##############ECHO OF PROBLEM#################
##############temp/tanh_sqrtpostode.ode#################
diff  (  y  ,  x  ,  1  )   =  tanh ( sqrt ( 2.0 * x  +  3.0 )  )  ; 
!
#BEGIN FIRST INPUT BLOCK
# Digits:=32; ELIMINATED in preodein.rb
max_terms=30 
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start=0.1 
x_end=5.0 
$array_y_init[0 + 1] = exact_soln_y(x_start)
$glob_look_poles=true 
$glob_max_h=0.1 
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
$glob_type_given_pole=1 
#  ELIMINATED in preodein.rb
$array_given_rad_poles[1][1]=-1.5 
#  ELIMINATED in preodein.rb
$array_given_rad_poles[1][2]=0.0 
#  ELIMINATED in preodein.rb
$array_given_ord_poles[1][1]=0.5 
#  ELIMINATED in preodein.rb
$array_given_ord_poles[1][2]=0.0 
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE  BLOCK
$glob_desired_digits_correct=16 
$glob_max_minutes=3.0 
$glob_subiter_method=3 
$glob_max_iter=100000000 
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
def exact_soln_y (x)
return(0.0) 
end
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   1.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               4900000.000000001
step_error                    1.5058465048420852e-21
est_needed_step_err           1.5058465048420852e-21
opt_iter                        1
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   1.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               4900000.000000001
step_error                    1.5058465048420852e-21
est_needed_step_err           1.5058465048420852e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      5.333536604452221e-166
estimated_step_error          5.333536604452221e-166
Double H and LOOP
opt_iter                        2
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   2.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               2450000.0000000005
step_error                    2.1295885499997994e-21
est_needed_step_err           2.1295885499997994e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      3.5792748051884397e-158
estimated_step_error          3.5792748051884397e-158
Double H and LOOP
opt_iter                        3
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   4.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               1225000.0000000002
step_error                    3.0116930096841704e-21
est_needed_step_err           3.0116930096841704e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      2.4020092907261174e-150
estimated_step_error          2.4020092907261174e-150
Double H and LOOP
opt_iter                        4
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   8.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               612500.0000000001
step_error                    4.259177099999599e-21
est_needed_step_err           4.259177099999599e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.6119593087647697e-142
estimated_step_error          1.6119593087647697e-142
Double H and LOOP
opt_iter                        5
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   1.6e-05
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               306250.00000000006
step_error                    6.023386019368341e-21
est_needed_step_err           6.023386019368341e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.0817651114404241e-134
estimated_step_error          1.0817651114404241e-134
Double H and LOOP
opt_iter                        6
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   3.2e-05
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               153125.00000000003
step_error                    8.518354199999198e-21
est_needed_step_err           8.518354199999198e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      7.259569638728824e-127
estimated_step_error          7.259569638728824e-127
Double H and LOOP
opt_iter                        7
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   6.4e-05
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               76562.50000000001
step_error                    1.2046772038736681e-20
est_needed_step_err           1.2046772038736681e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      4.871770242559357e-119
estimated_step_error          4.871770242559357e-119
Double H and LOOP
opt_iter                        8
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.000128
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               38281.25000000001
step_error                    1.7036708399998395e-20
est_needed_step_err           1.7036708399998395e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      3.269329977084842e-111
estimated_step_error          3.269329977084842e-111
Double H and LOOP
opt_iter                        9
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.000256
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               19140.625000000004
step_error                    2.4093544077473363e-20
est_needed_step_err           2.4093544077473363e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      2.1939300986958585e-103
estimated_step_error          2.1939300986958585e-103
Double H and LOOP
opt_iter                        10
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.000512
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               9570.312500000002
step_error                    3.407341679999679e-20
est_needed_step_err           3.407341679999679e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.4722140570703459e-95
estimated_step_error          1.4722140570703459e-95
Double H and LOOP
opt_iter                        11
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.001024
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               4785.156250000001
step_error                    4.8187088154946726e-20
est_needed_step_err           4.8187088154946726e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      9.878418647563098e-88
estimated_step_error          9.878418647563098e-88
Double H and LOOP
opt_iter                        12
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.002048
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               2392.5781250000005
step_error                    6.814683359999358e-20
est_needed_step_err           6.814683359999358e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      6.6273590995876485e-80
estimated_step_error          6.6273590995876485e-80
Double H and LOOP
opt_iter                        13
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.004096
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               1196.2890625000002
step_error                    9.637417630989345e-20
est_needed_step_err           9.637417630989345e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      4.4449499877800826e-72
estimated_step_error          4.4449499877800826e-72
Double H and LOOP
opt_iter                        14
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.008192
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               598.1445312500001
step_error                    1.3629366719998716e-19
est_needed_step_err           1.3629366719998716e-19
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      2.9794780426569276e-64
estimated_step_error          2.9794780426569276e-64
Double H and LOOP
opt_iter                        15
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.016384
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               299.07226562500006
step_error                    1.927483526197869e-19
est_needed_step_err           1.927483526197869e-19
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.9948429157191004e-56
estimated_step_error          1.9948429157191004e-56
Double H and LOOP
opt_iter                        16
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.032768
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               149.53613281250003
step_error                    2.7258733439997433e-19
est_needed_step_err           2.7258733439997433e-19
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.3325175019395825e-48
estimated_step_error          1.3325175019395825e-48
Double H and LOOP
opt_iter                        17
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.065536
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               74.76806640625001
step_error                    3.854967052395738e-19
est_needed_step_err           3.854967052395738e-19
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      8.860320865731363e-41
estimated_step_error          8.860320865731363e-41
Double H and LOOP
opt_iter                        18
SETTING H FOR MAX H
SETTING H FOR DISPLAY INTERVAL
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                             0.1 
y[1] (closed_form)               0.0 
y[1] (numeric)                   0.0 
absolute error                   0.0 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         -16 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           1.6 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.2 
y[1] (closed_form)               0.0 
y[1] (numeric)                   0.09456094207139262 
absolute error                   0.09456094207139262 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           1.7 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.30000000000000004 
y[1] (closed_form)               0.0 
y[1] (numeric)                   0.18967535843578154 
absolute error                   0.18967535843578154 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           1.8 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.4 
y[1] (closed_form)               0.0 
y[1] (numeric)                   0.2852744451025021 
absolute error                   0.2852744451025021 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           1.9 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.5 
y[1] (closed_form)               0.0 
y[1] (numeric)                   0.3812996744686154 
absolute error                   0.3812996744686154 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           2.0 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.6 
y[1] (closed_form)               0.0 
y[1] (numeric)                   0.4777009870006675 
absolute error                   0.4777009870006675 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           2.1 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.7 
y[1] (closed_form)               0.0 
y[1] (numeric)                   0.574435350577862 
absolute error                   0.574435350577862 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           2.2 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.7999999999999999 
y[1] (closed_form)               0.0 
y[1] (numeric)                   0.6714656026487241 
absolute error                   0.6714656026487241 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           2.3 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.8999999999999999 
y[1] (closed_form)               0.0 
y[1] (numeric)                   0.7687595122370581 
absolute error                   0.7687595122370581 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           2.4 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.9999999999999999 
y[1] (closed_form)               0.0 
y[1] (numeric)                   0.8662890144920525 
absolute error                   0.8662890144920525 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           2.5 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.0999999999999999 
y[1] (closed_form)               0.0 
y[1] (numeric)                   0.9640295818423824 
absolute error                   0.9640295818423824 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           2.5999999999999996 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.2 
y[1] (closed_form)               0.0 
y[1] (numeric)                   1.061959704169107 
absolute error                   1.061959704169107 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           2.7 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.3 
y[1] (closed_form)               0.0 
y[1] (numeric)                   1.1600604566264032 
absolute error                   1.1600604566264032 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           2.8 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.4000000000000001 
y[1] (closed_form)               0.0 
y[1] (numeric)                   1.2583151384107858 
absolute error                   1.2583151384107858 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           2.9000000000000004 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.5000000000000002 
y[1] (closed_form)               0.0 
y[1] (numeric)                   1.356708969326004 
absolute error                   1.356708969326004 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           3.0 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.6000000000000003 
y[1] (closed_form)               0.0 
y[1] (numeric)                   1.4552288337077086 
absolute error                   1.4552288337077086 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           3.1000000000000005 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.7000000000000004 
y[1] (closed_form)               0.0 
y[1] (numeric)                   1.5538630633708266 
absolute error                   1.5538630633708266 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           3.2 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.8000000000000005 
y[1] (closed_form)               0.0 
y[1] (numeric)                   1.6526012528766618 
absolute error                   1.6526012528766618 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           3.3000000000000007 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.9000000000000006 
y[1] (closed_form)               0.0 
y[1] (numeric)                   1.7514341016982442 
absolute error                   1.7514341016982442 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           3.4000000000000004 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.0000000000000004 
y[1] (closed_form)               0.0 
y[1] (numeric)                   1.850353278874289 
absolute error                   1.850353278874289 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           3.5000000000000004 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.1000000000000005 
y[1] (closed_form)               0.0 
y[1] (numeric)                   1.9493513065461718 
absolute error                   1.9493513065461718 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           3.6000000000000005 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.2000000000000006 
y[1] (closed_form)               0.0 
y[1] (numeric)                   2.0484214594150645 
absolute error                   2.0484214594150645 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           3.7000000000000006 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.3000000000000007 
y[1] (closed_form)               0.0 
y[1] (numeric)                   2.1475576776730834 
absolute error                   2.1475576776730834 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           3.8000000000000007 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.400000000000001 
y[1] (closed_form)               0.0 
y[1] (numeric)                   2.2467544913799142 
absolute error                   2.2467544913799142 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           3.900000000000001 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.500000000000001 
y[1] (closed_form)               0.0 
y[1] (numeric)                   2.346006954595585 
absolute error                   2.346006954595585 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           4.000000000000001 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.600000000000001 
y[1] (closed_form)               0.0 
y[1] (numeric)                   2.445310587856914 
absolute error                   2.445310587856914 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           4.100000000000001 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.700000000000001 
y[1] (closed_form)               0.0 
y[1] (numeric)                   2.5446613278121486 
absolute error                   2.5446613278121486 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           4.200000000000001 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.800000000000001 
y[1] (closed_form)               0.0 
y[1] (numeric)                   2.6440554830152023 
absolute error                   2.6440554830152023 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           4.300000000000001 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.9000000000000012 
y[1] (closed_form)               0.0 
y[1] (numeric)                   2.7434896950354206 
absolute error                   2.7434896950354206 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           4.400000000000001 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.0000000000000013 
y[1] (closed_form)               0.0 
y[1] (numeric)                   2.8429609041670743 
absolute error                   2.8429609041670743 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           4.500000000000002 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.1000000000000014 
y[1] (closed_form)               0.0 
y[1] (numeric)                   2.9424663191296174 
absolute error                   2.9424663191296174 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           4.600000000000001 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.2000000000000015 
y[1] (closed_form)               0.0 
y[1] (numeric)                   3.0420033902390937 
absolute error                   3.0420033902390937 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           4.700000000000001 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.3000000000000016 
y[1] (closed_form)               0.0 
y[1] (numeric)                   3.141569785606022 
absolute error                   3.141569785606022 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           4.800000000000002 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.4000000000000017 
y[1] (closed_form)               0.0 
y[1] (numeric)                   3.241163369978171 
absolute error                   3.241163369978171 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           4.900000000000002 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.5000000000000018 
y[1] (closed_form)               0.0 
y[1] (numeric)                   3.3407821858999007 
absolute error                   3.3407821858999007 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           5.000000000000002 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.600000000000002 
y[1] (closed_form)               0.0 
y[1] (numeric)                   3.44042443690485 
absolute error                   3.44042443690485 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           5.100000000000001 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.700000000000002 
y[1] (closed_form)               0.0 
y[1] (numeric)                   3.5400884724970525 
absolute error                   3.5400884724970525 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           5.200000000000002 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.800000000000002 
y[1] (closed_form)               0.0 
y[1] (numeric)                   3.6397727747082027 
absolute error                   3.6397727747082027 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           5.3000000000000025 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.900000000000002 
y[1] (closed_form)               0.0 
y[1] (numeric)                   3.739475946046632 
absolute error                   3.739475946046632 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           5.400000000000002 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.000000000000002 
y[1] (closed_form)               0.0 
y[1] (numeric)                   3.8391966986774277 
absolute error                   3.8391966986774277 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           5.500000000000002 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.100000000000001 
y[1] (closed_form)               0.0 
y[1] (numeric)                   3.9389338446935853 
absolute error                   3.9389338446935853 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           5.600000000000001 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.200000000000001 
y[1] (closed_form)               0.0 
y[1] (numeric)                   4.038686287355694 
absolute error                   4.038686287355694 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           5.700000000000001 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.300000000000001 
y[1] (closed_form)               0.0 
y[1] (numeric)                   4.138453013192855 
absolute error                   4.138453013192855 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           5.800000000000001 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.4 
y[1] (closed_form)               0.0 
y[1] (numeric)                   4.238233084870636 
absolute error                   4.238233084870636 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           5.9 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.5 
y[1] (closed_form)               0.0 
y[1] (numeric)                   4.338025634743251 
absolute error                   4.338025634743251 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           6.0 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.6 
y[1] (closed_form)               0.0 
y[1] (numeric)                   4.437829859017002 
absolute error                   4.437829859017002 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           6.1 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.699999999999999 
y[1] (closed_form)               0.0 
y[1] (numeric)                   4.5376450124606125 
absolute error                   4.5376450124606125 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           6.199999999999999 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.799999999999999 
y[1] (closed_form)               0.0 
y[1] (numeric)                   4.637470403605537 
absolute error                   4.637470403605537 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           6.299999999999999 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.899999999999999 
y[1] (closed_form)               0.0 
y[1] (numeric)                   4.737305390385884 
absolute error                   4.737305390385884 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           6.399999999999999 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.999999999999998 
y[1] (closed_form)               0.0 
y[1] (numeric)                   4.837149376173267 
absolute error                   4.837149376173267 
relative error                   -1.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   -16 
h                                0.1 
Radius of convergence (given) for eq  1           6.499999999999998 
Order of pole (given)                             0.5 
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff  (  y  ,  x  ,  1  )   =  tanh ( sqrt ( 2.0 * x  +  3.0 )  )  ; 
Iterations                      50 
Total Elapsed Time              0 Seconds
Elapsed Time(since restart)     0 Seconds
Time to Timeout                 3 Minutes 0.0 Seconds
Percent Done                    104.08163265306118%