[1] (numeric) = 1.3997638517482411445029651037132 absolute error = 5e-31 relative error = 3.5720310920697289584952781350503e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.928 y[1] (analytic) = 1.4005639745673265999420895217925 y[1] (numeric) = 1.4005639745673265999420895217921 absolute error = 4e-31 relative error = 2.8559923521063805182660482920099e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.929 y[1] (analytic) = 1.4013646968223875350541597083728 y[1] (numeric) = 1.4013646968223875350541597083723 absolute error = 5e-31 relative error = 3.5679505922602191108973742572889e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (analytic) = 1.402166017712701761505092915567 y[1] (numeric) = 1.4021660177127017615050929155666 absolute error = 4e-31 relative error = 2.8527292413811615322941882236874e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.931 y[1] (analytic) = 1.4029679364369484557574013260696 y[1] (numeric) = 1.4029679364369484557574013260692 absolute error = 4e-31 relative error = 2.8510986574351880586540321412164e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.932 y[1] (analytic) = 1.4037704521932089603909488139114 y[1] (numeric) = 1.403770452193208960390948813911 absolute error = 4e-31 relative error = 2.8494687245699748565866752497968e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.933 y[1] (analytic) = 1.4045735641789675860215415380431 y[1] (numeric) = 1.4045735641789675860215415380428 absolute error = 3e-31 relative error = 2.1358795840313471732216195383026e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.934 y[1] (analytic) = 1.4053772715911124138165504502244 y[1] (numeric) = 1.405377271591112413816550450224 absolute error = 4e-31 relative error = 2.8462108224301639858543838039964e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.935 y[1] (analytic) = 1.4061815736259360986067632016613 y[1] (numeric) = 1.4061815736259360986067632016609 absolute error = 4e-31 relative error = 2.8445828583045106533402137700699e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.936 y[1] (analytic) = 1.4069864694791366725936623366093 y[1] (numeric) = 1.4069864694791366725936623366089 absolute error = 4e-31 relative error = 2.8429555555575394341468210758077e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.937 y[1] (analytic) = 1.4077919583458183496513260657285 y[1] (numeric) = 1.4077919583458183496513260657282 absolute error = 3e-31 relative error = 2.1309966875539306372409730514911e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.938 y[1] (analytic) = 1.4085980394204923302221473173594 y[1] (numeric) = 1.4085980394204923302221473173591 absolute error = 3e-31 relative error = 2.1297772082901820785738306201500e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.939 y[1] (analytic) = 1.409404711897077606805566171065 y[1] (numeric) = 1.4094047118970776068055661710647 absolute error = 3e-31 relative error = 2.1285582307738703708583576151411e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = 1.410211974968901770039010184776 y[1] (numeric) = 1.4102119749689017700390101847757 absolute error = 3e-31 relative error = 2.1273397568944601402672531483574e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.941 y[1] (analytic) = 1.4110198278287018153702365346646 y[1] (numeric) = 1.4110198278287018153702365346643 absolute error = 3e-31 relative error = 2.1261217885339317872984902964924e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.942 y[1] (analytic) = 1.4118282696686249503202692954725 y[1] (numeric) = 1.4118282696686249503202692954722 absolute error = 3e-31 relative error = 2.1249043275667941378678592218864e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.943 y[1] (analytic) = 1.4126372996802294023361245984231 y[1] (numeric) = 1.4126372996802294023361245984229 absolute error = 2e-31 relative error = 1.4157915839067314171538159893535e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.944 y[1] (analytic) = 1.41344691705448522723251581406 y[1] (numeric) = 1.4134469170544852272325158140598 absolute error = 2e-31 relative error = 1.4149806235156296705822055344966e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.945 y[1] (analytic) = 1.4142571209817751182217303183736 y[1] (numeric) = 1.4142571209817751182217303183734 absolute error = 2e-31 relative error = 1.4141700051060043990101513953748e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.946 y[1] (analytic) = 1.4150679106518952155308688124071 y[1] (numeric) = 1.4150679106518952155308688124069 absolute error = 2e-31 relative error = 1.4133597299076887089109219766218e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.2MB, time=3.80 x[1] = 0.947 y[1] (analytic) = 1.4158792852540559166056375781701 y[1] (numeric) = 1.4158792852540559166056375781699 absolute error = 2e-31 relative error = 1.4125497991455771358551665963546e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.948 y[1] (analytic) = 1.4166912439768826868998834671338 y[1] (numeric) = 1.4166912439768826868998834671337 absolute error = 1e-31 relative error = 7.0587010701981710015565669499950e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.949 y[1] (analytic) = 1.4175037860084168712500608318425 y[1] (numeric) = 1.4175037860084168712500608318424 absolute error = 1e-31 relative error = 7.0546548790245149145369811271292e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (analytic) = 1.4183169105361165058338190262395 y[1] (numeric) = 1.4183169105361165058338190262395 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.951 y[1] (analytic) = 1.4191306167468571307118985161905 y[1] (numeric) = 1.4191306167468571307118985161905 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.952 y[1] (analytic) = 1.419944903826932602952523058373 y[1] (numeric) = 1.419944903826932602952523058373 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.953 y[1] (analytic) = 1.4207597709620559103374748232099 y[1] (numeric) = 1.4207597709620559103374748232099 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.954 y[1] (analytic) = 1.4215752173373599856490387558386 y[1] (numeric) = 1.4215752173373599856490387558387 absolute error = 1e-31 relative error = 7.0344501494125709695354772957629e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.955 y[1] (analytic) = 1.4223912421373985215370018882395 y[1] (numeric) = 1.4223912421373985215370018882395 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.956 y[1] (analytic) = 1.4232078445461467859648927355918 y[1] (numeric) = 1.4232078445461467859648927355918 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.957 y[1] (analytic) = 1.4240250237470024382346453306867 y[1] (numeric) = 1.4240250237470024382346453306867 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.958 y[1] (analytic) = 1.4248427789227863455888718718004 y[1] (numeric) = 1.4248427789227863455888718718005 absolute error = 1e-31 relative error = 7.0183181947696911447366640051319e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.959 y[1] (analytic) = 1.4256611092557434003899273818234 y[1] (numeric) = 1.4256611092557434003899273818235 absolute error = 1e-31 relative error = 7.0142896759107298528142905540120e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (analytic) = 1.4264800139275433378749491996481 y[1] (numeric) = 1.4264800139275433378749491996482 absolute error = 1e-31 relative error = 7.0102629566234779749643425416400e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.961 y[1] (analytic) = 1.4272994921192815544860535488458 y[1] (numeric) = 1.4272994921192815544860535488459 absolute error = 1e-31 relative error = 7.0062380426912427116371897107466e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.962 y[1] (analytic) = 1.4281195430114799267748708535018 y[1] (numeric) = 1.4281195430114799267748708535019 absolute error = 1e-31 relative error = 7.0022149398732897846972099849154e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.963 y[1] (analytic) = 1.4289401657840876308806008967442 y[1] (numeric) = 1.4289401657840876308806008967442 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.964 y[1] (analytic) = 1.4297613596164819625807683439772 y[1] (numeric) = 1.4297613596164819625807683439772 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.965 y[1] (analytic) = 1.4305831236874691579138585801337 y[1] (numeric) = 1.4305831236874691579138585801337 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.966 y[1] (analytic) = 1.4314054571752852143730132383785 y[1] (numeric) = 1.4314054571752852143730132383785 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.967 y[1] (analytic) = 1.4322283592575967126699642266353 y[1] (numeric) = 1.4322283592575967126699642266354 absolute error = 1e-31 relative error = 6.9821267923947225030713399666178e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.968 y[1] (analytic) = 1.4330518291115016390683844880724 y[1] (numeric) = 1.4330518291115016390683844880724 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.969 y[1] (analytic) = 1.4338758659135302082858331622636 y[1] (numeric) = 1.4338758659135302082858331622637 absolute error = 1e-31 relative error = 6.9741044100975539787305325039587e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (analytic) = 1.4347004688396456869634722451501 y[1] (numeric) = 1.4347004688396456869634722451502 absolute error = 1e-31 relative error = 6.9700960006570437358545324033530e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.971 y[1] (analytic) = 1.4355256370652452177027312781524 y[1] (numeric) = 1.4355256370652452177027312781524 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.972 y[1] (analytic) = 1.4363513697651606436680960298383 y[1] (numeric) = 1.4363513697651606436680960298383 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.973 y[1] (analytic) = 1.4371776661136593337551965674268 y[1] (numeric) = 1.4371776661136593337551965674267 absolute error = 1e-31 relative error = 6.9580819656357984619361504950992e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.974 y[1] (analytic) = 1.4380045252844450083233695501071 y[1] (numeric) = 1.4380045252844450083233695501071 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.975 y[1] (analytic) = 1.4388319464506585654918690116816 y[1] (numeric) = 1.4388319464506585654918690116816 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.976 y[1] (analytic) = 1.4396599287848789079988993363884 y[1] (numeric) = 1.4396599287848789079988993363885 absolute error = 1e-31 relative error = 6.9460848357711353338663165625435e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.977 y[1] (analytic) = 1.4404884714591237706226435689417 y[1] (numeric) = 1.4404884714591237706226435689417 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.978 y[1] (analytic) = 1.4413175736448505481634596378282 y[1] (numeric) = 1.4413175736448505481634596378282 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.979 y[1] (analytic) = 1.4421472345129571239864165097351 y[1] (numeric) = 1.4421472345129571239864165097351 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (analytic) = 1.4429774532337826991233417326401 y[1] (numeric) = 1.4429774532337826991233417326401 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.981 y[1] (analytic) = 1.4438082289771086219335512655861 y[1] (numeric) = 1.4438082289771086219335512655861 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.982 y[1] (analytic) = 1.4446395609121592183224319344801 y[1] (numeric) = 1.4446395609121592183224319344801 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.983 y[1] (analytic) = 1.4454714482076026225170462954026 y[1] (numeric) = 1.4454714482076026225170462954025 absolute error = 1e-31 relative error = 6.9181580946480045841511094776152e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.984 y[1] (analytic) = 1.4463038900315516083979291298914 y[1] (numeric) = 1.4463038900315516083979291298913 absolute error = 1e-31 relative error = 6.9141762453406985019674850747968e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.985 y[1] (analytic) = 1.4471368855515644213862442404742 y[1] (numeric) = 1.4471368855515644213862442404741 absolute error = 1e-31 relative error = 6.9101963330777665568800804955532e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.986 y[1] (analytic) = 1.4479704339346456108854696593607 y[1] (numeric) = 1.4479704339346456108854696593605 absolute error = 2e-31 relative error = 1.3812436726109770390807584317099e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.987 y[1] (analytic) = 1.4488045343472468632767788286789 y[1] (numeric) = 1.4488045343472468632767788286788 absolute error = 1e-31 relative error = 6.9022423404448139294022707608052e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.988 y[1] (analytic) = 1.4496391859552678354672847569453 y[1] (numeric) = 1.4496391859552678354672847569452 absolute error = 1e-31 relative error = 6.8982682703974411404068014346532e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.989 y[1] (analytic) = 1.4504743879240569889903136035916 y[1] (numeric) = 1.4504743879240569889903136035915 absolute error = 1e-31 relative error = 6.8942961580398299380616553354598e-30 % Correct digits = 31 h = 0.001 NO POLE memory used=83.9MB, alloc=4.3MB, time=3.98 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (analytic) = 1.4513101394184124246568735913464 y[1] (numeric) = 1.4513101394184124246568735913462 absolute error = 2e-31 relative error = 1.3780652016952528143424110141293e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.991 y[1] (analytic) = 1.4521464396025827177574845950707 y[1] (numeric) = 1.4521464396025827177574845950705 absolute error = 2e-31 relative error = 1.3772715653576587788311044450426e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.992 y[1] (analytic) = 1.4529832876402677538135332052885 y[1] (numeric) = 1.4529832876402677538135332052884 absolute error = 1e-31 relative error = 6.8823916180347823765819967747718e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.993 y[1] (analytic) = 1.4538206826946195648773175151265 y[1] (numeric) = 1.4538206826946195648773175151264 absolute error = 1e-31 relative error = 6.8784273872519511737327352825419e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.994 y[1] (analytic) = 1.4546586239282431663799453306873 y[1] (numeric) = 1.4546586239282431663799453306872 absolute error = 1e-31 relative error = 6.8744651394534267383126073313572e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.995 y[1] (analytic) = 1.4554971105031973945262489570286 y[1] (numeric) = 1.4554971105031973945262489570285 absolute error = 1e-31 relative error = 6.8705048796302864836950175261879e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.996 y[1] (analytic) = 1.4563361415809957442358791649033 y[1] (numeric) = 1.4563361415809957442358791649031 absolute error = 2e-31 relative error = 1.3733093225502209987926566997728e-29 % Correct digits = 30 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.997 y[1] (analytic) = 1.4571757163226072076297403972349 y[1] (numeric) = 1.4571757163226072076297403972348 absolute error = 1e-31 relative error = 6.8625903437620002803368985375585e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.998 y[1] (analytic) = 1.4580158338884571130609287289657 y[1] (numeric) = 1.4580158338884571130609287289656 absolute error = 1e-31 relative error = 6.8586360775866800830357006332495e-30 % Correct digits = 31 h = 0.001 NO POLE TOP MAIN SOLVE Loop x[1] = 0.999 y[1] (analytic) = 1.4588564934384279646893335494061 y[1] (numeric) = 1.458856493438427964689333549406 absolute error = 1e-31 relative error = 6.8546838191264882176395577691515e-30 % Correct digits = 31 h = 0.001 NO POLE Finished! diff ( y , x , 1 ) = sin(x); Iterations = 900 Total Elapsed Time = 3 Seconds Elapsed Time(since restart) = 3 Seconds Time to Timeout = 2 Minutes 56 Seconds Percent Done = 100.1 % > quit memory used=84.8MB, alloc=4.3MB, time=4.02