(%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 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , omniout_str(ALWAYS, "WARNING: ar\ 1 1 1 ctan of linear function has low precision in testing."), array_tmp3 : arctan(array_tmp2 ), array_tmp3_a1 : sin(array_tmp3 ), 1 1 1 1 array_tmp3_a2 : cos(array_tmp3 ), array_tmp4 : 1 1 1 array_tmp3 + array_const_0D0 , if not array_y_set_initial 1 1 1, 2 then (if 1 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1), array_y : temporary, 1 2 temporary 1.0 array_y_higher : temporary, temporary : -------------, 1, 2 glob_h array_y_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp2 array_tmp3_a2 2 1 array_tmp3 : -------------------------------------------, 2 array_tmp2 array_tmp3_a1 + array_tmp3_a2 1 1 1 array_tmp3_a1 : array_tmp3_a2 array_tmp3 , 2 1 2 array_tmp3_a2 : array_tmp3_a1 array_tmp3 , array_tmp4 : array_tmp3 , 2 1 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_tmp3 : (- att(2, array_tmp3_a2, array_tmp3, 2) 3 - array_tmp2 att(2, array_tmp3_a1, array_tmp3, 2) 1 + array_tmp2 array_tmp3_a2 )/(array_tmp2 array_tmp3_a1 + array_tmp3_a2 ), 2 2 1 1 1 array_tmp3_a1 : att(2, array_tmp3_a2, array_tmp3, 1), 3 array_tmp3_a2 : - att(2, array_tmp3_a1, array_tmp3, 1), 3 array_tmp4 : array_tmp3 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 2, 3 array_tmp3 : (- att(3, array_tmp3_a2, array_tmp3, 2) 4 - array_tmp2 att(3, array_tmp3_a1, array_tmp3, 2) 1 + array_tmp2 array_tmp3_a2 )/(array_tmp2 array_tmp3_a1 + array_tmp3_a2 ), 2 3 1 1 1 array_tmp3_a1 : att(3, array_tmp3_a2, array_tmp3, 1), 4 array_tmp3_a2 : - att(3, array_tmp3_a1, array_tmp3, 1), 4 array_tmp4 : array_tmp3 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 array_tmp3 : (- att(4, array_tmp3_a2, array_tmp3, 2) 5 - array_tmp2 att(4, array_tmp3_a1, array_tmp3, 2) 1 + array_tmp2 array_tmp3_a2 )/(array_tmp2 array_tmp3_a1 + array_tmp3_a2 ), 2 4 1 1 1 array_tmp3_a1 : att(4, array_tmp3_a2, array_tmp3, 1), 5 array_tmp3_a2 : - att(4, array_tmp3_a1, array_tmp3, 1), 5 array_tmp4 : array_tmp3 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp3 : kkk (- att(kkk - 1, array_tmp3_a2, array_tmp3, 2) - array_tmp2 att(kkk - 1, array_tmp3_a1, array_tmp3, 2) 1 + array_tmp2 array_tmp3_a2 )/(array_tmp2 array_tmp3_a1 2 kkk - 1 1 1 + array_tmp3_a2 ), array_tmp3_a1 : 1 kkk att(kkk - 1, array_tmp3_a2, array_tmp3, 1), array_tmp3_a2 : - att(kkk - 1, array_tmp3_a1, array_tmp3, 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 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , omniout_str(ALWAYS, "WARNING: ar\ 1 1 1 ctan of linear function has low precision in testing."), array_tmp3 : arctan(array_tmp2 ), array_tmp3_a1 : sin(array_tmp3 ), 1 1 1 1 array_tmp3_a2 : cos(array_tmp3 ), array_tmp4 : 1 1 1 array_tmp3 + array_const_0D0 , if not array_y_set_initial 1 1 1, 2 then (if 1 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1), array_y : temporary, 1 2 temporary 1.0 array_y_higher : temporary, temporary : -------------, 1, 2 glob_h array_y_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp2 array_tmp3_a2 2 1 array_tmp3 : -------------------------------------------, 2 array_tmp2 array_tmp3_a1 + array_tmp3_a2 1 1 1 array_tmp3_a1 : array_tmp3_a2 array_tmp3 , 2 1 2 array_tmp3_a2 : array_tmp3_a1 array_tmp3 , array_tmp4 : array_tmp3 , 2 1 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_tmp3 : (- att(2, array_tmp3_a2, array_tmp3, 2) 3 - array_tmp2 att(2, array_tmp3_a1, array_tmp3, 2) 1 + array_tmp2 array_tmp3_a2 )/(array_tmp2 array_tmp3_a1 + array_tmp3_a2 ), 2 2 1 1 1 array_tmp3_a1 : att(2, array_tmp3_a2, array_tmp3, 1), 3 array_tmp3_a2 : - att(2, array_tmp3_a1, array_tmp3, 1), 3 array_tmp4 : array_tmp3 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 2, 3 array_tmp3 : (- att(3, array_tmp3_a2, array_tmp3, 2) 4 - array_tmp2 att(3, array_tmp3_a1, array_tmp3, 2) 1 + array_tmp2 array_tmp3_a2 )/(array_tmp2 array_tmp3_a1 + array_tmp3_a2 ), 2 3 1 1 1 array_tmp3_a1 : att(3, array_tmp3_a2, array_tmp3, 1), 4 array_tmp3_a2 : - att(3, array_tmp3_a1, array_tmp3, 1), 4 array_tmp4 : array_tmp3 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 array_tmp3 : (- att(4, array_tmp3_a2, array_tmp3, 2) 5 - array_tmp2 att(4, array_tmp3_a1, array_tmp3, 2) 1 + array_tmp2 array_tmp3_a2 )/(array_tmp2 array_tmp3_a1 + array_tmp3_a2 ), 2 4 1 1 1 array_tmp3_a1 : att(4, array_tmp3_a2, array_tmp3, 1), 5 array_tmp3_a2 : - att(4, array_tmp3_a1, array_tmp3, 1), 5 array_tmp4 : array_tmp3 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp3 : kkk (- att(kkk - 1, array_tmp3_a2, array_tmp3, 2) - array_tmp2 att(kkk - 1, array_tmp3_a1, array_tmp3, 2) 1 + array_tmp2 array_tmp3_a2 )/(array_tmp2 array_tmp3_a1 2 kkk - 1 1 1 + array_tmp3_a2 ), array_tmp3_a1 : 1 kkk att(kkk - 1, array_tmp3_a2, array_tmp3, 1), array_tmp3_a2 : - att(kkk - 1, array_tmp3_a1, array_tmp3, 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) (%i55) exact_soln_y(x) := block(10.0 (0.2 + 0.1 x) arctan(0.2 + 0.1 x) - 5.0 ln(expt(0.2 + 0.1 x, 2) + 1.0)) (%o55) exact_soln_y(x) := block(10.0 (0.2 + 0.1 x) arctan(0.2 + 0.1 x) - 5.0 ln(expt(0.2 + 0.1 x, 2) + 1.0)) (%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/lin_arctanpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = arctan (0.1 * x + 0.2 ) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-1.0,"), omniout_str(ALWAYS, "x_end:5.00,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.00001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:100,"), 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, " (10.\ 0 * (0.1 * x + 0.2) * arctan(0.1 * x + 0.2) - 5.0 * ln(1.0 +"), omniout_str(ALWAYS, "expt((0.1 * x + 0.2) , 2))) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3_a1, 1 + max_terms), array(array_tmp3_a2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3_a1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3_a2 : 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, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a1 : 0.0, term : 1 + term), term array(array_tmp3_a2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), iiif, jjjf x_start : - 1.0, x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_h : 1.0E-5, glob_look_poles : true, glob_max_iter : 100, 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 ) = arctan (0.1 * x + 0.2 ) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-12T23:47:22-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "lin_arctan"), logitem_str(html_log_file, "diff ( y , x , 1 ) = arctan (0.1 * x + 0.2 ) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), 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, "lin_arctan diffeq.max"), logitem_str(html_log_file, "lin_arctan 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/lin_arctanpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = arctan (0.1 * x + 0.2 ) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-1.0,"), omniout_str(ALWAYS, "x_end:5.00,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.00001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:100,"), 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, " (10.\ 0 * (0.1 * x + 0.2) * arctan(0.1 * x + 0.2) - 5.0 * ln(1.0 +"), omniout_str(ALWAYS, "expt((0.1 * x + 0.2) , 2))) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3_a1, 1 + max_terms), array(array_tmp3_a2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3_a1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3_a2 : 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, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a1 : 0.0, term : 1 + term), term array(array_tmp3_a2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), iiif, jjjf x_start : - 1.0, x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_h : 1.0E-5, glob_look_poles : true, glob_max_iter : 100, 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 ) = arctan (0.1 * x + 0.2 ) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-12T23:47:22-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "lin_arctan"), logitem_str(html_log_file, "diff ( y , x , 1 ) = arctan (0.1 * x + 0.2 ) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), 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, "lin_arctan diffeq.max"), logitem_str(html_log_file, "lin_arctan 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/lin_arctanpostode.ode#################" "diff ( y , x , 1 ) = arctan (0.1 * x + 0.2 ) ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:-1.0," "x_end:5.00," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_h:0.00001," "glob_look_poles:true," "glob_max_iter:100," "/* 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(" " (10.0 * (0.1 * x + 0.2) * arctan(0.1 * x + 0.2) - 5.0 * ln(1.0 +" "expt((0.1 * x + 0.2) , 2))) " "));" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 "WARNING: arctan of linear function has low precision in testing." glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 6. "" estimated_steps = 6000. "" step_error = 1.666666666666666900000000000000E-14 "" est_needed_step_err = 1.666666666666666900000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 9.68699257807887500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-107 "" max_value3 = 9.68699257807887500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-107 "" value3 = 9.68699257807887500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-107 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = -1. " " y[1] (analytic) = 4.99169982253215900E-2 " " y[1] (numeric) = 4.99169982253215900E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -1. " " y[1] (analytic) = 4.99169982253215900E-2 " " y[1] (numeric) = 4.99169982253215900E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.999 " " y[1] (analytic) = 5.00167163824360800E-2 " " y[1] (numeric) = 5.001671638276640000E-2 " " absolute error = 3.3033298318940750000000000000E-13 " " relative error = 6.6044516130092780000000000E-10 "%" Correct digits = 12 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.998 " " y[1] (analytic) = 5.01165335474904200E-2 " " y[1] (numeric) = 5.011653354815083000E-2 " " absolute error = 6.6041616619827440000000000000E-13 " " relative error = 1.3177610649636495000000000E-9 "%" Correct digits = 11 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.997 " " y[1] (analytic) = 5.02164497185201500E-2 " " y[1] (numeric) = 5.021644971951147000E-2 " " absolute error = 9.9132507758170620000000000000E-13 " " relative error = 1.9741042688967697000000000E-9 "%" Correct digits = 11 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.996 " " y[1] (analytic) = 5.03164648935610700E-2 " " y[1] (numeric) = 5.03164648948830200E-2 " " absolute error = 1.3219494943150778000000000000E-12 " " relative error = 2.6272702128647474000000000E-9 "%" Correct digits = 11 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.995 " " y[1] (analytic) = 5.041657907064498000E-2 " " y[1] (numeric) = 5.041657907229830000E-2 " " absolute error = 1.6533094338022636000000000000E-12 " " relative error = 3.279297136534402000000000E-9 "%" Correct digits = 11 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.994 " " y[1] (analytic) = 5.05167922478037700E-2 " " y[1] (numeric) = 5.05167922497882300E-2 " " absolute error = 1.98447508426014000000000000E-12 " " relative error = 3.9283473790765405000000000E-9 "%" Correct digits = 11 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.993 " " y[1] (analytic) = 5.061710442306543000E-2 " " y[1] (numeric) = 5.06171044253819000E-2 " " absolute error = 2.3164664630925813000000000000E-12 " " relative error = 4.576449975745755500000000E-9 "%" Correct digits = 11 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.992 " " y[1] (analytic) = 5.071751559445717000E-2 " " y[1] (numeric) = 5.071751559710644000E-2 " " absolute error = 2.6492696925117800000000000000E-12 " " relative error = 5.223579391576731000000000E-9 "%" Correct digits = 11 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.991 " " y[1] (analytic) = 5.08180257600054300E-2 " " y[1] (numeric) = 5.08180257629871800E-2 " " absolute error = 2.9817606717053025000000000000E-12 " " relative error = 5.867525601618303000000000E-9 "%" Correct digits = 11 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.99 " " y[1] (analytic) = 5.091863491773351000E-2 " " y[1] (numeric) = 5.09186349210475100E-2 " " absolute error = 3.3140087896121884000000000000E-12 " " relative error = 6.508439974807757000000000E-9 "%" Correct digits = 11 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.989 " " y[1] (analytic) = 5.1019343065660790E-2 " " y[1] (numeric) = 5.10193430693089800E-2 " " absolute error = 3.648172042236552700000000000E-12 " " relative error = 7.150566477387672000000000E-9 "%" Correct digits = 11 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.988 " " y[1] (analytic) = 5.11201502018103200E-2 " " y[1] (numeric) = 5.11201502057912000E-2 " " absolute error = 3.980885066035000400000000E-12 " " relative error = 7.787310972912644000000000E-9 "%" Correct digits = 11 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.987 " " y[1] (analytic) = 5.122105632419637000E-2 " " y[1] (numeric) = 5.12210563285119900E-2 " " absolute error = 4.315624246853389000000000000E-12 " " relative error = 8.425488571610592000000000E-9 "%" Correct digits = 11 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.986 " " y[1] (analytic) = 5.13220614308382400E-2 " " y[1] (numeric) = 5.132206143548721000E-2 " " absolute error = 4.648961771103188300000000000E-12 " " relative error = 9.058408102659988000000000E-9 "%" Correct digits = 11 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.985 " " y[1] (analytic) = 5.14231655197466900E-2 " " y[1] (numeric) = 5.14231655247308600E-2 " " absolute error = 4.984172796707042600000000000E-12 " " relative error = 9.692465927234878000000000E-9 "%" Correct digits = 11 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.984 " " y[1] (analytic) = 5.15243685889359400E-2 " " y[1] (numeric) = 5.15243685942550900E-2 " " absolute error = 5.319147899918164000000000000E-12 " " relative error = 1.032355765939530400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.983 " " y[1] (analytic) = 5.16256706364162800E-2 " " y[1] (numeric) = 5.162567064207014000E-2 " " absolute error = 5.653866264054841000000000000E-12 " " relative error = 1.095165679081107200000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.982 " " y[1] (analytic) = 5.17270716601950600E-2 " " y[1] (numeric) = 5.17270716661843900E-2 " " absolute error = 5.98933402873314000000000000E-12 " " relative error = 1.157872239139731400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.981 " " y[1] (analytic) = 5.18285716582786200E-2 " " y[1] (numeric) = 5.18285716646043200E-2 " " absolute error = 6.325696910725043000000000000E-12 " " relative error = 1.22050380867762800000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.98 " " y[1] (analytic) = 5.19301706286728200E-2 " " y[1] (numeric) = 5.19301706353345500E-2 " " absolute error = 6.661726725809558000000000000E-12 " " relative error = 1.282823962479210400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.979 " " y[1] (analytic) = 5.203186856938031000E-2 " " y[1] (numeric) = 5.20318685763778000E-2 " " absolute error = 6.997492862925725000000000000E-12 " " relative error = 1.344847505062235200000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.978 " " y[1] (analytic) = 5.21336654784008900E-2 " " y[1] (numeric) = 5.213366548573496000E-2 " " absolute error = 7.334063911734745000000000000E-12 " " relative error = 1.406780790192714600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.977 " " y[1] (analytic) = 5.2235561353733510E-2 " " y[1] (numeric) = 5.22355613614049700E-2 " " absolute error = 7.671467627812234000000000000E-12 " " relative error = 1.468629307123148500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.976 " " y[1] (analytic) = 5.233755619337633000E-2 " " y[1] (numeric) = 5.233755620138494000E-2 " " absolute error = 8.008607665921375000000000000E-12 " " relative error = 1.530183724347243500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.975 " " y[1] (analytic) = 5.24396499953235600E-2 " " y[1] (numeric) = 5.2439650003670100E-2 " " absolute error = 8.346552615723368000000000000E-12 " " relative error = 1.591649184627986000000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.974 " " y[1] (analytic) = 5.25418427575685100E-2 " " y[1] (numeric) = 5.254184276625380000E-2 " " absolute error = 8.685281660536504000000000000E-12 " " relative error = 1.65302189734969130000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.973 " " y[1] (analytic) = 5.26441344781037400E-2 " " y[1] (numeric) = 5.264413448712748000E-2 " " absolute error = 9.02374702738129000000000000E-12 " " relative error = 1.714103027210853700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.972 " " y[1] (analytic) = 5.27465251549187900E-2 " " y[1] (numeric) = 5.27465251642807800E-2 " " absolute error = 9.361983410727248000000000000E-12 " " relative error = 1.77490050448455230000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.971 " " y[1] (analytic) = 5.28490147860003500E-2 " " y[1] (numeric) = 5.28490147957013500E-2 " " absolute error = 9.701010827978251000000000000E-12 " " relative error = 1.83560864232951400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.97 " " y[1] (analytic) = 5.29516033693341800E-2 " " y[1] (numeric) = 5.29516033793750900E-2 " " absolute error = 1.004090560696724300000000000E-11 " " relative error = 1.896242033868652300000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.969 " " y[1] (analytic) = 5.30542909029054700E-2 " " y[1] (numeric) = 5.305429091328592000E-2 " " absolute error = 1.038044650236713600000000000E-11 " " relative error = 1.956570585659954700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.968 " " y[1] (analytic) = 5.31570773846961900E-2 " " y[1] (numeric) = 5.31570773954159300E-2 " " absolute error = 1.071974453648039100000000000E-11 " " relative error = 2.016616613231370600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.967 " " y[1] (analytic) = 5.325996281268439000E-2 " " y[1] (numeric) = 5.32599628237453500E-2 " " absolute error = 1.106096464420502900000000000E-11 " " relative error = 2.076787902219629500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.966 " " y[1] (analytic) = 5.33629471848517100E-2 " " y[1] (numeric) = 5.3362947196252500E-2 " " absolute error = 1.140079003425498200000000000E-11 " " relative error = 2.13646184022822430000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.965 " " y[1] (analytic) = 5.34660304991713700E-2 " " y[1] (numeric) = 5.34660305109138300E-2 " " absolute error = 1.174246810897727800000000000E-11 " " relative error = 2.196248346725359600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.964 " " y[1] (analytic) = 5.35692127536210200E-2 " " y[1] (numeric) = 5.35692127657039400E-2 " " absolute error = 1.20829318772663900000000000E-11 " " relative error = 2.25557391198541400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.963 " " y[1] (analytic) = 5.367249394617036000E-2 " " y[1] (numeric) = 5.367249395859555000E-2 " " absolute error = 1.242517894128880600000000000E-11 " " relative error = 2.314999365177694800000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.962 " " y[1] (analytic) = 5.37758740747922300E-2 " " y[1] (numeric) = 5.377587408755945000E-2 " " absolute error = 1.276722477738801000000000000E-11 " " relative error = 2.37415476680698400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.961 " " y[1] (analytic) = 5.38793531374556800E-2 " " y[1] (numeric) = 5.38793531505646500E-2 " " absolute error = 1.31089653021554400000000000E-11 " " relative error = 2.433022027698100000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.96 " " y[1] (analytic) = 5.398293113212665000E-2 " " y[1] (numeric) = 5.39829311455782000E-2 " " absolute error = 1.34515384941913400000000000E-11 " " relative error = 2.491813284696943500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.959 " " y[1] (analytic) = 5.40866080567704200E-2 " " y[1] (numeric) = 5.40866080705653200E-2 " " absolute error = 1.379489578123838000000000000E-11 " " relative error = 2.55051967147930100000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.958 " " y[1] (analytic) = 5.41903839093513600E-2 " " y[1] (numeric) = 5.419038392348936000E-2 " " absolute error = 1.413799632921097800000000000E-11 " " relative error = 2.608949283854632000000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.957 " " y[1] (analytic) = 5.42942586878298900E-2 " " y[1] (numeric) = 5.42942587023117700E-2 " " absolute error = 1.448188097219471600000000000E-11 " " relative error = 2.667295092002212600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.956 " " y[1] (analytic) = 5.43982323901665800E-2 " " y[1] (numeric) = 5.43982324049921500E-2 " " absolute error = 1.482557132614914500000000000E-11 " " relative error = 2.72537740193725900000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.955 " " y[1] (analytic) = 5.45023050143182000E-2 " " y[1] (numeric) = 5.45023050294882200E-2 " " absolute error = 1.517002495843300400000000000E-11 " " relative error = 2.783373098522662000000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.954 " " y[1] (analytic) = 5.460647655824161000E-2 " " y[1] (numeric) = 5.46064765737558200E-2 " " absolute error = 1.55142079738546100000000000E-11 " " relative error = 2.84109302626541500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.953 " " y[1] (analytic) = 5.47107470198897600E-2 " " y[1] (numeric) = 5.47107470357489300E-2 " " absolute error = 1.585916814539345400000000000E-11 " " relative error = 2.898729958782677600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.952 " " y[1] (analytic) = 5.48151163972157500E-2 " " y[1] (numeric) = 5.48151164134196400E-2 " " absolute error = 1.620389239453956500000000000E-11 " " relative error = 2.95609924042095400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.951 " " y[1] (analytic) = 5.49195846881687500E-2 " " y[1] (numeric) = 5.491958470471819000E-2 " " absolute error = 1.654943543316633700000000000E-11 " " relative error = 3.013394133829194000000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.95 " " y[1] (analytic) = 5.50241518906971300E-2 " " y[1] (numeric) = 5.502415190759294000E-2 " " absolute error = 1.689581807795548200000000000E-11 " " relative error = 3.07061853702320140000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.949 " " y[1] (analytic) = 5.51288180027485300E-2 " " y[1] (numeric) = 5.512881801999038000E-2 " " absolute error = 1.724184683915552800000000000E-11 " " relative error = 3.12755605213518500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.948 " " y[1] (analytic) = 5.52335830222674400E-2 " " y[1] (numeric) = 5.5233583039855100E-2 " " absolute error = 1.758766049464455300000000000E-11 " " relative error = 3.18423312996987400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.947 " " y[1] (analytic) = 5.53384469471944900E-2 " " y[1] (numeric) = 5.533844696512986000E-2 " " absolute error = 1.79353823459571520000000000E-11 " " relative error = 3.24103463963699600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.946 " " y[1] (analytic) = 5.54434097754737800E-2 " " y[1] (numeric) = 5.54434097937555400E-2 " " absolute error = 1.82817511129584900000000000E-11 " " relative error = 3.29737135342020260000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.945 " " y[1] (analytic) = 5.55484715050422100E-2 " " y[1] (numeric) = 5.55484715236711300E-2 " " absolute error = 1.862891785275877500000000000E-11 " " relative error = 3.35363284497716600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.944 " " y[1] (analytic) = 5.565363213383689000E-2 " " y[1] (numeric) = 5.56536321528137600E-2 " " absolute error = 1.897686868757020300000000000E-11 " " relative error = 3.409816746898796700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.943 " " y[1] (analytic) = 5.57588916597930600E-2 " " y[1] (numeric) = 5.57588916791187200E-2 " " absolute error = 1.9325652189650100000000000E-11 " " relative error = 3.465931910476899300000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.942 " " y[1] (analytic) = 5.586425008084624000E-2 " " y[1] (numeric) = 5.586425010051935000E-2 " " absolute error = 1.96731103629943500000000000E-11 " " relative error = 3.5215921335243200000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.941 " " y[1] (analytic) = 5.59697073949247700E-2 " " y[1] (numeric) = 5.59697074149472200E-2 " " absolute error = 2.002245591548046400000000000E-11 " " relative error = 3.57737369863328300000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.94 " " y[1] (analytic) = 5.607526359996046000E-2 " " y[1] (numeric) = 5.60752636203319700E-2 " " absolute error = 2.037151003442261300000000000E-11 " " relative error = 3.632887074727363400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.939 " " y[1] (analytic) = 5.618091869388110000E-2 " " y[1] (numeric) = 5.618091871460138000E-2 " " absolute error = 2.072027965871470200000000000E-11 " " relative error = 3.688134715563388700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.938 " " y[1] (analytic) = 5.6286672674610390E-2 " " y[1] (numeric) = 5.628667269568135000E-2 " " absolute error = 2.107095747883036600000000000E-11 " " relative error = 3.74350738417959130000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9369999999999999 " " y[1] (analytic) = 5.63925255400756900E-2 " " y[1] (numeric) = 5.63925255614959700E-2 " " absolute error = 2.14202683368469600000000000E-11 " " relative error = 3.79842330729176400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9359999999999999 " " y[1] (analytic) = 5.64984772881969600E-2 " " y[1] (numeric) = 5.64984773099673700E-2 " " absolute error = 2.177040492323811800000000000E-11 " " relative error = 3.85327286117605700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9349999999999999 " " y[1] (analytic) = 5.66045279168944800E-2 " " y[1] (numeric) = 5.660452793901587000E-2 " " absolute error = 2.21214019324733600000000000E-11 " " relative error = 3.908062260487627500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9339999999999999 " " y[1] (analytic) = 5.67106774240878900E-2 " " y[1] (numeric) = 5.671067744655993000E-2 " " absolute error = 2.247204505811950500000000000E-11 " " relative error = 3.96257743318271350000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9329999999999999 " " y[1] (analytic) = 5.68169258076925800E-2 " " y[1] (numeric) = 5.681692583051613000E-2 " " absolute error = 2.282355554550363800000000000E-11 " " relative error = 4.017034575709745000000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9319999999999999 " " y[1] (analytic) = 5.69232730656243500E-2 " " y[1] (numeric) = 5.69232730887991500E-2 " " absolute error = 2.317480929381332500000000000E-11 " " relative error = 4.071236252893628600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9309999999999999 " " y[1] (analytic) = 5.70297191957950100E-2 " " y[1] (numeric) = 5.70297192193218500E-2 " " absolute error = 2.35268401982402500000000000E-11 " " relative error = 4.12536490272162600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9299999999999999 " " y[1] (analytic) = 5.713626419611550000E-2 " " y[1] (numeric) = 5.713626421999519000E-2 " " absolute error = 2.387968989214783700000000000E-11 " " relative error = 4.17942793917760800000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9289999999999999 " " y[1] (analytic) = 5.72429080644960300E-2 " " y[1] (numeric) = 5.72429080887283000E-2 " " absolute error = 2.423226203029926800000000000E-11 " " relative error = 4.233233923579946500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9279999999999999 " " y[1] (analytic) = 5.73496507988438200E-2 " " y[1] (numeric) = 5.734965082342838000E-2 " " absolute error = 2.45845566126945410000000000E-11 " " relative error = 4.286784011802591000000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9269999999999999 " " y[1] (analytic) = 5.74564923970631300E-2 " " y[1] (numeric) = 5.74564924220008300E-2 " " absolute error = 2.493769774014609200000000000E-11 " " relative error = 4.34027499761206700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9259999999999999 " " y[1] (analytic) = 5.756343285705755000E-2 " " y[1] (numeric) = 5.75634328823491500E-2 " " absolute error = 2.52915952070331700000000000E-11 " " relative error = 4.39369126400742400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9249999999999999 " " y[1] (analytic) = 5.767047217672976000E-2 " " y[1] (numeric) = 5.76704722023749900E-2 " " absolute error = 2.5645235934845800000000000E-11 " " relative error = 4.44685728534640700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9239999999999999 " " y[1] (analytic) = 5.777761035397839000E-2 " " y[1] (numeric) = 5.777761037997813000E-2 " " absolute error = 2.599973014660861300000000000E-11 " " relative error = 4.49996633424600400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9229999999999999 " " y[1] (analytic) = 5.788484738670253000E-2 " " y[1] (numeric) = 5.78848474130564600E-2 " " absolute error = 2.635392598593356000000000000E-11 " " relative error = 4.552819464112062300000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9219999999999999 " " y[1] (analytic) = 5.7992183272797100E-2 " " y[1] (numeric) = 5.79921832995060400E-2 " " absolute error = 2.670894061473916300000000000E-11 " " relative error = 4.60561046462062700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9209999999999999 " " y[1] (analytic) = 5.80996180101562700E-2 " " y[1] (numeric) = 5.80996180372210600E-2 " " absolute error = 2.70647740330254300000000000E-11 " " relative error = 4.6583394108192400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9199999999999999 " " y[1] (analytic) = 5.820715159667456000E-2 " " y[1] (numeric) = 5.8207151624093800E-2 " " absolute error = 2.74192474281065300000000000E-11 " " relative error = 4.71063205739705450000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9189999999999999 " " y[1] (analytic) = 5.83147840302391200E-2 " " y[1] (numeric) = 5.831478405801476000E-2 " " absolute error = 2.77756359579051100000000000E-11 " " relative error = 4.763052186475055000000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9179999999999999 " " y[1] (analytic) = 5.84225153087407700E-2 " " y[1] (numeric) = 5.842251533687249000E-2 " " absolute error = 2.81317261152658200000000000E-11 " " relative error = 4.815219948439458700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9169999999999999 " " y[1] (analytic) = 5.8530345430065100E-2 " " y[1] (numeric) = 5.85303454585537500E-2 " " absolute error = 2.848864893989500000000000E-11 " " relative error = 4.86732971257356100000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9159999999999999 " " y[1] (analytic) = 5.86382743920980800E-2 " " y[1] (numeric) = 5.86382744209433700E-2 " " absolute error = 2.884529420876802400000000000E-11 " " relative error = 4.91919220130651300000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9149999999999999 " " y[1] (analytic) = 5.87463021927227400E-2 " " y[1] (numeric) = 5.87463022219243600E-2 " " absolute error = 2.92016202885214700000000000E-11 " " relative error = 4.970801428951701600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9139999999999999 " " y[1] (analytic) = 5.885442882981794000E-2 " " y[1] (numeric) = 5.88544288593778600E-2 " " absolute error = 2.95599170141436200000000000E-11 " " relative error = 5.022547597839810000000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9129999999999999 " " y[1] (analytic) = 5.89626543012663800E-2 " " y[1] (numeric) = 5.89626543311831300E-2 " " absolute error = 2.99167496331520500000000000E-11 " " relative error = 5.07384716439224300000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9119999999999999 " " y[1] (analytic) = 5.90709786049420100E-2 " " y[1] (numeric) = 5.90709786352175900E-2 " " absolute error = 3.027558065360480600000000000E-11 " " relative error = 5.125288486599050000000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9109999999999999 " " y[1] (analytic) = 5.91794017387237400E-2 " " y[1] (numeric) = 5.917940176935679000E-2 " " absolute error = 3.06330447119584900000000000E-11 " " relative error = 5.17630185705542800000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9099999999999999 " " y[1] (analytic) = 5.92879237004820100E-2 " " y[1] (numeric) = 5.9287923731474400E-2 " " absolute error = 3.099238921056013400000000000E-11 " " relative error = 5.22743710289658300000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9089999999999999 " " y[1] (analytic) = 5.9396544488090800E-2 " " y[1] (numeric) = 5.939654451944225000E-2 " " absolute error = 3.13514561534056200000000000E-11 " " relative error = 5.27832998091188400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9079999999999999 " " y[1] (analytic) = 5.950526409942009000E-2 " " y[1] (numeric) = 5.95052641311303100E-2 " " absolute error = 3.17102247238132400000000000E-11 " " relative error = 5.3289780666854100000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9069999999999999 " " y[1] (analytic) = 5.961408253233685000E-2 " " y[1] (numeric) = 5.96140825644066800E-2 " " absolute error = 3.206981902259542500000000000E-11 " " relative error = 5.379571010792557000000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9059999999999999 " " y[1] (analytic) = 5.97229997847073200E-2 " " y[1] (numeric) = 5.97229998171375800E-2 " " absolute error = 3.243025986643388600000000000E-11 " " relative error = 5.43011234923567600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9049999999999999 " " y[1] (analytic) = 5.98320158543970200E-2 " " y[1] (numeric) = 5.9832015887187410E-2 " " absolute error = 3.279037458225886300000000000E-11 " " relative error = 5.48040611936846700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9039999999999999 " " y[1] (analytic) = 5.99411307392672900E-2 " " y[1] (numeric) = 5.994113077241867000E-2 " " absolute error = 3.31513774765035400000000000E-11 " " relative error = 5.5306560065918400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9029999999999999 " " y[1] (analytic) = 6.00503444371799900E-2 " " y[1] (numeric) = 6.005034447069203000E-2 " " absolute error = 3.35120334260530230000000000E-11 " " relative error = 5.5806563209825900000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9019999999999999 " " y[1] (analytic) = 6.01596569459927500E-2 " " y[1] (numeric) = 6.01596569798662700E-2 " " absolute error = 3.38735359206587800000000000E-11 " " relative error = 5.63060656264515300000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.9009999999999999 " " y[1] (analytic) = 6.02690682635636200E-2 " " y[1] (numeric) = 6.026906829779837000E-2 " " absolute error = 3.423474698172057600000000000E-11 " " relative error = 5.68031794220014500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8999999999999999 " " y[1] (analytic) = 6.03785783877465600E-2 " " y[1] (numeric) = 6.03785784223433500E-2 " " absolute error = 3.459679764894474400000000000E-11 " " relative error = 5.729978838979412000000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8989999999999999 " " y[1] (analytic) = 6.04881873163958900E-2 " " y[1] (numeric) = 6.04881873513544800E-2 " " absolute error = 3.495859157709446700000000000E-11 " " relative error = 5.779408034536788000000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8979999999999999 " " y[1] (analytic) = 6.059789504736195000E-2 " " y[1] (numeric) = 6.05978950826830800E-2 " " absolute error = 3.53211349057858100000000000E-11 " " relative error = 5.8287725800012700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8969999999999999 " " y[1] (analytic) = 6.0707701578494100E-2 " " y[1] (numeric) = 6.07077016141786900E-2 " " absolute error = 3.56845872295785700000000000E-11 " " relative error = 5.87809887406772500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8959999999999999 " " y[1] (analytic) = 6.0817606907641200E-2 " " y[1] (numeric) = 6.08176069436889200E-2 " " absolute error = 3.604772036425174500000000000E-11 " " relative error = 5.92718493823581700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8949999999999999 " " y[1] (analytic) = 6.092761103264792000E-2 " " y[1] (numeric) = 6.09276110690595600E-2 " " absolute error = 3.641163759393606400000000000E-11 " " relative error = 5.97621291509771600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8939999999999999 " " y[1] (analytic) = 6.103771395135931000E-2 " " y[1] (numeric) = 6.10377139881345500E-2 " " absolute error = 3.677524257339470600000000000E-11 " " relative error = 6.02500326317934200000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8929999999999999 " " y[1] (analytic) = 6.11479156616173000E-2 " " y[1] (numeric) = 6.11479156987559400E-2 " " absolute error = 3.71386324471423300000000000E-11 " " relative error = 6.07357291664061400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8919999999999999 " " y[1] (analytic) = 6.12582161612600300E-2 " " y[1] (numeric) = 6.12582161987639500E-2 " " absolute error = 3.75039235778196200000000000E-11 " " relative error = 6.12226831403185300000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8909999999999999 " " y[1] (analytic) = 6.13686154481279800E-2 " " y[1] (numeric) = 6.136861548599692000E-2 " " absolute error = 3.78689440916346600000000000E-11 " " relative error = 6.17073463611762700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8899999999999999 " " y[1] (analytic) = 6.14791135200576900E-2 " " y[1] (numeric) = 6.14791135582913800E-2 " " absolute error = 3.82336801107996400000000000E-11 " " relative error = 6.21897062623159400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8889999999999999 " " y[1] (analytic) = 6.15897103748827200E-2 " " y[1] (numeric) = 6.15897104134819200E-2 " " absolute error = 3.85992002249757600000000000E-11 " " relative error = 6.2671507935385800000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8879999999999999 " " y[1] (analytic) = 6.1700406010436900E-2 " " y[1] (numeric) = 6.17004060494013700E-2 " " absolute error = 3.89644705389713400000000000E-11 " " relative error = 6.31510764003405900000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8869999999999999 " " y[1] (analytic) = 6.18112004245500700E-2 " " y[1] (numeric) = 6.181120046388062000E-2 " " absolute error = 3.93305527035536800000000000E-11 " " relative error = 6.3630138928562910000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8859999999999999 " " y[1] (analytic) = 6.192209361505127000E-2 " " y[1] (numeric) = 6.19220936547487600E-2 " " absolute error = 3.9697495290980100000000000E-11 " " relative error = 6.41087743863539600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8849999999999999 " " y[1] (analytic) = 6.20330855797688900E-2 " " y[1] (numeric) = 6.20330856198330000E-2 " " absolute error = 4.006410481149913500000000000E-11 " " relative error = 6.45850588231345600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8839999999999999 " " y[1] (analytic) = 6.21441763165271400E-2 " " y[1] (numeric) = 6.21441763569586800E-2 " " absolute error = 4.043154006039273400000000000E-11 " " relative error = 6.50608672556176900000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8829999999999999 " " y[1] (analytic) = 6.22553658231506100E-2 " " y[1] (numeric) = 6.22553658639493300E-2 " " absolute error = 4.07987185702118900000000000E-11 " " relative error = 6.55344612159362800000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8819999999999999 " " y[1] (analytic) = 6.236665409746098000E-2 " " y[1] (numeric) = 6.23666541386265900E-2 " " absolute error = 4.116559870759317600000000000E-11 " " relative error = 6.60057835446219200000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8809999999999999 " " y[1] (analytic) = 6.247804113727587000E-2 " " y[1] (numeric) = 6.24780411788102400E-2 " " absolute error = 4.153436622411632600000000000E-11 " " relative error = 6.64783425793673700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8799999999999999 " " y[1] (analytic) = 6.25895269404153600E-2 " " y[1] (numeric) = 6.25895269823182300E-2 " " absolute error = 4.19028700626711270000000000E-11 " " relative error = 6.69486927142974900000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8789999999999999 " " y[1] (analytic) = 6.2701111504695500E-2 " " y[1] (numeric) = 6.27011115469666600E-2 " " absolute error = 4.22711587955149070000000000E-11 " " relative error = 6.74169209781063300000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8779999999999999 " " y[1] (analytic) = 6.28127948279295500E-2 " " y[1] (numeric) = 6.28127948705697300E-2 " " absolute error = 4.2640183051112500000000000E-11 " " relative error = 6.78845499040788600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8769999999999999 " " y[1] (analytic) = 6.29245769079308700E-2 " " y[1] (numeric) = 6.29245769509398400E-2 " " absolute error = 4.300895750652955500000000000E-11 " " relative error = 6.83500146047208400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8759999999999999 " " y[1] (analytic) = 6.3036457742508900E-2 " " y[1] (numeric) = 6.30364577858874900E-2 " " absolute error = 4.337857850700288500000000000E-11 " " relative error = 6.88150636322166900000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8749999999999999 " " y[1] (analytic) = 6.31484373294723800E-2 " " y[1] (numeric) = 6.31484373732213600E-2 " " absolute error = 4.37489766635934530000000000E-11 " " relative error = 6.92795871342569400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8739999999999999 " " y[1] (analytic) = 6.3260515666629200E-2 " " y[1] (numeric) = 6.32605157107482700E-2 " " absolute error = 4.41190695088522500000000000E-11 " " relative error = 6.97418746020840100000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8729999999999999 " " y[1] (analytic) = 6.33726927517831400E-2 " " y[1] (numeric) = 6.33726927962731800E-2 " " absolute error = 4.44900366547429370000000000E-11 " " relative error = 7.02037971291524500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8719999999999999 " " y[1] (analytic) = 6.34849685827385100E-2 " " y[1] (numeric) = 6.34849686275992100E-2 " " absolute error = 4.486069848930185300000000000E-11 " " relative error = 7.06634964004682800000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8709999999999999 " " y[1] (analytic) = 6.35973431572954300E-2 " " y[1] (numeric) = 6.3597343202527610E-2 " " absolute error = 4.52321791133414300000000000E-11 " " relative error = 7.11227495800706500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8699999999999999 " " y[1] (analytic) = 6.37098164732543800E-2 " " y[1] (numeric) = 6.37098165188577800E-2 " " absolute error = 4.56033960594126600000000000E-11 " " relative error = 7.15798578364405300000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8689999999999999 " " y[1] (analytic) = 6.38223885284118800E-2 " " y[1] (numeric) = 6.38223885743872800E-2 " " absolute error = 4.597540403938893400000000000E-11 " " relative error = 7.20364829638458600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8679999999999999 " " y[1] (analytic) = 6.39350593205646600E-2 " " y[1] (numeric) = 6.39350593669118200E-2 " " absolute error = 4.63471622191846700000000000E-11 " " relative error = 7.24909974460243300000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8669999999999999 " " y[1] (analytic) = 6.40478288475055100E-2 " " y[1] (numeric) = 6.40478288942252400E-2 " " absolute error = 4.67197391884610600000000000E-11 " " relative error = 7.29450787468507100000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8659999999999999 " " y[1] (analytic) = 6.41606971070264500E-2 " " y[1] (numeric) = 6.41606971541195600E-2 " " absolute error = 4.7093107191642500000000000E-11 " " relative error = 7.339868379716400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8649999999999999 " " y[1] (analytic) = 6.42736640969187100E-2 " " y[1] (numeric) = 6.42736641443849300E-2 " " absolute error = 4.746621151685559400000000000E-11 " " relative error = 7.38501720475760600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8639999999999999 " " y[1] (analytic) = 6.43867298149705800E-2 " " y[1] (numeric) = 6.43867298628096200E-2 " " absolute error = 4.78390382863125300000000000E-11 " " relative error = 7.42995310117294600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8629999999999999 " " y[1] (analytic) = 6.44998942589674900E-2 " " y[1] (numeric) = 6.4499894307180110E-2 " " absolute error = 4.82126144563110870000000000E-11 " " relative error = 7.47483620093036600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8619999999999999 " " y[1] (analytic) = 6.46131574266938700E-2 " " y[1] (numeric) = 6.46131574752809700E-2 " " absolute error = 4.85871065603049600000000000E-11 " " relative error = 7.5196923498791900000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8609999999999999 " " y[1] (analytic) = 6.47265193159337000E-2 " " y[1] (numeric) = 6.47265193648949700E-2 " " absolute error = 4.896127947517925300000000000E-11 " " relative error = 7.56433066270666600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8599999999999999 " " y[1] (analytic) = 6.48399799244667300E-2 " " y[1] (numeric) = 6.48399799738030200E-2 " " absolute error = 4.933628505732201600000000000E-11 " " relative error = 7.60892972434518700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8589999999999999 " " y[1] (analytic) = 6.49535392500731800E-2 " " y[1] (numeric) = 6.49535392997841500E-2 " " absolute error = 4.9710971450345200000000000E-11 " " relative error = 7.65331220196583700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8579999999999999 " " y[1] (analytic) = 6.50671972905290700E-2 " " y[1] (numeric) = 6.50671973406155600E-2 " " absolute error = 5.00864905106368500000000000E-11 " " relative error = 7.69765605347923200000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8569999999999999 " " y[1] (analytic) = 6.51809540436097800E-2 " " y[1] (numeric) = 6.51809540940726100E-2 " " absolute error = 5.04628283604091600000000000E-11 " " relative error = 7.74195915062038700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8559999999999999 " " y[1] (analytic) = 6.52948095070899000E-2 " " y[1] (numeric) = 6.52948095579288100E-2 " " absolute error = 5.083890253221313000000000000E-11 " " relative error = 7.78605572418323500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8549999999999999 " " y[1] (analytic) = 6.5408763678741100E-2 " " y[1] (numeric) = 6.54087637299558100E-2 " " absolute error = 5.12147130260487400000000000E-11 " " relative error = 7.82994665326388800000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8539999999999999 " " y[1] (analytic) = 6.55228165563321200E-2 " " y[1] (numeric) = 6.55228166079234300E-2 " " absolute error = 5.1591314553789400000000000E-11 " " relative error = 7.8737937813516700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8529999999999999 " " y[1] (analytic) = 6.5636968137630890E-2 " " y[1] (numeric) = 6.56369681895996200E-2 " " absolute error = 5.196872099322292000000000000E-11 " " relative error = 7.91759925355666900000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8519999999999999 " " y[1] (analytic) = 6.57512184204046100E-2 " " y[1] (numeric) = 6.57512184727505000E-2 " " absolute error = 5.23458776324758900000000000E-11 " " relative error = 7.96120268034932200000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8509999999999999 " " y[1] (analytic) = 6.58655674024165100E-2 " " y[1] (numeric) = 6.58655674551403200E-2 " " absolute error = 5.272379755005829000000000000E-11 " " relative error = 8.00475872741421600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8499999999999999 " " y[1] (analytic) = 6.59800150814300800E-2 " " y[1] (numeric) = 6.5980015134531500E-2 " " absolute error = 5.31014260340967300000000000E-11 " " relative error = 8.04810759266437400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8489999999999999 " " y[1] (analytic) = 6.60945614552047600E-2 " " y[1] (numeric) = 6.60945615086846300E-2 " " absolute error = 5.34798733076158300000000000E-11 " " relative error = 8.09141813337569800000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8479999999999999 " " y[1] (analytic) = 6.6209206521500300E-2 " " y[1] (numeric) = 6.62092065753584400E-2 " " absolute error = 5.38581401698934300000000000E-11 " " relative error = 8.13453943937599200000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8469999999999999 " " y[1] (analytic) = 6.63239502780726300E-2 " " y[1] (numeric) = 6.63239503323097800E-2 " " absolute error = 5.42371564327126500000000000E-11 " " relative error = 8.17761249221670800000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8459999999999999 " " y[1] (analytic) = 6.64387927226778200E-2 " " y[1] (numeric) = 6.64387927772937100E-2 " " absolute error = 5.461589513977572000000000000E-11 " " relative error = 8.22048277844962400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8449999999999999 " " y[1] (analytic) = 6.65537338530679500E-2 " " y[1] (numeric) = 6.6553733908063410E-2 " " absolute error = 5.49954526363194400000000000E-11 " " relative error = 8.26331588814145800000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8439999999999999 " " y[1] (analytic) = 6.66687736669943600E-2 " " y[1] (numeric) = 6.66687737223702200E-2 " " absolute error = 5.537585667791944000000000000E-11 " " relative error = 8.30611598685132300000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8429999999999999 " " y[1] (analytic) = 6.67839121622076700E-2 " " y[1] (numeric) = 6.67839122179636400E-2 " " absolute error = 5.57559692859754800000000000E-11 " " relative error = 8.3487126586045090000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8419999999999999 " " y[1] (analytic) = 6.68991493364544400E-2 " " y[1] (numeric) = 6.68991493925913200E-2 " " absolute error = 5.613687292793657000000000000E-11 " " relative error = 8.39126857138475900000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8409999999999999 " " y[1] (analytic) = 6.7014485187481600E-2 " " y[1] (numeric) = 6.70144852439990700E-2 " " absolute error = 5.651747125856588000000000000E-11 " " relative error = 8.43362014950215900000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8399999999999999 " " y[1] (analytic) = 6.71299197130330100E-2 " " y[1] (numeric) = 6.71299197699308700E-2 " " absolute error = 5.68978475445902600000000000E-11 " " relative error = 8.47578066349806300000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8389999999999999 " " y[1] (analytic) = 6.72454529108487200E-2 " " y[1] (numeric) = 6.72454529681288000E-2 " " absolute error = 5.728008345418090000000000000E-11 " " relative error = 8.51806047467930500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8379999999999999 " " y[1] (analytic) = 6.73610847786711100E-2 " " y[1] (numeric) = 6.73610848363331800E-2 " " absolute error = 5.76620695635909900000000000E-11 " " relative error = 8.56014563201464700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8369999999999999 " " y[1] (analytic) = 6.74768153142385900E-2 " " y[1] (numeric) = 6.74768153722824300E-2 " " absolute error = 5.80438336283961600000000000E-11 " " relative error = 8.60204106522912100000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8359999999999999 " " y[1] (analytic) = 6.75926445152867800E-2 " " y[1] (numeric) = 6.75926445737131100E-2 " " absolute error = 5.84263332159551400000000000E-11 " " relative error = 8.64388923305721700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8349999999999999 " " y[1] (analytic) = 6.77085723795514200E-2 " " y[1] (numeric) = 6.77085724383600E-2 " " absolute error = 5.88085691255457700000000000E-11 " " relative error = 8.68554262167643500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8339999999999999 " " y[1] (analytic) = 6.7824598904764400E-2 " " y[1] (numeric) = 6.78245989639559800E-2 " " absolute error = 5.91915821912536400000000000E-11 " " relative error = 8.72715550804321500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8329999999999999 " " y[1] (analytic) = 6.79407240886566600E-2 " " y[1] (numeric) = 6.79407241482321500E-2 " " absolute error = 5.95754834353812200000000000E-11 " " relative error = 8.76874425972270500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8319999999999999 " " y[1] (analytic) = 6.80569479289586200E-2 " " y[1] (numeric) = 6.80569479889176800E-2 " " absolute error = 5.9959051612601400000000000E-11 " " relative error = 8.81012937506245100000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8309999999999998 " " y[1] (analytic) = 6.81732704233965500E-2 " " y[1] (numeric) = 6.81732704837399800E-2 " " absolute error = 6.03434247015144400000000000E-11 " " relative error = 8.85147864063816800000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8299999999999998 " " y[1] (analytic) = 6.828969156969700E-2 " " y[1] (numeric) = 6.82896916304245500E-2 " " absolute error = 6.07275618680347400000000000E-11 " " relative error = 8.89263964621303300000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8289999999999998 " " y[1] (analytic) = 6.84062113655837400E-2 " " y[1] (numeric) = 6.84062114266951300E-2 " " absolute error = 6.11113937232232700000000000E-11 " " relative error = 8.93360303154713000000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8279999999999998 " " y[1] (analytic) = 6.85228298087764400E-2 " " y[1] (numeric) = 6.85228298702735400E-2 " " absolute error = 6.14970990797658600000000000E-11 " " relative error = 8.97468759702175500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8269999999999998 " " y[1] (analytic) = 6.86395468969972100E-2 " " y[1] (numeric) = 6.8639546958879800E-2 " " absolute error = 6.18825962694913300000000000E-11 " " relative error = 9.01558927280717800000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8259999999999998 " " y[1] (analytic) = 6.87563626279642300E-2 " " y[1] (numeric) = 6.87563626902320900E-2 " " absolute error = 6.22678575368240700000000000E-11 " " relative error = 9.05630477774849700000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8249999999999998 " " y[1] (analytic) = 6.88732769993928900E-2 " " y[1] (numeric) = 6.88732770620467100E-2 " " absolute error = 6.265382657133500000000000E-11 " " relative error = 9.09697190274354100000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8239999999999998 " " y[1] (analytic) = 6.89902900089986600E-2 " " y[1] (numeric) = 6.89902900720381700E-2 " " absolute error = 6.30395180500897800000000000E-11 " " relative error = 9.13744789909816300000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8229999999999998 " " y[1] (analytic) = 6.91074016544929800E-2 " " y[1] (numeric) = 6.91074017179191400E-2 " " absolute error = 6.34261532184154900000000000E-11 " " relative error = 9.17791028166834100000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8219999999999998 " " y[1] (analytic) = 6.9224611933586890E-2 " " y[1] (numeric) = 6.9224611997400400E-2 " " absolute error = 6.38135100317072100000000000E-11 " " relative error = 9.21832687092980500000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8209999999999998 " " y[1] (analytic) = 6.93419208439903800E-2 " " y[1] (numeric) = 6.93419209081909200E-2 " " absolute error = 6.42005476558793500000000000E-11 " " relative error = 9.25854762522682300000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8199999999999998 " " y[1] (analytic) = 6.94593283834093600E-2 " " y[1] (numeric) = 6.94593284479978600E-2 " " absolute error = 6.4588501214046800000000000E-11 " " relative error = 9.298751185373400000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8189999999999998 " " y[1] (analytic) = 6.95768345495504100E-2 " " y[1] (numeric) = 6.95768346145264800E-2 " " absolute error = 6.49760800719434400000000000E-11 " " relative error = 9.33875197004967800000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" "WARNING: arctan of linear function has low precision in testing." x[1] = -0.8179999999999998 " " y[1] (analytic) = 6.96944393401157800E-2 " " y[1] (numeric) = 6.96944394054802700E-2 " " absolute error = 6.53644915971085500000000000E-11 " " relative error = 9.37872407268008100000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE" "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = arctan (0.1 * x + 0.2 ) ;" Iterations = 183 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Expected Time Remaining "= 0 Years 0 Days 1 Hours 35 Minutes 34 Seconds "Optimized Time Remaining "= 0 Years 0 Days 1 Hours 34 Minutes 52 Seconds "Expected Total Time "= 0 Years 0 Days 1 Hours 37 Minutes 53 Seconds "Time to Timeout " Unknown Percent Done = 3.0666666666666695 "%" (%o57) true (%o57) diffeq.max