(%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 > 1.0E-34 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 > 1.0E-34 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 (rad_c : glob_large_float, ord_no : glob_large_float) 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 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) 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 (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float 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 (rad_c : glob_large_float, ord_no : glob_large_float) 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 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) 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 (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float 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 : sin(array_x ), array_tmp1_g : cos(array_x ), 1 1 1 1 array_tmp2 : sin(array_x ), array_tmp2_g : cos(array_x ), 1 1 1 1 array_tmp3 : array_tmp1 array_tmp2 , 1 1 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 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1_g array_x - array_tmp1 array_x 1 2 1 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 2 1 2 1 array_tmp2_g array_x - array_tmp2 array_x 1 2 1 2 array_tmp2 : ----------------------, array_tmp2_g : ----------------------, 2 1 2 1 array_tmp3 : ats(2, array_tmp1, array_tmp2, 1), array_tmp4 : array_tmp3 , 2 2 2 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 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 array_tmp1_g array_x - array_tmp1 array_x 2 2 2 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 3 2 3 2 array_tmp2_g array_x - array_tmp2 array_x 2 2 2 2 array_tmp2 : ----------------------, array_tmp2_g : ----------------------, 3 2 3 2 array_tmp3 : ats(3, array_tmp1, array_tmp2, 1), array_tmp4 : array_tmp3 , 3 3 3 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 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp1_g array_x - array_tmp1 array_x 3 2 3 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 4 3 4 3 array_tmp2_g array_x - array_tmp2 array_x 3 2 3 2 array_tmp2 : ----------------------, array_tmp2_g : ----------------------, 4 3 4 3 array_tmp3 : ats(4, array_tmp1, array_tmp2, 1), array_tmp4 : array_tmp3 , 4 4 4 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 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 array_tmp1_g array_x - array_tmp1 array_x 4 2 4 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 5 4 5 4 array_tmp2_g array_x - array_tmp2 array_x 4 2 4 2 array_tmp2 : ----------------------, array_tmp2_g : ----------------------, 5 4 5 4 array_tmp3 : ats(5, array_tmp1, array_tmp2, 1), array_tmp4 : array_tmp3 , 5 5 5 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 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 array_tmp1_g array_x kkk - 1 2 while kkk <= glob_max_terms do (array_tmp1 : ----------------------------, kkk kkk - 1 - array_tmp1 array_x kkk - 1 2 array_tmp1_g : ----------------------------, kkk kkk - 1 array_tmp2_g array_x kkk - 1 2 array_tmp2 : ----------------------------, kkk kkk - 1 - array_tmp2 array_x kkk - 1 2 array_tmp2_g : ----------------------------, kkk kkk - 1 array_tmp3 : ats(kkk, array_tmp1, array_tmp2, 1), kkk array_tmp4 : array_tmp3 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp4 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ), 1 1 1 1 array_tmp2 : sin(array_x ), array_tmp2_g : cos(array_x ), 1 1 1 1 array_tmp3 : array_tmp1 array_tmp2 , 1 1 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 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1_g array_x - array_tmp1 array_x 1 2 1 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 2 1 2 1 array_tmp2_g array_x - array_tmp2 array_x 1 2 1 2 array_tmp2 : ----------------------, array_tmp2_g : ----------------------, 2 1 2 1 array_tmp3 : ats(2, array_tmp1, array_tmp2, 1), array_tmp4 : array_tmp3 , 2 2 2 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 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 array_tmp1_g array_x - array_tmp1 array_x 2 2 2 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 3 2 3 2 array_tmp2_g array_x - array_tmp2 array_x 2 2 2 2 array_tmp2 : ----------------------, array_tmp2_g : ----------------------, 3 2 3 2 array_tmp3 : ats(3, array_tmp1, array_tmp2, 1), array_tmp4 : array_tmp3 , 3 3 3 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 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp1_g array_x - array_tmp1 array_x 3 2 3 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 4 3 4 3 array_tmp2_g array_x - array_tmp2 array_x 3 2 3 2 array_tmp2 : ----------------------, array_tmp2_g : ----------------------, 4 3 4 3 array_tmp3 : ats(4, array_tmp1, array_tmp2, 1), array_tmp4 : array_tmp3 , 4 4 4 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 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 array_tmp1_g array_x - array_tmp1 array_x 4 2 4 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 5 4 5 4 array_tmp2_g array_x - array_tmp2 array_x 4 2 4 2 array_tmp2 : ----------------------, array_tmp2_g : ----------------------, 5 4 5 4 array_tmp3 : ats(5, array_tmp1, array_tmp2, 1), array_tmp4 : array_tmp3 , 5 5 5 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 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 array_tmp1_g array_x kkk - 1 2 while kkk <= glob_max_terms do (array_tmp1 : ----------------------------, kkk kkk - 1 - array_tmp1 array_x kkk - 1 2 array_tmp1_g : ----------------------------, kkk kkk - 1 array_tmp2_g array_x kkk - 1 2 array_tmp2 : ----------------------------, kkk kkk - 1 - array_tmp2 array_x kkk - 1 2 array_tmp2_g : ----------------------------, kkk kkk - 1 array_tmp3 : ats(kkk, array_tmp1, array_tmp2, 1), kkk array_tmp4 : array_tmp3 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp4 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term 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 > + 1.0E-34 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 > + 1.0E-34 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) Si(x) := 0.0 (%o46) Si(x) := 0.0 (%i47) Ci(x) := 0.0 (%o47) Ci(x) := 0.0 (%i48) ln(x) := log(x) (%o48) ln(x) := log(x) (%i49) arcsin(x) := asin(x) (%o49) arcsin(x) := asin(x) (%i50) arccos(x) := acos(x) (%o50) arccos(x) := acos(x) (%i51) arctan(x) := atan(x) (%o51) arctan(x) := atan(x) (%i52) omniabs(x) := abs(x) (%o52) omniabs(x) := abs(x) (%i53) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%o53) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i54) 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) (%o54) 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) x - sin(x) cos(x) (%i55) exact_soln_y(x) := block(--- + ---------------) 2.0 2.0 x - sin(x) cos(x) (%o55) exact_soln_y(x) := block(--- + ---------------) 2.0 2.0 (%i56) 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, repeat_it], 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/mult_sin_sinpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x) * sin(x);"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), 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, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (-(sin(x) * cos(x))/2.0 + x/2.0) "), 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_g, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2_g, 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_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2_g : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0, term term : 1 + term), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 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_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_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_g : 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_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2_g : 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_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), x_start : 0.1, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_h : 0.05, 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(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(), display_alot(current_iter), 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 : 2, 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 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 ) = sin(x) * sin(x);"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-13T01:19:26-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mult_sin_sin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(x) * sin(x);"), 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, " 156 "), logitem_str(html_log_file, "mult_sin_sin diffeq.max"), logitem_str(html_log_file, "mult_sin_sin maxima results"), logitem_str(html_log_file, "Languages compared - single equations"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o56) 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, repeat_it], 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/mult_sin_sinpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x) * sin(x);"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), 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, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (-(sin(x) * cos(x))/2.0 + x/2.0) "), 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_g, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2_g, 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_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2_g : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0, term term : 1 + term), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 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_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_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_g : 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_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2_g : 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_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), x_start : 0.1, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_h : 0.05, 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(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(), display_alot(current_iter), 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 : 2, 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 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 ) = sin(x) * sin(x);"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-13T01:19:26-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mult_sin_sin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(x) * sin(x);"), 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, " 156 "), logitem_str(html_log_file, "mult_sin_sin diffeq.max"), logitem_str(html_log_file, "mult_sin_sin maxima results"), logitem_str(html_log_file, "Languages compared - single equations"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i57) main() "##############ECHO OF PROBLEM#################" "##############temp/mult_sin_sinpostode.ode#################" "diff ( y , x , 1 ) = sin(x) * sin(x);" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.1," "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," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.001," "glob_look_poles:true," "glob_max_iter:10000000," "glob_max_minutes:3," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (-(sin(x) * cos(x))/2.0 + x/2.0) " "));" "/* 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 = 4.9 "" estimated_steps = 4900. "" step_error = 2.040816326530612300000000000000E-14 "" est_needed_step_err = 2.040816326530612300000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 8.266297664164387000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-99 "" max_value3 = 8.266297664164387000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-99 "" value3 = 8.266297664164387000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-99 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = 0.1 " " y[1] (analytic) = 3.32667301234691740000E-4 " " y[1] (numeric) = 3.32667301234691740000E-4 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (analytic) = 3.32667301234691740000E-4 " " y[1] (numeric) = 3.32667301234691740000E-4 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.101 " " y[1] (analytic) = 3.42733673635152450000E-4 " " y[1] (numeric) = 3.4273367363515084000E-4 " " absolute error = 1.6263032587282567000000000000000000E-18 " " relative error = 4.7450933008102736000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10200000000000001 " " y[1] (analytic) = 3.53000675034048640000E-4 " " y[1] (numeric) = 3.53000675034039040000E-4 " " absolute error = 9.595189226496714000000000000000000E-18 " " relative error = 2.7181787189418866000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10300000000000001 " " y[1] (analytic) = 3.634702643627030000E-4 " " y[1] (numeric) = 3.6347026436269780000E-4 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 1.4318008756659212000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10400000000000001 " " y[1] (analytic) = 3.7414439974212120000E-4 " " y[1] (numeric) = 3.7414439974211710000E-4 " " absolute error = 4.119968255444917000000000000000000E-18 " " relative error = 1.101170633125766900000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10500000000000001 " " y[1] (analytic) = 3.85025038475109160000E-4 " " y[1] (numeric) = 3.8502503847510294000E-4 " " absolute error = 6.2341624917916500000000000000000000E-18 " " relative error = 1.6191576829605778000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10600000000000001 " " y[1] (analytic) = 3.961141370384530000E-4 " " y[1] (numeric) = 3.9611413703844820000E-4 " " absolute error = 4.7704895589362195000000000000000000E-18 " " relative error = 1.204321965028256900000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10700000000000001 " " y[1] (analytic) = 4.0741365107511280000E-4 " " y[1] (numeric) = 4.0741365107510690000E-4 " " absolute error = 5.908901840045999000000000000000000E-18 " " relative error = 1.4503445882221078000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10800000000000001 " " y[1] (analytic) = 4.18925535386374670000E-4 " " y[1] (numeric) = 4.18925535386371200000E-4 " " absolute error = 3.5236570605778894000000000000000000E-18 " " relative error = 8.4111775552856270000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10900000000000001 " " y[1] (analytic) = 4.3065174392405840000E-4 " " y[1] (numeric) = 4.30651743924052500000E-4 " " absolute error = 5.9631119486702740000000000000000000E-18 " " relative error = 1.384671496818974000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11000000000000001 " " y[1] (analytic) = 4.4259422978266960000E-4 " " y[1] (numeric) = 4.4259422978266560000E-4 " " absolute error = 4.0115480381963664000000000000000000E-18 " " relative error = 9.0637151780451080000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11100000000000002 " " y[1] (analytic) = 4.54754945191614130000E-4 " " y[1] (numeric) = 4.5475494519161640000E-4 " " absolute error = 2.2768245622195593000000000000000000E-18 " " relative error = 5.0067065488649130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11200000000000002 " " y[1] (analytic) = 4.671358415073920000E-4 " " y[1] (numeric) = 4.6713584150739285000E-4 " " absolute error = 8.1315162936412830000000000000000000E-19 " " relative error = 1.7407177037415590000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11300000000000002 " " y[1] (analytic) = 4.7973886920576330000E-4 " " y[1] (numeric) = 4.7973886920575940000E-4 " " absolute error = 3.903127820947816000000000000000000E-18 " " relative error = 8.1359424292838310000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11400000000000002 " " y[1] (analytic) = 4.9256597787396270000E-4 " " y[1] (numeric) = 4.9256597787395545000E-4 " " absolute error = 7.26415455565288000000000000000000E-18 " " relative error = 1.4747576734809775000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11500000000000002 " " y[1] (analytic) = 5.0561911620290020000E-4 " " y[1] (numeric) = 5.0561911620289680000E-4 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 6.8617796297111470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11600000000000002 " " y[1] (analytic) = 5.1890023197938280000E-4 " " y[1] (numeric) = 5.1890023197938080000E-4 " " absolute error = 1.951563910473908000000000000000000E-18 " " relative error = 3.76096172289136400000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11700000000000002 " " y[1] (analytic) = 5.3241127207830790000E-4 " " y[1] (numeric) = 5.3241127207829550000E-4 " " absolute error = 1.2251484549086200000000000000000E-17 " " relative error = 2.3011316986700153000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11800000000000002 " " y[1] (analytic) = 5.4615418245482900000E-4 " " y[1] (numeric) = 5.4615418245483180000E-4 " " absolute error = 2.710505431213761000000000000000000E-18 " " relative error = 4.9628942124560943000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11900000000000002 " " y[1] (analytic) = 5.6013090813670360000E-4 " " y[1] (numeric) = 5.6013090813669970000E-4 " " absolute error = 3.903127820947816000000000000000000E-18 " " relative error = 6.9682421809782210000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12000000000000002 " " y[1] (analytic) = 5.7434339321635330000E-4 " " y[1] (numeric) = 5.7434339321634880000E-4 " " absolute error = 4.553649124439118600000000000000000E-18 " " relative error = 7.9284434681810180000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12100000000000002 " " y[1] (analytic) = 5.8879358084319010000E-4 " " y[1] (numeric) = 5.8879358084319060000E-4 " " absolute error = 4.3368086899420180000000000000000000E-19 " " relative error = 7.36558418950734700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12200000000000003 " " y[1] (analytic) = 6.0348341321583150000E-4 " " y[1] (numeric) = 6.0348341321582740000E-4 " " absolute error = 4.0115480381963664000000000000000000E-18 " " relative error = 6.6473211199288840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12300000000000003 " " y[1] (analytic) = 6.1841483157429320000E-4 " " y[1] (numeric) = 6.1841483157428280000E-4 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 1.6830677927572370000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12400000000000003 " " y[1] (analytic) = 6.3358977619223930000E-4 " " y[1] (numeric) = 6.3358977619223640000E-4 " " absolute error = 2.927345865710862000000000000000000E-18 " " relative error = 4.6202542649972740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12500000000000003 " " y[1] (analytic) = 6.4901018636927270000E-4 " " y[1] (numeric) = 6.4901018636926330000E-4 " " absolute error = 9.324138683375338000000000000000000E-18 " " relative error = 1.436670622311328000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12600000000000003 " " y[1] (analytic) = 6.6467800042308010000E-4 " " y[1] (numeric) = 6.6467800042307690000E-4 " " absolute error = 3.2526065174565133000000000000000000E-18 " " relative error = 4.8935071047727890000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12700000000000003 " " y[1] (analytic) = 6.8059515568177910000E-4 " " y[1] (numeric) = 6.805951556817750000E-4 " " absolute error = 4.119968255444917000000000000000000E-18 " " relative error = 6.053478666502969000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12800000000000003 " " y[1] (analytic) = 6.9676358847609030000E-4 " " y[1] (numeric) = 6.9676358847609110000E-4 " " absolute error = 7.5894152073985310000000000000000000E-19 " " relative error = 1.08923820545754090000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12900000000000003 " " y[1] (analytic) = 7.1318523413164970000E-4 " " y[1] (numeric) = 7.131852341316490000E-4 " " absolute error = 6.5052130349130270000000000000000000E-19 " " relative error = 9.12135126133613100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13000000000000003 " " y[1] (analytic) = 7.2986202696122270000E-4 " " y[1] (numeric) = 7.2986202696122140000E-4 " " absolute error = 1.3010426069826053000000000000000000E-18 " " relative error = 1.78258706292679790000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13100000000000003 " " y[1] (analytic) = 7.4679590025700240000E-4 " " y[1] (numeric) = 7.4679590025699240000E-4 " " absolute error = 9.974659986866641000000000000000000E-18 " " relative error = 1.3356607854212860000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13200000000000003 " " y[1] (analytic) = 7.6398878628283760000E-4 " " y[1] (numeric) = 7.6398878628282480000E-4 " " absolute error = 1.279358563532895200000000000000000E-17 " " relative error = 1.6745776724781164000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13300000000000003 " " y[1] (analytic) = 7.814426162665450000E-4 " " y[1] (numeric) = 7.8144261626653080000E-4 " " absolute error = 1.420304845956010800000000000000000E-17 " " relative error = 1.8175420899639727000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13400000000000004 " " y[1] (analytic) = 7.991593203921510000E-4 " " y[1] (numeric) = 7.9915932039214690000E-4 " " absolute error = 4.119968255444917000000000000000000E-18 " " relative error = 5.1553778455880750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13500000000000004 " " y[1] (analytic) = 8.1714082779223150000E-4 " " y[1] (numeric) = 8.1714082779221360000E-4 " " absolute error = 1.788933584601082300000000000000000E-17 " " relative error = 2.1892598237129593000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13600000000000004 " " y[1] (analytic) = 8.3538906654005710000E-4 " " y[1] (numeric) = 8.3538906654005880000E-4 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 2.07654558272055980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13700000000000004 " " y[1] (analytic) = 8.5390596364208480000E-4 " " y[1] (numeric) = 8.5390596364208490000E-4 " " absolute error = 1.08420217248550440000000000000000000E-19 " " relative error = 1.269697388997213200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13800000000000004 " " y[1] (analytic) = 8.7269344503006220000E-4 " " y[1] (numeric) = 8.7269344503006170000E-4 " " absolute error = 4.3368086899420180000000000000000000E-19 " " relative error = 4.96945257769482300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13900000000000004 " " y[1] (analytic) = 8.9175343555342180000E-4 " " y[1] (numeric) = 8.9175343555342210000E-4 " " absolute error = 3.25260651745651330000000000000000000E-19 " " relative error = 3.64742807571909900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14000000000000004 " " y[1] (analytic) = 9.1108785897156540000E-4 " " y[1] (numeric) = 9.1108785897156260000E-4 " " absolute error = 2.8189256484623115000000000000000000E-18 " " relative error = 3.0940217463157840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14100000000000004 " " y[1] (analytic) = 9.3069863794614790000E-4 " " y[1] (numeric) = 9.3069863794614860000E-4 " " absolute error = 6.5052130349130270000000000000000000E-19 " " relative error = 6.9896019717710500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14200000000000004 " " y[1] (analytic) = 9.5058769403343070000E-4 " " y[1] (numeric) = 9.5058769403342370000E-4 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 7.2995831394206940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14300000000000004 " " y[1] (analytic) = 9.7075694767653760000E-4 " " y[1] (numeric) = 9.7075694767652350000E-4 " " absolute error = 1.409462824231155800000000000000000E-17 " " relative error = 1.4519214388366117000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14400000000000004 " " y[1] (analytic) = 9.9120831819780870000E-4 " " y[1] (numeric) = 9.9120831819779380000E-4 " " absolute error = 1.49619899802999600000000000000000E-17 " " relative error = 1.5094697759905298000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14500000000000005 " " y[1] (analytic) = 1.0119437237911255000E-3 " " y[1] (numeric) = 1.0119437237911127000E-3 " " absolute error = 1.279358563532895200000000000000000E-17 " " relative error = 1.2642586079193535000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14600000000000005 " " y[1] (analytic) = 1.0329650815142227000E-3 " " y[1] (numeric) = 1.0329650815142193000E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 3.3587262667850830000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14700000000000005 " " y[1] (analytic) = 1.0542743072810556000E-3 " " y[1] (numeric) = 1.0542743072810434000E-3 " " absolute error = 1.21430643318376500000000000000000E-17 " " relative error = 1.1517936316929014000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14800000000000005 " " y[1] (analytic) = 1.0758733158540423000E-3 " " y[1] (numeric) = 1.0758733158540446000E-3 " " absolute error = 2.168404344971009000000000000000000E-18 " " relative error = 2.01548296906100070000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14900000000000005 " " y[1] (analytic) = 1.0977640208365558000E-3 " " y[1] (numeric) = 1.09776402083655000E-3 " " absolute error = 5.854691731421724000000000000000000E-18 " " relative error = 5.333288047608020000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000005 " " y[1] (analytic) = 1.1199483346651107000E-3 " " y[1] (numeric) = 1.1199483346651022000E-3 " " absolute error = 8.456776945386935000000000000000000E-18 " " relative error = 7.5510420290197570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15100000000000005 " " y[1] (analytic) = 1.1424281686018001E-3 " " y[1] (numeric) = 1.1424281686018092000E-3 " " absolute error = 9.107298248878237000000000000000000E-18 " " relative error = 7.9718782319806750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15200000000000005 " " y[1] (analytic) = 1.1652054327267042000E-3 " " y[1] (numeric) = 1.1652054327266984000E-3 " " absolute error = 5.854691731421724000000000000000000E-18 " " relative error = 5.0246004412467640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15300000000000005 " " y[1] (analytic) = 1.1882820359300772000E-3 " " y[1] (numeric) = 1.188282035930076900E-3 " " absolute error = 2.1684043449710090000000000000000000E-19 " " relative error = 1.824822962398638400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15400000000000005 " " y[1] (analytic) = 1.2116598859049088000E-3 " " y[1] (numeric) = 1.2116598859048962000E-3 " " absolute error = 1.257674520083185100000000000000000E-17 " " relative error = 1.0379765268402123000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15500000000000005 " " y[1] (analytic) = 1.2353408891391249000E-3 " " y[1] (numeric) = 1.2353408891391207000E-3 " " absolute error = 4.119968255444917000000000000000000E-18 " " relative error = 3.33508612211161350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15600000000000006 " " y[1] (analytic) = 1.2593269509081073000E-3 " " y[1] (numeric) = 1.2593269509081026000E-3 " " absolute error = 4.7704895589362195000000000000000000E-18 " " relative error = 3.7881263126277050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15700000000000006 " " y[1] (analytic) = 1.2836199752669641000E-3 " " y[1] (numeric) = 1.2836199752669597000E-3 " " absolute error = 4.336808689942018000000000000000000E-18 " " relative error = 3.378576816740530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15800000000000006 " " y[1] (analytic) = 1.3082218650429522000E-3 " " y[1] (numeric) = 1.308221865042960800E-3 " " absolute error = 8.673617379884035000000000000000000E-18 " " relative error = 6.6300813429679670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15900000000000006 " " y[1] (analytic) = 1.333134521827914000E-3 " " y[1] (numeric) = 1.3331345218279125000E-3 " " absolute error = 1.3010426069826053000000000000000000E-18 " " relative error = 9.75927474444734800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000006 " " y[1] (analytic) = 1.358359845970561000E-3 " " y[1] (numeric) = 1.3583598459705545000E-3 " " absolute error = 6.288372600415926000000000000000000E-18 " " relative error = 4.6293864023364330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16100000000000006 " " y[1] (analytic) = 1.3838997365689665000E-3 " " y[1] (numeric) = 1.3838997365689573000E-3 " " absolute error = 9.107298248878237000000000000000000E-18 " " relative error = 6.5808945606547390000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16200000000000006 " " y[1] (analytic) = 1.4097560914629326000E-3 " " y[1] (numeric) = 1.4097560914629256000E-3 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.9220527904983880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16300000000000006 " " y[1] (analytic) = 1.4359308072264126000E-3 " " y[1] (numeric) = 1.4359308072264076000E-3 " " absolute error = 4.9873299934333204000000000000000000E-18 " " relative error = 3.47323838191524740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16400000000000006 " " y[1] (analytic) = 1.4624257791599204000E-3 " " y[1] (numeric) = 1.4624257791599088000E-3 " " absolute error = 1.170938346284344800000000000000000E-17 " " relative error = 8.0068223835399120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16500000000000006 " " y[1] (analytic) = 1.4892429012829111000E-3 " " y[1] (numeric) = 1.4892429012829098000E-3 " " absolute error = 1.3010426069826053000000000000000000E-18 " " relative error = 8.7362686494044710000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16600000000000006 " " y[1] (analytic) = 1.5163840663262873000E-3 " " y[1] (numeric) = 1.5163840663262915000E-3 " " absolute error = 4.119968255444917000000000000000000E-18 " " relative error = 2.7169688385253743000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16700000000000007 " " y[1] (analytic) = 1.54385116572478000E-3 " " y[1] (numeric) = 1.5438511657247628000E-3 " " absolute error = 1.71303943252709700000000000000000E-17 " " relative error = 1.1095884568140281000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16800000000000007 " " y[1] (analytic) = 1.571646089609302000E-3 " " y[1] (numeric) = 1.5716460896092965000E-3 " " absolute error = 5.421010862427522000000000000000000E-18 " " relative error = 3.4492567367855315000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16900000000000007 " " y[1] (analytic) = 1.5997707267995792000E-3 " " y[1] (numeric) = 1.5997707267995676000E-3 " " absolute error = 1.170938346284344800000000000000000E-17 " " relative error = 7.3194135051268570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000007 " " y[1] (analytic) = 1.628226964796406000E-3 " " y[1] (numeric) = 1.6282269647963976000E-3 " " absolute error = 8.456776945386935000000000000000000E-18 " " relative error = 5.1938563408108000000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17100000000000007 " " y[1] (analytic) = 1.6570166897742072000E-3 " " y[1] (numeric) = 1.657016689774205900E-3 " " absolute error = 1.3010426069826053000000000000000000E-18 " " relative error = 7.85171697431660500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17200000000000007 " " y[1] (analytic) = 1.6861417865734750000E-3 " " y[1] (numeric) = 1.6861417865734646000E-3 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.1728740363005590000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17300000000000007 " " y[1] (analytic) = 1.7156041386931636000E-3 " " y[1] (numeric) = 1.7156041386931586000E-3 " " absolute error = 4.9873299934333204000000000000000000E-18 " " relative error = 2.90704008048869900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17400000000000007 " " y[1] (analytic) = 1.7454056282832642000E-3 " " y[1] (numeric) = 1.745405628283252000E-3 " " absolute error = 1.21430643318376500000000000000000E-17 " " relative error = 6.9571589177131590000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17500000000000007 " " y[1] (analytic) = 1.775548136137159000E-3 " " y[1] (numeric) = 1.7755481361371594000E-3 " " absolute error = 6.5052130349130270000000000000000000E-19 " " relative error = 3.66377734431104550000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17600000000000007 " " y[1] (analytic) = 1.8060335416842377000E-3 " " y[1] (numeric) = 1.8060335416842233000E-3 " " absolute error = 1.45283091113057600000000000000000E-17 " " relative error = 8.0443185444702290000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17700000000000007 " " y[1] (analytic) = 1.836863722982196000E-3 " " y[1] (numeric) = 1.8368637229821946000E-3 " " absolute error = 1.3010426069826053000000000000000000E-18 " " relative error = 7.08295662168301100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17800000000000007 " " y[1] (analytic) = 1.8680405567097352000E-3 " " y[1] (numeric) = 1.8680405567097236000E-3 " " absolute error = 1.170938346284344800000000000000000E-17 " " relative error = 6.2682704723861650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17900000000000008 " " y[1] (analytic) = 1.8995659181588603000E-3 " " y[1] (numeric) = 1.8995659181588498000E-3 " " absolute error = 1.062518129035794300000000000000000E-17 " " relative error = 5.5934785883378650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000008 " " y[1] (analytic) = 1.931441681227497000E-3 " " y[1] (numeric) = 1.9314416812275026000E-3 " " absolute error = 5.637851296924623000000000000000000E-18 " " relative error = 2.9189860360378970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18100000000000008 " " y[1] (analytic) = 1.9636697184120117000E-3 " " y[1] (numeric) = 1.963669718412006000E-3 " " absolute error = 5.637851296924623000000000000000000E-18 " " relative error = 2.87107920647870600000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18200000000000008 " " y[1] (analytic) = 1.996251900799592000E-3 " " y[1] (numeric) = 1.9962519007995874000E-3 " " absolute error = 4.7704895589362195000000000000000000E-18 " " relative error = 2.38972323934941060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18300000000000008 " " y[1] (analytic) = 2.0291900980609068000E-3 " " y[1] (numeric) = 2.0291900980608937000E-3 " " absolute error = 1.301042606982605300000000000000000E-17 " " relative error = 6.4116349090500750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18400000000000008 " " y[1] (analytic) = 2.062486178442513000E-3 " " y[1] (numeric) = 2.0624861784425136000E-3 " " absolute error = 4.3368086899420180000000000000000000E-19 " " relative error = 2.102709213410079700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18500000000000008 " " y[1] (analytic) = 2.0961420087595023000E-3 " " y[1] (numeric) = 2.0961420087595029000E-3 " " absolute error = 4.3368086899420180000000000000000000E-19 " " relative error = 2.068947939509376600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18600000000000008 " " y[1] (analytic) = 2.1301594543879226000E-3 " " y[1] (numeric) = 2.1301594543879182000E-3 " " absolute error = 4.336808689942018000000000000000000E-18 " " relative error = 2.0359080072661280000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18700000000000008 " " y[1] (analytic) = 2.164540379257368000E-3 " " y[1] (numeric) = 2.164540379257356700E-3 " " absolute error = 1.127570259384924600000000000000000E-17 " " relative error = 5.2092826273436510000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18800000000000008 " " y[1] (analytic) = 2.1992866458435123000E-3 " " y[1] (numeric) = 2.1992866458434976000E-3 " " absolute error = 1.47451495458028600000000000000000E-17 " " relative error = 6.7045146541812060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18900000000000008 " " y[1] (analytic) = 2.2344001151606563000E-3 " " y[1] (numeric) = 2.234400115160654000E-3 " " absolute error = 2.168404344971009000000000000000000E-18 " " relative error = 9.70463763521198100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000009 " " y[1] (analytic) = 2.2698826467543315000E-3 " " y[1] (numeric) = 2.2698826467543293000E-3 " " absolute error = 2.168404344971009000000000000000000E-18 " " relative error = 9.55293591090083500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1910000000000001 " " y[1] (analytic) = 2.305736098693778000E-3 " " y[1] (numeric) = 2.305736098693777200E-3 " " absolute error = 8.6736173798840350000000000000000000E-19 " " relative error = 3.761756336641354000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1920000000000001 " " y[1] (analytic) = 2.3419623275645757000E-3 " " y[1] (numeric) = 2.3419623275645712000E-3 " " absolute error = 4.336808689942018000000000000000000E-18 " " relative error = 1.8517841379847890000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1930000000000001 " " y[1] (analytic) = 2.3785631884611774000E-3 " " y[1] (numeric) = 2.378563188461178000E-3 " " absolute error = 4.3368086899420180000000000000000000E-19 " " relative error = 1.82328924914865800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1940000000000001 " " y[1] (analytic) = 2.4155405349795406000E-3 " " y[1] (numeric) = 2.4155405349795353000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 2.1544537765227360000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1950000000000001 " " y[1] (analytic) = 2.4528962192096465000E-3 " " y[1] (numeric) = 2.4528962192096404000E-3 " " absolute error = 6.071532165918825000000000000000000E-18 " " relative error = 2.47525032586790320000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1960000000000001 " " y[1] (analytic) = 2.4906320917281455000E-3 " " y[1] (numeric) = 2.490632091728139000E-3 " " absolute error = 6.5052130349130270000000000000000000E-18 " " relative error = 2.61187232611273860000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1970000000000001 " " y[1] (analytic) = 2.528750001590932000E-3 " " y[1] (numeric) = 2.528750001590925000E-3 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.7440015420827320000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1980000000000001 " " y[1] (analytic) = 2.567251796325748000E-3 " " y[1] (numeric) = 2.567251796325743000E-3 " " absolute error = 4.7704895589362195000000000000000000E-18 " " relative error = 1.85820867503676380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1990000000000001 " " y[1] (analytic) = 2.6061393219247997000E-3 " " y[1] (numeric) = 2.606139321924798600E-3 " " absolute error = 8.6736173798840350000000000000000000E-19 " " relative error = 3.32814800303078860000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2000000000000001 " " y[1] (analytic) = 2.645414422837389000E-3 " " y[1] (numeric) = 2.645414422837375000E-3 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 5.2459787351312530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2010000000000001 " " y[1] (analytic) = 2.68507894196246000E-3 " " y[1] (numeric) = 2.685078941962454000E-3 " " absolute error = 6.071532165918825000000000000000000E-18 " " relative error = 2.2612117919636610000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2020000000000001 " " y[1] (analytic) = 2.7251347206413423000E-3 " " y[1] (numeric) = 2.725134720641345000E-3 " " absolute error = 2.6020852139652106000000000000000000E-18 " " relative error = 9.5484645006938500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2030000000000001 " " y[1] (analytic) = 2.7655835986503260000E-3 " " y[1] (numeric) = 2.76558359865032000E-3 " " absolute error = 5.637851296924623000000000000000000E-18 " " relative error = 2.0385756191481740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2040000000000001 " " y[1] (analytic) = 2.8064274141932630000E-3 " " y[1] (numeric) = 2.806427414193255000E-3 " " absolute error = 8.239936510889834000000000000000000E-18 " " relative error = 2.93609464802726370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2050000000000001 " " y[1] (analytic) = 2.8476680038942714000E-3 " " y[1] (numeric) = 2.847668003894275000E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.21834671289245850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2060000000000001 " " y[1] (analytic) = 2.889307202790417000E-3 " " y[1] (numeric) = 2.8893072027904100000E-3 " " absolute error = 7.37257477290143000000000000000000E-18 " " relative error = 2.55167562860092960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2070000000000001 " " y[1] (analytic) = 2.9313468443242646000E-3 " " y[1] (numeric) = 2.9313468443242524000E-3 " " absolute error = 1.21430643318376500000000000000000E-17 " " relative error = 4.1424863643650040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2080000000000001 " " y[1] (analytic) = 2.973788760336632000E-3 " " y[1] (numeric) = 2.9737887603366264000E-3 " " absolute error = 5.637851296924623000000000000000000E-18 " " relative error = 1.89584794055325580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2090000000000001 " " y[1] (analytic) = 3.016634781059263000E-3 " " y[1] (numeric) = 3.016634781059257000E-3 " " absolute error = 6.071532165918825000000000000000000E-18 " " relative error = 2.01268387013255300000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2100000000000001 " " y[1] (analytic) = 3.059886735107459000E-3 " " y[1] (numeric) = 3.0598867351074520000E-3 " " absolute error = 6.5052130349130270000000000000000000E-18 " " relative error = 2.12596530462248380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2110000000000001 " " y[1] (analytic) = 3.103546449472791000E-3 " " y[1] (numeric) = 3.103546449472787000E-3 " " absolute error = 3.903127820947816000000000000000000E-18 " " relative error = 1.25763473641931550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2120000000000001 " " y[1] (analytic) = 3.147615749515803000E-3 " " y[1] (numeric) = 3.1476157495157960000E-3 " " absolute error = 7.37257477290143000000000000000000E-18 " " relative error = 2.3422728057055730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2130000000000001 " " y[1] (analytic) = 3.192096458958682000E-3 " " y[1] (numeric) = 3.1920964589586690000E-3 " " absolute error = 1.257674520083185100000000000000000E-17 " " relative error = 3.93996402130485900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2140000000000001 " " y[1] (analytic) = 3.236990399877973000E-3 " " y[1] (numeric) = 3.2369903998779637000E-3 " " absolute error = 9.540979117872439000000000000000000E-18 " " relative error = 2.9474845270570194000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2150000000000001 " " y[1] (analytic) = 3.2822993926973076000E-3 " " y[1] (numeric) = 3.2822993926973076000E-3 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2160000000000001 " " y[1] (analytic) = 3.328025256180131000E-3 " " y[1] (numeric) = 3.328025256180124000E-3 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.084988354887550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2170000000000001 " " y[1] (analytic) = 3.3741698074223614000E-3 " " y[1] (numeric) = 3.374169807422353000E-3 " " absolute error = 8.239936510889834000000000000000000E-18 " " relative error = 2.4420633759344170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2180000000000001 " " y[1] (analytic) = 3.420734861845187000E-3 " " y[1] (numeric) = 3.4207348618451844000E-3 " " absolute error = 2.6020852139652106000000000000000000E-18 " " relative error = 7.60680181030345400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2190000000000001 " " y[1] (analytic) = 3.467722233187795000E-3 " " y[1] (numeric) = 3.4677222331877960000E-3 " " absolute error = 1.3010426069826053000000000000000000E-18 " " relative error = 3.751865113448223400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2200000000000001 " " y[1] (analytic) = 3.5151337335000976000E-3 " " y[1] (numeric) = 3.515133733500099000E-3 " " absolute error = 1.3010426069826053000000000000000000E-18 " " relative error = 3.701260622272621300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2210000000000001 " " y[1] (analytic) = 3.56297117313549000E-3 " " y[1] (numeric) = 3.5629711731354874000E-3 " " absolute error = 2.6020852139652106000000000000000000E-18 " " relative error = 7.30313294024021100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22200000000000011 " " y[1] (analytic) = 3.6112363607436054000E-3 " " y[1] (numeric) = 3.611236360743601000E-3 " " absolute error = 4.336808689942018000000000000000000E-18 " " relative error = 1.2009207530932721000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22300000000000011 " " y[1] (analytic) = 3.659931103263084000E-3 " " y[1] (numeric) = 3.659931103263086600E-3 " " absolute error = 3.0357660829594124000000000000000000E-18 " " relative error = 8.2945989891799200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22400000000000012 " " y[1] (analytic) = 3.7090572059143845000E-3 " " y[1] (numeric) = 3.7090572059143730000E-3 " " absolute error = 1.170938346284344800000000000000000E-17 " " relative error = 3.1569703061392290000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22500000000000012 " " y[1] (analytic) = 3.758616472192458000E-3 " " y[1] (numeric) = 3.7586164721924470000E-3 " " absolute error = 1.084202172485504400000000000000000E-17 " " relative error = 2.88457782406586650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22600000000000012 " " y[1] (analytic) = 3.808610703859655000E-3 " " y[1] (numeric) = 3.808610703859644000E-3 " " absolute error = 1.084202172485504400000000000000000E-17 " " relative error = 2.8467130320953290000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22700000000000012 " " y[1] (analytic) = 3.85904170093844000E-3 " " y[1] (numeric) = 3.859041700938437000E-3 " " absolute error = 2.6020852139652106000000000000000000E-18 " " relative error = 6.74282740539558600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22800000000000012 " " y[1] (analytic) = 3.909911261704243600E-3 " " y[1] (numeric) = 3.909911261704238600E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 1.33102008705487580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22900000000000012 " " y[1] (analytic) = 3.961221182678207000E-3 " " y[1] (numeric) = 3.961221182678205700E-3 " " absolute error = 8.6736173798840350000000000000000000E-19 " " relative error = 2.189632181563703500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23000000000000012 " " y[1] (analytic) = 4.012973258620059000E-3 " " y[1] (numeric) = 4.012973258620058000E-3 " " absolute error = 8.6736173798840350000000000000000000E-19 " " relative error = 2.161394263281642700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23100000000000012 " " y[1] (analytic) = 4.065169282520889000E-3 " " y[1] (numeric) = 4.065169282520893500E-3 " " absolute error = 4.336808689942018000000000000000000E-18 " " relative error = 1.06682117976958630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23200000000000012 " " y[1] (analytic) = 4.117811045596026000E-3 " " y[1] (numeric) = 4.117811045596018000E-3 " " absolute error = 7.806255641895632000000000000000000E-18 " " relative error = 1.89572944349750440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23300000000000012 " " y[1] (analytic) = 4.170900337277794000E-3 " " y[1] (numeric) = 4.170900337277785000E-3 " " absolute error = 9.540979117872439000000000000000000E-18 " " relative error = 2.2875106922596750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23400000000000012 " " y[1] (analytic) = 4.224438945208436300E-3 " " y[1] (numeric) = 4.22443894520843000E-3 " " absolute error = 6.071532165918825000000000000000000E-18 " " relative error = 1.43723989023570840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23500000000000013 " " y[1] (analytic) = 4.278428655232924000E-3 " " y[1] (numeric) = 4.278428655232927600E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 8.1091616374393690000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23600000000000013 " " y[1] (analytic) = 4.33287125139184000E-3 " " y[1] (numeric) = 4.332871251391841600E-3 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 4.00363494627163300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23700000000000013 " " y[1] (analytic) = 4.387768515914214400E-3 " " y[1] (numeric) = 4.387768515914194400E-3 " " absolute error = 1.994931997373328200000000000000000E-17 " " relative error = 4.5465753039108847000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23800000000000013 " " y[1] (analytic) = 4.443122229210339000E-3 " " y[1] (numeric) = 4.443122229210334000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 1.1712868022663740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23900000000000013 " " y[1] (analytic) = 4.498934169864826600E-3 " " y[1] (numeric) = 4.498934169864814000E-3 " " absolute error = 1.301042606982605300000000000000000E-17 " " relative error = 2.8918907409167450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24000000000000013 " " y[1] (analytic) = 4.555206114629284400E-3 " " y[1] (numeric) = 4.555206114629279400E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 1.14246650908220230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24100000000000013 " " y[1] (analytic) = 4.611939838415374000E-3 " " y[1] (numeric) = 4.6119398384153590000E-3 " " absolute error = 1.47451495458028600000000000000000E-17 " " relative error = 3.1971686670720270000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24200000000000013 " " y[1] (analytic) = 4.669137114287583000E-3 " " y[1] (numeric) = 4.669137114287569300E-3 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 2.9722382247778410000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24300000000000013 " " y[1] (analytic) = 4.7267997134562145000E-3 " " y[1] (numeric) = 4.726799713456213400E-3 " " absolute error = 8.6736173798840350000000000000000000E-19 " " relative error = 1.834987286470389800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24400000000000013 " " y[1] (analytic) = 4.784929405270310600E-3 " " y[1] (numeric) = 4.784929405270307300E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 7.25077980906516200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24500000000000013 " " y[1] (analytic) = 4.8435279572105056000E-3 " " y[1] (numeric) = 4.8435279572104930000E-3 " " absolute error = 1.301042606982605300000000000000000E-17 " " relative error = 2.6861465825664493000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24600000000000014 " " y[1] (analytic) = 4.902597134881975000E-3 " " y[1] (numeric) = 4.9025971348819736000E-3 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 3.538376554814693400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24700000000000014 " " y[1] (analytic) = 4.962138702007471000E-3 " " y[1] (numeric) = 4.962138702007452000E-3 " " absolute error = 1.908195823574487800000000000000000E-17 " " relative error = 3.8455108536214690000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24800000000000014 " " y[1] (analytic) = 5.022154420420075000E-3 " " y[1] (numeric) = 5.022154420420072000E-3 " " absolute error = 2.6020852139652106000000000000000000E-18 " " relative error = 5.18121307338765800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24900000000000014 " " y[1] (analytic) = 5.082646050056385000E-3 " " y[1] (numeric) = 5.082646050056374000E-3 " " absolute error = 1.21430643318376500000000000000000E-17 " " relative error = 2.3891225578658850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (analytic) = 5.143615348949249000E-3 " " y[1] (numeric) = 5.143615348949251000E-3 " " absolute error = 2.6020852139652106000000000000000000E-18 " " relative error = 5.05886431514901600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2510000000000001 " " y[1] (analytic) = 5.2050640732209390000E-3 " " y[1] (numeric) = 5.205064073220924000E-3 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 2.66620883289660660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2520000000000001 " " y[1] (analytic) = 5.266993977075918000E-3 " " y[1] (numeric) = 5.2669939770759120000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 9.88072219292649700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2530000000000001 " " y[1] (analytic) = 5.329406812794022000E-3 " " y[1] (numeric) = 5.3294068127940140000E-3 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 1.30200116967040260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2540000000000001 " " y[1] (analytic) = 5.39230433072331000E-3 " " y[1] (numeric) = 5.392304330723304000E-3 " " absolute error = 6.071532165918825000000000000000000E-18 " " relative error = 1.12596244453888310000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2550000000000001 " " y[1] (analytic) = 5.455688279273132000E-3 " " y[1] (numeric) = 5.455688279273129000E-3 " " absolute error = 4.336808689942018000000000000000000E-18 " " relative error = 7.94915044251724700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2560000000000001 " " y[1] (analytic) = 5.5195604049071150000E-3 " " y[1] (numeric) = 5.519560404907109000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 9.42859584126246900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2570000000000001 " " y[1] (analytic) = 5.583922452136153000E-3 " " y[1] (numeric) = 5.583922452136163000E-3 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 1.86398377575589140000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2580000000000001 " " y[1] (analytic) = 5.648776163511517000E-3 " " y[1] (numeric) = 5.648776163511521000E-3 " " absolute error = 2.6020852139652106000000000000000000E-18 " " relative error = 4.60645835247195300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2590000000000001 " " y[1] (analytic) = 5.714123279617775000E-3 " " y[1] (numeric) = 5.714123279617755000E-3 " " absolute error = 1.908195823574487800000000000000000E-17 " " relative error = 3.3394376183324653000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (analytic) = 5.779965539065818000E-3 " " y[1] (numeric) = 5.779965539065824000E-3 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 1.20050783296343360000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2610000000000001 " " y[1] (analytic) = 5.846304678486112000E-3 " " y[1] (numeric) = 5.84630467848611100E-3 " " absolute error = 8.6736173798840350000000000000000000E-19 " " relative error = 1.48360680068594200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2620000000000001 " " y[1] (analytic) = 5.913142432521501000E-3 " " y[1] (numeric) = 5.913142432521477000E-3 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 4.10714420307293900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2630000000000001 " " y[1] (analytic) = 5.9804805338203320000E-3 " " y[1] (numeric) = 5.980480533820330000E-3 " " absolute error = 8.6736173798840350000000000000000000E-19 " " relative error = 1.4503211457396598000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2640000000000001 " " y[1] (analytic) = 6.048320713029687000E-3 " " y[1] (numeric) = 6.04832071302969000E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 5.73621525141599300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2650000000000001 " " y[1] (analytic) = 6.116664698788271000E-3 " " y[1] (numeric) = 6.1166646987882620000E-3 " " absolute error = 8.673617379884035000000000000000000E-18 " " relative error = 1.4180305455687808000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2660000000000001 " " y[1] (analytic) = 6.185514217719512000E-3 " " y[1] (numeric) = 6.185514217719528000E-3 " " absolute error = 1.561251128379126400000000000000000E-17 " " relative error = 2.52404419976376900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2670000000000001 " " y[1] (analytic) = 6.254870994424844000E-3 " " y[1] (numeric) = 6.254870994424837000E-3 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 1.10935843602403230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2680000000000001 " " y[1] (analytic) = 6.324736751476517000E-3 " " y[1] (numeric) = 6.324736751476507000E-3 " " absolute error = 9.540979117872439000000000000000000E-18 " " relative error = 1.5085179815025640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.26900000000000013 " " y[1] (analytic) = 6.395113209410941000E-3 " " y[1] (numeric) = 6.395113209410939000E-3 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 2.71257664903260400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (analytic) = 6.466002086721712000E-3 " " y[1] (numeric) = 6.466002086721726000E-3 " " absolute error = 1.47451495458028600000000000000000E-17 " " relative error = 2.28041212298443740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27100000000000013 " " y[1] (analytic) = 6.537405099852789000E-3 " " y[1] (numeric) = 6.537405099852788000E-3 " " absolute error = 8.6736173798840350000000000000000000E-19 " " relative error = 1.326767616111070000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27200000000000013 " " y[1] (analytic) = 6.609323963191527000E-3 " " y[1] (numeric) = 6.6093239631915000E-3 " " absolute error = 2.68882138776405100000000000000000E-17 " " relative error = 4.0682245305852220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27300000000000013 " " y[1] (analytic) = 6.681760389061847000E-3 " " y[1] (numeric) = 6.681760389061838000E-3 " " absolute error = 8.673617379884035000000000000000000E-18 " " relative error = 1.29810362462007640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27400000000000013 " " y[1] (analytic) = 6.754716087717522000E-3 " " y[1] (numeric) = 6.75471608771753000E-3 " " absolute error = 8.673617379884035000000000000000000E-18 " " relative error = 1.28408318976659270000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27500000000000013 " " y[1] (analytic) = 6.828192767335234000E-3 " " y[1] (numeric) = 6.82819276733521000E-3 " " absolute error = 2.341876692568689600000000000000000E-17 " " relative error = 3.4297167235403470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27600000000000013 " " y[1] (analytic) = 6.902192134007584000E-3 " " y[1] (numeric) = 6.902192134007592000E-3 " " absolute error = 7.806255641895632000000000000000000E-18 " " relative error = 1.13098208371129850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27700000000000014 " " y[1] (analytic) = 6.976715891736623000E-3 " " y[1] (numeric) = 6.976715891736641000E-3 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 2.4864470660636362000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27800000000000014 " " y[1] (analytic) = 7.051765742426747000E-3 " " y[1] (numeric) = 7.051765742426758000E-3 " " absolute error = 1.127570259384924600000000000000000E-17 " " relative error = 1.59898995594951550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27900000000000014 " " y[1] (analytic) = 7.127343385877977000E-3 " " y[1] (numeric) = 7.127343385877974000E-3 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 2.433899115081174800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (analytic) = 7.203450519779164000E-3 " " y[1] (numeric) = 7.203450519779151000E-3 " " absolute error = 1.301042606982605300000000000000000E-17 " " relative error = 1.80613804927265780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28100000000000014 " " y[1] (analytic) = 7.280088839701188000E-3 " " y[1] (numeric) = 7.280088839701186000E-3 " " absolute error = 8.6736173798840350000000000000000000E-19 " " relative error = 1.191416419616116300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28200000000000014 " " y[1] (analytic) = 7.357260039090235000E-3 " " y[1] (numeric) = 7.357260039090237000E-3 " " absolute error = 8.6736173798840350000000000000000000E-19 " " relative error = 1.178919507235002600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28300000000000014 " " y[1] (analytic) = 7.434965809260952000E-3 " " y[1] (numeric) = 7.4349658092609390000E-3 " " absolute error = 1.21430643318376500000000000000000E-17 " " relative error = 1.6332374140459820000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28400000000000014 " " y[1] (analytic) = 7.513207839389663000E-3 " " y[1] (numeric) = 7.5132078393896530000E-3 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 1.38533913587386760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28500000000000014 " " y[1] (analytic) = 7.591987816507689000E-3 " " y[1] (numeric) = 7.591987816507691000E-3 " " absolute error = 2.6020852139652106000000000000000000E-18 " " relative error = 3.427409628223255000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28600000000000014 " " y[1] (analytic) = 7.6713074254946000E-3 " " y[1] (numeric) = 7.671307425494588000E-3 " " absolute error = 1.21430643318376500000000000000000E-17 " " relative error = 1.58291978906773350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28700000000000014 " " y[1] (analytic) = 7.751168349071358000E-3 " " y[1] (numeric) = 7.751168349071345000E-3 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.79041238466677220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28800000000000014 " " y[1] (analytic) = 7.831572267793685000E-3 " " y[1] (numeric) = 7.831572267793706000E-3 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 2.6580463028257510000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28900000000000015 " " y[1] (analytic) = 7.912520860045458000E-3 " " y[1] (numeric) = 7.912520860045439000E-3 " " absolute error = 1.908195823574487800000000000000000E-17 " " relative error = 2.4116155360929123000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y[1] (analytic) = 7.994015802031629000E-3 " " y[1] (numeric) = 7.994015802031615000E-3 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.73602206343994300000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29100000000000015 " " y[1] (analytic) = 8.076058767771926000E-3 " " y[1] (numeric) = 8.076058767771908000E-3 " " absolute error = 1.908195823574487800000000000000000E-17 " " relative error = 2.36278100301755580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29200000000000015 " " y[1] (analytic) = 8.158651429093888000E-3 " " y[1] (numeric) = 8.158651429093897000E-3 " " absolute error = 8.673617379884035000000000000000000E-18 " " relative error = 1.06311900382871740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29300000000000015 " " y[1] (analytic) = 8.241795455626394000E-3 " " y[1] (numeric) = 8.241795455626382000E-3 " " absolute error = 1.21430643318376500000000000000000E-17 " " relative error = 1.47335181966303130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29400000000000015 " " y[1] (analytic) = 8.325492514792726000E-3 " " y[1] (numeric) = 8.3254925147927010E-3 " " absolute error = 2.602085213965210600000000000000000E-17 " " relative error = 3.12544298051055660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29500000000000015 " " y[1] (analytic) = 8.409744271804076000E-3 " " y[1] (numeric) = 8.40974427180406000E-3 " " absolute error = 1.561251128379126400000000000000000E-17 " " relative error = 1.8564787203026370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29600000000000015 " " y[1] (analytic) = 8.49455238965291000E-3 " " y[1] (numeric) = 8.49455238965288000E-3 " " absolute error = 2.94902990916057200000000000000000E-17 " " relative error = 3.47167193029822600000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29700000000000015 " " y[1] (analytic) = 8.57991852910614000E-3 " " y[1] (numeric) = 8.579918529106133000E-3 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 8.08736572540639900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29800000000000015 " " y[1] (analytic) = 8.665844348698715000E-3 " " y[1] (numeric) = 8.66584434869870900E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 6.00538183992641500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29900000000000015 " " y[1] (analytic) = 8.75233150472679000E-3 " " y[1] (numeric) = 8.75233150472678000E-3 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 1.18920779568732140000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y[1] (analytic) = 8.83938165124117900E-3 " " y[1] (numeric) = 8.839381651241167000E-3 " " absolute error = 1.21430643318376500000000000000000E-17 " " relative error = 1.37374590338370380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30100000000000016 " " y[1] (analytic) = 8.926996440040746000E-3 " " y[1] (numeric) = 8.926996440040736000E-3 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 1.1659398461475509000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30200000000000016 " " y[1] (analytic) = 9.015177520665801000E-3 " " y[1] (numeric) = 9.01517752066578000E-3 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 2.3090706382656237000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30300000000000016 " " y[1] (analytic) = 9.10392654039141000E-3 " " y[1] (numeric) = 9.103926540391428000E-3 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 1.90546734783102160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30400000000000016 " " y[1] (analytic) = 9.19324514422104000E-3 " " y[1] (numeric) = 9.193245144221053000E-3 " " absolute error = 1.21430643318376500000000000000000E-17 " " relative error = 1.32086810928466250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30500000000000016 " " y[1] (analytic) = 9.283134974879703000E-3 " " y[1] (numeric) = 9.283134974879693000E-3 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 1.1212096866011280000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30600000000000016 " " y[1] (analytic) = 9.373597672807488000E-3 " " y[1] (numeric) = 9.373597672807478000E-3 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 1.11038911836968550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30700000000000016 " " y[1] (analytic) = 9.464634876153066000E-3 " " y[1] (numeric) = 9.464634876153069000E-3 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.832847752370867500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30800000000000016 " " y[1] (analytic) = 9.556248220767116000E-3 " " y[1] (numeric) = 9.556248220767107000E-3 " " absolute error = 8.673617379884035000000000000000000E-18 " " relative error = 9.07638351318146400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30900000000000016 " " y[1] (analytic) = 9.648439340195686000E-3 " " y[1] (numeric) = 9.648439340195671000E-3 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.43834534461953660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (analytic) = 9.741209865673728000E-3 " " y[1] (numeric) = 9.74120986567374000E-3 " " absolute error = 1.21430643318376500000000000000000E-17 " " relative error = 1.2465663402476960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31100000000000017 " " y[1] (analytic) = 9.83456142611866000E-3 " " y[1] (numeric) = 9.834561426118666000E-3 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 7.05562109305544700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31200000000000017 " " y[1] (analytic) = 9.928495648123675000E-3 " " y[1] (numeric) = 9.928495648123669000E-3 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 6.98886734690624200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31300000000000017 " " y[1] (analytic) = 1.002301415595130400E-2 " " y[1] (numeric) = 1.002301415595131700E-2 " " absolute error = 1.21430643318376500000000000000000E-17 " " relative error = 1.2115182262441020000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31400000000000017 " " y[1] (analytic) = 1.011811857152705700E-2 " " y[1] (numeric) = 1.011811857152703800E-2 " " absolute error = 1.908195823574487800000000000000000E-17 " " relative error = 1.8859196105333811000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31500000000000017 " " y[1] (analytic) = 1.021381051443262500E-2 " " y[1] (numeric) = 1.02138105144326310E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 5.09522907300528800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31600000000000017 " " y[1] (analytic) = 1.031009160189977300E-2 " " y[1] (numeric) = 1.031009160189978500E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 1.00952942590179950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31700000000000017 " " y[1] (analytic) = 1.040696344880362400E-2 " " y[1] (numeric) = 1.04069634488036100E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.3335098058223540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31800000000000017 " " y[1] (analytic) = 1.050442766765616300E-2 " " y[1] (numeric) = 1.050442766765618400E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 1.98170546462208900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3190000000000002 " " y[1] (analytic) = 1.060248586860010300E-2 " " y[1] (numeric) = 1.060248586860009200E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 9.81688727045208000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y[1] (analytic) = 1.070113965940200400E-2 " " y[1] (numeric) = 1.070113965940199700E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 6.48425693408339700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3210000000000002 " " y[1] (analytic) = 1.08003906454461900E-2 " " y[1] (numeric) = 1.080039064544619800E-2 " " absolute error = 8.673617379884035000000000000000000E-18 " " relative error = 8.03083672120797500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3220000000000002 " " y[1] (analytic) = 1.09002404297282310E-2 " " y[1] (numeric) = 1.090024042972821800E-2 " " absolute error = 1.21430643318376500000000000000000E-17 " " relative error = 1.11401802649415560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3230000000000002 " " y[1] (analytic) = 1.10006906128483900E-2 " " y[1] (numeric) = 1.100069061284838800E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 3.15384467580738240000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3240000000000002 " " y[1] (analytic) = 1.110174279300543700E-2 " " y[1] (numeric) = 1.110174279300543800E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.56256860595775620000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3250000000000002 " " y[1] (analytic) = 1.12033985659901190E-2 " " y[1] (numeric) = 1.120339856599012000E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.548390397573522500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3260000000000002 " " y[1] (analytic) = 1.130565952517881300E-2 " " y[1] (numeric) = 1.13056595251788100E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 3.068770065317123500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3270000000000002 " " y[1] (analytic) = 1.140852726152713500E-2 " " y[1] (numeric) = 1.140852726152713800E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 3.04109976022373800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3280000000000002 " " y[1] (analytic) = 1.151200336356364400E-2 " " y[1] (numeric) = 1.151200336356363200E-2 " " absolute error = 1.21430643318376500000000000000000E-17 " " relative error = 1.05481764974733770000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3290000000000002 " " y[1] (analytic) = 1.161608941738334600E-2 " " y[1] (numeric) = 1.161608941738335500E-2 " " absolute error = 8.673617379884035000000000000000000E-18 " " relative error = 7.46689963224978800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y[1] (analytic) = 1.172078700664155900E-2 " " y[1] (numeric) = 1.172078700664156100E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.96008019767585500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3310000000000002 " " y[1] (analytic) = 1.18260977125473900E-2 " " y[1] (numeric) = 1.18260977125473700E-2 " " absolute error = 1.908195823574487800000000000000000E-17 " " relative error = 1.61354647150421220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3320000000000002 " " y[1] (analytic) = 1.193202311385746500E-2 " " y[1] (numeric) = 1.193202311385743200E-2 " " absolute error = 3.295974604355933500000000000000000E-17 " " relative error = 2.7622931776993420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3330000000000002 " " y[1] (analytic) = 1.203856478686959900E-2 " " y[1] (numeric) = 1.203856478686961300E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.15277759878410820000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3340000000000002 " " y[1] (analytic) = 1.214572430541668900E-2 " " y[1] (numeric) = 1.214572430541669700E-2 " " absolute error = 8.673617379884035000000000000000000E-18 " " relative error = 7.14129282188285800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3350000000000002 " " y[1] (analytic) = 1.225350324086010900E-2 " " y[1] (numeric) = 1.225350324086008800E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 1.69883512515074860000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3360000000000002 " " y[1] (analytic) = 1.23619031620835200E-2 " " y[1] (numeric) = 1.23619031620835200E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3370000000000002 " " y[1] (analytic) = 1.247092563548679600E-2 " " y[1] (numeric) = 1.247092563548678800E-2 " " absolute error = 8.673617379884035000000000000000000E-18 " " relative error = 6.9550710455707610000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3380000000000002 " " y[1] (analytic) = 1.258057222497949200E-2 " " y[1] (numeric) = 1.258057222497947200E-2 " " absolute error = 1.908195823574487800000000000000000E-17 " " relative error = 1.5167798327850690000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3390000000000002 " " y[1] (analytic) = 1.269084449197471800E-2 " " y[1] (numeric) = 1.269084449197469800E-2 " " absolute error = 1.908195823574487800000000000000000E-17 " " relative error = 1.50360035124626230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y[1] (analytic) = 1.280174399538289200E-2 " " y[1] (numeric) = 1.28017439953828800E-2 " " absolute error = 1.21430643318376500000000000000000E-17 " " relative error = 9.4854766164806890000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3410000000000002 " " y[1] (analytic) = 1.291327229160552000E-2 " " y[1] (numeric) = 1.291327229160548200E-2 " " absolute error = 3.989863994746656300000000000000000E-17 " " relative error = 3.0897389171761920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3420000000000002 " " y[1] (analytic) = 1.302543093452879200E-2 " " y[1] (numeric) = 1.302543093452879800E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 5.32718951010909500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3430000000000002 " " y[1] (analytic) = 1.31382214755177700E-2 " " y[1] (numeric) = 1.313822147551774700E-2 " " absolute error = 2.255140518769849200000000000000000E-17 " " relative error = 1.71647320984210700000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3440000000000002 " " y[1] (analytic) = 1.325164546340967800E-2 " " y[1] (numeric) = 1.325164546340964500E-2 " " absolute error = 3.46944695195361400000000000000000E-17 " " relative error = 2.6181253954713923000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3450000000000002 " " y[1] (analytic) = 1.336570444450804800E-2 " " y[1] (numeric) = 1.336570444450802300E-2 " " absolute error = 2.602085213965210600000000000000000E-17 " " relative error = 1.94683731393926220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3460000000000002 " " y[1] (analytic) = 1.348039996257646700E-2 " " y[1] (numeric) = 1.348039996257644200E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 1.80158813767374050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3470000000000002 " " y[1] (analytic) = 1.35957335588323400E-2 " " y[1] (numeric) = 1.359573355883232000E-2 " " absolute error = 1.908195823574487800000000000000000E-17 " " relative error = 1.40352546283524840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3480000000000002 " " y[1] (analytic) = 1.37117067719407800E-2 " " y[1] (numeric) = 1.371170677194075700E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 1.51816852985219240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3490000000000002 " " y[1] (analytic) = 1.382832113800841500E-2 " " y[1] (numeric) = 1.38283211380083900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 1.7562600999280120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = sin(x) * sin(x);" Iterations = 250 "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 0 Hours 55 Minutes 45 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 55 Minutes 31 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 58 Minutes 31 Seconds "Time to Timeout " Unknown Percent Done = 5.122448979591840 "%" (%o57) true (%o57) diffeq.max