|\^/| 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_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 1 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > if (min_size < 1.0) then # if number 1 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 4 > # Begin Function number 5 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms; > max_value3 := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > value3 := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (value3 > max_value3) then # if number 1 > max_value3 := value3; > omniout_float(ALWAYS,"value3",32,value3,32,""); > fi;# end if 1; > omniout_float(ALWAYS,"max_value3",32,max_value3,32,""); > max_value3; > end; test_suggested_h := proc() local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; max_value3 := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); value3 := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_value3 < value3 then max_value3 := value3; omniout_float(ALWAYS, "value3", 32, value3, 32, "") end if; omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""); max_value3 end proc > # End Function number 5 > # Begin Function number 6 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1 > ret := true; > else > ret := false; > fi;# end if 1; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 6 > # Begin Function number 7 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 1 > if (iter >= 0) then # if number 2 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 3 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 4 > glob_good_digits := -trunc(log10(relerr)) + 2; > else > glob_good_digits := Digits; > fi;# end if 4; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 3; > if (glob_iter = 1) then # if number 3 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 3; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 2; > #BOTTOM DISPLAY ALOT > fi;# end if 1; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 2 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 7 > # Begin Function number 8 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 2 > fi;# end if 1; > if ( not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 8 > # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 1; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 9 > # Begin Function number 10 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc,hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, 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 * glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float * 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)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > glob_small_float * glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > 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_sing := 0; > #TOP WHICH RADII EQ = 1 > if (1 <> found_sing 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_sing := 1; > 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 for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing 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] > -1.0 * glob_smallish_float) 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_sing := 1; > 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 for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing 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_sing := 1; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 3 > omniout_str(ALWAYS,"NO POLE for equation 1"); > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing 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] > -1.0 * glob_smallish_float))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found_sing := 1; > 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 for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing 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_sing := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing ) 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 for equation 1"); > 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, hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, 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_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and ( omniabs(array_y_higher[1, m]) < glob_small_float*glob_small_float or omniabs(array_y_higher[1, m - 1]) < glob_small_float*glob_small_float or omniabs(array_y_higher[1, m - 2]) < glob_small_float*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)*rm0 - convfloat(m - 1)*rm1; if glob_small_float*glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; 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_sing := 0; if 1 <> found_sing 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_sing := 1; array_type_pole[1] := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1") end if end if end if; if 1 <> found_sing 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 -1.0*glob_smallish_float < 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_sing := 1; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1") end if end if end if; if 1 <> found_sing 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_sing := 1; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1") end if end if; if 1 <> found_sing and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and -1.0*glob_smallish_float < 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_sing := 1; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1") end if end if end if; if 1 <> found_sing 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_sing := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1") end if end if end if; if 1 <> found_sing 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 for equation 1") 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_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 2 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 3; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 2; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 11 > # Begin Function number 12 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D1[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp3[1] := sqrt(array_tmp2[1]); > #emit pre arcsin FULL $eq_no = 1 > array_tmp4[1] := arcsin(array_tmp3[1]); > array_tmp4_a1[1] := cos(array_tmp4[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D1[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/2.0; > #emit pre arcsin FULL $eq_no = 1 > temp := att(1,array_tmp4_a1,array_tmp4,2); > array_tmp4[2] := (array_tmp3[2] - temp) / array_tmp4_a1[1]; > temp2 := att(1,array_tmp3,array_tmp4,1); > array_tmp4_a1[2] := -temp2; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp4[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := 0.0; > array_tmp3[3] := -ats(3,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre arcsin FULL $eq_no = 1 > temp := att(2,array_tmp4_a1,array_tmp4,2); > array_tmp4[3] := (array_tmp3[3] - temp) / array_tmp4_a1[1]; > temp2 := att(2,array_tmp3,array_tmp4,1); > array_tmp4_a1[3] := -temp2; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp4[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := 0.0; > array_tmp3[4] := -ats(4,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre arcsin FULL $eq_no = 1 > temp := att(3,array_tmp4_a1,array_tmp4,2); > array_tmp4[4] := (array_tmp3[4] - temp) / array_tmp4_a1[1]; > temp2 := att(3,array_tmp3,array_tmp4,1); > array_tmp4_a1[4] := -temp2; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp4[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := 0.0; > array_tmp3[5] := -ats(5,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre arcsin FULL $eq_no = 1 > temp := att(4,array_tmp4_a1,array_tmp4,2); > array_tmp4[5] := (array_tmp3[5] - temp) / array_tmp4_a1[1]; > temp2 := att(4,array_tmp3,array_tmp4,1); > array_tmp4_a1[5] := -temp2; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp4[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sqrt LINEAR $eq_no = 1 > array_tmp3[kkk] := 0.0; > array_tmp3[kkk] := -ats(kkk,array_tmp3,array_tmp3,2) /array_tmp3[1] / 2.0; > #emit arcsin $eq_no = 1 > temp := att(kkk-1,array_tmp4_a1,array_tmp4,2); > array_tmp4[kkk] := (array_tmp3[kkk] - temp) / array_tmp4_a1[1]; > temp2 := att(kkk-1,array_tmp3,array_tmp4,1); > array_tmp4_a1[kkk] := -temp2; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[kkk] := array_tmp4[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 2 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; Warning, `temp` is implicitly declared local to procedure `atomall` Warning, `temp2` is implicitly declared local to procedure `atomall` atomall := proc() local kkk, order_d, adj2, adj3, temporary, term, temp, temp2; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; array_tmp1[1] := array_const_0D1[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; array_tmp3[1] := sqrt(array_tmp2[1]); array_tmp4[1] := arcsin(array_tmp3[1]); array_tmp4_a1[1] := cos(array_tmp4[1]); array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_const_0D1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*2.0); temp := att(1, array_tmp4_a1, array_tmp4, 2); array_tmp4[2] := (array_tmp3[2] - temp)/array_tmp4_a1[1]; temp2 := att(1, array_tmp3, array_tmp4, 1); array_tmp4_a1[2] := -temp2; array_tmp5[2] := array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp3[3] := 0.; array_tmp3[3] := -ats(3, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; temp := att(2, array_tmp4_a1, array_tmp4, 2); array_tmp4[3] := (array_tmp3[3] - temp)/array_tmp4_a1[1]; temp2 := att(2, array_tmp3, array_tmp4, 1); array_tmp4_a1[3] := -temp2; array_tmp5[3] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp3[4] := 0.; array_tmp3[4] := -ats(4, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; temp := att(3, array_tmp4_a1, array_tmp4, 2); array_tmp4[4] := (array_tmp3[4] - temp)/array_tmp4_a1[1]; temp2 := att(3, array_tmp3, array_tmp4, 1); array_tmp4_a1[4] := -temp2; array_tmp5[4] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp3[5] := 0.; array_tmp3[5] := -ats(5, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; temp := att(4, array_tmp4_a1, array_tmp4, 2); array_tmp4[5] := (array_tmp3[5] - temp)/array_tmp4_a1[1]; temp2 := att(4, array_tmp3, array_tmp4, 1); array_tmp4_a1[5] := -temp2; array_tmp5[5] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp3[kkk] := 0.; array_tmp3[kkk] := -ats(kkk, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0); temp := att(kkk - 1, array_tmp4_a1, array_tmp4, 2); array_tmp4[kkk] := (array_tmp3[kkk] - temp)/array_tmp4_a1[1]; temp2 := att(kkk - 1, array_tmp3, array_tmp4, 1); array_tmp4_a1[kkk] := -temp2; array_tmp5[kkk] := array_tmp4[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp5[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 12 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, "\n") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > 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 16 > # Begin Function number 17 > 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 17 > # Begin Function number 18 > 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 18 > # Begin Function number 19 > 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 19 > # Begin Function number 20 > 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 20 > # Begin Function number 21 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 21 > # Begin Function number 22 > 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 22 > # Begin Function number 23 > 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 23 > # Begin Function number 24 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 24 > # Begin Function number 25 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc > # End Function number 25 > # Begin Function number 26 > 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 26 > # Begin Function number 27 > 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 27 > # Begin Function number 28 > 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 28 > # Begin Function number 29 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 29 > # Begin Function number 30 > 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 30 > # Begin Function number 31 > 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 31 > # Begin Function number 32 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 33 > # Begin Function number 34 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 34 > # Begin Function number 35 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 35 > # Begin Function number 36 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 36 > # Begin Function number 37 > 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 37 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(10.0 * (0.1 * x + 0.2) * arcsin(sqrt ( 0.1 * x + 0.2)) + 5.0 * sqrt( 0.1 * x + > 0.2) * sqrt( 0.8 - 0.1 * x) - 5.0 * arcsin(sqrt( 0.1 * x + 0.2))); > end; exact_soln_y := proc(x) return 10.0*(0.1*x + 0.2)*arcsin(sqrt(0.1*x + 0.2)) + 5.0*sqrt(0.1*x + 0.2)*sqrt(0.8 - 0.1*x) - 5.0*arcsin(sqrt(0.1*x + 0.2)) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, 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_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_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > 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_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_value3 := 0.0; > glob_ratio_of_radius := 0.01; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_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_max_h := 0.1; > 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_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-200; > 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_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/arcsin_sqrtpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = arcsin(sqrt(0.1 * x + 0.2));"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.0;"); > omniout_str(ALWAYS,"x_end := 0.5 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"glob_display_interval := 0.1;"); > omniout_str(ALWAYS,"glob_max_minutes := 10;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.001;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(10.0 * (0.1 * x + 0.2) * arcsin(sqrt ( 0.1 * x + 0.2)) + 5.0 * sqrt( 0.1 * x +"); > omniout_str(ALWAYS,"0.2) * sqrt( 0.8 - 0.1 * x) - 5.0 * arcsin(sqrt( 0.1 * x + 0.2)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4_a1:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4_a1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp4_a1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4_a1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D0[1] := 0.0; > array_const_0D1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D1[1] := 0.1; > array_const_0D2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D2[1] := 0.2; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3; > iiif := iiif + 1; > od;# end do number 2; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.0; > x_end := 0.5 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 1000000; > glob_display_interval := 0.1; > glob_max_minutes := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.001; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > if (glob_display_interval < glob_h) then # if number 2 > glob_h := glob_display_interval; > fi;# end if 2; > if (glob_max_h < glob_h) then # if number 2 > glob_h := glob_max_h; > 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_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 ) = arcsin(sqrt(0.1 * x + 0.2));"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 3 > logstart(html_log_file); > logitem_str(html_log_file,"2013-01-28T12:06:42-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"arcsin_sqrt") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = arcsin(sqrt(0.1 * x + 0.2));") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 4 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 4; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 4 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 4; > log_revs(html_log_file," 165 ") > ; > logitem_str(html_log_file,"arcsin_sqrt diffeq.mxt") > ; > logitem_str(html_log_file,"arcsin_sqrt maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > 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, 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_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_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, 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_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_value3 := 0.; glob_ratio_of_radius := 0.01; glob_percent_done := 0.; glob_subiter_method := 3; glob_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_max_h := 0.1; 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_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^(-200); 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_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/arcsin_sqrtpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = arcsin(sqrt(0.1 * x + 0.2));") ; omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.0;"); omniout_str(ALWAYS, "x_end := 0.5 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "glob_display_interval := 0.1;"); omniout_str(ALWAYS, "glob_max_minutes := 10;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.001;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(10.0 * (0.1 * x + 0.2) * arcsin(sqrt ( 0.\ 1 * x + 0.2)) + 5.0 * sqrt( 0.1 * x +"); omniout_str(ALWAYS, "0.2) * sqrt( 0.8 - 0.1 * x) - 5.0 * arcsin(sqrt(\ 0.1 * x + 0.2)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4_a1 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4_a1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4_a1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_a1[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_0D1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D1[term] := 0.; term := term + 1 end do; array_const_0D1[1] := 0.1; array_const_0D2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D2[term] := 0.; term := term + 1 end do; array_const_0D2[1] := 0.2; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.; x_end := 0.5; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_display_interval := 0.1; glob_max_minutes := 10; glob_desired_digits_correct := 10; glob_display_interval := 0.001; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_max_h < glob_h then glob_h := glob_max_h 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_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 ) = arcsin(sqrt(0.1 * x + 0.2));"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-01-28T12:06:42-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "arcsin_sqrt"); logitem_str(html_log_file, "diff ( y , x , 1 ) = arcsin(sqrt(0.1 * x + 0.2));"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 165 "); logitem_str(html_log_file, "arcsin_sqrt diffeq.mxt"); logitem_str(html_log_file, "arcsin_sqrt maple results"); logitem_str(html_log_file, "All Tests - All Languages"); 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/arcsin_sqrtpostode.ode################# diff ( y , x , 1 ) = arcsin(sqrt(0.1 * x + 0.2)); ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 0.5 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_display_interval := 0.1; glob_max_minutes := 10; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.001; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(10.0 * (0.1 * x + 0.2) * arcsin(sqrt ( 0.1 * x + 0.2)) + 5.0 * sqrt( 0.1 * x + 0.2) * sqrt( 0.8 - 0.1 * x) - 5.0 * arcsin(sqrt( 0.1 * x + 0.2))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 0.5 estimated_steps = 500 step_error = 2.0000000000000000000000000000000e-13 est_needed_step_err = 2.0000000000000000000000000000000e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 1.1718309454379427110227424203722e-90 max_value3 = 1.1718309454379427110227424203722e-90 value3 = 1.1718309454379427110227424203722e-90 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 0.6090571729975816513572313056163 y[1] (numeric) = 0.6090571729975816513572313056163 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.001 y[1] (analytic) = 0.6095208831026770820978879838655 y[1] (numeric) = 0.60952088310267708209788798386545 absolute error = 5e-32 relative error = 8.2031643847020135928787867007718e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.8MB, time=0.13 x[1] = 0.002 y[1] (analytic) = 0.6099847181843472541779969702107 y[1] (numeric) = 0.60998471818434725417799697021069 absolute error = 1e-32 relative error = 1.6393853324334984658192728658359e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.003 y[1] (analytic) = 0.6104486782191861298431324520456 y[1] (numeric) = 0.61044867821918612984313245204548 absolute error = 1.2e-31 relative error = 1.9657672181397222901078238641304e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.004 y[1] (analytic) = 0.6109127631838086164442505419117 y[1] (numeric) = 0.6109127631838086164442505419117 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.005 y[1] (analytic) = 0.6113769730548505410074765302546 y[1] (numeric) = 0.61137697305485054100747653025455 absolute error = 5e-32 relative error = 8.1782602557251007235327047029670e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.006 y[1] (analytic) = 0.6118413078089686248489230972898 y[1] (numeric) = 0.6118413078089686248489230972897 absolute error = 1.0e-31 relative error = 1.6344107323858946277117925364759e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.8MB, time=0.27 x[1] = 0.007 y[1] (analytic) = 0.6123057674228404582344384153974 y[1] (numeric) = 0.61230576742284045823443841539743 absolute error = 3e-32 relative error = 4.8995128898210879084248664485216e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.008 y[1] (analytic) = 0.6127703518731644750841833511355 y[1] (numeric) = 0.61277035187316447508418335113545 absolute error = 5e-32 relative error = 8.1596637055229709110119341743027e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.009 y[1] (analytic) = 0.6132350611366599277219372527391 y[1] (numeric) = 0.61323506113665992772193725273911 absolute error = 1e-32 relative error = 1.6306960631808186744711612244906e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (analytic) = 0.6136998951900668616690320848583 y[1] (numeric) = 0.61369989519006686166903208485818 absolute error = 1.2e-31 relative error = 1.9553531121727699994384824642355e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.011 y[1] (analytic) = 0.6141648540101460904828149472665 y[1] (numeric) = 0.61416485401014609048281494726634 absolute error = 1.6e-31 relative error = 2.6051637268933786515637906762677e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.1MB, time=0.42 x[1] = 0.012 y[1] (analytic) = 0.614629937573679170639539288377 y[1] (numeric) = 0.61462993757367917063953928837691 absolute error = 9e-32 relative error = 1.4642957411948582543910877742619e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.013 y[1] (analytic) = 0.6150951458574683764615853976086 y[1] (numeric) = 0.6150951458574683764615853976086 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.014 y[1] (analytic) = 0.6155604788383366750889110329727 y[1] (numeric) = 0.61556047883833667508891103297269 absolute error = 1e-32 relative error = 1.6245357432419371577124896761349e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.015 y[1] (analytic) = 0.6160259364931277014946333117 y[1] (numeric) = 0.61602593649312770149463331169984 absolute error = 1.6e-31 relative error = 2.5972932391586882063779294420356e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.016 y[1] (analytic) = 0.6164915187987057335446432622956 y[1] (numeric) = 0.61649151879870573354464326229554 absolute error = 6e-32 relative error = 9.7324939874137915561132465820690e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.1MB, time=0.57 x[1] = 0.017 y[1] (analytic) = 0.61695722573195566710115470611 y[1] (numeric) = 0.61695722573195566710115470611004 absolute error = 4e-32 relative error = 6.4834316435056181832915716351622e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.018 y[1] (analytic) = 0.6174230572697829911700894053354 y[1] (numeric) = 0.61742305726978299117008940533541 absolute error = 1e-32 relative error = 1.6196350107525220299561710247658e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.019 y[1] (analytic) = 0.6178890133891137630922006823022 y[1] (numeric) = 0.61788901338911376309220068230217 absolute error = 3e-32 relative error = 4.8552408846777130646988045810291e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.02 y[1] (analytic) = 0.6183550940668945837778379820439 y[1] (numeric) = 0.61835509406689458377783798204398 absolute error = 8e-32 relative error = 1.2937550085314810994243921347664e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.021 y[1] (analytic) = 0.6188212992800925729852551163342 y[1] (numeric) = 0.6188212992800925729852551163343 absolute error = 1.0e-31 relative error = 1.6159754054415268127495267795049e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.022 y[1] (analytic) = 0.6192876290056953446423651927772 y[1] (numeric) = 0.61928762900569534464236519277707 absolute error = 1.3e-31 relative error = 2.0991861279180250047155951537056e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.2MB, time=0.72 x[1] = 0.023 y[1] (analytic) = 0.6197540832207109822118454970576 y[1] (numeric) = 0.61975408322071098221184549705746 absolute error = 1.4e-31 relative error = 2.2589605101503181335667807210264e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.024 y[1] (analytic) = 0.6202206619021680140994958601316 y[1] (numeric) = 0.62022066190216801409949586013159 absolute error = 1e-32 relative error = 1.6123293876296842653680501617926e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.025 y[1] (analytic) = 0.6206873650271153891057543049593 y[1] (numeric) = 0.62068736502711538910575430495927 absolute error = 3e-32 relative error = 4.8333511668453921281710569318793e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.026 y[1] (analytic) = 0.6211541925726224519202740293642 y[1] (numeric) = 0.62115419257262245192027402936429 absolute error = 9e-32 relative error = 1.4489156006055230746244869500834e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.027 y[1] (analytic) = 0.6216211445157789186594660427454 y[1] (numeric) = 0.62162114451577891865946604274544 absolute error = 4e-32 relative error = 6.4347875475115309735041848610248e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.2MB, time=0.87 x[1] = 0.028 y[1] (analytic) = 0.6220882208336948524469120346621 y[1] (numeric) = 0.62208822083369485244691203466203 absolute error = 7e-32 relative error = 1.1252423314845782813343503428000e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.029 y[1] (analytic) = 0.6225554215035006390365523127825 y[1] (numeric) = 0.62255542150350063903655231278252 absolute error = 2e-32 relative error = 3.2125653892305778726416288451921e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.03 y[1] (analytic) = 0.6230227465023469624785539063179 y[1] (numeric) = 0.62302274650234696247855390631784 absolute error = 6e-32 relative error = 9.6304669992934160956861736723055e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.031 y[1] (analytic) = 0.6234901958074047808277641888643 y[1] (numeric) = 0.6234901958074047808277641888644 absolute error = 1.0e-31 relative error = 1.6038744582102435381417814956972e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.032 y[1] (analytic) = 0.6239577693958653018946556315594 y[1] (numeric) = 0.62395776939586530189465563155938 absolute error = 2e-32 relative error = 3.2053451340728719748077647615098e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.033 y[1] (analytic) = 0.6244254672449399590386675536054 y[1] (numeric) = 0.6244254672449399590386675536053 absolute error = 1.0e-31 relative error = 1.6014721571369469391441551323806e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.3MB, time=1.03 x[1] = 0.034 y[1] (analytic) = 0.6248932893318603870038509925553 y[1] (numeric) = 0.62489328933186038700385099255529 absolute error = 1e-32 relative error = 1.6002732259602370412413480865567e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.035 y[1] (analytic) = 0.6253612356338783977967230712678 y[1] (numeric) = 0.6253612356338783977967230712678 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.036 y[1] (analytic) = 0.6258293061282659566062374921429 y[1] (numeric) = 0.62582930612826595660623749214304 absolute error = 1.4e-31 relative error = 2.2370317054360905693089370207238e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.037 y[1] (analytic) = 0.6262975007923151577657780421459 y[1] (numeric) = 0.62629750079231515776577804214588 absolute error = 2e-32 relative error = 3.1933705586719475999844244493334e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.038 y[1] (analytic) = 0.6267658196033382007570822442044 y[1] (numeric) = 0.62676581960333820075708224420431 absolute error = 9e-32 relative error = 1.4359430138828944748408376067800e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.3MB, time=1.18 x[1] = 0.039 y[1] (analytic) = 0.6272342625386673662560025418522 y[1] (numeric) = 0.62723426253866736625600254185213 absolute error = 7e-32 relative error = 1.1160104634061612899629232855888e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.04 y[1] (analytic) = 0.6277028295756549922200126544619 y[1] (numeric) = 0.62770282957565499222001265446191 absolute error = 1e-32 relative error = 1.5931105499015011748351245036004e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.041 y[1] (analytic) = 0.6281715206916734500173669900926 y[1] (numeric) = 0.62817152069167345001736699009256 absolute error = 4e-32 relative error = 6.3676875952536650377879377765953e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.042 y[1] (analytic) = 0.6286403358641151205978212518581 y[1] (numeric) = 0.62864033586411512059782125185804 absolute error = 6e-32 relative error = 9.5444082374264650467924422701450e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.043 y[1] (analytic) = 0.6291092750703923707048226218127 y[1] (numeric) = 0.62910927507039237070482262181269 absolute error = 1e-32 relative error = 1.5895489696732064229593416852484e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.044 y[1] (analytic) = 0.6295783382879375291290781536472 y[1] (numeric) = 0.6295783382879375291290781536472 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.3MB, time=1.33 x[1] = 0.045 y[1] (analytic) = 0.6300475254942028630034102520006 y[1] (numeric) = 0.63004752549420286300341025200062 absolute error = 2e-32 relative error = 3.1743637091999057796461969185240e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.046 y[1] (analytic) = 0.6305168366666605541388083619203 y[1] (numeric) = 0.63051683666666055413880836192028 absolute error = 2e-32 relative error = 3.1720009422323373045070722918199e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.047 y[1] (analytic) = 0.6309862717828026754015862369468 y[1] (numeric) = 0.63098627178280267540158623694682 absolute error = 2e-32 relative error = 3.1696410673867046663317150034104e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.048 y[1] (analytic) = 0.6314558308201411671315543984676 y[1] (numeric) = 0.63145583082014116713155439846755 absolute error = 5e-32 relative error = 7.9182101992881273193136205764165e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.049 y[1] (analytic) = 0.631925513756207813601117642372 y[1] (numeric) = 0.63192551375620781360111764237196 absolute error = 4e-32 relative error = 6.3298599485621819606712245469793e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.3MB, time=1.49 x[1] = 0.05 y[1] (analytic) = 0.6323953205685542195152076916603 y[1] (numeric) = 0.63239532056855421951520769166033 absolute error = 3e-32 relative error = 4.7438681192372735522204302786030e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.051 y[1] (analytic) = 0.6328652512347517865519613355036 y[1] (numeric) = 0.6328652512347517865519613355036 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.052 y[1] (analytic) = 0.6333353057323916899440546363321 y[1] (numeric) = 0.63333530573239168994405463633216 absolute error = 6e-32 relative error = 9.4736547065879645214087561222086e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.053 y[1] (analytic) = 0.6338054840390848551006040268464 y[1] (numeric) = 0.6338054840390848551006040268463 absolute error = 1.0e-31 relative error = 1.5777711382792848218372927067981e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.054 y[1] (analytic) = 0.6342757861324619342695453583944 y[1] (numeric) = 0.63427578613246193426954535839438 absolute error = 2e-32 relative error = 3.1532025086360788437263190651000e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.055 y[1] (analytic) = 0.6347462119901732832404022009587 y[1] (numeric) = 0.63474621199017328324040220095872 absolute error = 2e-32 relative error = 3.1508655935562521541057094010402e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.3MB, time=1.64 x[1] = 0.056 y[1] (analytic) = 0.6352167615898889380873549330273 y[1] (numeric) = 0.63521676158988893808735493302736 absolute error = 6e-32 relative error = 9.4455945793724864321870247221227e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.057 y[1] (analytic) = 0.6356874349092985919525223969142 y[1] (numeric) = 0.63568743490929859195252239691412 absolute error = 8e-32 relative error = 1.2584801209955422808916392476381e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.058 y[1] (analytic) = 0.6361582319261115718693681316233 y[1] (numeric) = 0.63615823192611157186936813162315 absolute error = 1.5e-31 relative error = 2.3579039376074941927857426888512e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.059 y[1] (analytic) = 0.6366291526180568156261434311398 y[1] (numeric) = 0.63662915261805681562614343113977 absolute error = 3e-32 relative error = 4.7123195468867231305147031759747e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.06 y[1] (analytic) = 0.6371001969628828486692797110698 y[1] (numeric) = 0.63710019696288284866927971106981 absolute error = 1e-32 relative error = 1.5696118205065623601937599878036e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.3MB, time=1.79 x[1] = 0.061 y[1] (analytic) = 0.6375713649383577610466429008477 y[1] (numeric) = 0.63757136493835776104664290084752 absolute error = 1.8e-31 relative error = 2.8232133671405226817135803841750e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.062 y[1] (analytic) = 0.6380426565222691843905628122902 y[1] (numeric) = 0.63804265652226918439056281229002 absolute error = 1.8e-31 relative error = 2.8211279944998094034189469165497e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.063 y[1] (analytic) = 0.6385140716924242689405506680971 y[1] (numeric) = 0.6385140716924242689405506680972 absolute error = 1.0e-31 relative error = 1.5661361970448561793713098146774e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.064 y[1] (analytic) = 0.6389856104266496606056182059822 y[1] (numeric) = 0.6389856104266496606056182059821 absolute error = 1.0e-31 relative error = 1.5649804685465477293615329668156e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.065 y[1] (analytic) = 0.6394572727027914780661120054716 y[1] (numeric) = 0.63945727270279147806611200547154 absolute error = 6e-32 relative error = 9.3829568543959538920819570757282e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.066 y[1] (analytic) = 0.6399290584987152899149769150421 y[1] (numeric) = 0.639929058498715289914976915042 absolute error = 1.0e-31 relative error = 1.5626732162249631332228049931747e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.3MB, time=1.95 x[1] = 0.067 y[1] (analytic) = 0.6404009677923060918383626871547 y[1] (numeric) = 0.64040096779230609183836268715467 absolute error = 3e-32 relative error = 4.6845650629512409262345302233266e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.068 y[1] (analytic) = 0.6408730005614682838354881579287 y[1] (numeric) = 0.64087300056146828383548815792862 absolute error = 8e-32 relative error = 1.2482972434462376929682953646742e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.069 y[1] (analytic) = 0.6413451567841256474776775366449 y[1] (numeric) = 0.64134515678412564747767753664482 absolute error = 8e-32 relative error = 1.2473782510675089923531230357627e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.07 y[1] (analytic) = 0.6418174364382213232064835980089 y[1] (numeric) = 0.64181743643822132320648359800889 absolute error = 1e-32 relative error = 1.5580754638725927485806052089351e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.071 y[1] (analytic) = 0.6422898395017177876708127971197 y[1] (numeric) = 0.64228983950171778767081279711963 absolute error = 7e-32 relative error = 1.0898506514489676400803685269619e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.3MB, time=2.10 x[1] = 0.072 y[1] (analytic) = 0.6427623659525968311029675533963 y[1] (numeric) = 0.64276236595259683110296755339624 absolute error = 6e-32 relative error = 9.3347095564747093698237981278891e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.073 y[1] (analytic) = 0.643235015768859534733521175312 y[1] (numeric) = 0.64323501576885953473352117531195 absolute error = 5e-32 relative error = 7.7732086677891662976354725219823e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.074 y[1] (analytic) = 0.6437077889285262482449411226685 y[1] (numeric) = 0.64370778892852624824494112266846 absolute error = 4e-32 relative error = 6.2139996886757228148973380853199e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.075 y[1] (analytic) = 0.6441806854096365672638765273268 y[1] (numeric) = 0.64418068540963656726387652732674 absolute error = 6e-32 relative error = 9.3141569374818816946877272022654e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.076 y[1] (analytic) = 0.6446537051902493108920261167875 y[1] (numeric) = 0.64465370519024931089202611678747 absolute error = 3e-32 relative error = 4.6536613003948284831078318783337e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.077 y[1] (analytic) = 0.6451268482484424992755029077918 y[1] (numeric) = 0.64512684824844249927550290779172 absolute error = 8e-32 relative error = 1.2400662012006588411379054445679e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.3MB, time=2.25 x[1] = 0.078 y[1] (analytic) = 0.6456001145623133312126122591918 y[1] (numeric) = 0.64560011456231333121261225919171 absolute error = 9e-32 relative error = 1.3940517972338928211751843643381e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.079 y[1] (analytic) = 0.6460735041099781617999600947252 y[1] (numeric) = 0.64607350410997816179996009472517 absolute error = 3e-32 relative error = 4.6434345022905065752388098162810e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.08 y[1] (analytic) = 0.6465470168695724801168083270176 y[1] (numeric) = 0.64654701686957248011680832701747 absolute error = 1.3e-31 relative error = 2.0106813055828361759538783202293e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.081 y[1] (analytic) = 0.647020652819250886947594734136 y[1] (numeric) = 0.64702065281925088694759473413591 absolute error = 9e-32 relative error = 1.3909911470034951358571696390334e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.082 y[1] (analytic) = 0.6474944119371870725425347593326 y[1] (numeric) = 0.64749441193718707254253475933259 absolute error = 1e-32 relative error = 1.5444148730306095975758043623074e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.3MB, time=2.41 x[1] = 0.083 y[1] (analytic) = 0.6479682942015737944162229232389 y[1] (numeric) = 0.6479682942015737944162229232389 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.084 y[1] (analytic) = 0.6484422995906228551841517557181 y[1] (numeric) = 0.64844229959062285518415175571818 absolute error = 8e-32 relative error = 1.2337258079941101139796928757729e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.085 y[1] (analytic) = 0.6489164280825650804370663718461 y[1] (numeric) = 0.64891642808256508043706637184598 absolute error = 1.2e-31 relative error = 1.8492365858971867985105668721379e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.086 y[1] (analytic) = 0.649390679655650296653073033072 y[1] (numeric) = 0.64939067965565029665307303307206 absolute error = 6e-32 relative error = 9.2394304198846757766555272546497e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.087 y[1] (analytic) = 0.6498650542881473091474202505273 y[1] (numeric) = 0.64986505428814730914742025052725 absolute error = 5e-32 relative error = 7.6939050145986492346571940814242e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.088 y[1] (analytic) = 0.6503395519583438800598712026741 y[1] (numeric) = 0.65033955195834388005987120267406 absolute error = 4e-32 relative error = 6.1506331391885134978746727334811e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.3MB, time=2.56 x[1] = 0.089 y[1] (analytic) = 0.6508141726445467063795864540647 y[1] (numeric) = 0.6508141726445467063795864540647 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.09 y[1] (analytic) = 0.6512889163250813980074361758667 y[1] (numeric) = 0.65128891632508139800743617586664 absolute error = 6e-32 relative error = 9.2125013179330495353017431156290e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.091 y[1] (analytic) = 0.6517637829782924558556612820461 y[1] (numeric) = 0.65176378297829245585566128204605 absolute error = 5e-32 relative error = 7.6714910072972392049801919078231e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.092 y[1] (analytic) = 0.6522387725825432499848031076663 y[1] (numeric) = 0.65223877258254324998480310766619 absolute error = 1.1e-31 relative error = 1.6864989421658322163264216445438e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.093 y[1] (analytic) = 0.6527138851162159977778214676633 y[1] (numeric) = 0.65271388511621599777782146766322 absolute error = 8e-32 relative error = 1.2256518793951497506565691812849e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.3MB, time=2.71 x[1] = 0.094 y[1] (analytic) = 0.6531891205577117421513211457083 y[1] (numeric) = 0.6531891205577117421513211457083 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.095 y[1] (analytic) = 0.6536644788854503298038070733548 y[1] (numeric) = 0.65366447888545032980380707335481 absolute error = 1e-32 relative error = 1.5298368387786332586324899712303e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.096 y[1] (analytic) = 0.6541399600778703895008886696053 y[1] (numeric) = 0.65413996007787038950088866960523 absolute error = 7e-32 relative error = 1.0701073817851921496626057060768e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.097 y[1] (analytic) = 0.6546155641134293103973540203162 y[1] (numeric) = 0.65461556411342931039735402031615 absolute error = 5e-32 relative error = 7.6380707610759143221424629256862e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.098 y[1] (analytic) = 0.6550912909706032203960347854942 y[1] (numeric) = 0.65509129097060322039603478549407 absolute error = 1.3e-31 relative error = 1.9844562397919843857531583479756e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.099 y[1] (analytic) = 0.655567140627886964543382930522 y[1] (numeric) = 0.65556714062788696454338293052205 absolute error = 5e-32 relative error = 7.6269838589089688909792982155491e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.4MB, time=2.87 x[1] = 0.1 y[1] (analytic) = 0.6560431130637940834616805846994 y[1] (numeric) = 0.65604311306379408346168058469938 absolute error = 2e-32 relative error = 3.0485801316620461567761785830013e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.101 y[1] (analytic) = 0.6565192082568567918178045371763 y[1] (numeric) = 0.65651920825685679181780453717623 absolute error = 7e-32 relative error = 1.0662292758479836721905415609440e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.102 y[1] (analytic) = 0.6569954261856259568284670864246 y[1] (numeric) = 0.65699542618562595682846708642464 absolute error = 4e-32 relative error = 6.0883224457484264441861052590640e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.103 y[1] (analytic) = 0.6574717668286710768018551648088 y[1] (numeric) = 0.65747176682867107680185516480874 absolute error = 6e-32 relative error = 9.1258671515905944480370937759837e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.104 y[1] (analytic) = 0.6579482301645802597155898646028 y[1] (numeric) = 0.65794823016458025971558986460275 absolute error = 5e-32 relative error = 7.5993820953805008656445107532005e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.4MB, time=3.02 x[1] = 0.105 y[1] (analytic) = 0.6584248161719602018309286959577 y[1] (numeric) = 0.65842481617196020183092869595767 absolute error = 3e-32 relative error = 4.5563288720522538256726440602833e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.106 y[1] (analytic) = 0.6589015248294361663431331108386 y[1] (numeric) = 0.65890152482943616634313311083869 absolute error = 9e-32 relative error = 1.3659097241169305215594653257296e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.107 y[1] (analytic) = 0.6593783561156519620679240298475 y[1] (numeric) = 0.65937835611565196206792402984747 absolute error = 3e-32 relative error = 4.5497398757107727334552915196441e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.108 y[1] (analytic) = 0.6598553100092699221639483111091 y[1] (numeric) = 0.65985531000926992216394831110912 absolute error = 2e-32 relative error = 3.0309675009994284461911481373755e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.109 y[1] (analytic) = 0.6603323864889708828911793020446 y[1] (numeric) = 0.6603323864889708828911793020445 absolute error = 1.0e-31 relative error = 1.5143888448619994680789061859245e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 0.6608095855334541624051748158676 y[1] (numeric) = 0.66080958553345416240517481586755 absolute error = 5e-32 relative error = 7.5664761974716692066732939179987e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.4MB, time=3.17 x[1] = 0.111 y[1] (analytic) = 0.661286907121437539587116075046 y[1] (numeric) = 0.66128690712143753958711607504594 absolute error = 6e-32 relative error = 9.0732175934313043631985411909562e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.112 y[1] (analytic) = 0.6617643512316572329095513637445 y[1] (numeric) = 0.66176435123165723290955136374442 absolute error = 8e-32 relative error = 1.2088895367528674795939881700343e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.113 y[1] (analytic) = 0.6622419178428678793377683304356 y[1] (numeric) = 0.66224191784286787933776833043558 absolute error = 2e-32 relative error = 3.0200444069059155843880577279614e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.114 y[1] (analytic) = 0.6627196069338425132667190804147 y[1] (numeric) = 0.66271960693384251326671908041469 absolute error = 1e-32 relative error = 1.5089337776297710569697103286977e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.115 y[1] (analytic) = 0.6631974184833725454934223958961 y[1] (numeric) = 0.66319741848337254549342239589593 absolute error = 1.7e-31 relative error = 2.5633392902638715675787653092608e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.4MB, time=3.33 x[1] = 0.116 y[1] (analytic) = 0.663675352470267742224767618699 y[1] (numeric) = 0.66367535247026774222476761869896 absolute error = 4e-32 relative error = 6.0270431696937209991443630606705e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.117 y[1] (analytic) = 0.6641534088733562041206449272595 y[1] (numeric) = 0.66415340887335620412064492725946 absolute error = 4e-32 relative error = 6.0227049150970152016627455374861e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.118 y[1] (analytic) = 0.6646315876714843453723269358173 y[1] (numeric) = 0.66463158767148434537232693581719 absolute error = 1.1e-31 relative error = 1.6550522430837436680479513120522e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.119 y[1] (analytic) = 0.6651098888435168728160267391523 y[1] (numeric) = 0.66510988884351687281602673915234 absolute error = 4e-32 relative error = 6.0140437950112877964813068093466e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 0.665588312368336765081557721158 y[1] (numeric) = 0.66558831236833676508155772115794 absolute error = 6e-32 relative error = 9.0145813688501162562981840562195e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.121 y[1] (analytic) = 0.6660668582248452517760206398544 y[1] (numeric) = 0.66606685822484525177602063985426 absolute error = 1.4e-31 relative error = 2.1018910980365874424819182558834e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.4MB, time=3.48 x[1] = 0.122 y[1] (analytic) = 0.6665455263919617927024436951737 y[1] (numeric) = 0.66654552639196179270244369517368 absolute error = 2e-32 relative error = 3.0005452303101962647377347741537e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.123 y[1] (analytic) = 0.6670243168486240571133014789723 y[1] (numeric) = 0.66702431684862405711330147897226 absolute error = 4e-32 relative error = 5.9967828742707871351555935421854e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.124 y[1] (analytic) = 0.6675032295737879029988388992606 y[1] (numeric) = 0.66750322957378790299883889926049 absolute error = 1.1e-31 relative error = 1.6479321016954009297889502358256e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.125 y[1] (analytic) = 0.6679822645464273564101263625918 y[1] (numeric) = 0.66798226454642735641012636259178 absolute error = 2e-32 relative error = 2.9940914694165390497802346751214e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.126 y[1] (analytic) = 0.6684614217455345908167726899054 y[1] (numeric) = 0.66846142174553459081677268990542 absolute error = 2e-32 relative error = 2.9919452865020332939775366248130e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.127 y[1] (analytic) = 0.6689407011501199064992224318933 y[1] (numeric) = 0.66894070115011990649922243189329 absolute error = 1e-32 relative error = 1.4949008159926355404670977482856e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 memory used=91.5MB, alloc=4.4MB, time=3.64 TOP MAIN SOLVE Loop x[1] = 0.128 y[1] (analytic) = 0.6694201027392117099755644401484 y[1] (numeric) = 0.66942010273921170997556444014838 absolute error = 2e-32 relative error = 2.9876605017031388336013399063594e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.129 y[1] (analytic) = 0.6698996264918564934627787399603 y[1] (numeric) = 0.66989962649185649346277873996024 absolute error = 6e-32 relative error = 8.9565656745039816067450437942941e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 0.6703792723871188143723489396501 y[1] (numeric) = 0.67037927238711881437234893965009 absolute error = 1e-32 relative error = 1.4916928986171541617707934915930e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.131 y[1] (analytic) = 0.6708590404040812748401675997883 y[1] (numeric) = 0.67085904040408127484016759978817 absolute error = 1.3e-31 relative error = 1.9378139395974535468500408627796e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.132 y[1] (analytic) = 0.6713389305218445012906621735106 y[1] (numeric) = 0.67133893052184450129066217351048 absolute error = 1.2e-31 relative error = 1.7874726839797853055503388545061e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.4MB, time=3.80 x[1] = 0.133 y[1] (analytic) = 0.6718189427195271240350693164531 y[1] (numeric) = 0.671818942719527124035069316453 absolute error = 1.0e-31 relative error = 1.4884962843589881235862661113392e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.134 y[1] (analytic) = 0.672299076976265756903785551551 y[1] (numeric) = 0.67229907697626575690378555155086 absolute error = 1.4e-31 relative error = 2.0824065478367811937833537835391e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.135 y[1] (analytic) = 0.6727793332712149769127224601103 y[1] (numeric) = 0.6727793332712149769127224601101 absolute error = 2.0e-31 relative error = 2.9727429204394832346396502840342e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.136 y[1] (analytic) = 0.6732597115835473039635947561522 y[1] (numeric) = 0.67325971158354730396359475615218 absolute error = 2e-32 relative error = 2.9706218352140510557974773211427e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.137 y[1] (analytic) = 0.6737402118924531805780697860585 y[1] (numeric) = 0.67374021189245318057806978605837 absolute error = 1.3e-31 relative error = 1.9295271041466566092976211009857e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.138 y[1] (analytic) = 0.6742208341771409516657071800052 y[1] (numeric) = 0.67422083417714095166570718000503 absolute error = 1.7e-31 relative error = 2.5214290538422484551179272512152e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.4MB, time=3.95 x[1] = 0.139 y[1] (analytic) = 0.6747015784168368443256175655827 y[1] (numeric) = 0.67470157841683684432561756558268 absolute error = 2e-32 relative error = 2.9642734862024905391480450671527e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 0.6751824445907849476817694373346 y[1] (numeric) = 0.67518244459078494768176943733446 absolute error = 1.4e-31 relative error = 2.0735136276366204805811912000800e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.141 y[1] (analytic) = 0.6756634326782471927518734587348 y[1] (numeric) = 0.67566343267824719275187345873467 absolute error = 1.3e-31 relative error = 1.9240348628117390191115182901036e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.142 y[1] (analytic) = 0.6761445426585033323497736553574 y[1] (numeric) = 0.67614454265850333234977365535735 absolute error = 5e-32 relative error = 7.3948685296500617628840718182296e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.143 y[1] (analytic) = 0.6766257745108509210212751396609 y[1] (numeric) = 0.6766257745108509210212751396608 absolute error = 1.0e-31 relative error = 1.4779218257284450919086321054780e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=103.0MB, alloc=4.4MB, time=4.10 x[1] = 0.144 y[1] (analytic) = 0.677107128214605295013338188938 y[1] (numeric) = 0.67710712821460529501333818893786 absolute error = 1.4e-31 relative error = 2.0676196449024501720063654877639e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.145 y[1] (analytic) = 0.6775886037490995522765686785562 y[1] (numeric) = 0.67758860374909955227656867855609 absolute error = 1.1e-31 relative error = 1.6234039266801375721484580794231e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.146 y[1] (analytic) = 0.6780702010936845325009350526384 y[1] (numeric) = 0.67807020109368453250093505263836 absolute error = 4e-32 relative error = 5.8990942140625733180930287324903e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.147 y[1] (analytic) = 0.6785519202277287971846421938149 y[1] (numeric) = 0.67855192022772879718464219381481 absolute error = 9e-32 relative error = 1.3263539210057072963970632483184e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.148 y[1] (analytic) = 0.6790337611306186097360927326137 y[1] (numeric) = 0.67903376113061860973609273261357 absolute error = 1.3e-31 relative error = 1.9144850733716797055628132570268e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.149 y[1] (analytic) = 0.679515723781757915608866515452 y[1] (numeric) = 0.67951572378175791560886651545186 absolute error = 1.4e-31 relative error = 2.0602908085900925532057233508706e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.4MB, time=4.26 x[1] = 0.15 y[1] (analytic) = 0.6799978081605683224696491280433 y[1] (numeric) = 0.6799978081605683224696491280432 absolute error = 1.0e-31 relative error = 1.4705929754465757820455995020002e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.151 y[1] (analytic) = 0.6804800142464890803990405483521 y[1] (numeric) = 0.680480014246489080399040548352 absolute error = 1.0e-31 relative error = 1.4695508744769273361062685272543e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.152 y[1] (analytic) = 0.6809623420189770621251751800064 y[1] (numeric) = 0.68096234201897706212517518000626 absolute error = 1.4e-31 relative error = 2.0559139817470035555128698180933e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.153 y[1] (analytic) = 0.6814447914575067432900846933234 y[1] (numeric) = 0.68144479145750674329008469332334 absolute error = 6e-32 relative error = 8.8048218655643588638662325157754e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.154 y[1] (analytic) = 0.6819273625415701827487352768161 y[1] (numeric) = 0.68192736254157018274873527681605 absolute error = 5e-32 relative error = 7.3321592220098087077393489713252e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.4MB, time=4.41 x[1] = 0.155 y[1] (analytic) = 0.682410055250677002900671077227 y[1] (numeric) = 0.68241005525067700290067107722689 absolute error = 1.1e-31 relative error = 1.6119340439611857785217589926657e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.156 y[1] (analytic) = 0.6828928695643543700541957807906 y[1] (numeric) = 0.68289286956435437005419578079056 absolute error = 4e-32 relative error = 5.8574341280672114508793931306699e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.157 y[1] (analytic) = 0.6833758054621469748230244625494 y[1] (numeric) = 0.68337580546214697482302446254938 absolute error = 2e-32 relative error = 2.9266473644724058881998319183281e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.158 y[1] (analytic) = 0.6838588629236170125553380041459 y[1] (numeric) = 0.68385886292361701255533800414583 absolute error = 7e-32 relative error = 1.0236030238862106506351128203046e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.159 y[1] (analytic) = 0.6843420419283441637951725535923 y[1] (numeric) = 0.68434204192834416379517255359218 absolute error = 1.2e-31 relative error = 1.7535091028729302605949447299728e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 0.6848253424559255747760766730715 y[1] (numeric) = 0.68482534245592557477607667307149 absolute error = 1e-32 relative error = 1.4602263351028932408652737240844e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.4MB, time=4.57 x[1] = 0.161 y[1] (analytic) = 0.6853087644859758379469689928586 y[1] (numeric) = 0.68530876448597583794696899285844 absolute error = 1.6e-31 relative error = 2.3347140484918494109869767894935e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.162 y[1] (analytic) = 0.6857923079981269725301293609648 y[1] (numeric) = 0.68579230799812697253012936096471 absolute error = 9e-32 relative error = 1.3123506774626262924911529366328e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.163 y[1] (analytic) = 0.6862759729720284051112566491137 y[1] (numeric) = 0.68627597297202840511125664911357 absolute error = 1.3e-31 relative error = 1.8942816755920232102236661384080e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.164 y[1] (analytic) = 0.6867597593873469502615265461338 y[1] (numeric) = 0.6867597593873469502615265461337 absolute error = 1.0e-31 relative error = 1.4561132715348555608011965726562e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.165 y[1] (analytic) = 0.6872436672237667911915828398352 y[1] (numeric) = 0.68724366722376679119158283983508 absolute error = 1.2e-31 relative error = 1.7461055768583452919394895600924e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.4MB, time=4.72 x[1] = 0.166 y[1] (analytic) = 0.6877276964609894604373958578915 y[1] (numeric) = 0.68772769646098946043739585789148 absolute error = 2e-32 relative error = 2.9081277521494259504907582764615e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.167 y[1] (analytic) = 0.6882118470787338205779219072069 y[1] (numeric) = 0.68821184707873382057792190720678 absolute error = 1.2e-31 relative error = 1.7436491468341663710452112206287e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.168 y[1] (analytic) = 0.6886961190567360449844977196877 y[1] (numeric) = 0.68869611905673604498449771968762 absolute error = 8e-32 relative error = 1.1616153741300443394522361983133e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.169 y[1] (analytic) = 0.6891805123747495986019040802846 y[1] (numeric) = 0.68918051237474959860190408028443 absolute error = 1.7e-31 relative error = 2.4666977221137762217594905336857e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 0.6896650270125452187610329805987 y[1] (numeric) = 0.68966502701254521876103298059859 absolute error = 1.1e-31 relative error = 1.5949772091023990143448995864653e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.171 y[1] (analytic) = 0.6901496629499108960230928082872 y[1] (numeric) = 0.69014966294991089602309280828714 absolute error = 6e-32 relative error = 8.6937664713971800819915243456635e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.4MB, time=4.87 x[1] = 0.172 y[1] (analytic) = 0.6906344201666518550552862489296 y[1] (numeric) = 0.69063442016665185505528624892961 absolute error = 1e-32 relative error = 1.4479440508607975807342216467565e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.173 y[1] (analytic) = 0.6911192986425905355378957429561 y[1] (numeric) = 0.69111929864259053553789574295599 absolute error = 1.1e-31 relative error = 1.5916210155909137979505025957910e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.174 y[1] (analytic) = 0.6916042983575665731027115056725 y[1] (numeric) = 0.69160429835756657310271150567243 absolute error = 7e-32 relative error = 1.0121394584480918919053356086786e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.175 y[1] (analytic) = 0.6920894192914367803027372833639 y[1] (numeric) = 0.69208941929143678030273728336367 absolute error = 2.3e-31 relative error = 3.3232699935721411354168337025967e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.176 y[1] (analytic) = 0.6925746614240751276131091828998 y[1] (numeric) = 0.69257466142407512761310918289984 absolute error = 4e-32 relative error = 5.7755505980758551648556669579736e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.4MB, time=5.03 x[1] = 0.177 y[1] (analytic) = 0.6930600247353727244631630762324 y[1] (numeric) = 0.69306002473537272446316307623235 absolute error = 5e-32 relative error = 7.2143823356557353631320164616672e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.178 y[1] (analytic) = 0.6935455092052378002995862446305 y[1] (numeric) = 0.69354550920523780029958624463039 absolute error = 1.1e-31 relative error = 1.5860530929838116103173373437163e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.179 y[1] (analytic) = 0.694031114813595685680589090488 y[1] (numeric) = 0.69403111481359568568058909048803 absolute error = 3e-32 relative error = 4.3225727722679208895560207242954e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 0.6945168415403887934010329070236 y[1] (numeric) = 0.69451684154038879340103290702344 absolute error = 1.6e-31 relative error = 2.3037598288492388132059561641577e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.181 y[1] (analytic) = 0.6950026893655765996484498581985 y[1] (numeric) = 0.69500268936557659964844985819847 absolute error = 3e-32 relative error = 4.3165300593851049382194145733871e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.182 y[1] (analytic) = 0.69548865826913562518989148271 y[1] (numeric) = 0.69548865826913562518989148270995 absolute error = 5e-32 relative error = 7.1891898459473265719340409813740e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.4MB, time=5.18 x[1] = 0.183 y[1] (analytic) = 0.6959747482310594165895421969455 y[1] (numeric) = 0.69597474823105941658954219694546 absolute error = 4e-32 relative error = 5.7473349574344386095320189392936e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.184 y[1] (analytic) = 0.6964609592313585274570344323578 y[1] (numeric) = 0.69646095923135852745703443235773 absolute error = 7e-32 relative error = 1.0050814632489196464612863967068e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.185 y[1] (analytic) = 0.6969472912500604997264022027948 y[1] (numeric) = 0.69694729125006049972640220279478 absolute error = 2e-32 relative error = 2.8696574692366686008096930728494e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.186 y[1] (analytic) = 0.6974337442672098449656100569291 y[1] (numeric) = 0.69743374426720984496561005692892 absolute error = 1.8e-31 relative error = 2.5808903208307636710757832781687e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.187 y[1] (analytic) = 0.6979203182628680257165945300589 y[1] (numeric) = 0.6979203182628680257165945300588 absolute error = 1.0e-31 relative error = 1.4328283241402283508852387512258e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.188 y[1] (analytic) = 0.6984070132171134368657553682163 y[1] (numeric) = 0.69840701321711343686575536821613 absolute error = 1.7e-31 relative error = 2.4341107231572456377718836077625e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 memory used=133.5MB, alloc=4.4MB, time=5.34 TOP MAIN SOLVE Loop x[1] = 0.189 y[1] (analytic) = 0.6988938291100413870448339556942 y[1] (numeric) = 0.69889382911004138704483395569424 absolute error = 4e-32 relative error = 5.7233299728708819823762047444248e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 0.6993807659217640800621165348311 y[1] (numeric) = 0.69938076592176408006211653483092 absolute error = 1.8e-31 relative error = 2.5737053229189837393778057116017e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.191 y[1] (analytic) = 0.6998678236324105963638999641248 y[1] (numeric) = 0.69986782363241059636389996412467 absolute error = 1.3e-31 relative error = 1.8574935953660800999739812199881e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.192 y[1] (analytic) = 0.7003550022221268745261579175431 y[1] (numeric) = 0.70035500222212687452615791754294 absolute error = 1.6e-31 relative error = 2.2845556823659821402904328837684e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.193 y[1] (analytic) = 0.7008423016710756927763455841952 y[1] (numeric) = 0.70084230167107569277634558419514 absolute error = 6e-32 relative error = 8.5611270690905909247674059683368e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.4MB, time=5.49 x[1] = 0.194 y[1] (analytic) = 0.7013297219594366505452810833935 y[1] (numeric) = 0.70132972195943665054528108339338 absolute error = 1.2e-31 relative error = 1.7110354265998230828417288758602e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.195 y[1] (analytic) = 0.7018172630674061500490419655119 y[1] (numeric) = 0.70181726306740615004904196551192 absolute error = 2e-32 relative error = 2.8497446632456370393211715902026e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.196 y[1] (analytic) = 0.7023049249751973779008153239836 y[1] (numeric) = 0.70230492497519737790081532398353 absolute error = 7e-32 relative error = 9.9671805665426769048875678003106e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.197 y[1] (analytic) = 0.7027927076630402867526401982392 y[1] (numeric) = 0.7027927076630402867526401982391 absolute error = 1.0e-31 relative error = 1.4228946730612039603232466409710e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.198 y[1] (analytic) = 0.7032806111111815769669811014075 y[1] (numeric) = 0.70328061111118157696698110140753 absolute error = 3e-32 relative error = 4.2657226043243359569136803217350e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.199 y[1] (analytic) = 0.7037686352998846783180716601475 y[1] (numeric) = 0.70376863529988467831807166014745 absolute error = 5e-32 relative error = 7.1046076071142855537522038492403e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.4MB, time=5.65 x[1] = 0.2 y[1] (analytic) = 0.7042567802094297317229675070826 y[1] (numeric) = 0.70425678020942973172296750708252 absolute error = 8e-32 relative error = 1.1359493049709772645838593580654e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.201 y[1] (analytic) = 0.7047450458201135710022477189595 y[1] (numeric) = 0.70474504582011357100224771895944 absolute error = 6e-32 relative error = 8.5137171741559176280548734326552e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.202 y[1] (analytic) = 0.7052334321122497046703042458437 y[1] (numeric) = 0.70523343211224970467030424584366 absolute error = 4e-32 relative error = 5.6718808523010194579148327014279e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.203 y[1] (analytic) = 0.7057219390661682977551589284141 y[1] (numeric) = 0.70572193906616829775515892841404 absolute error = 6e-32 relative error = 8.5019320894846683036289140567505e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.204 y[1] (analytic) = 0.7062105666622161536477478517158 y[1] (numeric) = 0.70621056666221615364774785171567 absolute error = 1.3e-31 relative error = 1.8408107459284110855937632507824e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.4MB, time=5.80 x[1] = 0.205 y[1] (analytic) = 0.706699314880756695980612934581 y[1] (numeric) = 0.70669931488075669598061293458102 absolute error = 2e-32 relative error = 2.8300579297115428194593207592860e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.206 y[1] (analytic) = 0.707188183702169950535940804336 y[1] (numeric) = 0.70718818370216995053594080433593 absolute error = 7e-32 relative error = 9.8983554325732734359375793585828e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.207 y[1] (analytic) = 0.7076771731068525271828891563688 y[1] (numeric) = 0.70767717310685252718288915636882 absolute error = 2e-32 relative error = 2.8261473960218001952476841993834e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.208 y[1] (analytic) = 0.708166283075217601844140947662 y[1] (numeric) = 0.70816628307521760184414094766197 absolute error = 3e-32 relative error = 4.2362931866403983904331624868430e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.209 y[1] (analytic) = 0.7086555135876948984916269224629 y[1] (numeric) = 0.70865551358769489849162692246278 absolute error = 1.2e-31 relative error = 1.6933474403166441576135082340716e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 0.7091448646247306711713571169135 y[1] (numeric) = 0.7091448646247306711713571169134 absolute error = 1.0e-31 relative error = 1.4101491104066384379877121972699e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.4MB, time=5.96 x[1] = 0.211 y[1] (analytic) = 0.7096343361667876860573021376597 y[1] (numeric) = 0.70963433616678768605730213765957 absolute error = 1.3e-31 relative error = 1.8319293948235006700930470118215e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.212 y[1] (analytic) = 0.710123928194345203534265157226 y[1] (numeric) = 0.71012392819434520353426515722575 absolute error = 2.5e-31 relative error = 3.5205122665797642675782058115708e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.213 y[1] (analytic) = 0.7106136406878989603096857162753 y[1] (numeric) = 0.71061364068789896030968571627529 absolute error = 1e-32 relative error = 1.4072344558879630862175737381478e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.214 y[1] (analytic) = 0.7111034736279611515543165697729 y[1] (numeric) = 0.71110347362796115155431656977279 absolute error = 1.1e-31 relative error = 1.5468916139418322891236557009788e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.215 y[1] (analytic) = 0.7115934269950604130717149605324 y[1] (numeric) = 0.71159342699506041307171496053228 absolute error = 1.2e-31 relative error = 1.6863562175769365322268150147027e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.4MB, time=6.12 x[1] = 0.216 y[1] (analytic) = 0.7120835007697418034964898496711 y[1] (numeric) = 0.71208350076974180349648984967106 absolute error = 4e-32 relative error = 5.6173187493827829672158528602641e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.217 y[1] (analytic) = 0.7125736949325667865212467790967 y[1] (numeric) = 0.71257369493256678652124677909661 absolute error = 9e-32 relative error = 1.2630272579528353017788817684217e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.218 y[1] (analytic) = 0.7130640094641132131521721863338 y[1] (numeric) = 0.71306400946411321315217218633378 absolute error = 2e-32 relative error = 2.8047972881187115396406522690743e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.219 y[1] (analytic) = 0.7135544443449753039931991367536 y[1] (numeric) = 0.7135544443449753039931991367536 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 0.7140449995557636315586965825946 y[1] (numeric) = 0.7140449995557636315586965825945 absolute error = 1.0e-31 relative error = 1.4004719599214903508593961172008e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.221 y[1] (analytic) = 0.7145356750771051026146244020733 y[1] (numeric) = 0.71453567507710510261462440207328 absolute error = 2e-32 relative error = 2.7990204964702164624589626272560e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.4MB, time=6.27 x[1] = 0.222 y[1] (analytic) = 0.7150264708896429405480966153678 y[1] (numeric) = 0.71502647088964294054809661536773 absolute error = 7e-32 relative error = 9.7898473482954154376207644802094e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.223 y[1] (analytic) = 0.7155173869740366677652953173176 y[1] (numeric) = 0.7155173869740366677652953173176 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.224 y[1] (analytic) = 0.7160084233109620881176780093363 y[1] (numeric) = 0.71600842331096208811767800933616 absolute error = 1.4e-31 relative error = 1.9552842598221511755903958163412e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.225 y[1] (analytic) = 0.7164995798811112693564211552532 y[1] (numeric) = 0.71649957988111126935642115525313 absolute error = 7e-32 relative error = 9.7697196154134655093868724987916e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.226 y[1] (analytic) = 0.716990856665192525615042927622 y[1] (numeric) = 0.71699085666519252561504292762193 absolute error = 7e-32 relative error = 9.7630254764444421668885463740285e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.4MB, time=6.43 x[1] = 0.227 y[1] (analytic) = 0.7174822536439303999201482524222 y[1] (numeric) = 0.71748225364393039992014825242215 absolute error = 5e-32 relative error = 6.9688134788088886006518028462698e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.228 y[1] (analytic) = 0.7179737707980656467302394010729 y[1] (numeric) = 0.71797377079806564673023940107277 absolute error = 1.3e-31 relative error = 1.8106511029713265938731535351185e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.229 y[1] (analytic) = 0.7184654081083552145025355192442 y[1] (numeric) = 0.71846540810835521450253551924421 absolute error = 1e-32 relative error = 1.3918554584734929969524430429514e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = 0.7189571655555722282877446221203 y[1] (numeric) = 0.71895716555557222828774462212016 absolute error = 1.4e-31 relative error = 1.9472648261571379450200363636562e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.231 y[1] (analytic) = 0.7194490431205059723527317255132 y[1] (numeric) = 0.71944904312050597235273172551307 absolute error = 1.3e-31 relative error = 1.8069382570326848684889084282987e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.232 y[1] (analytic) = 0.7199410407839618728310269215833 y[1] (numeric) = 0.71994104078396187283102692158327 absolute error = 3e-32 relative error = 4.1670078937758912695042074413665e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.4MB, time=6.58 x[1] = 0.233 y[1] (analytic) = 0.720433158526761480401117346851 y[1] (numeric) = 0.72043315852676148040111734685101 absolute error = 1e-32 relative error = 1.3880538231262624828458815617824e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.234 y[1] (analytic) = 0.7209253963297424529924671287255 y[1] (numeric) = 0.72092539632974245299246712872539 absolute error = 1.1e-31 relative error = 1.5258166872746337024881589536330e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.235 y[1] (analytic) = 0.7214177541737585385192095349051 y[1] (numeric) = 0.72141775417375853851920953490501 absolute error = 9e-32 relative error = 1.2475434584095759194852748581171e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.236 y[1] (analytic) = 0.7219102320396795576414556877343 y[1] (numeric) = 0.72191023203967955764145568773431 absolute error = 1e-32 relative error = 1.3852137781377717472837310822134e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.237 y[1] (analytic) = 0.7224028299083913865541643429273 y[1] (numeric) = 0.72240282990839138655416434292722 absolute error = 8e-32 relative error = 1.1074153739146464679726163367853e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.238 y[1] (analytic) = 0.7228955477607959398035173689986 y[1] (numeric) = 0.72289554776079593980351736899859 absolute error = 1e-32 relative error = 1.3833257143408180561163497145094e-30 % Correct digits = 31 h = 0.001 memory used=167.8MB, alloc=4.4MB, time=6.74 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.239 y[1] (analytic) = 0.723388385577811153130745700274 y[1] (numeric) = 0.72338838557781115313074570027399 absolute error = 1e-32 relative error = 1.3823832673249841165728739666768e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 0.7238813433403709663433506724822 y[1] (numeric) = 0.72388134334037096634335067248219 absolute error = 1e-32 relative error = 1.3814418746938160749962799796264e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.241 y[1] (analytic) = 0.7243744210294253062136657856727 y[1] (numeric) = 0.72437442102942530621366578567254 absolute error = 1.6e-31 relative error = 2.2088024556778286782936844502926e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.242 y[1] (analytic) = 0.7248676186259400694047040745436 y[1] (numeric) = 0.72486761862594006940470407454353 absolute error = 7e-32 relative error = 9.6569357219587328619780952926201e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.243 y[1] (analytic) = 0.7253609361108971054232364012199 y[1] (numeric) = 0.72536093611089710542323640121978 absolute error = 1.2e-31 relative error = 1.6543488079657732020961963920195e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.4MB, time=6.90 x[1] = 0.244 y[1] (analytic) = 0.7258543734652941996000461200743 y[1] (numeric) = 0.72585437346529419960004612007421 absolute error = 9e-32 relative error = 1.2399181335827996512807510092850e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.245 y[1] (analytic) = 0.7263479306701450560973056983617 y[1] (numeric) = 0.7263479306701450560973056983616 absolute error = 1.0e-31 relative error = 1.3767506697201950382213613610672e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.246 y[1] (analytic) = 0.7268416077064792809430210102102 y[1] (numeric) = 0.72684160770647928094302101021003 absolute error = 1.7e-31 relative error = 2.3388864671139074878331832770606e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.247 y[1] (analytic) = 0.7273354045553423650924891549096 y[1] (numeric) = 0.72733540455534236509248915490957 absolute error = 3e-32 relative error = 4.1246445329222694484993633503239e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.248 y[1] (analytic) = 0.7278293211977956675167157834441 y[1] (numeric) = 0.72782932119779566751671578344408 absolute error = 2e-32 relative error = 2.7478969886903991339128934343614e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.249 y[1] (analytic) = 0.7283233576149163983177380498334 y[1] (numeric) = 0.72832335761491639831773804983339 absolute error = 1e-32 relative error = 1.3730165173814542766353052076948e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.4MB, time=7.05 x[1] = 0.25 y[1] (analytic) = 0.7288175137877976018707994360911 y[1] (numeric) = 0.72881751378779760187079943609093 absolute error = 1.7e-31 relative error = 2.3325454833882761842087504543316e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.251 y[1] (analytic) = 0.7293117896975481399933228314572 y[1] (numeric) = 0.72931178969754813999332283145712 absolute error = 8e-32 relative error = 1.0969245407807912547884636793271e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.252 y[1] (analytic) = 0.729806185325292675140628378043 y[1] (numeric) = 0.72980618532529267514062837804294 absolute error = 6e-32 relative error = 8.2213608498339206810930137489737e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.253 y[1] (analytic) = 0.7303007006521716536283427261124 y[1] (numeric) = 0.73030070065217165362834272611228 absolute error = 1.2e-31 relative error = 1.6431587686118586887572375919203e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.254 y[1] (analytic) = 0.7307953356593412888814464729472 y[1] (numeric) = 0.73079533565934128888144647294718 absolute error = 2e-32 relative error = 2.7367443419648422608361269922999e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.4MB, time=7.21 x[1] = 0.255 y[1] (analytic) = 0.7312900903279735447099066895784 y[1] (numeric) = 0.7312900903279735447099066895783 absolute error = 1.0e-31 relative error = 1.3674463981202230671657483515545e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.256 y[1] (analytic) = 0.7317849646392561186108415696249 y[1] (numeric) = 0.73178496463925611861084156962491 absolute error = 1e-32 relative error = 1.3665216536567737837336899077912e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.257 y[1] (analytic) = 0.732279958574392425097164364076 y[1] (numeric) = 0.73227995857439242509716436407591 absolute error = 9e-32 relative error = 1.2290381423958755960549161948423e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.258 y[1] (analytic) = 0.732775072114601579052653895057 y[1] (numeric) = 0.73277507211460157905265389505695 absolute error = 5e-32 relative error = 6.8233762177134081206568641633587e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.259 y[1] (analytic) = 0.7332703052411183791133990704699 y[1] (numeric) = 0.73327030524111837911339907046978 absolute error = 1.2e-31 relative error = 1.6365042896499248503830870081907e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = 0.7337656579351932910755649498601 y[1] (numeric) = 0.73376565793519329107556494986003 absolute error = 7e-32 relative error = 9.5398304953353990547478719028386e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.4MB, time=7.36 x[1] = 0.261 y[1] (analytic) = 0.7342611301780924313294280399698 y[1] (numeric) = 0.73426113017809243132942803996975 absolute error = 5e-32 relative error = 6.8095665077453681149323332909251e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.262 y[1] (analytic) = 0.7347567219510975503196286261624 y[1] (numeric) = 0.73475672195109755031962862616239 absolute error = 1e-32 relative error = 1.3609946940595066438078772097262e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.263 y[1] (analytic) = 0.735252433235506016031588073272 y[1] (numeric) = 0.73525243323550601603158807327185 absolute error = 1.5e-31 relative error = 2.0401156557880312239125771150687e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.264 y[1] (analytic) = 0.7357482640126307975040391564251 y[1] (numeric) = 0.73574826401263079750403915642503 absolute error = 7e-32 relative error = 9.5141237056045966151897433375251e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.265 y[1] (analytic) = 0.73624421426380044836761760902 y[1] (numeric) = 0.73624421426380044836761760901988 absolute error = 1.2e-31 relative error = 1.6298939628339588442765386346291e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.4MB, time=7.52 x[1] = 0.266 y[1] (analytic) = 0.7367402839703590904094632013101 y[1] (numeric) = 0.73674028397035909040946320130997 absolute error = 1.3e-31 relative error = 1.7645295476367656594590830955858e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.267 y[1] (analytic) = 0.7372364731136663971637787889528 y[1] (numeric) = 0.73723647311366639716377878895272 absolute error = 8e-32 relative error = 1.0851335075993409020466204584576e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.268 y[1] (analytic) = 0.7377327816750975775282958964235 y[1] (numeric) = 0.73773278167509757752829589642334 absolute error = 1.6e-31 relative error = 2.1688069714985915305488112444828e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.269 y[1] (analytic) = 0.7382292096360433594065955253814 y[1] (numeric) = 0.73822920963604335940659552538132 absolute error = 8e-32 relative error = 1.0836742702099398733939543951317e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 0.7387257569779099733762330029017 y[1] (numeric) = 0.73872575697790997337623300290162 absolute error = 8e-32 relative error = 1.0829458597365819246420012600351e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.271 y[1] (analytic) = 0.7392224236821191363826158089509 y[1] (numeric) = 0.73922242368211913638261580895088 absolute error = 2e-32 relative error = 2.7055456327174961108653811626293e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.4MB, time=7.67 x[1] = 0.272 y[1] (analytic) = 0.7397192097301080354585834465999 y[1] (numeric) = 0.73971920973010803545858344659988 absolute error = 2e-32 relative error = 2.7037286225535695220458598143850e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.273 y[1] (analytic) = 0.7402161151033293114696385422192 y[1] (numeric) = 0.74021611510332931146963854221915 absolute error = 5e-32 relative error = 6.7547840393910267896337563698941e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.274 y[1] (analytic) = 0.7407131397832510428847784863063 y[1] (numeric) = 0.74071313978325104288477848630625 absolute error = 5e-32 relative error = 6.7502515230972005949519861857454e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.275 y[1] (analytic) = 0.7412102837513567295728770486412 y[1] (numeric) = 0.74121028375135672957287704864119 absolute error = 1e-32 relative error = 1.3491447999599743483076047010818e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.276 y[1] (analytic) = 0.7417075469891452766245655241632 y[1] (numeric) = 0.74170754698914527662456552416306 absolute error = 1.4e-31 relative error = 1.8875364093072773945821685975827e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.4MB, time=7.83 x[1] = 0.277 y[1] (analytic) = 0.7422049294781309781995630883063 y[1] (numeric) = 0.7422049294781309781995630883062 absolute error = 1.0e-31 relative error = 1.3473367802921132948642571676804e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.278 y[1] (analytic) = 0.7427024311998435013994061625305 y[1] (numeric) = 0.74270243119984350139940616253032 absolute error = 1.8e-31 relative error = 2.4235816719922153489513064280383e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.279 y[1] (analytic) = 0.7432000521358278701655267124262 y[1] (numeric) = 0.74320005213582787016552671242616 absolute error = 4e-32 relative error = 5.3821309464453005939676176279375e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 0.7436977922676444492026295220786 y[1] (numeric) = 0.74369779226764444920262952207851 absolute error = 9e-32 relative error = 1.2101689817523419370818670191552e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.281 y[1] (analytic) = 0.7441956515768689279273186093222 y[1] (numeric) = 0.74419565157686892792731860932209 absolute error = 1.1e-31 relative error = 1.4781059223729951912842740354335e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.282 y[1] (analytic) = 0.7446936300450923044419230671348 y[1] (numeric) = 0.74469363004509230444192306713475 absolute error = 5e-32 relative error = 6.7141704967950948900738384673685e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.4MB, time=7.98 x[1] = 0.283 y[1] (analytic) = 0.7451917276539208695334727366772 y[1] (numeric) = 0.74519172765392086953347273667711 absolute error = 9e-32 relative error = 1.2077428755596366525969036177751e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.284 y[1] (analytic) = 0.7456899443849761906977742374102 y[1] (numeric) = 0.74568994438497619069777423741005 absolute error = 1.5e-31 relative error = 2.0115599134666583718249276583501e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.285 y[1] (analytic) = 0.7461882802198950961885379993017 y[1] (numeric) = 0.74618828021989509618853799930178 absolute error = 8e-32 relative error = 1.0721154716665438181804002081949e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.286 y[1] (analytic) = 0.7466867351403296590915070613761 y[1] (numeric) = 0.74668673514032965909150706137603 absolute error = 7e-32 relative error = 9.3747480309589868430523923662237e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.287 y[1] (analytic) = 0.7471853091279471814235385197536 y[1] (numeric) = 0.74718530912794718142353851975357 absolute error = 3e-32 relative error = 4.0150682345472658860407204042790e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.288 memory used=202.1MB, alloc=4.4MB, time=8.14 y[1] (analytic) = 0.7476840021644301782565886269014 y[1] (numeric) = 0.74768400216443017825658862690121 absolute error = 1.9e-31 relative error = 2.5411804913570335276800499236918e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.289 y[1] (analytic) = 0.7481828142314763618665526620276 y[1] (numeric) = 0.74818281423147636186655266202751 absolute error = 9e-32 relative error = 1.2029145589563805648394220611761e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = 0.7486817453107986259069108104533 y[1] (numeric) = 0.74868174531079862590691081045327 absolute error = 3e-32 relative error = 4.0070430710910635593967761519648e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.291 y[1] (analytic) = 0.7491807953841250296071314073389 y[1] (numeric) = 0.74918079538412502960713140733879 absolute error = 1.1e-31 relative error = 1.4682704185389597206738953767557e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.292 y[1] (analytic) = 0.7496799644331987819957830183699 y[1] (numeric) = 0.74967996443319878199578301836984 absolute error = 6e-32 relative error = 8.0034151700137077380175110820180e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.293 y[1] (analytic) = 0.7501792524397782261483069468916 y[1] (numeric) = 0.75017925243977822614830694689153 absolute error = 7e-32 relative error = 9.3311031693214357255897207227141e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=206.0MB, alloc=4.4MB, time=8.29 x[1] = 0.294 y[1] (analytic) = 0.7506786593856368234594018735347 y[1] (numeric) = 0.75067865938563682345940187353472 absolute error = 2e-32 relative error = 2.6642558370272849892294965712244e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.295 y[1] (analytic) = 0.7511781852525631379399724506047 y[1] (numeric) = 0.75117818525256313793997245060459 absolute error = 1.1e-31 relative error = 1.4643662736693492487785766810255e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.296 y[1] (analytic) = 0.7516778300223608205385937893963 y[1] (numeric) = 0.75167783002236082053859378939617 absolute error = 1.3e-31 relative error = 1.7294643370835185578515430814630e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.297 y[1] (analytic) = 0.7521775936768485934874438941689 y[1] (numeric) = 0.75217759367684859348744389416875 absolute error = 1.5e-31 relative error = 1.9942098948568677152117528095956e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.298 y[1] (analytic) = 0.7526774761978602346726562117504 y[1] (numeric) = 0.75267747619786023467265621175034 absolute error = 6e-32 relative error = 7.9715418485868824632340927454747e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.299 y[1] (analytic) = 0.7531774775672445620290445806569 y[1] (numeric) = 0.75317747756724456202904458065676 absolute error = 1.4e-31 relative error = 1.8587916416751938392266951719292e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 memory used=209.8MB, alloc=4.4MB, time=8.45 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 0.753677597766865417959152978198 y[1] (numeric) = 0.75367759776686541795915297819773 absolute error = 2.7e-31 relative error = 3.5824336665970389842357498227129e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.301 y[1] (analytic) = 0.7541778367786016537765825783062 y[1] (numeric) = 0.75417783677860165377658257830617 absolute error = 3e-32 relative error = 3.9778416358855259753857084220923e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.302 y[1] (analytic) = 0.7546781945843471141735487467675 y[1] (numeric) = 0.75467819458434711417354874676747 absolute error = 3e-32 relative error = 3.9752042943977003823677535459428e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.303 y[1] (analytic) = 0.7551786711660106217126207141443 y[1] (numeric) = 0.75517867116601062171262071414415 absolute error = 1.5e-31 relative error = 1.9862849114686603840122093378180e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.304 y[1] (analytic) = 0.7556792665055159613425967799888 y[1] (numeric) = 0.75567926650551596134259677998875 absolute error = 5e-32 relative error = 6.6165636952320740831603464097832e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.4MB, time=8.60 x[1] = 0.305 y[1] (analytic) = 0.7561799805848018649384680149155 y[1] (numeric) = 0.75617998058480186493846801491539 absolute error = 1.1e-31 relative error = 1.4546801399705138203424690369756e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.306 y[1] (analytic) = 0.7566808133858219958654235397591 y[1] (numeric) = 0.75668081338582199586542353975906 absolute error = 4e-32 relative error = 5.2862447801493950240939746731639e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.307 y[1] (analytic) = 0.7571817648905449335668505733925 y[1] (numeric) = 0.75718176489054493356685057339237 absolute error = 1.3e-31 relative error = 1.7168929050845837881273276985162e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.308 y[1] (analytic) = 0.7576828350809541581762825527935 y[1] (numeric) = 0.75768283508095415817628255279342 absolute error = 8e-32 relative error = 1.0558507636173709679876417302412e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.309 y[1] (analytic) = 0.7581840239390480351532487406665 y[1] (numeric) = 0.75818402393904803515324874066646 absolute error = 4e-32 relative error = 5.2757640278655728883654467903594e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = 0.7586853314468397999429788473102 y[1] (numeric) = 0.75868533144683979994297884731009 absolute error = 1.1e-31 relative error = 1.4498764565571091741722185410824e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.4MB, time=8.76 x[1] = 0.311 y[1] (analytic) = 0.7591867575863575426599163045076 y[1] (numeric) = 0.75918675758635754265991630450747 absolute error = 1.3e-31 relative error = 1.7123586350913463030485262453182e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.312 y[1] (analytic) = 0.7596883023396441927949939399795 y[1] (numeric) = 0.75968830233964419279499393997943 absolute error = 7e-32 relative error = 9.2143053650316899208054801614316e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.313 y[1] (analytic) = 0.7601899656887575039466259113965 y[1] (numeric) = 0.76018996568875750394662591139643 absolute error = 7e-32 relative error = 9.2082246753385729800235849194084e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.314 y[1] (analytic) = 0.7606917476157700385753698690896 y[1] (numeric) = 0.76069174761577003857536986908957 absolute error = 3e-32 relative error = 3.9437788163245830063397348789496e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.315 y[1] (analytic) = 0.7611936481027691527822134264352 y[1] (numeric) = 0.76119364810276915278221342643515 absolute error = 5e-32 relative error = 6.5686307452278521685374526714991e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.4MB, time=8.91 x[1] = 0.316 y[1] (analytic) = 0.7616956671318569811104391264134 y[1] (numeric) = 0.76169566713185698111043912641334 absolute error = 6e-32 relative error = 7.8771617837775375286105864901104e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.317 y[1] (analytic) = 0.7621978046851504213710222020593 y[1] (numeric) = 0.76219780468515042137102220205923 absolute error = 7e-32 relative error = 9.1839676747580877021021294197006e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.318 y[1] (analytic) = 0.7627000607447811194915155374362 y[1] (numeric) = 0.76270006074478111949151553743613 absolute error = 7e-32 relative error = 9.1779198144608230475063888665043e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.319 y[1] (analytic) = 0.7632024352928954543883763443664 y[1] (numeric) = 0.76320243529289545438837634436644 absolute error = 4e-32 relative error = 5.2410734230229669252573140878543e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = 0.7637049283116545228626891784563 y[1] (numeric) = 0.76370492831165452286268917845631 absolute error = 1e-32 relative error = 1.3094062417676550890195046943506e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.321 y[1] (analytic) = 0.7642075397832341245192400259476 y[1] (numeric) = 0.76420753978323412451924002594749 absolute error = 1.1e-31 relative error = 1.4393995645633288396751419989332e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.4MB, time=9.07 x[1] = 0.322 y[1] (analytic) = 0.764710269689824746708896300624 y[1] (numeric) = 0.76471026968982474670889630062398 absolute error = 2e-32 relative error = 2.6153696102593508144098147174843e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.323 y[1] (analytic) = 0.7652131180136315494942476973938 y[1] (numeric) = 0.76521311801363154949424769739379 absolute error = 1e-32 relative error = 1.3068254796726915805349506783211e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.324 y[1] (analytic) = 0.7657160847368743506384629562579 y[1] (numeric) = 0.7657160847368743506384629562578 absolute error = 1.0e-31 relative error = 1.3059670809235167577977565195323e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.325 y[1] (analytic) = 0.7662191698417876106173176971697 y[1] (numeric) = 0.76621916984178761061731769716959 absolute error = 1.1e-31 relative error = 1.4356205682339335889328046034331e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.326 y[1] (analytic) = 0.7667223733106204176543485927833 y[1] (numeric) = 0.76672237331062041765434859278322 absolute error = 8e-32 relative error = 1.0434024463714167583401684134158e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.4MB, time=9.22 x[1] = 0.327 y[1] (analytic) = 0.7672256951256364727790892522811 y[1] (numeric) = 0.76722569512563647277908925228106 absolute error = 4e-32 relative error = 5.2135897238751668458849232746269e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.328 y[1] (analytic) = 0.7677291352691140749083432953719 y[1] (numeric) = 0.76772913526911407490834329537187 absolute error = 3e-32 relative error = 3.9076281753308766359505864482267e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.329 y[1] (analytic) = 0.7682326937233461059504502011517 y[1] (numeric) = 0.76823269372334610595045020115162 absolute error = 8e-32 relative error = 1.0413511512022343728228255550064e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 0.7687363704706400159324996218269 y[1] (numeric) = 0.7687363704706400159324996218267 absolute error = 2.0e-31 relative error = 2.6016721425259858348973778874948e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.331 y[1] (analytic) = 0.7692401654933178081504499563123 y[1] (numeric) = 0.76924016549331780815044995631219 absolute error = 1.1e-31 relative error = 1.4299825325612894268767612579465e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.332 y[1] (analytic) = 0.7697440787737160243421070834381 y[1] (numeric) = 0.76974407877371602434210708343792 absolute error = 1.8e-31 relative error = 2.3384395536599527374056523556492e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.4MB, time=9.38 x[1] = 0.333 y[1] (analytic) = 0.7702481102941857298829192589228 y[1] (numeric) = 0.77024811029418572988291925892266 absolute error = 1.4e-31 relative error = 1.8175961502395496301956442598980e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.334 y[1] (analytic) = 0.7707522600370924990045442844134 y[1] (numeric) = 0.77075226003709249900454428441343 absolute error = 3e-32 relative error = 3.8923012692244649649757823331210e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.335 y[1] (analytic) = 0.7712565279848164000361451607332 y[1] (numeric) = 0.77125652798481640003614516073313 absolute error = 7e-32 relative error = 9.0760982189544693806329248370827e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.336 y[1] (analytic) = 0.7717609141197519806683705410363 y[1] (numeric) = 0.7717609141197519806683705410363 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.337 y[1] (analytic) = 0.7722654184243082532399764028416 y[1] (numeric) = 0.77226541842430825323997640284151 absolute error = 9e-32 relative error = 1.1654024361680146190204474726726e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.338 y[1] (analytic) = 0.7727700408809086800470454608894 y[1] (numeric) = 0.77277004088090868004704546088944 absolute error = 4e-32 relative error = 5.1761841018581083903714386026413e-30 % Correct digits = 31 h = 0.001 memory used=236.5MB, alloc=4.4MB, time=9.54 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.339 y[1] (analytic) = 0.7732747814719911586747609454703 y[1] (numeric) = 0.77327478147199115867476094547023 absolute error = 7e-32 relative error = 9.0524095285700811414561842611130e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = 0.773779640180008007351691473272 y[1] (numeric) = 0.77377964018000800735169147327197 absolute error = 3e-32 relative error = 3.8770728049940624568715528926735e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.341 y[1] (analytic) = 0.7742846169874259503265438399263 y[1] (numeric) = 0.77428461698742595032654383992631 absolute error = 1e-32 relative error = 1.2915147454314458769146076005976e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.342 y[1] (analytic) = 0.774789711876726103267340665267 y[1] (numeric) = 0.77478971187672610326734066526694 absolute error = 6e-32 relative error = 7.7440367470375466036753797775635e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.343 y[1] (analytic) = 0.7752949248304039586829799238739 y[1] (numeric) = 0.77529492483040395868297992387382 absolute error = 8e-32 relative error = 1.0318653900320581684724428874012e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.4MB, time=9.69 x[1] = 0.344 y[1] (analytic) = 0.7758002558309693713671334947511 y[1] (numeric) = 0.775800255830969371367133494751 absolute error = 1.0e-31 relative error = 1.2889915831864317631888953650428e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.345 y[1] (analytic) = 0.7763057048609465438644419649799 y[1] (numeric) = 0.77630570486094654386444196497976 absolute error = 1.4e-31 relative error = 1.8034132574753792982786806698130e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.346 y[1] (analytic) = 0.7768112719028740119589630229027 y[1] (numeric) = 0.77681127190287401195896302290255 absolute error = 1.5e-31 relative error = 1.9309709504158012030464909542729e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.347 y[1] (analytic) = 0.7773169569393046301848308768273 y[1] (numeric) = 0.77731695693930463018483087682733 absolute error = 3e-32 relative error = 3.8594295071247873230308481008573e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.348 y[1] (analytic) = 0.7778227599528055573590842353981 y[1] (numeric) = 0.77782275995280555735908423539805 absolute error = 5e-32 relative error = 6.4281996586257970904237483095887e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.349 y[1] (analytic) = 0.7783286809259582421366204856551 y[1] (numeric) = 0.77832868092595824213662048565511 absolute error = 1e-32 relative error = 1.2848042536609660995537761570455e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.4MB, time=9.85 x[1] = 0.35 y[1] (analytic) = 0.7788347198413584085872338044118 y[1] (numeric) = 0.77883471984135840858723380441161 absolute error = 1.9e-31 relative error = 2.4395419870174930351573398074596e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.351 y[1] (analytic) = 0.7793408766816160417946950378968 y[1] (numeric) = 0.77934087668161604179469503789682 absolute error = 2e-32 relative error = 2.5662711399354195088122894992675e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.352 y[1] (analytic) = 0.7798471514293553734778312836697 y[1] (numeric) = 0.77984715142935537347783128366957 absolute error = 1.3e-31 relative error = 1.6669933301894789587189791992589e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.353 y[1] (analytic) = 0.7803535440672148676335632075812 y[1] (numeric) = 0.78035354406721486763356320758118 absolute error = 2e-32 relative error = 2.5629408813548391700609572162663e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.354 y[1] (analytic) = 0.7808600545778472062018582270715 y[1] (numeric) = 0.7808600545778472062018582270714 absolute error = 1.0e-31 relative error = 1.2806392056264491830135151212750e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.4MB, time=10.00 x[1] = 0.355 y[1] (analytic) = 0.7813666829439192747525577903125 y[1] (numeric) = 0.78136668294391927475255779031249 absolute error = 1e-32 relative error = 1.2798088552129533385523697632866e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.356 y[1] (analytic) = 0.7818734291481121481940370786768 y[1] (numeric) = 0.78187342914811214819403707867677 absolute error = 3e-32 relative error = 3.8369381643633049537848735085219e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.357 y[1] (analytic) = 0.7823802931731210765036555576927 y[1] (numeric) = 0.7823802931731210765036555576926 absolute error = 1.0e-31 relative error = 1.2781508030375774777396173028365e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.358 y[1] (analytic) = 0.7828872750016554704799568990739 y[1] (numeric) = 0.78288727500165547047995689907388 absolute error = 2e-32 relative error = 2.5546461973031441322553499121503e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.359 y[1] (analytic) = 0.7833943746164388875165768935592 y[1] (numeric) = 0.78339437461643888751657689355916 absolute error = 4e-32 relative error = 5.1059850946191148273382535782322e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 0.78390159200020901739781807118 y[1] (numeric) = 0.78390159200020901739781807117988 absolute error = 1.2e-31 relative error = 1.5308043920896642792497313157981e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.4MB, time=10.16 x[1] = 0.361 y[1] (analytic) = 0.7844089271357176681158498421933 y[1] (numeric) = 0.78440892713571766811584984219324 absolute error = 6e-32 relative error = 7.6490715396484592116167972234369e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.362 y[1] (analytic) = 0.7849163800057307517094930682652 y[1] (numeric) = 0.78491638000573075170949306826518 absolute error = 2e-32 relative error = 2.5480421239080241939180244166674e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.363 y[1] (analytic) = 0.7854239505930282701245480695735 y[1] (numeric) = 0.78542395059302827012454806957338 absolute error = 1.2e-31 relative error = 1.5278372897770042472116686796084e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.364 y[1] (analytic) = 0.7859316388804043010956251693202 y[1] (numeric) = 0.78593163888040430109562516932005 absolute error = 1.5e-31 relative error = 1.9085629408390007808460670591108e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.365 y[1] (analytic) = 0.7864394448506669840494369727006 y[1] (numeric) = 0.78643944485066698404943697270053 absolute error = 7e-32 relative error = 8.9008760252726065405531867641879e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.4MB, time=10.31 x[1] = 0.366 y[1] (analytic) = 0.7869473684866385060295116726672 y[1] (numeric) = 0.78694736848663850602951167266701 absolute error = 1.9e-31 relative error = 2.4143927231802667802086487665351e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.367 y[1] (analytic) = 0.7874554097711550876422867698579 y[1] (numeric) = 0.78745540977115508764228676985782 absolute error = 8e-32 relative error = 1.0159305404130635606178028155158e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.368 y[1] (analytic) = 0.787963568687066969024542688833 y[1] (numeric) = 0.78796356868706696902454268883294 absolute error = 6e-32 relative error = 7.6145652393516291866923404563031e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.369 y[1] (analytic) = 0.7884718452172383958321358672659 y[1] (numeric) = 0.78847184521723839583213586726582 absolute error = 8e-32 relative error = 1.0146208832346897395534918105286e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = 0.7889802393445476052499909889917 y[1] (numeric) = 0.78898023934454760524999098899181 absolute error = 1.1e-31 relative error = 1.3942047533583792217161171603526e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.371 y[1] (analytic) = 0.7894887510518868120233121258048 y[1] (numeric) = 0.78948875105188681202331212580473 absolute error = 7e-32 relative error = 8.8664974525266487468617193095641e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.4MB, time=10.47 x[1] = 0.372 y[1] (analytic) = 0.7899973803221621945099726466266 y[1] (numeric) = 0.78999738032216219450997264662655 absolute error = 5e-32 relative error = 6.3291349117651402938526964588223e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.373 y[1] (analytic) = 0.7905061271382938807540438461515 y[1] (numeric) = 0.79050612713829388075404384615142 absolute error = 8e-32 relative error = 1.0120098662562867501140028722877e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.374 y[1] (analytic) = 0.7910149914832159345804223382854 y[1] (numeric) = 0.79101499148321593458042233828532 absolute error = 8e-32 relative error = 1.0113588346788933302333226067457e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.375 y[1] (analytic) = 0.7915239733398763417105163526672 y[1] (numeric) = 0.79152397333987634171051635266704 absolute error = 1.6e-31 relative error = 2.0214169802699939091728753716687e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.376 y[1] (analytic) = 0.7920330726912369958989511652662 y[1] (numeric) = 0.79203307269123699589895116526612 absolute error = 8e-32 relative error = 1.0100588316112764134119600503429e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.4MB, time=10.62 x[1] = 0.377 y[1] (analytic) = 0.7925422895202736850912539865094 y[1] (numeric) = 0.79254228952027368509125398650926 absolute error = 1.4e-31 relative error = 1.7664672516685776162808260520670e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.378 y[1] (analytic) = 0.7930516238099760776024787225898 y[1] (numeric) = 0.79305162380997607760247872258971 absolute error = 9e-32 relative error = 1.1348567646532553267664353941505e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.379 y[1] (analytic) = 0.7935610755433477083167311175649 y[1] (numeric) = 0.79356107554334770831673111756474 absolute error = 1.6e-31 relative error = 2.0162279241134492111886376426115e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = 0.7940706447034059649075548755455 y[1] (numeric) = 0.79407064470340596490755487554535 absolute error = 1.5e-31 relative error = 1.8890006953477877758919485169377e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.381 y[1] (analytic) = 0.7945803312731820740791394537311 y[1] (numeric) = 0.79458033127318207407913945373107 absolute error = 3e-32 relative error = 3.7755779773619638934867322763072e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.382 y[1] (analytic) = 0.7950901352357210878283103082411 y[1] (numeric) = 0.79509013523572108782831030824108 absolute error = 2e-32 relative error = 2.5154380759699127701636246492403e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.4MB, time=10.77 x[1] = 0.383 y[1] (analytic) = 0.7956000565740818697272624656426 y[1] (numeric) = 0.79560005657408186972726246564254 absolute error = 6e-32 relative error = 7.5414775934487546625394948167360e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.384 y[1] (analytic) = 0.7961100952713370812269983837782 y[1] (numeric) = 0.79611009527133708122699838377808 absolute error = 1.2e-31 relative error = 1.5073292087710628666803413795108e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.385 y[1] (analytic) = 0.7966202513105731679814311559483 y[1] (numeric) = 0.79662025131057316798143115594815 absolute error = 1.5e-31 relative error = 1.8829548929144719090770591041802e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.386 y[1] (analytic) = 0.7971305246748903461921142027108 y[1] (numeric) = 0.79713052467489034619211420271071 absolute error = 9e-32 relative error = 1.1290497254098567676352465038238e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.387 y[1] (analytic) = 0.7976409153474025889735586855218 y[1] (numeric) = 0.79764091534740258897355868552181 absolute error = 1e-32 relative error = 1.2536969716059041759107841120328e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.388 y[1] (analytic) = 0.7981514233112376127390999661562 y[1] (numeric) = 0.79815142331123761273909996615612 absolute error = 8e-32 relative error = 1.0023160726583601396846494413992e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 memory used=270.8MB, alloc=4.4MB, time=10.93 TOP MAIN SOLVE Loop x[1] = 0.389 y[1] (analytic) = 0.7986620485495368636072745253181 y[1] (numeric) = 0.79866204854953686360727452531802 absolute error = 8e-32 relative error = 1.0016752410520732915547064622509e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = 0.7991727910454555038286688430814 y[1] (numeric) = 0.79917279104545550382866884308125 absolute error = 1.5e-31 relative error = 1.8769407777731545808968209676936e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.391 y[1] (analytic) = 0.79968365078216239823320183278 y[1] (numeric) = 0.79968365078216239823320183277994 absolute error = 6e-32 relative error = 7.5029669471564929191032386041149e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.392 y[1] (analytic) = 0.8001946277428401006978025087165 y[1] (numeric) = 0.80019462774284010069780250871648 absolute error = 2e-32 relative error = 2.4993919362362219940312211905920e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.393 y[1] (analytic) = 0.8007057219106848406344446565529 y[1] (numeric) = 0.80070572191068484063444465655286 absolute error = 4e-32 relative error = 4.9955931255930030635372576975982e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.4MB, time=11.09 x[1] = 0.394 y[1] (analytic) = 0.8012169332689065094985003635128 y[1] (numeric) = 0.80121693326890650949850036351271 absolute error = 9e-32 relative error = 1.1232912868279827791769951927924e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.395 y[1] (analytic) = 0.8017282618007286473173743535422 y[1] (numeric) = 0.80172826180072864731737435354198 absolute error = 2.2e-31 relative error = 2.7440719066815370925552099211102e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.396 y[1] (analytic) = 0.8022397074893884292393811603581 y[1] (numeric) = 0.80223970748938842923938116035801 absolute error = 9e-32 relative error = 1.1218592044222701209677762992762e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.397 y[1] (analytic) = 0.8027512703181366521028272588598 y[1] (numeric) = 0.80275127031813665210282725885978 absolute error = 2e-32 relative error = 2.4914317472302276706376035985114e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.398 y[1] (analytic) = 0.803262950270237721025260362678 y[1] (numeric) = 0.80326295027023772102526036267794 absolute error = 6e-32 relative error = 7.4695341021037384173227724297102e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.399 y[1] (analytic) = 0.8037747473289696360128481827122 y[1] (numeric) = 0.80377474732896963601284818271204 absolute error = 1.6e-31 relative error = 1.9906074498072662038888858976907e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.4MB, time=11.24 x[1] = 0.4 y[1] (analytic) = 0.8042866614776239785898490283349 y[1] (numeric) = 0.80428666147762397858984902833491 absolute error = 1e-32 relative error = 1.2433377897413022719926098970569e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.401 y[1] (analytic) = 0.8047986926995058984481367195416 y[1] (numeric) = 0.8047986926995058984481367195416 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.402 y[1] (analytic) = 0.8053108409779341001167423646828 y[1] (numeric) = 0.80531084097793410011674236468278 absolute error = 2e-32 relative error = 2.4835130712648644832899898643507e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.403 y[1] (analytic) = 0.8058231062962408296513756445515 y[1] (numeric) = 0.80582310629624082965137564455131 absolute error = 1.9e-31 relative error = 2.3578375764537983354477526359213e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.404 y[1] (analytic) = 0.8063354886377718613438883294862 y[1] (numeric) = 0.8063354886377718613438883294862 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.4MB, time=11.40 x[1] = 0.405 y[1] (analytic) = 0.8068479879858864844516428418212 y[1] (numeric) = 0.80684798798588648445164284182115 absolute error = 5e-32 relative error = 6.1969541654077481680055189161513e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.406 y[1] (analytic) = 0.8073606043239574899467487614365 y[1] (numeric) = 0.80736060432395748994674876143644 absolute error = 6e-32 relative error = 7.4316234503714648935090518966486e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.407 y[1] (analytic) = 0.807873337635371157285130257373 y[1] (numeric) = 0.80787333763537115728513025737299 absolute error = 1e-32 relative error = 1.2378178031310943857978308654489e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.408 y[1] (analytic) = 0.8083861879035272411953875134378 y[1] (numeric) = 0.80838618790352724119538751343771 absolute error = 9e-32 relative error = 1.1133292644868963862145563737658e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.409 y[1] (analytic) = 0.8088991551118389584874153004696 y[1] (numeric) = 0.80889915511183895848741530046951 absolute error = 9e-32 relative error = 1.1126232414911663190978806265492e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 0.8094122392437329748807419324471 y[1] (numeric) = 0.80941223924373297488074193244716 absolute error = 6e-32 relative error = 7.4127863517433908363896403725499e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.4MB, time=11.55 x[1] = 0.411 y[1] (analytic) = 0.8099254402826493918525519279037 y[1] (numeric) = 0.80992544028264939185255192790359 absolute error = 1.1e-31 relative error = 1.3581497077263307238088872409624e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.412 y[1] (analytic) = 0.8104387582120417335053557821674 y[1] (numeric) = 0.81043875821204173350535578216724 absolute error = 1.6e-31 relative error = 1.9742392423702160709020768972501e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.413 y[1] (analytic) = 0.8109521930153769334542703397805 y[1] (numeric) = 0.81095219301537693345427033978047 absolute error = 3e-32 relative error = 3.6993549383534563859169594057943e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.414 y[1] (analytic) = 0.8114657446761353217338733400484 y[1] (numeric) = 0.81146574467613532173387334004832 absolute error = 8e-32 relative error = 9.8587032816682677916844174697429e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.415 y[1] (analytic) = 0.8119794131778106117245957920491 y[1] (numeric) = 0.81197941317781061172459579204901 absolute error = 9e-32 relative error = 1.1084024858188298376962560430496e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.4MB, time=11.71 x[1] = 0.416 y[1] (analytic) = 0.8124931985039098870986159185909 y[1] (numeric) = 0.81249319850390988709861591859076 absolute error = 1.4e-31 relative error = 1.7230913471988441603820398218167e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.417 y[1] (analytic) = 0.8130071006379535887852184915294 y[1] (numeric) = 0.81300710063795358878521849152927 absolute error = 1.3e-31 relative error = 1.5990020246808557020965961947502e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.418 y[1] (analytic) = 0.8135211195634755019555834635663 y[1] (numeric) = 0.81352111956347550195558346356619 absolute error = 1.1e-31 relative error = 1.3521468263666531664992964364874e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.419 y[1] (analytic) = 0.8140352552640227430269678841331 y[1] (numeric) = 0.81403525526402274302696788413294 absolute error = 1.6e-31 relative error = 1.9655168368365800732705573740765e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = 0.8145495077231557466862451692259 y[1] (numeric) = 0.81454950772315574668624516922587 absolute error = 3e-32 relative error = 3.6830173875933667602311799391249e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.421 y[1] (analytic) = 0.8150638769244482529327658770997 y[1] (numeric) = 0.81506387692444825293276587709971 absolute error = 1e-32 relative error = 1.2268977049668639223512374325562e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.4MB, time=11.87 x[1] = 0.422 y[1] (analytic) = 0.8155783628514872941405042235466 y[1] (numeric) = 0.81557836285148729414050422354653 absolute error = 7e-32 relative error = 8.5828662441780161472393118971152e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.423 y[1] (analytic) = 0.8160929654878731821394546520879 y[1] (numeric) = 0.81609296548787318213945465208789 absolute error = 1e-32 relative error = 1.2253505939757541060050407035247e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.424 y[1] (analytic) = 0.8166076848172194953162428557894 y[1] (numeric) = 0.8166076848172194953162428557894 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.425 y[1] (analytic) = 0.8171225208231530657339157285699 y[1] (numeric) = 0.81712252082315306573391572856988 absolute error = 2e-32 relative error = 2.4476133615620330200897135822101e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.426 y[1] (analytic) = 0.8176374734893139662708748048227 y[1] (numeric) = 0.81763747348931396627087480482262 absolute error = 8e-32 relative error = 9.7842873637622667312649987295611e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.427 y[1] (analytic) = 0.8181525427993554977789178268946 y[1] (numeric) = 0.81815254279935549777891782689447 absolute error = 1.3e-31 relative error = 1.5889457429930804818865596321217e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 memory used=297.5MB, alloc=4.4MB, time=12.02 TOP MAIN SOLVE Loop x[1] = 0.428 y[1] (analytic) = 0.8186677287369441762603531604804 y[1] (numeric) = 0.81866772873694417626035316048027 absolute error = 1.3e-31 relative error = 1.5879458226668641490271361516137e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.429 y[1] (analytic) = 0.8191830312857597200641518582865 y[1] (numeric) = 0.81918303128575972006415185828638 absolute error = 1.2e-31 relative error = 1.4648740930540564251991256101174e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = 0.819698450429495037101102252398 y[1] (numeric) = 0.81969845042949503710110225239798 absolute error = 2e-32 relative error = 2.4399216552770909328216773003929e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.431 y[1] (analytic) = 0.8202139861518562120779320356516 y[1] (numeric) = 0.82021398615185621207793203565153 absolute error = 7e-32 relative error = 8.5343582506333959093728084576388e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.432 y[1] (analytic) = 0.8207296384365624937503628719667 y[1] (numeric) = 0.82072963843656249375036287196675 absolute error = 5e-32 relative error = 6.0921401711831443506266115217821e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.4MB, time=12.18 x[1] = 0.433 y[1] (analytic) = 0.8212454072673462821950626550325 y[1] (numeric) = 0.82124540726734628219506265503236 absolute error = 1.4e-31 relative error = 1.7047279505141236306190267664173e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.434 y[1] (analytic) = 0.8217612926279531161004606139672 y[1] (numeric) = 0.82176129262795311610046061396718 absolute error = 2e-32 relative error = 2.4337967946921619165505108063175e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.435 y[1] (analytic) = 0.822277294502141660076390543594 y[1] (numeric) = 0.822277294502141660076390543594 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.436 y[1] (analytic) = 0.8227934128736836919825275157683 y[1] (numeric) = 0.82279341287368369198252751576823 absolute error = 7e-32 relative error = 8.5076033551992583172342823318696e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.437 y[1] (analytic) = 0.8233096477263640902755835067975 y[1] (numeric) = 0.82330964772636409027558350679746 absolute error = 4e-32 relative error = 4.8584393624516877698308980060271e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.438 y[1] (analytic) = 0.8238259990439808213752274543724 y[1] (numeric) = 0.82382599904398082137522745437236 absolute error = 4e-32 relative error = 4.8553942272298397975006053118622e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.4MB, time=12.33 x[1] = 0.439 y[1] (analytic) = 0.8243424668103449270486953356048 y[1] (numeric) = 0.8243424668103449270486953356047 absolute error = 1.0e-31 relative error = 1.2130880553434696500144302848026e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 0.8248590510092805118140559357349 y[1] (numeric) = 0.82485905100928051181405593573482 absolute error = 8e-32 relative error = 9.6986266807782070157691944187268e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.441 y[1] (analytic) = 0.8253757516246247303620980548297 y[1] (numeric) = 0.82537575162462473036209805482972 absolute error = 2e-32 relative error = 2.4231387898945526287119798039921e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.442 y[1] (analytic) = 0.8258925686402277749968049773448 y[1] (numeric) = 0.82589256864022777499680497734462 absolute error = 1.8e-31 relative error = 2.1794602207930862893387812328336e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.443 y[1] (analytic) = 0.8264095020399528630943821067657 y[1] (numeric) = 0.82640950203995286309438210676571 absolute error = 1e-32 relative error = 1.2100538504597868045517102719400e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=309.0MB, alloc=4.4MB, time=12.48 x[1] = 0.444 y[1] (analytic) = 0.826926551807676224580803744691 y[1] (numeric) = 0.82692655180767622458080374469095 absolute error = 5e-32 relative error = 6.0464862194470725590441601737611e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.445 y[1] (analytic) = 0.8274437179272870894278450706394 y[1] (numeric) = 0.82744371792728708942784507063936 absolute error = 4e-32 relative error = 4.8341656517978498384468490224472e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.446 y[1] (analytic) = 0.8279610003826876751675654556086 y[1] (numeric) = 0.82796100038268767516756545560849 absolute error = 1.1e-31 relative error = 1.3285649921814850600850193500519e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.447 y[1] (analytic) = 0.8284783991577931744252093189246 y[1] (numeric) = 0.82847839915779317442520931892446 absolute error = 1.4e-31 relative error = 1.6898449029246856784750692861218e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.448 y[1] (analytic) = 0.8289959142365317424704908142506 y[1] (numeric) = 0.82899591423653174247049081425065 absolute error = 5e-32 relative error = 6.0313928140463478185124328195464e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.449 y[1] (analytic) = 0.8295135456028444847872287067398 y[1] (numeric) = 0.82951354560284448478722870673972 absolute error = 8e-32 relative error = 9.6442065863867759377552615573596e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.4MB, time=12.64 x[1] = 0.45 y[1] (analytic) = 0.8300312932406854446612978792303 y[1] (numeric) = 0.83003129324068544466129787923028 absolute error = 2e-32 relative error = 2.4095477077634191540346544800750e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.451 y[1] (analytic) = 0.8305491571340215907868639811044 y[1] (numeric) = 0.83054915713402159078686398110431 absolute error = 9e-32 relative error = 1.0836203881124058160667020232849e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.452 y[1] (analytic) = 0.8310671372668328048908678089355 y[1] (numeric) = 0.83106713726683280489086780893552 absolute error = 2e-32 relative error = 2.4065444418575956715812356856918e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.453 y[1] (analytic) = 0.8315852336231118693757260833726 y[1] (numeric) = 0.83158523362311186937572608337248 absolute error = 1.2e-31 relative error = 1.4430270662355938049685995831817e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.454 y[1] (analytic) = 0.8321034461868644549802153618143 y[1] (numeric) = 0.83210344618686445498021536181421 absolute error = 9e-32 relative error = 1.0815962896491695322531866854047e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.4MB, time=12.79 x[1] = 0.455 y[1] (analytic) = 0.832621774942109108458505901351 y[1] (numeric) = 0.83262177494210910845850590135081 absolute error = 1.9e-31 relative error = 2.2819484875135580406769014526009e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.456 y[1] (analytic) = 0.8331402198728772402773123611579 y[1] (numeric) = 0.83314021987287724027731236115794 absolute error = 4e-32 relative error = 4.8011125913598681892383142042491e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.457 y[1] (analytic) = 0.8336587809632131123311283080525 y[1] (numeric) = 0.83365878096321311233112830805244 absolute error = 6e-32 relative error = 7.1971892301878868972682660697851e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.458 y[1] (analytic) = 0.8341774581971738256755115632374 y[1] (numeric) = 0.83417745819717382567551156323733 absolute error = 7e-32 relative error = 8.3914998316166628840319627484565e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.459 y[1] (analytic) = 0.8346962515588293082783875023893 y[1] (numeric) = 0.83469625155882930827838750238916 absolute error = 1.4e-31 relative error = 1.6772568432953219511418213509334e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = 0.8352151610322623027893374951687 y[1] (numeric) = 0.83521516103226230278933749516863 absolute error = 7e-32 relative error = 8.3810739155507346634919188334035e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.4MB, time=12.95 x[1] = 0.461 y[1] (analytic) = 0.8357341866015683543268397439686 y[1] (numeric) = 0.83573418660156835432683974396855 absolute error = 5e-32 relative error = 5.9827635151937637714849068545730e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.462 y[1] (analytic) = 0.8362533282508557982834298552511 y[1] (numeric) = 0.83625332825085579828342985525106 absolute error = 4e-32 relative error = 4.7832395577624494934824591124256e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.463 y[1] (analytic) = 0.8367725859642457481487485501695 y[1] (numeric) = 0.83677258596424574814874855016954 absolute error = 4e-32 relative error = 4.7802713271140971926474577818606e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.464 y[1] (analytic) = 0.837291959725872083350443994321 y[1] (numeric) = 0.83729195972587208335044399432089 absolute error = 1.1e-31 relative error = 1.3137591818750272814116432787667e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.465 y[1] (analytic) = 0.8378114495198814371128962994305 y[1] (numeric) = 0.83781144951988143711289629943038 absolute error = 1.2e-31 relative error = 1.4323031759564462176529616304221e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.466 y[1] (analytic) = 0.8383310553304331843337318225359 y[1] (numeric) = 0.83833105533043318433373182253576 absolute error = 1.4e-31 relative error = 1.6699846571330721512577672959117e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 memory used=324.2MB, alloc=4.4MB, time=13.10 TOP MAIN SOLVE Loop x[1] = 0.467 y[1] (analytic) = 0.8388507771416994294780949608097 y[1] (numeric) = 0.83885077714169942947809496080961 absolute error = 9e-32 relative error = 1.0728964251146794713789271307661e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.468 y[1] (analytic) = 0.8393706149378649944906452125399 y[1] (numeric) = 0.83937061493786499449064521253995 absolute error = 5e-32 relative error = 5.9568442247291782411538385075344e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.469 y[1] (analytic) = 0.8398905687031274067252473469794 y[1] (numeric) = 0.83989056870312740672524734697937 absolute error = 3e-32 relative error = 3.5718939011689240736578523796011e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = 0.840410638421696886892322597773 y[1] (numeric) = 0.84041063842169688689232259777285 absolute error = 1.5e-31 relative error = 1.7848417564263837742134445012405e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.471 y[1] (analytic) = 0.8409308240777963370238288664851 y[1] (numeric) = 0.8409308240777963370238288664851 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.4MB, time=13.26 x[1] = 0.472 y[1] (analytic) = 0.8414511256556613284558379943694 y[1] (numeric) = 0.84145112565566132845583799436941 absolute error = 1e-32 relative error = 1.1884231531817096288476700448060e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.473 y[1] (analytic) = 0.8419715431395400898286782319531 y[1] (numeric) = 0.84197154313954008982867823195306 absolute error = 4e-32 relative error = 4.7507543842691121764730487374018e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.474 y[1] (analytic) = 0.8424920765136934951046101072593 y[1] (numeric) = 0.84249207651369349510461010725927 absolute error = 3e-32 relative error = 3.5608643495073147094005232843583e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.475 y[1] (analytic) = 0.8430127257623950516030039645435 y[1] (numeric) = 0.84301272576239505160300396454348 absolute error = 2e-32 relative error = 2.3724434268667307141167190269304e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.476 y[1] (analytic) = 0.8435334908699308880529875162926 y[1] (numeric) = 0.84353349086993088805298751629264 absolute error = 4e-32 relative error = 4.7419575432326043904979961369886e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.477 y[1] (analytic) = 0.8440543718205997426635318219209 y[1] (numeric) = 0.84405437182059974266353182192094 absolute error = 4e-32 relative error = 4.7390311969738643996534646091340e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.4MB, time=13.41 x[1] = 0.478 y[1] (analytic) = 0.8445753685987129512109441770946 y[1] (numeric) = 0.84457536859871295121094417709462 absolute error = 2e-32 relative error = 2.3680539053824447526178321319207e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.479 y[1] (analytic) = 0.8450964811885944351437364679326 y[1] (numeric) = 0.84509648118859443514373646793257 absolute error = 3e-32 relative error = 3.5498905353157072247589182923453e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = 0.845617709574580689704837614459 y[1] (numeric) = 0.84561770957458068970483761445897 absolute error = 3e-32 relative error = 3.5477024263236647673084893329906e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.481 y[1] (analytic) = 0.8461390537410207720711187976299 y[1] (numeric) = 0.84613905374102077207111879762991 absolute error = 1e-32 relative error = 1.1818388426567906780575313821632e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.482 y[1] (analytic) = 0.8466605136722762895102002340184 y[1] (numeric) = 0.84666051367227628951020023401825 absolute error = 1.5e-31 relative error = 1.7716664185671673976790735052162e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=335.7MB, alloc=4.4MB, time=13.57 x[1] = 0.483 y[1] (analytic) = 0.8471820893527213875545083318205 y[1] (numeric) = 0.84718208935272138755450833182035 absolute error = 1.5e-31 relative error = 1.7705756753498598705860231566948e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.484 y[1] (analytic) = 0.8477037807667427381925521312454 y[1] (numeric) = 0.84770378076674273819255213124541 absolute error = 1e-32 relative error = 1.1796573551854473143391269183306e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.485 y[1] (analytic) = 0.8482255878987395280773880015639 y[1] (numeric) = 0.84822558789873952807738800156382 absolute error = 8e-32 relative error = 9.4314532762657395919901603671269e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.486 y[1] (analytic) = 0.848747510733123446752241636125 y[1] (numeric) = 0.84874751073312344675224163612496 absolute error = 4e-32 relative error = 4.7128267823076337336275086045323e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.487 y[1] (analytic) = 0.8492695492543186748932564555087 y[1] (numeric) = 0.84926954925431867489325645550864 absolute error = 6e-32 relative error = 7.0648947737124922194627586457860e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.488 y[1] (analytic) = 0.8497917034467618725693375976481 y[1] (numeric) = 0.849791703446761872569337597648 absolute error = 1.0e-31 relative error = 1.1767589586294995446430489690191e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.4MB, time=13.72 x[1] = 0.489 y[1] (analytic) = 0.8503139732949021675190607422556 y[1] (numeric) = 0.85031397329490216751906074225549 absolute error = 1.1e-31 relative error = 1.2936398019399627323529547015024e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = 0.8508363587832011434446150851991 y[1] (numeric) = 0.85083635878320114344461508519894 absolute error = 1.6e-31 relative error = 1.8805026177868014891516719972584e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.491 y[1] (analytic) = 0.851358859896132828322749846611 y[1] (numeric) = 0.85135885989613282832274984661094 absolute error = 6e-32 relative error = 7.0475568912644073517131748534814e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.492 y[1] (analytic) = 0.8518814766181836827326937644736 y[1] (numeric) = 0.85188147661818368273269376447361 absolute error = 1e-32 relative error = 1.1738722198419200608143280522385e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.493 y[1] (analytic) = 0.8524042089338525882010170932022 y[1] (numeric) = 0.8524042089338525882010170932022 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.4MB, time=13.88 x[1] = 0.494 y[1] (analytic) = 0.8529270568276508355634056943552 y[1] (numeric) = 0.8529270568276508355634056943551 absolute error = 1.0e-31 relative error = 1.1724332016378604374137076257869e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.495 y[1] (analytic) = 0.8534500202841021133433168740263 y[1] (numeric) = 0.8534500202841021133433168740263 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.496 y[1] (analytic) = 0.8539730992877424961474866887285 y[1] (numeric) = 0.85397309928774249614748668872844 absolute error = 6e-32 relative error = 7.0259824402013467578421400088706e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.497 y[1] (analytic) = 0.8544962938231204330782585086519 y[1] (numeric) = 0.85449629382312043307825850865177 absolute error = 1.3e-31 relative error = 1.5213641175477096056804153792371e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.498 y[1] (analytic) = 0.8550196038747967361627026940869 y[1] (numeric) = 0.85501960387479673616270269408673 absolute error = 1.7e-31 relative error = 1.9882585057651338416260015471403e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.499 y[1] (analytic) = 0.8555430294273445687984973075261 y[1] (numeric) = 0.85554302942734456879849730752593 absolute error = 1.7e-31 relative error = 1.9870420791551424814414285656502e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 Finished! diff ( y , x , 1 ) = arcsin(sqrt(0.1 * x + 0.2)); Iterations = 500 Total Elapsed Time = 13 Seconds Elapsed Time(since restart) = 13 Seconds Time to Timeout = 2 Minutes 46 Seconds Percent Done = 100.2 % > quit memory used=346.8MB, alloc=4.4MB, time=14.01