(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac (%i3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%o3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%o4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i5) test_suggested_h() := block([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 hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%o5) test_suggested_h() := block([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 hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%i6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%o6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 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) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr # 0.0 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "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, " ")))) (%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 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) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr # 0.0 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "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, " ")))) (%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 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))), 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 ), hnew : sz2), return(hnew)) 1 (%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 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))), 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 ), hnew : sz2), return(hnew)) 1 (%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], 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(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 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(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 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))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], 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(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 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(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 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))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 elseif (omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 5 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 elseif (omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 5 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%i11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%o11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_0D2 array_x , 1 1 1 array_tmp2 1 array_tmp2 : array_const_0D3 + array_tmp1 , array_tmp3 : ----------------, 1 1 1 1 array_const_2D0 1 array_tmp4 : array_tmp3 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1), 1 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 2 1, 2 glob_h array_y_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1 : array_const_0D2 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp2 2 array_tmp3 : ----------------, array_tmp4 : array_tmp3 , 2 array_const_2D0 2 2 1 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), 2 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 3 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (order_d : 1, if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp4 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d temporary convfp(adj2) then (if adj2 > 1 then temporary : ---------------------- glob_h temporary else temporary : ---------, array_y_higher : temporary), glob_h adj3, term term : term - 1, adj2 : adj2 - 1, adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_0D2 array_x , 1 1 1 array_tmp2 1 array_tmp2 : array_const_0D3 + array_tmp1 , array_tmp3 : ----------------, 1 1 1 1 array_const_2D0 1 array_tmp4 : array_tmp3 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1), 1 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 2 1, 2 glob_h array_y_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1 : array_const_0D2 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp2 2 array_tmp3 : ----------------, array_tmp4 : array_tmp3 , 2 array_const_2D0 2 2 1 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), 2 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 3 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (order_d : 1, if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp4 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d temporary convfp(adj2) then (if adj2 > 1 then temporary : ---------------------- glob_h temporary else temporary : ---------, array_y_higher : temporary), glob_h adj3, term term : term - 1, adj2 : adj2 - 1, adj3 : 1 + adj3))), kkk : 1 + kkk)) log(x) (%i13) log10(x) := --------- log(10.0) log(x) (%o13) log10(x) := --------- log(10.0) (%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, 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 : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, 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 : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i27) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%o27) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error # 0.0 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error # 0.0 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%i32) log_revs(file, revs) := printf(file, revs) (%o32) log_revs(file, revs) := printf(file, revs) (%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i34) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%o34) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%i35) logstart(file) := printf(file, "") (%o35) logstart(file) := printf(file, "") (%i36) logend(file) := printf(file, "~%") (%o36) logend(file) := printf(file, "~%") (%i37) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o37) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i40) factorial_2(nnn) := nnn! (%o40) factorial_2(nnn) := nnn! (%i41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%o41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%o42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i43) convfp(mmm) := mmm (%o43) convfp(mmm) := mmm (%i44) convfloat(mmm) := mmm (%o44) convfloat(mmm) := mmm (%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i46) arcsin(x) := asin(x) (%o46) arcsin(x) := asin(x) (%i47) arccos(x) := acos(x) (%o47) arccos(x) := acos(x) (%i48) arctan(x) := atan(x) (%o48) arctan(x) := atan(x) (%i49) omniabs(x) := abs(x) (%o49) omniabs(x) := abs(x) y (%i50) expt(x, y) := x y (%o50) expt(x, y) := x (%i51) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], 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, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%o51) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], 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, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%i52) exact_soln_y(x) := block(0.15 x + 0.05 x x) (%o52) exact_soln_y(x) := block(0.15 x + 0.05 x x) (%i53) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, 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/div_lin_cpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.2 * x + 0.3) / 2.0;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-5.0,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter: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, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (0.05 * x * x + 0.15 * x) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_const_0D3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term), term array_const_0D3 : 0.3, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), iiif, jjjf x_start : - 5.0, x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_h : 0.05, glob_look_poles : true, glob_max_iter : 1000000, glob_display_interval : 0.1, glob_max_minutes : 10, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 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, 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 (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), 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 (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 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")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = (0.2 * x + 0.3) / 2.0;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-12-14T21:25:29-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "div_lin_c"), logitem_str(html_log_file, "diff ( y , x , 1 ) = (0.2 * x + 0.3) / 2.0;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 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) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), 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), log_revs(html_log_file, " 151 "), logitem_str(html_log_file, "div_lin_c diffeq.max"), logitem_str(html_log_file, "div_lin_c maxima results"), logitem_str(html_log_file, "Languages compared"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o53) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, 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/div_lin_cpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.2 * x + 0.3) / 2.0;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-5.0,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter: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, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (0.05 * x * x + 0.15 * x) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_const_0D3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term), term array_const_0D3 : 0.3, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), iiif, jjjf x_start : - 5.0, x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_h : 0.05, glob_look_poles : true, glob_max_iter : 1000000, glob_display_interval : 0.1, glob_max_minutes : 10, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 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, 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 (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), 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 (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 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")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = (0.2 * x + 0.3) / 2.0;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-12-14T21:25:29-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "div_lin_c"), logitem_str(html_log_file, "diff ( y , x , 1 ) = (0.2 * x + 0.3) / 2.0;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 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) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), 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), log_revs(html_log_file, " 151 "), logitem_str(html_log_file, "div_lin_c diffeq.max"), logitem_str(html_log_file, "div_lin_c maxima results"), logitem_str(html_log_file, "Languages compared"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i54) main() "##############ECHO OF PROBLEM#################" "##############temp/div_lin_cpostode.ode#################" "diff ( y , x , 1 ) = (0.2 * x + 0.3) / 2.0;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:-5.0," "x_end:5.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_h:0.05," "glob_look_poles:true," "glob_max_iter: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," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (0.05 * x * x + 0.15 * x) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 10. "" estimated_steps = 10000. "" step_error = 1.00000000000000E-14 "" est_needed_step_err = 1.00000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_value3 = 0.0 "" value3 = 0.0 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = -5. " " y[1] (analytic) = 0.5 " " y[1] (numeric) = 0.5 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.999 " " y[1] (analytic) = 0.49965005000000007 " " y[1] (numeric) = 0.49965005 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.111000613954863400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.998000000000000 " " y[1] (analytic) = 0.49930019999999986 " " y[1] (numeric) = 0.4993002 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.33533721183715770000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.996999999999999 " " y[1] (analytic) = 0.4989504499999998 " " y[1] (numeric) = 0.49895045000000005 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.450233583816416400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.995999999999999 " " y[1] (analytic) = 0.4986007999999996 " " y[1] (numeric) = 0.49860080000000007 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.90670873071328800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.994999999999998 " " y[1] (analytic) = 0.49825124999999937 " " y[1] (numeric) = 0.4982512500000001 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 1.44835555556830560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.993999999999998 " " y[1] (analytic) = 0.4979017999999995 " " y[1] (numeric) = 0.4979018000000001 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 1.2263917574586730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.992999999999998 " " y[1] (analytic) = 0.49755244999999915 " " y[1] (numeric) = 0.4975524500000001 " " absolute error = 9.436895709313831000000000000000E-16 " " relative error = 1.89666349935847900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.991999999999997 " " y[1] (analytic) = 0.4972031999999992 " " y[1] (numeric) = 0.49720320000000007 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.78634896094821330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.990999999999997 " " y[1] (analytic) = 0.49685404999999905 " " y[1] (numeric) = 0.49685405000000005 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 2.0110548000215410000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.989999999999997 " " y[1] (analytic) = 0.49650499999999886 " " y[1] (numeric) = 0.49650500000000003 " " absolute error = 1.1657341758564144000000000000000E-15 " " relative error = 2.34788003314451430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.988999999999996 " " y[1] (analytic) = 0.49615604999999885 " " y[1] (numeric) = 0.49615605 " " absolute error = 1.1657341758564144000000000000000E-15 " " relative error = 2.34953131349787460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.987999999999996 " " y[1] (analytic) = 0.49580719999999856 " " y[1] (numeric) = 0.4958072 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 2.9109902639830720000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.986999999999996 " " y[1] (analytic) = 0.49545844999999866 " " y[1] (numeric) = 0.49545845 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 2.6889593457336160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.985999999999995 " " y[1] (analytic) = 0.4951097999999984 " " y[1] (numeric) = 0.4951098 " " absolute error = 1.609823385706477000000000000000E-15 " " relative error = 3.2514472258607730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.984999999999995 " " y[1] (analytic) = 0.49476124999999826 " " y[1] (numeric) = 0.49476125 " " absolute error = 1.7208456881689926000000000000000E-15 " " relative error = 3.4781335202969080000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.983999999999995 " " y[1] (analytic) = 0.4944127999999983 " " y[1] (numeric) = 0.4944128 " " absolute error = 1.6653345369377348000000000000000E-15 " " relative error = 3.36830789360174470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.982999999999994 " " y[1] (analytic) = 0.4940644499999981 " " y[1] (numeric) = 0.49406445 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 3.82010715780658400000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.981999999999994 " " y[1] (analytic) = 0.49371619999999805 " " y[1] (numeric) = 0.4937162 " " absolute error = 1.942890293094024000000000000000E-15 " " relative error = 3.93523707160921940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.980999999999994 " " y[1] (analytic) = 0.49336804999999784 " " y[1] (numeric) = 0.49336805 " " absolute error = 2.1649348980190553000000000000000E-15 " " relative error = 4.3880727542431347000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.979999999999993 " " y[1] (analytic) = 0.49301999999999757 " " y[1] (numeric) = 0.49302 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 4.9541411183630620000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.978999999999993 " " y[1] (analytic) = 0.4926720499999977 " " y[1] (numeric) = 0.49267205000000003 " " absolute error = 2.3314683517128287000000000000000E-15 " " relative error = 4.732292712186209600000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.977999999999993 " " y[1] (analytic) = 0.49232419999999755 " " y[1] (numeric) = 0.49232420000000005 " " absolute error = 2.4980018054066022000000000000000E-15 " " relative error = 5.0738960331558250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.976999999999992 " " y[1] (analytic) = 0.49197644999999735 " " y[1] (numeric) = 0.49197645000000007 " " absolute error = 2.7200464103316335000000000000000E-15 " " relative error = 5.5288142559092990000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.975999999999992 " " y[1] (analytic) = 0.4916287999999972 " " y[1] (numeric) = 0.4916288000000001 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 5.8714620950306900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.974999999999992 " " y[1] (analytic) = 0.491281249999997 " " y[1] (numeric) = 0.4912812500000001 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 6.3275862226585220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.973999999999991 " " y[1] (analytic) = 0.4909337999999972 " " y[1] (numeric) = 0.4909338000000001 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 5.8797741447531690000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.972999999999991 " " y[1] (analytic) = 0.4905864499999969 " " y[1] (numeric) = 0.49058645000000006 " " absolute error = 3.164135620181696000000000000000E-15 " " relative error = 6.4497003946638080000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.971999999999990 " " y[1] (analytic) = 0.49023919999999677 " " y[1] (numeric) = 0.49023920000000004 " " absolute error = 3.2751579226442120000000000000000E-15 " " relative error = 6.6807344713442610000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.97099999999999 " " y[1] (analytic) = 0.4898920499999967 " " y[1] (numeric) = 0.48989205 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 6.7987816374556230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.96999999999999 " " y[1] (analytic) = 0.48954499999999657 " " y[1] (numeric) = 0.489545 " " absolute error = 3.4416913763379850000000000000000E-15 " " relative error = 7.0303881692959990000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.96899999999999 " " y[1] (analytic) = 0.4891980499999966 " " y[1] (numeric) = 0.48919805 " " absolute error = 3.3861802251067274000000000000000E-15 " " relative error = 6.9219004963465220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.967999999999990 " " y[1] (analytic) = 0.4888511999999964 " " y[1] (numeric) = 0.4888512 " " absolute error = 3.608224830031759000000000000000E-15 " " relative error = 7.3810288898376140000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.966999999999989 " " y[1] (analytic) = 0.4885044499999963 " " y[1] (numeric) = 0.48850445 " " absolute error = 3.6637359812630166000000000000000E-15 " " relative error = 7.4999029819749730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.965999999999989 " " y[1] (analytic) = 0.4881577999999961 " " y[1] (numeric) = 0.4881578 " " absolute error = 3.885780586188048000000000000000E-15 " " relative error = 7.9600911553355880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.964999999999988 " " y[1] (analytic) = 0.48781124999999603 " " y[1] (numeric) = 0.48781125 " " absolute error = 3.941291737419305700000000000000E-15 " " relative error = 8.079542522685440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.963999999999988 " " y[1] (analytic) = 0.4874647999999959 " " y[1] (numeric) = 0.4874648 " " absolute error = 4.052314039881821400000000000000E-15 " " relative error = 8.3130393002363570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.962999999999988 " " y[1] (analytic) = 0.48711844999999576 " " y[1] (numeric) = 0.48711845 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 8.6608246794504120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.961999999999987 " " y[1] (analytic) = 0.48677219999999577 " " y[1] (numeric) = 0.4867722 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 8.6669852830043110000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.960999999999987 " " y[1] (analytic) = 0.4864260499999956 " " y[1] (numeric) = 0.48642605 " " absolute error = 4.385380947269368300000000000000E-15 " " relative error = 9.0155141717212880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.959999999999987 " " y[1] (analytic) = 0.4860799999999954 " " y[1] (numeric) = 0.48608 " " absolute error = 4.6074255521943996000000000000E-15 " " relative error = 9.4787392038233290000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.958999999999986 " " y[1] (analytic) = 0.48573404999999537 " " y[1] (numeric) = 0.48573405000000003 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 9.5997731751062170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.957999999999986 " " y[1] (analytic) = 0.4853881999999953 " " y[1] (numeric) = 0.48538820000000005 " " absolute error = 4.773959005888173000000000000000E-15 " " relative error = 9.8353421156266660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.956999999999986 " " y[1] (analytic) = 0.48504244999999513 " " y[1] (numeric) = 0.48504245000000007 " " absolute error = 4.9404924595819466000000000000000E-15 " " relative error = 1.018569088042087100000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.955999999999985 " " y[1] (analytic) = 0.48469679999999504 " " y[1] (numeric) = 0.4846968000000001 " " absolute error = 5.051514762044462000000000000000E-15 " " relative error = 1.0422009722458480000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.954999999999985 " " y[1] (analytic) = 0.4843512499999949 " " y[1] (numeric) = 0.4843512500000001 " " absolute error = 5.218048215738236000000000000000E-15 " " relative error = 1.0773272941358758000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.953999999999985 " " y[1] (analytic) = 0.48400579999999493 " " y[1] (numeric) = 0.4840058000000001 " " absolute error = 5.162537064506978000000000000000E-15 " " relative error = 1.0666271074658674000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.952999999999984 " " y[1] (analytic) = 0.4836604499999947 " " y[1] (numeric) = 0.4836604500000001 " " absolute error = 5.384581669432009000000000000000E-15 " " relative error = 1.1132979075365927000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.951999999999984 " " y[1] (analytic) = 0.4833151999999946 " " y[1] (numeric) = 0.48331520000000006 " " absolute error = 5.440092820663267000000000000000E-15 " " relative error = 1.1255786742612951000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.950999999999984 " " y[1] (analytic) = 0.4829700499999944 " " y[1] (numeric) = 0.48297005000000004 " " absolute error = 5.662137425588298000000000000000E-15 " " relative error = 1.1723578771785878000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.949999999999983 " " y[1] (analytic) = 0.4826249999999943 " " y[1] (numeric) = 0.482625 " " absolute error = 5.717648576819556000000000000000E-15 " " relative error = 1.1846979698149959000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.948999999999983 " " y[1] (analytic) = 0.4822800499999942 " " y[1] (numeric) = 0.48228005 " " absolute error = 5.828670879282072000000000000000E-15 " " relative error = 1.2085656205937073000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.947999999999983 " " y[1] (analytic) = 0.481935199999994 " " y[1] (numeric) = 0.4819352 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 1.2439855675567836000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.946999999999982 " " y[1] (analytic) = 0.481590449999994 " " y[1] (numeric) = 0.48159045 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 1.2448760836050467000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.945999999999982 " " y[1] (analytic) = 0.48124579999999384 " " y[1] (numeric) = 0.4812458 " " absolute error = 6.161737786669619000000000000000E-15 " " relative error = 1.2803722726867847000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.944999999999982 " " y[1] (analytic) = 0.4809012499999936 " " y[1] (numeric) = 0.48090125 " " absolute error = 6.38378239159465000000000000000E-15 " " relative error = 1.3274622163271016000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.943999999999981 " " y[1] (analytic) = 0.4805567999999938 " " y[1] (numeric) = 0.4805568 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 1.2937594344520684000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.942999999999981 " " y[1] (analytic) = 0.48021244999999346 " " y[1] (numeric) = 0.48021245 " " absolute error = 6.5503158452884240000000000000000E-15 " " relative error = 1.3640454022565454000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.941999999999980 " " y[1] (analytic) = 0.4798681999999933 " " y[1] (numeric) = 0.4798682 " " absolute error = 6.716849298982197000000000000000E-15 " " relative error = 1.3997279459197945000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.94099999999998 " " y[1] (analytic) = 0.4795240499999932 " " y[1] (numeric) = 0.47952405000000003 " " absolute error = 6.827871601444713000000000000000E-15 " " relative error = 1.423885121391682000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.93999999999998 " " y[1] (analytic) = 0.47917999999999306 " " y[1] (numeric) = 0.47918000000000005 " " absolute error = 6.994405055138486000000000000000E-15 " " relative error = 1.4596613078881812000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.93899999999998 " " y[1] (analytic) = 0.4788360499999931 " " y[1] (numeric) = 0.47883605000000007 " " absolute error = 6.994405055138486000000000000000E-15 " " relative error = 1.460709788901355000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.937999999999980 " " y[1] (analytic) = 0.47849219999999304 " " y[1] (numeric) = 0.4784922000000001 " " absolute error = 7.049916206369744000000000000000E-15 " " relative error = 1.4733607374101076000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.936999999999979 " " y[1] (analytic) = 0.47814844999999295 " " y[1] (numeric) = 0.4781484500000001 " " absolute error = 7.16093850883226000000000000000E-15 " " relative error = 1.4976391764591865000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.935999999999979 " " y[1] (analytic) = 0.4778047999999927 " " y[1] (numeric) = 0.47780480000000014 " " absolute error = 7.438494264988549000000000000000E-15 " " relative error = 1.5568060984294554000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.934999999999978 " " y[1] (analytic) = 0.4774612499999926 " " y[1] (numeric) = 0.47746125000000017 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 1.5811789056077705000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.933999999999978 " " y[1] (analytic) = 0.4771177999999925 " " y[1] (numeric) = 0.47711780000000015 " " absolute error = 7.66053886991358000000000000000E-15 " " relative error = 1.6055864756908464000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.932999999999978 " " y[1] (analytic) = 0.4767744499999923 " " y[1] (numeric) = 0.4767744500000001 " " absolute error = 7.827072323607354000000000000000E-15 " " relative error = 1.641671931792377000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.931999999999977 " " y[1] (analytic) = 0.4764311999999923 " " y[1] (numeric) = 0.4764312000000001 " " absolute error = 7.827072323607354000000000000000E-15 " " relative error = 1.642854692053643800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.930999999999977 " " y[1] (analytic) = 0.4760880499999921 " " y[1] (numeric) = 0.4760880500000001 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 1.6790183616877719000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.929999999999977 " " y[1] (analytic) = 0.4757449999999921 " " y[1] (numeric) = 0.4757450000000001 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 1.6802290675259351000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.928999999999976 " " y[1] (analytic) = 0.475402049999992 " " y[1] (numeric) = 0.4754020500000001 " " absolute error = 8.049116928532385000000000000000E-15 " " relative error = 1.6931178417368037000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.927999999999976 " " y[1] (analytic) = 0.4750591999999919 " " y[1] (numeric) = 0.47505920000000007 " " absolute error = 8.1601392309949010000000000000E-15 " " relative error = 1.7177099677250834000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.926999999999976 " " y[1] (analytic) = 0.47471644999999174 " " y[1] (numeric) = 0.47471645000000007 " " absolute error = 8.326672684688674000000000000000E-15 " " relative error = 1.7540307871549046000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.925999999999975 " " y[1] (analytic) = 0.47437379999999163 " " y[1] (numeric) = 0.47437380000000007 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 1.7787017299756727000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.924999999999975 " " y[1] (analytic) = 0.47403124999999147 " " y[1] (numeric) = 0.47403125000000007 " " absolute error = 8.604228440844963000000000000000E-15 " " relative error = 1.815118400072805000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.923999999999975 " " y[1] (analytic) = 0.47368879999999147 " " y[1] (numeric) = 0.4736888000000001 " " absolute error = 8.604228440844963000000000000000E-15 " " relative error = 1.8164306272061145000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.922999999999974 " " y[1] (analytic) = 0.4733464499999912 " " y[1] (numeric) = 0.4733464500000001 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 1.8763812841527422000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.921999999999974 " " y[1] (analytic) = 0.4730041999999911 " " y[1] (numeric) = 0.4730042000000001 " " absolute error = 8.992806499463768000000000000000E-15 " " relative error = 1.901210707952263000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.920999999999974 " " y[1] (analytic) = 0.47266204999999106 " " y[1] (numeric) = 0.4726620500000001 " " absolute error = 9.048317650695026000000000000000E-15 " " relative error = 1.914331317840135000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.919999999999973 " " y[1] (analytic) = 0.47231999999999097 " " y[1] (numeric) = 0.47232000000000013 " " absolute error = 9.159339953157541000000000000000E-15 " " relative error = 1.9392233979415896000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.918999999999973 " " y[1] (analytic) = 0.4719780499999908 " " y[1] (numeric) = 0.47197805000000015 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 1.975912525349748000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.917999999999973 " " y[1] (analytic) = 0.4716361999999906 " " y[1] (numeric) = 0.47163620000000017 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 2.024424336337316000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.916999999999972 " " y[1] (analytic) = 0.4712944499999906 " " y[1] (numeric) = 0.4712944500000002 " " absolute error = 9.603429163007604000000000000000E-15 " " relative error = 2.0376707519063283000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.915999999999972 " " y[1] (analytic) = 0.4709527999999904 " " y[1] (numeric) = 0.4709528000000002 " " absolute error = 9.825473767932635000000000000000E-15 " " relative error = 2.086296921460672000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.914999999999972 " " y[1] (analytic) = 0.4706112499999904 " " y[1] (numeric) = 0.4706112500000002 " " absolute error = 9.825473767932635000000000000000E-15 " " relative error = 2.0878110686756504000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.913999999999971 " " y[1] (analytic) = 0.4702697999999903 " " y[1] (numeric) = 0.4702698000000002 " " absolute error = 9.880984919163893000000000000000E-15 " " relative error = 2.1011310781947082000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.912999999999971 " " y[1] (analytic) = 0.46992844999999017 " " y[1] (numeric) = 0.46992845000000016 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 2.12628267593218000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.911999999999970 " " y[1] (analytic) = 0.46958719999999 " " y[1] (numeric) = 0.46958720000000015 " " absolute error = 1.015854067532018200000000000000E-14 " " relative error = 2.163291647498142800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.91099999999997 " " y[1] (analytic) = 0.46924604999998987 " " y[1] (numeric) = 0.46924605000000014 " " absolute error = 1.026956297778269800000000000000E-14 " " relative error = 2.1885241181642165000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.90999999999997 " " y[1] (analytic) = 0.4689049999999897 " " y[1] (numeric) = 0.4689050000000001 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 2.2256312966329428000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.90899999999997 " " y[1] (analytic) = 0.4685640499999897 " " y[1] (numeric) = 0.4685640500000001 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 2.2272507742488354000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.907999999999970 " " y[1] (analytic) = 0.4682231999999896 " " y[1] (numeric) = 0.4682232000000001 " " absolute error = 1.04916075827077300000000000000E-14 " " relative error = 2.240727837216942900000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.906999999999969 " " y[1] (analytic) = 0.4678824499999895 " " y[1] (numeric) = 0.4678824500000001 " " absolute error = 1.060262988517024500000000000000E-14 " " relative error = 2.2660883914689434000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.905999999999969 " " y[1] (analytic) = 0.46754179999998946 " " y[1] (numeric) = 0.4675418000000001 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 2.2796124402998283000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.904999999999968 " " y[1] (analytic) = 0.46720124999998913 " " y[1] (numeric) = 0.4672012500000001 " " absolute error = 1.09912079437890500000000000000E-14 " " relative error = 2.3525638991311143000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.903999999999968 " " y[1] (analytic) = 0.4668607999999892 " " y[1] (numeric) = 0.46686080000000013 " " absolute error = 1.093569679255779200000000000000E-14 " " relative error = 2.342389164512858000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.902999999999968 " " y[1] (analytic) = 0.466520449999989 " " y[1] (numeric) = 0.46652045000000014 " " absolute error = 1.115774139748282300000000000000E-14 " " relative error = 2.3916939541413643000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.901999999999967 " " y[1] (analytic) = 0.46618019999998894 " " y[1] (numeric) = 0.46618020000000016 " " absolute error = 1.121325254871408100000000000000E-14 " " relative error = 2.4053472345488602000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.900999999999967 " " y[1] (analytic) = 0.46584004999998896 " " y[1] (numeric) = 0.46584005000000017 " " absolute error = 1.121325254871408100000000000000E-14 " " relative error = 2.407103586030086000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.899999999999967 " " y[1] (analytic) = 0.4654999999999887 " " y[1] (numeric) = 0.4655000000000002 " " absolute error = 1.14908083048703700000000000000E-14 " " relative error = 2.4684872835382704000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.898999999999966 " " y[1] (analytic) = 0.4651600499999886 " " y[1] (numeric) = 0.4651600500000002 " " absolute error = 1.160183060733288600000000000000E-14 " " relative error = 2.494158861521571000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.897999999999966 " " y[1] (analytic) = 0.46482019999998847 " " y[1] (numeric) = 0.46482020000000024 " " absolute error = 1.17683640610266600000000000000E-14 " " relative error = 2.5318099473789980000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.896999999999966 " " y[1] (analytic) = 0.4644804499999885 " " y[1] (numeric) = 0.46448045000000027 " " absolute error = 1.17683640610266600000000000000E-14 " " relative error = 2.533661871242794000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.895999999999965 " " y[1] (analytic) = 0.46414079999998836 " " y[1] (numeric) = 0.4641408000000003 " " absolute error = 1.193489751472043300000000000000E-14 " " relative error = 2.5713959028641165000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.894999999999965 " " y[1] (analytic) = 0.4638012499999882 " " y[1] (numeric) = 0.4638012500000003 " " absolute error = 1.210143096841420600000000000000E-14 " " relative error = 2.609184638552508000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.893999999999965 " " y[1] (analytic) = 0.46346179999998816 " " y[1] (numeric) = 0.46346180000000026 " " absolute error = 1.210143096841420600000000000000E-14 " " relative error = 2.6110956649317196000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.892999999999964 " " y[1] (analytic) = 0.46312244999998786 " " y[1] (numeric) = 0.46312245000000024 " " absolute error = 1.237898672457049500000000000000E-14 " " relative error = 2.6729403259485307000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.891999999999964 " " y[1] (analytic) = 0.46278319999998774 " " y[1] (numeric) = 0.4627832000000002 " " absolute error = 1.249000902703301100000000000000E-14 " " relative error = 2.698889896399294700000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.890999999999964 " " y[1] (analytic) = 0.46244404999998767 " " y[1] (numeric) = 0.4624440500000002 " " absolute error = 1.254552017826427000000000000000E-14 " " relative error = 2.712873087731284000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.889999999999963 " " y[1] (analytic) = 0.46210499999998755 " " y[1] (numeric) = 0.4621050000000002 " " absolute error = 1.265654248072678500000000000000E-14 " " relative error = 2.738888884718219000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.888999999999963 " " y[1] (analytic) = 0.4617660499999876 " " y[1] (numeric) = 0.4617660500000002 " " absolute error = 1.260103132949552700000000000000E-14 " " relative error = 2.728877822329265300000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.887999999999963 " " y[1] (analytic) = 0.4614271999999874 " " y[1] (numeric) = 0.4614272000000002 " " absolute error = 1.282307593442055800000000000000E-14 " " relative error = 2.779003044125034000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.886999999999962 " " y[1] (analytic) = 0.4610884499999873 " " y[1] (numeric) = 0.4610884500000002 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 2.7930838618170045000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.885999999999962 " " y[1] (analytic) = 0.4607497999999871 " " y[1] (numeric) = 0.4607498000000002 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 2.8433287850753736000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.884999999999962 " " y[1] (analytic) = 0.46041124999998706 " " y[1] (numeric) = 0.4604112500000002 " " absolute error = 1.315614284180810500000000000000E-14 " " relative error = 2.8574764065405606000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.883999999999961 " " y[1] (analytic) = 0.46007279999998696 " " y[1] (numeric) = 0.4600728000000002 " " absolute error = 1.32671651442706200000000000000E-14 " " relative error = 2.8837099572656755000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.882999999999961 " " y[1] (analytic) = 0.4597344499999868 " " y[1] (numeric) = 0.45973445000000024 " " absolute error = 1.343369859796439400000000000000E-14 " " relative error = 2.9220561126025640000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.881999999999960 " " y[1] (analytic) = 0.4593961999999868 " " y[1] (numeric) = 0.45939620000000025 " " absolute error = 1.343369859796439400000000000000E-14 " " relative error = 2.924207600751765000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.88099999999996 " " y[1] (analytic) = 0.4590580499999867 " " y[1] (numeric) = 0.4590580500000003 " " absolute error = 1.360023205165816800000000000000E-14 " " relative error = 2.9626388322040237000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.87999999999996 " " y[1] (analytic) = 0.45871999999998647 " " y[1] (numeric) = 0.4587200000000003 " " absolute error = 1.382227665658320000000000000000E-14 " " relative error = 3.0132273841523380000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.87899999999996 " " y[1] (analytic) = 0.45838204999998644 " " y[1] (numeric) = 0.4583820500000003 " " absolute error = 1.387778780781445700000000000000E-14 " " relative error = 3.0275591742335606000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.877999999999960 " " y[1] (analytic) = 0.45804419999998636 " " y[1] (numeric) = 0.45804420000000035 " " absolute error = 1.398881011027697200000000000000E-14 " " relative error = 3.0540306176297810000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.876999999999959 " " y[1] (analytic) = 0.4577064499999862 " " y[1] (numeric) = 0.4577064500000004 " " absolute error = 1.415534356397074600000000000000E-14 " " relative error = 3.0926685791670994000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.875999999999959 " " y[1] (analytic) = 0.45736879999998614 " " y[1] (numeric) = 0.45736880000000035 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 3.107088790315919000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.874999999999958 " " y[1] (analytic) = 0.457031249999986 " " y[1] (numeric) = 0.45703125000000033 " " absolute error = 1.43218770176645200000000000000E-14 " " relative error = 3.1336756551472045000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.873999999999958 " " y[1] (analytic) = 0.45669379999998605 " " y[1] (numeric) = 0.4566938000000003 " " absolute error = 1.42663658664332620000000000000E-14 " " relative error = 3.1238361165476075000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.872999999999958 " " y[1] (analytic) = 0.4563564499999858 " " y[1] (numeric) = 0.4563564500000003 " " absolute error = 1.448841047135829300000000000000E-14 " " relative error = 3.174801292138797000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.871999999999957 " " y[1] (analytic) = 0.45601919999998575 " " y[1] (numeric) = 0.4560192000000003 " " absolute error = 1.45439216225895500000000000000E-14 " " relative error = 3.1893222089311163000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.870999999999957 " " y[1] (analytic) = 0.4556820499999855 " " y[1] (numeric) = 0.4556820500000003 " " absolute error = 1.476596622751458200000000000000E-14 " " relative error = 3.240409892712484700000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.869999999999957 " " y[1] (analytic) = 0.45534499999998546 " " y[1] (numeric) = 0.4553450000000003 " " absolute error = 1.48214773787458400000000000000E-14 " " relative error = 3.2549994792402054000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.868999999999956 " " y[1] (analytic) = 0.45500804999998534 " " y[1] (numeric) = 0.4550080500000003 " " absolute error = 1.493249968120835500000000000000E-14 " " relative error = 3.2818099990118500000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.867999999999956 " " y[1] (analytic) = 0.4546711999999852 " " y[1] (numeric) = 0.4546712000000003 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 3.3208686045878033000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.866999999999956 " " y[1] (analytic) = 0.4543344499999852 " " y[1] (numeric) = 0.4543344500000003 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 3.3233300127037735000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.865999999999955 " " y[1] (analytic) = 0.453997799999985 " " y[1] (numeric) = 0.4539978000000003 " " absolute error = 1.526556658859590200000000000000E-14 " " relative error = 3.362475894948479000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.864999999999955 " " y[1] (analytic) = 0.4536612499999848 " " y[1] (numeric) = 0.4536612500000003 " " absolute error = 1.548761119352093400000000000000E-14 " " relative error = 3.4139153814705253000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.863999999999955 " " y[1] (analytic) = 0.453324799999985 " " y[1] (numeric) = 0.4533248000000003 " " absolute error = 1.53210777398271600000000000000E-14 " " relative error = 3.3797131195618835000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.862999999999954 " " y[1] (analytic) = 0.45298844999998467 " " y[1] (numeric) = 0.4529884500000003 " " absolute error = 1.565414464721470700000000000000E-14 " " relative error = 3.4557491801866560000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.861999999999954 " " y[1] (analytic) = 0.4526521999999845 " " y[1] (numeric) = 0.45265220000000034 " " absolute error = 1.58206781009084800000000000000E-14 " " relative error = 3.49510686149521000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.860999999999954 " " y[1] (analytic) = 0.4523160499999844 " " y[1] (numeric) = 0.45231605000000036 " " absolute error = 1.593170040337099600000000000000E-14 " " relative error = 3.522249631285811000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.859999999999953 " " y[1] (analytic) = 0.4519799999999843 " " y[1] (numeric) = 0.4519800000000004 " " absolute error = 1.60982338570647700000000000000E-14 " " relative error = 3.561713761021578000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.858999999999953 " " y[1] (analytic) = 0.4516440499999843 " " y[1] (numeric) = 0.4516440500000004 " " absolute error = 1.60982338570647700000000000000E-14 " " relative error = 3.5643630990080194000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.857999999999953 " " y[1] (analytic) = 0.45130819999998406 " " y[1] (numeric) = 0.45130820000000044 " " absolute error = 1.63757896132210600000000000000E-14 " " relative error = 3.6285158597210593000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.856999999999952 " " y[1] (analytic) = 0.450972449999984 " " y[1] (numeric) = 0.45097245000000047 " " absolute error = 1.648681191568357500000000000000E-14 " " relative error = 3.6558357202716396000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.855999999999952 " " y[1] (analytic) = 0.45063679999998396 " " y[1] (numeric) = 0.45063680000000045 " " absolute error = 1.648681191568357500000000000000E-14 " " relative error = 3.658558714176064000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.854999999999952 " " y[1] (analytic) = 0.45030124999998367 " " y[1] (numeric) = 0.45030125000000043 " " absolute error = 1.676436767183986400000000000000E-14 " " relative error = 3.722922748235869600000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.853999999999951 " " y[1] (analytic) = 0.44996579999998376 " " y[1] (numeric) = 0.4499658000000004 " " absolute error = 1.665334536937734800000000000000E-14 " " relative error = 3.701024693294012000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.852999999999951 " " y[1] (analytic) = 0.4496304499999836 " " y[1] (numeric) = 0.4496304500000004 " " absolute error = 1.681987882307112200000000000000E-14 " " relative error = 3.74082289646347000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.851999999999950 " " y[1] (analytic) = 0.4492951999999836 " " y[1] (numeric) = 0.4492952000000004 " " absolute error = 1.681987882307112200000000000000E-14 " " relative error = 3.7436141812936660000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.85099999999995 " " y[1] (analytic) = 0.4489600499999834 " " y[1] (numeric) = 0.4489600500000004 " " absolute error = 1.698641227676489500000000000000E-14 " " relative error = 3.7835019567477157000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.84999999999995 " " y[1] (analytic) = 0.4486249999999832 " " y[1] (numeric) = 0.4486250000000004 " " absolute error = 1.720845688168992600000000000000E-14 " " relative error = 3.835822096782518000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.84899999999995 " " y[1] (analytic) = 0.44829004999998334 " " y[1] (numeric) = 0.4482900500000004 " " absolute error = 1.704192342799615300000000000000E-14 " " relative error = 3.801539522904152000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.847999999999950 " " y[1] (analytic) = 0.447955199999983 " " y[1] (numeric) = 0.4479552000000004 " " absolute error = 1.7374990335383700000000000000E-14 " " relative error = 3.878733930398477000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.846999999999949 " " y[1] (analytic) = 0.44762044999998307 " " y[1] (numeric) = 0.4476204500000004 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 3.869233227425846000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.845999999999949 " " y[1] (analytic) = 0.44728579999998297 " " y[1] (numeric) = 0.4472858000000004 " " absolute error = 1.743050148661495800000000000000E-14 " " relative error = 3.8969494418592365000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.844999999999948 " " y[1] (analytic) = 0.4469512499999826 " " y[1] (numeric) = 0.4469512500000004 " " absolute error = 1.781907954523376200000000000000E-14 " " relative error = 3.986806065590924300000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.843999999999948 " " y[1] (analytic) = 0.4466167999999828 " " y[1] (numeric) = 0.4466168000000004 " " absolute error = 1.75970349403087300000000000000E-14 " " relative error = 3.940074565110271000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.842999999999948 " " y[1] (analytic) = 0.44628244999998257 " " y[1] (numeric) = 0.44628245000000044 " " absolute error = 1.78745906964650200000000000000E-14 " " relative error = 4.0052192723387886000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.841999999999947 " " y[1] (analytic) = 0.4459481999999825 " " y[1] (numeric) = 0.44594820000000046 " " absolute error = 1.798561299892753600000000000000E-14 " " relative error = 4.033117074792149000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.840999999999947 " " y[1] (analytic) = 0.44561404999998244 " " y[1] (numeric) = 0.4456140500000005 " " absolute error = 1.804112415015879400000000000000E-14 " " relative error = 4.048598591125998600000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.839999999999947 " " y[1] (analytic) = 0.44527999999998213 " " y[1] (numeric) = 0.4452800000000005 " " absolute error = 1.83741910575463400000000000000E-14 " " relative error = 4.126435289603637700000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.838999999999946 " " y[1] (analytic) = 0.4449460499999822 " " y[1] (numeric) = 0.44494605000000054 " " absolute error = 1.831867990631508300000000000000E-14 " " relative error = 4.117056417584967000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.837999999999946 " " y[1] (analytic) = 0.444612199999982 " " y[1] (numeric) = 0.44461220000000057 " " absolute error = 1.854072451124011400000000000000E-14 " " relative error = 4.170089014930509000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.836999999999946 " " y[1] (analytic) = 0.444278449999982 " " y[1] (numeric) = 0.44427845000000055 " " absolute error = 1.854072451124011400000000000000E-14 " " relative error = 4.173221661154365400000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.835999999999945 " " y[1] (analytic) = 0.4439447999999818 " " y[1] (numeric) = 0.44394480000000053 " " absolute error = 1.870725796493388800000000000000E-14 " " relative error = 4.213870275073535000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.834999999999945 " " y[1] (analytic) = 0.4436112499999816 " " y[1] (numeric) = 0.4436112500000005 " " absolute error = 1.89293025698589200000000000000E-14 " " relative error = 4.267092543270646400000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.833999999999945 " " y[1] (analytic) = 0.44327779999998174 " " y[1] (numeric) = 0.4432778000000005 " " absolute error = 1.876276911616514600000000000000E-14 " " relative error = 4.232733765635436400000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.832999999999944 " " y[1] (analytic) = 0.4429444499999814 " " y[1] (numeric) = 0.4429444500000005 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 4.31111305798131000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.831999999999944 " " y[1] (analytic) = 0.44261119999998144 " " y[1] (numeric) = 0.4426112000000005 " " absolute error = 1.904032487232143500000000000000E-14 " " relative error = 4.301817231991019000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.830999999999944 " " y[1] (analytic) = 0.4422780499999813 " " y[1] (numeric) = 0.4422780500000005 " " absolute error = 1.91513471747839500000000000000E-14 " " relative error = 4.330159992064892000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.829999999999943 " " y[1] (analytic) = 0.44194499999998116 " " y[1] (numeric) = 0.4419450000000005 " " absolute error = 1.931788062847772400000000000000E-14 " " relative error = 4.371105143961024300000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.828999999999943 " " y[1] (analytic) = 0.44161204999998116 " " y[1] (numeric) = 0.4416120500000005 " " absolute error = 1.931788062847772400000000000000E-14 " " relative error = 4.374400704980434500000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.827999999999943 " " y[1] (analytic) = 0.4412791999999809 " " y[1] (numeric) = 0.4412792000000005 " " absolute error = 1.959543638463401300000000000000E-14 " " relative error = 4.440598239081937600000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.826999999999942 " " y[1] (analytic) = 0.4409464499999808 " " y[1] (numeric) = 0.4409464500000005 " " absolute error = 1.97064586870965290000000000000E-14 " " relative error = 4.469127416060927000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.825999999999942 " " y[1] (analytic) = 0.44061379999998074 " " y[1] (numeric) = 0.4406138000000005 " " absolute error = 1.976196983832778600000000000000E-14 " " relative error = 4.485100066845081000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.824999999999942 " " y[1] (analytic) = 0.44028124999998064 " " y[1] (numeric) = 0.4402812500000005 " " absolute error = 1.987299214079030200000000000000E-14 " " relative error = 4.513703942829992400000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.823999999999941 " " y[1] (analytic) = 0.4399487999999807 " " y[1] (numeric) = 0.43994880000000053 " " absolute error = 1.981748098955904400000000000000E-14 " " relative error = 4.50449711183663000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.822999999999941 " " y[1] (analytic) = 0.4396164499999805 " " y[1] (numeric) = 0.43961645000000055 " " absolute error = 2.003952559448407600000000000000E-14 " " relative error = 4.558411222893266000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.821999999999940 " " y[1] (analytic) = 0.43928419999998025 " " y[1] (numeric) = 0.43928420000000057 " " absolute error = 2.031708135064036500000000000000E-14 " " relative error = 4.625042592162722500000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.82099999999994 " " y[1] (analytic) = 0.4389520499999803 " " y[1] (numeric) = 0.4389520500000006 " " absolute error = 2.031708135064036500000000000000E-14 " " relative error = 4.628542309038373700000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.81999999999994 " " y[1] (analytic) = 0.43861999999998 " " y[1] (numeric) = 0.4386200000000006 " " absolute error = 2.059463710679665400000000000000E-14 " " relative error = 4.695325590898179000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8189999999999396 " " y[1] (analytic) = 0.43828804999998017 " " y[1] (numeric) = 0.43828805000000065 " " absolute error = 2.048361480433413800000000000000E-14 " " relative error = 4.6735508313163143000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.817999999999940 " " y[1] (analytic) = 0.4379561999999798 " " y[1] (numeric) = 0.4379562000000007 " " absolute error = 2.087219286295294300000000000000E-14 " " relative error = 4.765817418032649000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.816999999999939 " " y[1] (analytic) = 0.43762444999997985 " " y[1] (numeric) = 0.43762445000000066 " " absolute error = 2.081668171172168500000000000000E-14 " " relative error = 4.756745586706283000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8159999999999386 " " y[1] (analytic) = 0.4372927999999797 " " y[1] (numeric) = 0.43729280000000065 " " absolute error = 2.0927704014184200000000000000E-14 " " relative error = 4.785741730525902000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.814999999999938 " " y[1] (analytic) = 0.43696124999997954 " " y[1] (numeric) = 0.43696125000000063 " " absolute error = 2.109423746787797400000000000000E-14 " " relative error = 4.827484695239901000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.813999999999938 " " y[1] (analytic) = 0.43662979999997953 " " y[1] (numeric) = 0.4366298000000006 " " absolute error = 2.109423746787797400000000000000E-14 " " relative error = 4.831149286621977000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8129999999999376 " " y[1] (analytic) = 0.43629844999997947 " " y[1] (numeric) = 0.4362984500000006 " " absolute error = 2.114974861910923200000000000000E-14 " " relative error = 4.84754154389277050000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.811999999999937 " " y[1] (analytic) = 0.43596719999997935 " " y[1] (numeric) = 0.4359672000000006 " " absolute error = 2.126077092157174800000000000000E-14 " " relative error = 4.876690476158012700000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.810999999999937 " " y[1] (analytic) = 0.4356360499999793 " " y[1] (numeric) = 0.4356360500000006 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 4.893140058726549000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8099999999999365 " " y[1] (analytic) = 0.43530499999997896 " " y[1] (numeric) = 0.4353050000000006 " " absolute error = 2.164934898019055300000000000000E-14 " " relative error = 4.973374755675124500000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.808999999999936 " " y[1] (analytic) = 0.434974049999979 " " y[1] (numeric) = 0.4349740500000006 " " absolute error = 2.159383782895929500000000000000E-14 " " relative error = 4.96439680228288050000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.807999999999936 " " y[1] (analytic) = 0.4346431999999788 " " y[1] (numeric) = 0.4346432000000006 " " absolute error = 2.181588243388432600000000000000E-14 " " relative error = 5.019262336069077000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8069999999999355 " " y[1] (analytic) = 0.43431244999997876 " " y[1] (numeric) = 0.4343124500000006 " " absolute error = 2.187139358511558400000000000000E-14 " " relative error = 5.035866133958780000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.805999999999935 " " y[1] (analytic) = 0.43398179999997877 " " y[1] (numeric) = 0.43398180000000064 " " absolute error = 2.187139358511558400000000000000E-14 " " relative error = 5.039702951855736000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.804999999999935 " " y[1] (analytic) = 0.4336512499999785 " " y[1] (numeric) = 0.43365125000000065 " " absolute error = 2.214894934127187300000000000000E-14 " " relative error = 5.107548828989417000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8039999999999345 " " y[1] (analytic) = 0.43332079999997863 " " y[1] (numeric) = 0.43332080000000067 " " absolute error = 2.203792703880935700000000000000E-14 " " relative error = 5.085822568132073000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.802999999999934 " " y[1] (analytic) = 0.43299044999997827 " " y[1] (numeric) = 0.4329904500000007 " " absolute error = 2.242650509742816200000000000000E-14 " " relative error = 5.1794456661640660000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.801999999999934 " " y[1] (analytic) = 0.4326601999999783 " " y[1] (numeric) = 0.4326602000000007 " " absolute error = 2.242650509742816200000000000000E-14 " " relative error = 5.183399142659595000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8009999999999335 " " y[1] (analytic) = 0.43233004999997815 " " y[1] (numeric) = 0.43233005000000074 " " absolute error = 2.259303855112193600000000000000E-14 " " relative error = 5.225877440423833000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.799999999999933 " " y[1] (analytic) = 0.43199999999997796 " " y[1] (numeric) = 0.4320000000000008 " " absolute error = 2.281508315604696700000000000000E-14 " " relative error = 5.281269249085215000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.798999999999933 " " y[1] (analytic) = 0.43167004999997793 " " y[1] (numeric) = 0.4316700500000008 " " absolute error = 2.287059430727822500000000000000E-14 " " relative error = 5.298165649268323000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7979999999999325 " " y[1] (analytic) = 0.43134019999997786 " " y[1] (numeric) = 0.4313402000000008 " " absolute error = 2.292610545850948300000000000000E-14 " " relative error = 5.3150866667448700000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.796999999999932 " " y[1] (analytic) = 0.43101044999997773 " " y[1] (numeric) = 0.43101045000000077 " " absolute error = 2.303712776097199800000000000000E-14 " " relative error = 5.344911651439818000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.795999999999932 " " y[1] (analytic) = 0.43068079999997766 " " y[1] (numeric) = 0.43068080000000075 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 5.361891895855226000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7949999999999315 " " y[1] (analytic) = 0.43035124999997754 " " y[1] (numeric) = 0.43035125000000074 " " absolute error = 2.320366121466577200000000000000E-14 " " relative error = 5.39179593754334000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.793999999999931 " " y[1] (analytic) = 0.4300217999999776 " " y[1] (numeric) = 0.43002180000000073 " " absolute error = 2.314815006343451400000000000000E-14 " " relative error = 5.3830178059427970000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.792999999999930 " " y[1] (analytic) = 0.42969244999997736 " " y[1] (numeric) = 0.4296924500000007 " " absolute error = 2.337019466835954500000000000000E-14 " " relative error = 5.438819013078023000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7919999999999305 " " y[1] (analytic) = 0.4293631999999773 " " y[1] (numeric) = 0.4293632000000007 " " absolute error = 2.342570581959080300000000000000E-14 " " relative error = 5.4559183971966030000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.79099999999993 " " y[1] (analytic) = 0.4290340499999771 " " y[1] (numeric) = 0.4290340500000007 " " absolute error = 2.364775042451583400000000000000E-14 " " relative error = 5.511858656560499000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.78999999999993 " " y[1] (analytic) = 0.428704999999977 " " y[1] (numeric) = 0.4287050000000007 " " absolute error = 2.370326157574709200000000000000E-14 " " relative error = 5.5290378175548140000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7889999999999295 " " y[1] (analytic) = 0.4283760499999769 " " y[1] (numeric) = 0.42837605000000073 " " absolute error = 2.381428387820960800000000000000E-14 " " relative error = 5.559200585142632000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.787999999999930 " " y[1] (analytic) = 0.42804719999997676 " " y[1] (numeric) = 0.42804720000000074 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 5.602376871500312000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.786999999999929 " " y[1] (analytic) = 0.42771844999997677 " " y[1] (numeric) = 0.42771845000000075 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 5.606682931705351000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7859999999999285 " " y[1] (analytic) = 0.4273897999999766 " " y[1] (numeric) = 0.42738980000000076 " " absolute error = 2.414735078559715500000000000000E-14 " " relative error = 5.649959541757542000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.784999999999928 " " y[1] (analytic) = 0.4270612499999764 " " y[1] (numeric) = 0.4270612500000008 " " absolute error = 2.436939539052218600000000000000E-14 " " relative error = 5.706299831821204000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.783999999999928 " " y[1] (analytic) = 0.4267327999999764 " " y[1] (numeric) = 0.4267328000000008 " " absolute error = 2.442490654175344400000000000000E-14 " " relative error = 5.723700297177718000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7829999999999275 " " y[1] (analytic) = 0.4264044499999763 " " y[1] (numeric) = 0.4264044500000008 " " absolute error = 2.45359288442159600000000000000E-14 " " relative error = 5.754144649338749000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.781999999999927 " " y[1] (analytic) = 0.42607619999997615 " " y[1] (numeric) = 0.42607620000000085 " " absolute error = 2.470246229790973300000000000000E-14 " " relative error = 5.797663023166071000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.780999999999927 " " y[1] (analytic) = 0.42574804999997606 " " y[1] (numeric) = 0.4257480500000009 " " absolute error = 2.48134846003722500000000000000E-14 " " relative error = 5.828208631929997000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7799999999999265 " " y[1] (analytic) = 0.42541999999997593 " " y[1] (numeric) = 0.4254200000000009 " " absolute error = 2.498001805406602200000000000000E-14 " " relative error = 5.871848538871570000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.778999999999926 " " y[1] (analytic) = 0.42509204999997596 " " y[1] (numeric) = 0.42509205000000094 " " absolute error = 2.498001805406602200000000000000E-14 " " relative error = 5.876378552378816000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.777999999999926 " " y[1] (analytic) = 0.4247641999999757 " " y[1] (numeric) = 0.4247642000000009 " " absolute error = 2.520206265899105300000000000000E-14 " " relative error = 5.9331889690780180000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7769999999999255 " " y[1] (analytic) = 0.42443644999997565 " " y[1] (numeric) = 0.4244364500000009 " " absolute error = 2.52575738102223100000000000000E-14 " " relative error = 5.950849369846478000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.775999999999925 " " y[1] (analytic) = 0.42410879999997564 " " y[1] (numeric) = 0.4241088000000009 " " absolute error = 2.52575738102223100000000000000E-14 " " relative error = 5.955446765128137000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.774999999999925 " " y[1] (analytic) = 0.42378124999997535 " " y[1] (numeric) = 0.4237812500000009 " " absolute error = 2.5535129566378600000000000000E-14 " " relative error = 6.0255449164822860000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7739999999999245 " " y[1] (analytic) = 0.42345379999997546 " " y[1] (numeric) = 0.4234538000000009 " " absolute error = 2.542410726391608500000000000000E-14 " " relative error = 6.003986093386707000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.772999999999924 " " y[1] (analytic) = 0.4231264499999753 " " y[1] (numeric) = 0.4231264500000009 " " absolute error = 2.559064071760986000000000000000E-14 " " relative error = 6.047988897316949000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.771999999999924 " " y[1] (analytic) = 0.42279919999997506 " " y[1] (numeric) = 0.4227992000000009 " " absolute error = 2.58126853225348900000000000000E-14 " " relative error = 6.105187834446332000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7709999999999235 " " y[1] (analytic) = 0.4224720499999751 " " y[1] (numeric) = 0.4224720500000009 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 6.096775910099886000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.769999999999923 " " y[1] (analytic) = 0.4221449999999749 " " y[1] (numeric) = 0.4221450000000009 " " absolute error = 2.597921877622866300000000000000E-14 " " relative error = 6.154098420265598000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.768999999999923 " " y[1] (analytic) = 0.42181804999997485 " " y[1] (numeric) = 0.4218180500000009 " " absolute error = 2.60347299274599200000000000000E-14 " " relative error = 6.172028420182938000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7679999999999225 " " y[1] (analytic) = 0.42149119999997475 " " y[1] (numeric) = 0.4214912000000009 " " absolute error = 2.614575222992243700000000000000E-14 " " relative error = 6.203154948412684000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.766999999999922 " " y[1] (analytic) = 0.4211644499999746 " " y[1] (numeric) = 0.4211644500000009 " " absolute error = 2.63122856836162100000000000000E-14 " " relative error = 6.247508706781353000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.765999999999922 " " y[1] (analytic) = 0.4208377999999745 " " y[1] (numeric) = 0.42083780000000093 " " absolute error = 2.642330798607872600000000000000E-14 " " relative error = 6.2787392164107700000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7649999999999215 " " y[1] (analytic) = 0.42051124999997436 " " y[1] (numeric) = 0.42051125000000095 " " absolute error = 2.6589841439772500000000000000E-14 " " relative error = 6.3232176165974440000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.763999999999921 " " y[1] (analytic) = 0.4201847999999744 " " y[1] (numeric) = 0.42018480000000097 " " absolute error = 2.6589841439772500000000000000E-14 " " relative error = 6.328130251207117000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.762999999999920 " " y[1] (analytic) = 0.4198584499999741 " " y[1] (numeric) = 0.419858450000001 " " absolute error = 2.686739719592879000000000000000E-14 " " relative error = 6.399156000297349000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7619999999999205 " " y[1] (analytic) = 0.41953219999997404 " " y[1] (numeric) = 0.419532200000001 " " absolute error = 2.697841949839130400000000000000E-14 " " relative error = 6.4305956726070070000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.76099999999992 " " y[1] (analytic) = 0.419206049999974 " " y[1] (numeric) = 0.41920605000000105 " " absolute error = 2.703393064962256000000000000000E-14 " " relative error = 6.448840766879256000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.75999999999992 " " y[1] (analytic) = 0.41887999999997394 " " y[1] (numeric) = 0.4188800000000011 " " absolute error = 2.714495295208508000000000000000E-14 " " relative error = 6.480365009569988000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7589999999999195 " " y[1] (analytic) = 0.41855404999997403 " " y[1] (numeric) = 0.41855405000000107 " " absolute error = 2.703393064962256000000000000000E-14 " " relative error = 6.458886408965399000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.757999999999920 " " y[1] (analytic) = 0.4182281999999736 " " y[1] (numeric) = 0.41822820000000105 " " absolute error = 2.742250870824136700000000000000E-14 " " relative error = 6.556829192350754000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.756999999999919 " " y[1] (analytic) = 0.4179024499999736 " " y[1] (numeric) = 0.41790245000000104 " " absolute error = 2.742250870824136700000000000000E-14 " " relative error = 6.561940162888037000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7559999999999185 " " y[1] (analytic) = 0.41757679999997366 " " y[1] (numeric) = 0.417576800000001 " " absolute error = 2.73669975570101100000000000000E-14 " " relative error = 6.553763896129247000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.754999999999918 " " y[1] (analytic) = 0.41725124999997343 " " y[1] (numeric) = 0.417251250000001 " " absolute error = 2.75890421619351400000000000000E-14 " " relative error = 6.612093351892151000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.753999999999918 " " y[1] (analytic) = 0.41692579999997337 " " y[1] (numeric) = 0.416925800000001 " " absolute error = 2.764455331316640000000000000000E-14 " " relative error = 6.630569111618462000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7529999999999175 " " y[1] (analytic) = 0.41660044999997325 " " y[1] (numeric) = 0.416600450000001 " " absolute error = 2.775557561562891400000000000000E-14 " " relative error = 6.662396935872417000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.751999999999917 " " y[1] (analytic) = 0.4162751999999731 " " y[1] (numeric) = 0.416275200000001 " " absolute error = 2.792210906932268700000000000000E-14 " " relative error = 6.707608108608077000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.750999999999917 " " y[1] (analytic) = 0.415950049999973 " " y[1] (numeric) = 0.415950050000001 " " absolute error = 2.803313137178520000000000000000E-14 " " relative error = 6.739542733986214000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7499999999999165 " " y[1] (analytic) = 0.4156249999999728 " " y[1] (numeric) = 0.415625000000001 " " absolute error = 2.819966482547897600000000000000E-14 " " relative error = 6.784881762521702000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.748999999999916 " " y[1] (analytic) = 0.41530004999997283 " " y[1] (numeric) = 0.41530005000000103 " " absolute error = 2.819966482547897600000000000000E-14 " " relative error = 6.790190568356739000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.747999999999916 " " y[1] (analytic) = 0.4149751999999728 " " y[1] (numeric) = 0.41497520000000104 " " absolute error = 2.825517597671023400000000000000E-14 " " relative error = 6.808883031253937000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7469999999999155 " " y[1] (analytic) = 0.4146504499999727 " " y[1] (numeric) = 0.41465045000000106 " " absolute error = 2.83661982791727500000000000000E-14 " " relative error = 6.840990593203171000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.745999999999915 " " y[1] (analytic) = 0.41432579999997265 " " y[1] (numeric) = 0.4143258000000011 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 6.859748881292423000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.744999999999915 " " y[1] (analytic) = 0.41400124999997234 " " y[1] (numeric) = 0.4140012500000011 " " absolute error = 2.875477633779155400000000000000E-14 " " relative error = 6.94557717827989000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7439999999999145 " " y[1] (analytic) = 0.4136767999999724 " " y[1] (numeric) = 0.4136768000000011 " " absolute error = 2.869926518656029700000000000000E-14 " " relative error = 6.9376056831232040000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.742999999999914 " " y[1] (analytic) = 0.4133524499999722 " " y[1] (numeric) = 0.41335245000000115 " " absolute error = 2.89213097914853300000000000000E-14 " " relative error = 6.9967674780897680000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.741999999999914 " " y[1] (analytic) = 0.4130281999999722 " " y[1] (numeric) = 0.4130282000000012 " " absolute error = 2.897682094271658600000000000000E-14 " " relative error = 7.015700366880164000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7409999999999135 " " y[1] (analytic) = 0.412704049999972 " " y[1] (numeric) = 0.4127040500000012 " " absolute error = 2.91988655476416170000000000000E-14 " " relative error = 7.0750130868944950000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.739999999999913 " " y[1] (analytic) = 0.41237999999997177 " " y[1] (numeric) = 0.41238000000000125 " " absolute error = 2.947642130379790600000000000000E-14 " " relative error = 7.147878486784016000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.738999999999913 " " y[1] (analytic) = 0.4120560499999719 " " y[1] (numeric) = 0.41205605000000123 " " absolute error = 2.93098878501041300000000000000E-14 " " relative error = 7.1130827590339050000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7379999999999125 " " y[1] (analytic) = 0.4117321999999718 " " y[1] (numeric) = 0.4117322000000012 " " absolute error = 2.94209101525666500000000000000E-14 " " relative error = 7.145642277327026000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.736999999999912 " " y[1] (analytic) = 0.4114084499999716 " " y[1] (numeric) = 0.4114084500000012 " " absolute error = 2.95874436062604200000000000000E-14 " " relative error = 7.191744264431726000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.735999999999912 " " y[1] (analytic) = 0.4110847999999715 " " y[1] (numeric) = 0.4110848000000012 " " absolute error = 2.96984659087229400000000000000E-14 " " relative error = 7.224413529453046000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7349999999999115 " " y[1] (analytic) = 0.4107612499999713 " " y[1] (numeric) = 0.4107612500000012 " " absolute error = 2.98649993624167100000000000000E-14 " " relative error = 7.270646722985382000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.733999999999911 " " y[1] (analytic) = 0.4104377999999713 " " y[1] (numeric) = 0.4104378000000012 " " absolute error = 2.98649993624167100000000000000E-14 " " relative error = 7.276376435703241000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.732999999999910 " " y[1] (analytic) = 0.41011444999997126 " " y[1] (numeric) = 0.4101144500000012 " " absolute error = 2.99205105136479700000000000000E-14 " " relative error = 7.295648937424679000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7319999999999105 " " y[1] (analytic) = 0.40979119999997116 " " y[1] (numeric) = 0.4097912000000012 " " absolute error = 3.003153281611048400000000000000E-14 " " relative error = 7.328496272275392000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.73099999999991 " " y[1] (analytic) = 0.4094680499999711 " " y[1] (numeric) = 0.4094680500000012 " " absolute error = 3.00870439673417400000000000000E-14 " " relative error = 7.347836776848369000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.72999999999991 " " y[1] (analytic) = 0.4091449999999708 " " y[1] (numeric) = 0.4091450000000012 " " absolute error = 3.04201108747292900000000000000E-14 " " relative error = 7.435044024668872000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7289999999999095 " " y[1] (analytic) = 0.40882204999997085 " " y[1] (numeric) = 0.4088220500000012 " " absolute error = 3.03645997234980300000000000000E-14 " " relative error = 7.427339039931968000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.727999999999910 " " y[1] (analytic) = 0.40849919999997064 " " y[1] (numeric) = 0.40849920000000123 " " absolute error = 3.05866443284230600000000000000E-14 " " relative error = 7.487565294724019000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.726999999999909 " " y[1] (analytic) = 0.4081764499999706 " " y[1] (numeric) = 0.40817645000000125 " " absolute error = 3.06421554796543200000000000000E-14 " " relative error = 7.50708559488342000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7259999999999085 " " y[1] (analytic) = 0.4078537999999706 " " y[1] (numeric) = 0.40785380000000127 " " absolute error = 3.06421554796543200000000000000E-14 " " relative error = 7.513024392479984000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.724999999999908 " " y[1] (analytic) = 0.40753124999997037 " " y[1] (numeric) = 0.4075312500000013 " " absolute error = 3.09197112358106100000000000000E-14 " " relative error = 7.587077367885987000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.723999999999908 " " y[1] (analytic) = 0.4072087999999705 " " y[1] (numeric) = 0.4072088000000013 " " absolute error = 3.080868893334809400000000000000E-14 " " relative error = 7.565821007146781000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7229999999999075 " " y[1] (analytic) = 0.40688644999997015 " " y[1] (numeric) = 0.40688645000000134 " " absolute error = 3.1197266991966900000000000000E-14 " " relative error = 7.667315289552942000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.721999999999907 " " y[1] (analytic) = 0.4065641999999702 " " y[1] (numeric) = 0.4065642000000014 " " absolute error = 3.1197266991966900000000000000E-14 " " relative error = 7.673392539719234000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.720999999999907 " " y[1] (analytic) = 0.40624204999997005 " " y[1] (numeric) = 0.4062420500000014 " " absolute error = 3.13638004456606700000000000000E-14 " " relative error = 7.720471193384089000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7199999999999065 " " y[1] (analytic) = 0.40591999999996986 " " y[1] (numeric) = 0.4059200000000014 " " absolute error = 3.153033389935444600000000000000E-14 " " relative error = 7.767622659478909000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.718999999999906 " " y[1] (analytic) = 0.40559804999996985 " " y[1] (numeric) = 0.4055980500000014 " " absolute error = 3.153033389935444600000000000000E-14 " " relative error = 7.77378833536226000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.717999999999906 " " y[1] (analytic) = 0.4052761999999698 " " y[1] (numeric) = 0.40527620000000136 " " absolute error = 3.158584505058570400000000000000E-14 " " relative error = 7.79365900356054900000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7169999999999055 " " y[1] (analytic) = 0.40495444999996966 " " y[1] (numeric) = 0.40495445000000135 " " absolute error = 3.16968673530482200000000000000E-14 " " relative error = 7.827267326745168000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.715999999999905 " " y[1] (analytic) = 0.4046327999999696 " " y[1] (numeric) = 0.40463280000000135 " " absolute error = 3.17523785042794770000000000000E-14 " " relative error = 7.84720826000310900000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.714999999999905 " " y[1] (analytic) = 0.4043112499999695 " " y[1] (numeric) = 0.40431125000000134 " " absolute error = 3.18634008067419900000000000000E-14 " " relative error = 7.88090878172308900000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7139999999999045 " " y[1] (analytic) = 0.40398979999996953 " " y[1] (numeric) = 0.40398980000000134 " " absolute error = 3.180788965551073500000000000000E-14 " " relative error = 7.873438798581829000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.712999999999904 " " y[1] (analytic) = 0.4036684499999693 " " y[1] (numeric) = 0.40366845000000134 " " absolute error = 3.202993426043576600000000000000E-14 " " relative error = 7.934713317436178000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.711999999999904 " " y[1] (analytic) = 0.40334719999996926 " " y[1] (numeric) = 0.40334720000000135 " " absolute error = 3.208544541166702400000000000000E-14 " " relative error = 7.954795623142907000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7109999999999035 " " y[1] (analytic) = 0.40302604999996905 " " y[1] (numeric) = 0.40302605000000136 " " absolute error = 3.230749001659205500000000000000E-14 " " relative error = 8.016228731764246000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.709999999999903 " " y[1] (analytic) = 0.402704999999969 " " y[1] (numeric) = 0.40270500000000137 " " absolute error = 3.23630011678233130000000000000E-14 " " relative error = 8.036404109168200000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.708999999999903 " " y[1] (analytic) = 0.4023840499999689 " " y[1] (numeric) = 0.4023840500000014 " " absolute error = 3.24740234702858300000000000000E-14 " " relative error = 8.07040524352005000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7079999999999025 " " y[1] (analytic) = 0.40206319999996876 " " y[1] (numeric) = 0.4020632000000014 " " absolute error = 3.2640556923979600000000000000E-14 " " relative error = 8.118265218995955000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.706999999999902 " " y[1] (analytic) = 0.4017424499999688 " " y[1] (numeric) = 0.4017424500000014 " " absolute error = 3.2640556923979600000000000000E-14 " " relative error = 8.124746818261834000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.705999999999902 " " y[1] (analytic) = 0.40142179999996863 " " y[1] (numeric) = 0.40142180000000144 " " absolute error = 3.280709037767337600000000000000E-14 " " relative error = 8.172722651753328000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7049999999999015 " " y[1] (analytic) = 0.40110124999996843 " " y[1] (numeric) = 0.40110125000000146 " " absolute error = 3.30291349825984070000000000000E-14 " " relative error = 8.234612827210338000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.703999999999901 " " y[1] (analytic) = 0.4007807999999684 " " y[1] (numeric) = 0.4007808000000015 " " absolute error = 3.308464613382966500000000000000E-14 " " relative error = 8.255047680385955000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.702999999999900 " " y[1] (analytic) = 0.4004604499999683 " " y[1] (numeric) = 0.4004604500000015 " " absolute error = 3.31956684362921800000000000000E-14 " " relative error = 8.28937500227421000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7019999999999005 " " y[1] (analytic) = 0.4001401999999682 " " y[1] (numeric) = 0.40014020000000156 " " absolute error = 3.336220188998595400000000000000E-14 " " relative error = 8.337628133836242000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7009999999999 " " y[1] (analytic) = 0.3998200499999681 " " y[1] (numeric) = 0.3998200500000016 " " absolute error = 3.34732241924484700000000000000E-14 " " relative error = 8.37207243419912000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.6999999999999 " " y[1] (analytic) = 0.399499999999968 " " y[1] (numeric) = 0.3995000000000016 " " absolute error = 3.358424649491098500000000000000E-14 " " relative error = 8.406569836023448000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.6989999999998995 " " y[1] (analytic) = 0.39918004999996803 " " y[1] (numeric) = 0.39918005000000156 " " absolute error = 3.35287353436797300000000000000E-14 " " relative error = 8.39940155919175000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = (0.2 * x + 0.3) / 2.0;" Iterations = 301 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds "Expected Time Remaining "= 0 Years 0 Days 1 Hours 36 Minutes 42 Seconds "Optimized Time Remaining "= 0 Years 0 Days 1 Hours 35 Minutes 56 Seconds "Expected Total Time "= 0 Years 0 Days 1 Hours 38 Minutes 56 Seconds "Time to Timeout " Unknown Percent Done = 3.0200000000010085 "%" (%o54) true (%o54) diffeq.max