##############ECHO OF PROBLEM#################
##############temp/sub_c_sinpostode.ode#################
diff  (  y  ,  x  ,  1  )   =  1.0  -  sin ( x )  ; 
!
#BEGIN FIRST INPUT BLOCK
# Digits:=32; ELIMINATED in preodein.rb
max_terms=40 
!
#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 
#  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=3 
#  ELIMINATED in preodein.rb
#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(2.0 + cos(x) + x) 
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                    1.129384878631564e-21
est_needed_step_err           1.129384878631564e-21
opt_iter                        1
NO POLE (given) for Equation 1
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                      3.095004165278026
$glob_desired_digits_correct  16
estimated_h                   1.0e-06
estimated_answer              3.095004165278026
desired_abs_gbl_error         3.0950041652780257e-16
range                         4.9
estimated_steps               4900000.000000001
step_error                    3.4954509035667076e-21
est_needed_step_err           3.4954509035667076e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      2.674790358513323e-258
estimated_step_error          2.674790358513323e-258
Double H and LOOP
opt_iter                        2
NO POLE (given) for Equation 1
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                      3.095004165278026
$glob_desired_digits_correct  16
estimated_h                   2.0e-06
estimated_answer              3.095004165278026
desired_abs_gbl_error         3.0950041652780257e-16
range                         4.9
estimated_steps               2450000.0000000005
step_error                    4.943314074433328e-21
est_needed_step_err           4.943314074433328e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.8381019356630983e-247
estimated_step_error          1.8381019356630983e-247
Double H and LOOP
opt_iter                        3
NO POLE (given) for Equation 1
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                      3.095004165278026
$glob_desired_digits_correct  16
estimated_h                   4.0e-06
estimated_answer              3.095004165278026
desired_abs_gbl_error         3.0950041652780257e-16
range                         4.9
estimated_steps               1225000.0000000002
step_error                    6.990901807133415e-21
est_needed_step_err           6.990901807133415e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.2631340286366648e-236
estimated_step_error          1.2631340286366648e-236
Double H and LOOP
opt_iter                        4
NO POLE (given) for Equation 1
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                      3.095004165278026
$glob_desired_digits_correct  16
estimated_h                   8.0e-06
estimated_answer              3.095004165278026
desired_abs_gbl_error         3.0950041652780257e-16
range                         4.9
estimated_steps               612500.0000000001
step_error                    9.886628148866656e-21
est_needed_step_err           9.886628148866656e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      8.68019090245767e-226
estimated_step_error          8.68019090245767e-226
Double H and LOOP
opt_iter                        5
NO POLE (given) for Equation 1
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                      3.095004165278026
$glob_desired_digits_correct  16
estimated_h                   1.6e-05
estimated_answer              3.095004165278026
desired_abs_gbl_error         3.0950041652780257e-16
range                         4.9
estimated_steps               306250.00000000006
step_error                    1.398180361426683e-20
est_needed_step_err           1.398180361426683e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      5.964981703152477e-215
estimated_step_error          5.964981703152477e-215
Double H and LOOP
opt_iter                        6
NO POLE (given) for Equation 1
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                      3.095004165278026
$glob_desired_digits_correct  16
estimated_h                   3.2e-05
estimated_answer              3.095004165278026
desired_abs_gbl_error         3.0950041652780257e-16
range                         4.9
estimated_steps               153125.00000000003
step_error                    1.9773256297733312e-20
est_needed_step_err           1.9773256297733312e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      4.099104124878063e-204
estimated_step_error          4.099104124878063e-204
Double H and LOOP
opt_iter                        7
NO POLE (given) for Equation 1
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                      3.095004165278026
$glob_desired_digits_correct  16
estimated_h                   6.4e-05
estimated_answer              3.095004165278026
desired_abs_gbl_error         3.0950041652780257e-16
range                         4.9
estimated_steps               76562.50000000001
step_error                    2.796360722853366e-20
est_needed_step_err           2.796360722853366e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      2.8168827832596326e-193
estimated_step_error          2.8168827832596326e-193
Double H and LOOP
opt_iter                        8
NO POLE (given) for Equation 1
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                      3.095004165278026
$glob_desired_digits_correct  16
estimated_h                   0.000128
estimated_answer              3.095004165278026
desired_abs_gbl_error         3.0950041652780257e-16
range                         4.9
estimated_steps               38281.25000000001
step_error                    3.9546512595466624e-20
est_needed_step_err           3.9546512595466624e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.9357469409419875e-182
estimated_step_error          1.9357469409419875e-182
Double H and LOOP
opt_iter                        9
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.09933466539749951 
Order of pole (three term test)                   32.00996671107996 
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE ACCURACY
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                             0.1 
y[1] (closed_form)               3.095004165278026 
y[1] (numeric)                   3.095004165278026 
absolute error                   0.0 
relative error                   0.0%
Desired digits                   16 
Estimated correct digits         14 
Correct digits                   16 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             0.2000959999999943 
y[1] (closed_form)               3.1801435010693635 
y[1] (numeric)                   3.1801435010693697 
absolute error                   6.217248937900877e-15 
relative error                   1.9550215063597752e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             0.3000639999999968 
y[1] (closed_form)               3.2553815738758614 
y[1] (numeric)                   3.2553815738758645 
absolute error                   3.1086244689504383e-15 
relative error                   9.549186165753547e-14%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   16 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             0.40003200000001005 
y[1] (closed_form)               3.3210805321443564 
y[1] (numeric)                   3.3210805321443484 
absolute error                   7.993605777301127e-15 
relative error                   2.4069292207556957e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             0.5000000000000233 
y[1] (closed_form)               3.377582561890385 
y[1] (numeric)                   3.3775825618903683 
absolute error                   1.687538997430238e-14 
relative error                   4.996292367419574e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             0.6000960000000366 
y[1] (closed_form)               3.425377405429185 
y[1] (numeric)                   3.4253774054291655 
absolute error                   1.9539925233402755e-14 
relative error                   5.704459077248595e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             0.7000640000000499 
y[1] (closed_form)               3.4648649557861546 
y[1] (numeric)                   3.464864955786125 
absolute error                   2.9753977059954195e-14 
relative error                   8.587341047813858e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             0.8000320000000631 
y[1] (closed_form)               3.4967157535955646 
y[1] (numeric)                   3.4967157535955296 
absolute error                   3.5083047578154947e-14 
relative error                   1.003314254013359e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             0.9000000000000764 
y[1] (closed_form)               3.5216099682706807 
y[1] (numeric)                   3.5216099682706408 
absolute error                   3.9968028886505635e-14 
relative error                   1.1349362719498521e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             1.0000960000000896 
y[1] (closed_form)               3.540317522164023 
y[1] (numeric)                   3.5403175221639827 
absolute error                   4.04121180963557e-14 
relative error                   1.141482871052022e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             1.1000640000000161 
y[1] (closed_form)               3.5536030832256094 
y[1] (numeric)                   3.553603083225581 
absolute error                   2.842170943040401e-14 
relative error                   7.997997740537076e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             1.2000319999999427 
y[1] (closed_form)               3.5623599290403964 
y[1] (numeric)                   3.562359929040372 
absolute error                   2.4424906541753444e-14 
relative error                   6.856383697402765e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             1.2999999999998693 
y[1] (closed_form)               3.567498828624583 
y[1] (numeric)                   3.5674988286245566 
absolute error                   2.6201263381153694e-14 
relative error                   7.344435034125956e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             1.4000959999997957 
y[1] (closed_form)               3.5699685389430957 
y[1] (numeric)                   3.5699685389430678 
absolute error                   2.7977620220553945e-14 
relative error                   7.836937473078359e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             1.5000639999997223 
y[1] (closed_form)               3.570737361843733 
y[1] (numeric)                   3.5707373618437006 
absolute error                   3.241851231905457e-14 
relative error                   9.078940575544159e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             1.6000319999996488 
y[1] (closed_form)               3.5708004913583693 
y[1] (numeric)                   3.570800491358335 
absolute error                   3.419486915845482e-14 
relative error                   9.576247466418024e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             1.6999999999995754 
y[1] (closed_form)               3.5711555057044717 
y[1] (numeric)                   3.5711555057044375 
absolute error                   3.419486915845482e-14 
relative error                   9.575295476165298e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             1.8000959999995019 
y[1] (closed_form)               3.5728004169814263 
y[1] (numeric)                   3.572800416981389 
absolute error                   3.730349362740526e-14 
relative error                   1.0440967665057006e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             1.9000639999994284 
y[1] (closed_form)               3.576713870592992 
y[1] (numeric)                   3.576713870592961 
absolute error                   3.108624468950438e-14 
relative error                   8.691286419383197e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             2.000031999999355 
y[1] (closed_form)               3.583856066148213 
y[1] (numeric)                   3.5838560661481833 
absolute error                   2.9753977059954195e-14 
relative error                   8.302224339029495e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             2.099999999999455 
y[1] (closed_form)               3.595153895400068 
y[1] (numeric)                   3.5951538954000246 
absolute error                   4.3520742565306136e-14 
relative error                   1.210539070969677e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             2.2000959999995553 
y[1] (closed_form)               3.611517269801735 
y[1] (numeric)                   3.6115172698016784 
absolute error                   5.639932965095795e-14 
relative error                   1.5616519439779438e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             2.3000639999996553 
y[1] (closed_form)               3.633740254951075 
y[1] (numeric)                   3.633740254950998 
absolute error                   7.682743330406083e-14 
relative error                   2.114279720444555e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             2.4000319999997553 
y[1] (closed_form)               3.6626166700144465 
y[1] (numeric)                   3.6626166700143443 
absolute error                   1.021405182655144e-13 
relative error                   2.788730775506232e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             2.4999999999998552 
y[1] (closed_form)               3.6988563844530082 
y[1] (numeric)                   3.6988563844528723 
absolute error                   1.3589129821411916e-13 
relative error                   3.673873329748512e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             2.6000959999999553 
y[1] (closed_form)               3.7431577624479555 
y[1] (numeric)                   3.743157762447778 
absolute error                   1.7763568394002505e-13 
relative error                   4.745610396711001e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             2.7000640000000553 
y[1] (closed_form)               3.7959645075221937 
y[1] (numeric)                   3.7959645075219663 
absolute error                   2.2737367544323206e-13 
relative error                   5.989878856682189e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             2.8000320000001553 
y[1] (closed_form)               3.8577989401930597 
y[1] (numeric)                   3.8577989401927764 
absolute error                   2.8332891588433995e-13 
relative error                   7.344315250140046e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             2.9000000000002553 
y[1] (closed_form)               3.9290418348506035 
y[1] (numeric)                   3.9290418348502474 
absolute error                   3.561595462997502e-13 
relative error                   9.064793943923294e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             3.0000960000003554 
y[1] (closed_form)               4.010089960440992 
y[1] (numeric)                   4.01008996044055 
absolute error                   4.4231285301066237e-13 
relative error                   1.1029998263730247e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             3.1000640000004553 
y[1] (closed_form)               4.100926190610991 
y[1] (numeric)                   4.100926190610451 
absolute error                   5.400124791776761e-13 
relative error                   1.3168061410469336e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             3.2000320000005553 
y[1] (closed_form)               4.201739092689551 
y[1] (numeric)                   4.201739092688897 
absolute error                   6.536993168992922e-13 
relative error                   1.5557827425235402e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             3.3000000000006553 
y[1] (closed_form)               4.312520230091893 
y[1] (numeric)                   4.31252023009114 
absolute error                   7.531752999057062e-13 
relative error                   1.7464852562318466e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             3.4000960000007554 
y[1] (closed_form)               4.43332234382225 
y[1] (numeric)                   4.4333223438213745 
absolute error                   8.757439218243235e-13 
relative error                   1.975367126292217e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             3.5000640000008554 
y[1] (closed_form)               4.563629764754779 
y[1] (numeric)                   4.563629764753769 
absolute error                   1.0098588631990424e-12 
relative error                   2.2128413461544374e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             3.6000320000009554 
y[1] (closed_form)               4.703287744780555 
y[1] (numeric)                   4.703287744779398 
absolute error                   1.1572964808692632e-12 
relative error                   2.460611690521308e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             3.7000000000010553 
y[1] (closed_form)               4.851899968291207 
y[1] (numeric)                   4.851899968289895 
absolute error                   1.311839525897085e-12 
relative error                   2.703764575672203e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             3.8000960000011554 
y[1] (closed_form)               5.009187030089665 
y[1] (numeric)                   5.009187030088199 
absolute error                   1.4654943925052066e-12 
relative error                   2.925613245626754e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             3.9000640000012554 
y[1] (closed_form)               5.174175714322846 
y[1] (numeric)                   5.174175714321218 
absolute error                   1.6280310433103296e-12 
relative error                   3.146454881313193e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             4.000032000001355 
y[1] (closed_form)               5.3464125971532805 
y[1] (numeric)                   5.346412597151479 
absolute error                   1.801225835151854e-12 
relative error                   3.369036344316045e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             4.100000000001455 
y[1] (closed_form)               5.5251760534693775 
y[1] (numeric)                   5.525176053467399 
absolute error                   1.978861519091879e-12 
relative error                   3.581535683101553e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             4.2000960000015555 
y[1] (closed_form)               5.709918852195357 
y[1] (numeric)                   5.709918852193204 
absolute error                   2.1529444893531036e-12 
relative error                   3.770534301946054e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             4.3000640000016555 
y[1] (closed_form)               5.899323463363945 
y[1] (numeric)                   5.899323463361602 
absolute error                   2.3430146711689304e-12 
relative error                   3.971666727073961e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             4.400032000001755 
y[1] (closed_form)               6.09272958144872 
y[1] (numeric)                   6.0927295814461795 
absolute error                   2.540190280342358e-12 
relative error                   4.169215532028184e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             4.500000000001855 
y[1] (closed_form)               6.28920420057289 
y[1] (numeric)                   6.289204200570154 
absolute error                   2.7355895326763857e-12 
relative error                   4.349659265996163e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             4.6000960000019555 
y[1] (closed_form)               6.488038867921845 
y[1] (numeric)                   6.488038867918915 
absolute error                   2.930100606590713e-12 
relative error                   4.516157603613803e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             4.7000640000020555 
y[1] (closed_form)               6.687739331655033 
y[1] (numeric)                   6.6877393316518985 
absolute error                   3.134381643121742e-12 
relative error                   4.686758092208818e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             4.8000320000021555 
y[1] (closed_form)               6.887562860666427 
y[1] (numeric)                   6.887562860663094 
absolute error                   3.33333360913457e-12 
relative error                   4.839641650562073e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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]                             4.900000000002255 
y[1] (closed_form)               7.086512369427046 
y[1] (numeric)                   7.086512369423512 
absolute error                   3.5340619319867983e-12 
relative error                   4.987025701434755e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
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  )   =  1.0  -  sin ( x )  ; 
Iterations                      38282 
Total Elapsed Time              6 Seconds
Elapsed Time(since restart)     6 Seconds
Time to Timeout                 2 Minutes 54.0 Seconds
Percent Done                    100.00457142861951%