##############ECHO OF PROBLEM#################
##############temp/subpostode.ode#################
diff  (  y  ,  x  ,  1  )   =  sin  (  x  )   -  cos  (  x  )  ; 
!
#BEGIN FIRST INPUT BLOCK
# Digits:=32; ELIMINATED in preodein.rb
max_terms=40 
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start=0.0 
x_end=10.0 
$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
#  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) - sin(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                         10.0
estimated_steps               10000000.0
step_error                    7.905694150420948e-22
est_needed_step_err           7.905694150420948e-22
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                      1.0
$glob_desired_digits_correct  16
estimated_h                   1.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         10.0
estimated_steps               10000000.0
step_error                    7.905694150420948e-22
est_needed_step_err           7.905694150420948e-22
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      2.688220302613934e-258
estimated_step_error          2.688220302613934e-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                      1.0
$glob_desired_digits_correct  16
estimated_h                   2.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         10.0
estimated_steps               5000000.0
step_error                    1.1180339887498947e-21
est_needed_step_err           1.1180339887498947e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.8473309504311414e-247
estimated_step_error          1.8473309504311414e-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                      1.0
$glob_desired_digits_correct  16
estimated_h                   4.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         10.0
estimated_steps               2500000.0
step_error                    1.5811388300841896e-21
est_needed_step_err           1.5811388300841896e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.2694761970286187e-236
estimated_step_error          1.2694761970286187e-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                      1.0
$glob_desired_digits_correct  16
estimated_h                   8.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         10.0
estimated_steps               1250000.0
step_error                    2.2360679774997895e-21
est_needed_step_err           2.2360679774997895e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      8.723774470416644e-226
estimated_step_error          8.723774470416644e-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                      1.0
$glob_desired_digits_correct  16
estimated_h                   1.6e-05
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         10.0
estimated_steps               625000.0
step_error                    3.1622776601683792e-21
est_needed_step_err           3.1622776601683792e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      5.994932815799572e-215
estimated_step_error          5.994932815799572e-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                      1.0
$glob_desired_digits_correct  16
estimated_h                   3.2e-05
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         10.0
estimated_steps               312500.0
step_error                    4.472135954999579e-21
est_needed_step_err           4.472135954999579e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      4.119687352434481e-204
estimated_step_error          4.119687352434481e-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                      1.0
$glob_desired_digits_correct  16
estimated_h                   6.4e-05
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         10.0
estimated_steps               156250.0
step_error                    6.3245553203367584e-21
est_needed_step_err           6.3245553203367584e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      2.831028815978219e-193
estimated_step_error          2.831028815978219e-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                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.000128
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         10.0
estimated_steps               78125.0
step_error                    8.944271909999158e-21
est_needed_step_err           8.944271909999158e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.945469871146985e-182
estimated_step_error          1.945469871146985e-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  0.49999999999993255 
Order of pole (three term test)                   32.50000000000047 
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE ACCURACY
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                             0.0 
y[1] (closed_form)               1.0 
y[1] (numeric)                   1.0 
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]                             0.1000960000000016 
y[1] (closed_form)               0.9050764867284197 
y[1] (numeric)                   0.905076486728421 
absolute error                   1.3322676295501878e-15 
relative error                   1.4719945210000274e-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]                             0.20006399999999588 
y[1] (closed_form)               0.8212140843539748 
y[1] (numeric)                   0.821214084353972 
absolute error                   2.7755575615628914e-15 
relative error                   3.3798221614115904e-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]                             0.3000319999999983 
y[1] (closed_form)               0.7491221907324588 
y[1] (numeric)                   0.7491221907324581 
absolute error                   6.661338147750939e-16 
relative error                   8.892191728078132e-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]                             0.40000000000001157 
y[1] (closed_form)               0.6895206636884582 
y[1] (numeric)                   0.6895206636884649 
absolute error                   6.661338147750939e-15 
relative error                   9.660824538770733e-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]                             0.5000960000000249 
y[1] (closed_form)               0.642953682684331 
y[1] (numeric)                   0.6429536826843425 
absolute error                   1.1546319456101628e-14 
relative error                   1.795824453154348e-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]                             0.6000640000000381 
y[1] (closed_form)               0.610005230180906 
y[1] (numeric)                   0.6100052301809218 
absolute error                   1.5765166949677223e-14 
relative error                   2.584431439219272e-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]                             0.7000320000000514 
y[1] (closed_form)               0.5909362662152521 
y[1] (numeric)                   0.5909362662152707 
absolute error                   1.865174681370263e-14 
relative error                   3.156304305565944e-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]                             0.8000000000000647 
y[1] (closed_form)               0.5859371997533132 
y[1] (numeric)                   0.5859371997533335 
absolute error                   2.0317081350640365e-14 
relative error                   3.4674503273036955e-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]                             0.900096000000078 
y[1] (closed_form)               0.5950786534021603 
y[1] (numeric)                   0.5950786534021798 
absolute error                   1.9539925233402755e-14 
relative error                   3.283586988323285e-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]                             1.000064000000091 
y[1] (closed_form)               0.6182459869493019 
y[1] (numeric)                   0.6182459869493175 
absolute error                   1.5654144647214707e-14 
relative error                   2.5320252743506117e-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]                             1.1000320000000177 
y[1] (closed_form)               0.6552105227611684 
y[1] (numeric)                   0.6552105227612098 
absolute error                   4.141131881851834e-14 
relative error                   6.320307348545626e-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]                             1.1999999999999442 
y[1] (closed_form)               0.7056031595560682 
y[1] (numeric)                   0.7056031595561456 
absolute error                   7.738254481637341e-14 
relative error                   1.0966864840154458e-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]                             1.3000959999998707 
y[1] (closed_form)               0.7690098133289898 
y[1] (numeric)                   0.7690098133291143 
absolute error                   1.2456702336294256e-13 
relative error                   1.6198365899090495e-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]                             1.4000639999997972 
y[1] (closed_form)               0.8446353203629654 
y[1] (numeric)                   0.8446353203631463 
absolute error                   1.80855330711438e-13 
relative error                   2.141223867286523e-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]                             1.5000319999997238 
y[1] (closed_form)               0.9317974685240344 
y[1] (numeric)                   0.9317974685242798 
absolute error                   2.453592884421596e-13 
relative error                   2.633182603842102e-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]                             1.5999999999996504 
y[1] (closed_form)               1.029625919259424 
y[1] (numeric)                   1.029625919259739 
absolute error                   3.1508129438861943e-13 
relative error                   3.060153095361537e-11%
Desired digits                   16 
Estimated correct digits         12 
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]                             1.7000959999995768 
y[1] (closed_form)               1.1372872567115486 
y[1] (numeric)                   1.1372872567119403 
absolute error                   3.9168668308775523e-13 
relative error                   3.444043541121811e-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]                             1.8000639999995034 
y[1] (closed_form)               1.2534313325258095 
y[1] (numeric)                   1.253431332526289 
absolute error                   4.793943020331426e-13 
relative error                   3.8246554844540825e-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]                             1.90003199999943 
y[1] (closed_form)               1.3770301063632853 
y[1] (numeric)                   1.3770301063638533 
absolute error                   5.679900993982301e-13 
relative error                   4.1247471407744524e-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]                             1.9999999999993565 
y[1] (closed_form)               1.5068494097206078 
y[1] (numeric)                   1.506849409721271 
absolute error                   6.632472349110685e-13 
relative error                   4.4015495552010365e-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]                             2.1000959999994566 
y[1] (closed_form)               1.6417680729266162 
y[1] (numeric)                   1.6417680729271469 
absolute error                   5.306866057708248e-13 
relative error                   3.232409099202561e-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]                             2.2000639999995566 
y[1] (closed_form)               1.7800941217269743 
y[1] (numeric)                   1.7800941217273678 
absolute error                   3.934630399271555e-13 
relative error                   2.210349638958606e-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]                             2.3000319999996566 
y[1] (closed_form)               1.92061599254275 
y[1] (numeric)                   1.9206159925430004 
absolute error                   2.504663143554353e-13 
relative error                   1.3040936622829893e-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]                             2.3999999999997566 
y[1] (closed_form)               2.0619305349897505 
y[1] (numeric)                   2.0619305349898633 
absolute error                   1.127986593019159e-13 
relative error                   5.470536343867501e-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]                             2.5000959999998567 
y[1] (closed_form)               2.2028058336215866 
y[1] (numeric)                   2.202805833621564 
absolute error                   2.2648549702353193e-14 
relative error                   1.0281682278422694e-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]                             2.6000639999999566 
y[1] (closed_form)               2.3414752138162145 
y[1] (numeric)                   2.3414752138160497 
absolute error                   1.6475709685437323e-13 
relative error                   7.036465553092344e-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]                             2.7000320000000566 
y[1] (closed_form)               2.4767348680039447 
y[1] (numeric)                   2.476734868003645 
absolute error                   2.9976021664879227e-13 
relative error                   1.2103040197046834e-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]                             2.8000000000001566 
y[1] (closed_form)               2.6072341905129535 
y[1] (numeric)                   2.6072341905125223 
absolute error                   4.312106227644108e-13 
relative error                   1.65390061365977e-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]                             2.9000960000002567 
y[1] (closed_form)               2.731825012483485 
y[1] (numeric)                   2.731825012482928 
absolute error                   5.568878691519785e-13 
relative error                   2.038519548679713e-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]                             3.0000640000003567 
y[1] (closed_form)               2.8489448780027393 
y[1] (numeric)                   2.848944878002067 
absolute error                   6.723510637129948e-13 
relative error                   2.360000254495441e-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]                             3.1000320000004566 
y[1] (closed_form)               2.957587790256197 
y[1] (numeric)                   2.9575877902554164 
absolute error                   7.807088309164101e-13 
relative error                   2.6396810045282957e-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]                             3.2000000000005566 
y[1] (closed_form)               3.056668919222856 
y[1] (numeric)                   3.0566689192219756 
absolute error                   8.806289031326742e-13 
relative error                   2.8810084651123092e-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]                             3.3000960000006567 
y[1] (closed_form)               3.1453051132466103 
y[1] (numeric)                   3.1453051132456413 
absolute error                   9.690026558928366e-13 
relative error                   3.080790641937513e-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]                             3.4000640000007567 
y[1] (closed_form)               3.222384812557244 
y[1] (numeric)                   3.222384812556201 
absolute error                   1.043165553937797e-12 
relative error                   3.237246991336066e-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]                             3.5000320000008567 
y[1] (closed_form)               3.287258655872555 
y[1] (numeric)                   3.287258655871451 
absolute error                   1.1040057756872557e-12 
relative error                   3.358439025523574e-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]                             3.6000000000009567 
y[1] (closed_form)               3.339278859629434 
y[1] (numeric)                   3.339278859628278 
absolute error                   1.155964213239713e-12 
relative error                   3.461718118887479e-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]                             3.7000960000010568 
y[1] (closed_form)               3.3779667196031777 
y[1] (numeric)                   3.3779667196019814 
absolute error                   1.1963763313360687e-12 
relative error                   3.54170550110278e-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]                             3.8000640000011567 
y[1] (closed_form)               3.4028370630128904 
y[1] (numeric)                   3.402837063011664 
absolute error                   1.2261303083960229e-12 
relative error                   3.603258944494981e-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]                             3.9000320000012567 
y[1] (closed_form)               3.4136996839769886 
y[1] (numeric)                   3.413699683975751 
absolute error                   1.2376766278521245e-12 
relative error                   3.6256166108033875e-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]                             4.000000000001356 
y[1] (closed_form)               3.4104461161714004 
y[1] (numeric)                   3.4104461161701694 
absolute error                   1.2310152897043736e-12 
relative error                   3.6095432907361785e-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]                             4.100096000001456 
y[1] (closed_form)               3.393077679674156 
y[1] (numeric)                   3.3930776796729463 
absolute error                   1.2096990076315706e-12 
relative error                   3.565196915113775e-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]                             4.200064000001556 
y[1] (closed_form)               3.3618121868078004 
y[1] (numeric)                   3.3618121868066213 
absolute error                   1.1790568521519162e-12 
relative error                   3.5072061930725714e-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]                             4.300032000001656 
y[1] (closed_form)               3.316948616417824 
y[1] (numeric)                   3.3169486164166817 
absolute error                   1.142197447734361e-12 
relative error                   3.443518666767561e-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]                             4.400000000001756 
y[1] (closed_form)               3.2589349438668043 
y[1] (numeric)                   3.258934943865715 
absolute error                   1.0893508317622036e-12 
relative error                   3.3426590297923e-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]                             4.500096000001856 
y[1] (closed_form)               3.1882523051242098 
y[1] (numeric)                   3.18825230512319 
absolute error                   1.0196288258157438e-12 
relative error                   3.198080729611581e-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]                             4.600064000001956 
y[1] (closed_form)               3.105787109839557 
y[1] (numeric)                   3.105787109838622 
absolute error                   9.348077867343818e-13 
relative error                   3.0098900976592485e-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]                             4.700032000002056 
y[1] (closed_form)               3.0122803193996512 
y[1] (numeric)                   3.0122803193988124 
absolute error                   8.388845174067683e-13 
relative error                   2.7848819779626564e-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]                             4.800000000002156 
y[1] (closed_form)               2.9086656253940575 
y[1] (numeric)                   2.9086656253933216 
absolute error                   7.358558207215538e-13 
relative error                   2.5298742292588623e-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]                             4.900096000002256 
y[1] (closed_form)               2.7958280188933227 
y[1] (numeric)                   2.7958280188927 
absolute error                   6.226130722097878e-13 
relative error                   2.2269362349985954e-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]                             5.000064000002356 
y[1] (closed_form)               2.6751825622806535 
y[1] (numeric)                   2.6751825622801584 
absolute error                   4.951594689828198e-13 
relative error                   1.8509371134681933e-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]                             5.100032000002456 
y[1] (closed_form)               2.547795217973462 
y[1] (numeric)                   2.5477952179730976 
absolute error                   3.645972412869014e-13 
relative error                   1.4310304011674263e-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]                             5.200000000002556 
y[1] (closed_form)               2.41493798441632 
y[1] (numeric)                   2.414937984416086 
absolute error                   2.34035013590983e-13 
relative error                   9.691139693905979e-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]                             5.3000960000026565 
y[1] (closed_form)               2.2777599871500027 
y[1] (numeric)                   2.2777599871499024 
absolute error                   1.0036416142611415e-13 
relative error                   4.40626589246976e-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]                             5.400064000002756 
y[1] (closed_form)               2.1379815340555 
y[1] (numeric)                   2.1379815340555384 
absolute error                   3.8191672047105385e-14 
relative error                   1.7863424654870738e-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]                             5.500032000002856 
y[1] (closed_form)               1.9968252965535067 
y[1] (numeric)                   1.9968252965536848 
absolute error                   1.780797731498751e-13 
relative error                   8.918144890153304e-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]                             5.600000000002956 
y[1] (closed_form)               1.8557007593579122 
y[1] (numeric)                   1.8557007593582322 
absolute error                   3.199662756969701e-13 
relative error                   1.7242342230203164e-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]                             5.7000960000030565 
y[1] (closed_form)               1.7158397608238118 
y[1] (numeric)                   1.7158397608242735 
absolute error                   4.616307336391401e-13 
relative error                   2.690407019228306e-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]                             5.8000640000031565 
y[1] (closed_form)               1.5789962555417074 
y[1] (numeric)                   1.5789962555423072 
absolute error                   5.997424779025096e-13 
relative error                   3.798251425851263e-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]                             5.9000320000032564 
y[1] (closed_form)               1.4463565910023557 
y[1] (numeric)                   1.4463565910030873 
absolute error                   7.316369732279782e-13 
relative error                   5.058482657592332e-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]                             6.000000000003356 
y[1] (closed_form)               1.3192452115443993 
y[1] (numeric)                   1.3192452115452595 
absolute error                   8.602007994795713e-13 
relative error                   6.520401150234693e-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]                             6.1000960000034565 
y[1] (closed_form)               1.19878218814665 
y[1] (numeric)                   1.1987821881476317 
absolute error                   9.816591983735634e-13 
relative error                   8.188803671593046e-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]                             6.2000640000035565 
y[1] (closed_form)               1.086478211245248 
y[1] (numeric)                   1.0864782112463411 
absolute error                   1.0931255900459291e-12 
relative error                   1.0061182808195135e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
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]                             6.3000320000036565 
y[1] (closed_form)               0.9832960062176336 
y[1] (numeric)                   0.9832960062188283 
absolute error                   1.194710996799131e-12 
relative error                   1.2150064571041334e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
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]                             6.4000000000037565 
y[1] (closed_form)               0.890265876388021 
y[1] (numeric)                   0.8902658763893092 
absolute error                   1.2881917754725691e-12 
relative error                   1.4469742238116658e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
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]                             6.500096000003857 
y[1] (closed_form)               0.8082192907795123 
y[1] (numeric)                   0.808219290780884 
absolute error                   1.371680546924381e-12 
relative error                   1.697163829882631e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
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]                             6.6000640000039565 
y[1] (closed_form)               0.738185170871086 
y[1] (numeric)                   0.7381851708725291 
absolute error                   1.4430678874077785e-12 
relative error                   1.9548860426238372e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
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]                             6.7000320000040565 
y[1] (closed_form)               0.6807506267581821 
y[1] (numeric)                   0.6807506267596815 
absolute error                   1.499356194756274e-12 
relative error                   2.2025043177652173e-10%
Desired digits                   16 
Estimated correct digits         10 
Correct digits                   12 
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]                             6.8000000000041565 
y[1] (closed_form)               0.6364891585100065 
y[1] (numeric)                   0.6364891585115513 
absolute error                   1.5447643164634428e-12 
relative error                   2.4270080578900495e-10%
Desired digits                   16 
Estimated correct digits         10 
Correct digits                   12 
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]                             6.900096000004257 
y[1] (closed_form)               0.6058123625175496 
y[1] (numeric)                   0.6058123625191231 
absolute error                   1.5735190928012344e-12 
relative error                   2.5973703908289785e-10%
Desired digits                   16 
Estimated correct digits         10 
Correct digits                   12 
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]                             7.000064000004357 
y[1] (closed_form)               0.5891049472250289 
y[1] (numeric)                   0.5891049472266207 
absolute error                   1.591726750405087e-12 
relative error                   2.701940898481493e-10%
Desired digits                   16 
Estimated correct digits         10 
Correct digits                   12 
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]                             7.100032000004457 
y[1] (closed_form)               0.5864857156711933 
y[1] (numeric)                   0.5864857156727873 
absolute error                   1.5939471964543372e-12 
relative error                   2.717793722614663e-10%
Desired digits                   16 
Estimated correct digits         10 
Correct digits                   12 
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]                             7.2000000000045565 
y[1] (closed_form)               0.5979808216194367 
y[1] (numeric)                   0.597980821621019 
absolute error                   1.5822898546957731e-12 
relative error                   2.6460545179536954e-10%
Desired digits                   16 
Estimated correct digits         10 
Correct digits                   12 
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]                             7.300096000004657 
y[1] (closed_form)               0.6235170068086826 
y[1] (numeric)                   0.6235170068102396 
absolute error                   1.5569767697343195e-12 
relative error                   2.497087894528041e-10%
Desired digits                   16 
Estimated correct digits         10 
Correct digits                   12 
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]                             7.400064000004757 
y[1] (closed_form)               0.662774029644018 
y[1] (numeric)                   0.6627740296455351 
absolute error                   1.5171197631502764e-12 
relative error                   2.2890452783207805e-10%
Desired digits                   16 
Estimated correct digits         10 
Correct digits                   12 
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]                             7.500032000004857 
y[1] (closed_form)               0.7153836297199236 
y[1] (numeric)                   0.7153836297213866 
absolute error                   1.4629408795485688e-12 
relative error                   2.0449739395369135e-10%
Desired digits                   16 
Estimated correct digits         10 
Correct digits                   12 
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]                             7.600000000004957 
y[1] (closed_form)               0.7808204853898105 
y[1] (numeric)                   0.7808204853912081 
absolute error                   1.397548743398147e-12 
relative error                   1.7898464109845248e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
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]                             7.700096000005057 
y[1] (closed_form)               0.8585380496091564 
y[1] (numeric)                   0.8585380496104762 
absolute error                   1.319833131674386e-12 
relative error                   1.5373030144385926e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
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]                             7.800064000005157 
y[1] (closed_form)               0.9475616898502808 
y[1] (numeric)                   0.9475616898515111 
absolute error                   1.2303491558895985e-12 
relative error                   1.2984369978950916e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
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]                             7.900032000005257 
y[1] (closed_form)               1.047094222484116 
y[1] (numeric)                   1.047094222485248 
absolute error                   1.1319833959078096e-12 
relative error                   1.0810711888203369e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
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]                             8.000000000005356 
y[1] (closed_form)               1.1561417871913098 
y[1] (numeric)                   1.1561417871923332 
absolute error                   1.0234035840994693e-12 
relative error                   8.851886467884618e-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]                             8.100096000005456 
y[1] (closed_form)               1.2737708359047475 
y[1] (numeric)                   1.273770835905654 
absolute error                   9.066081219089028e-13 
relative error                   7.117513577432063e-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]                             8.200064000005556 
y[1] (closed_form)               1.3985062182098749 
y[1] (numeric)                   1.3985062182106542 
absolute error                   7.793765632868599e-13 
relative error                   5.57292168700174e-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]                             8.300032000005656 
y[1] (closed_form)               1.529247685020628 
y[1] (numeric)                   1.5292476850212755 
absolute error                   6.474820679613913e-13 
relative error                   4.23399083290198e-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]                             8.400000000005756 
y[1] (closed_form)               1.6646897460363126 
y[1] (numeric)                   1.6646897460368246 
absolute error                   5.120348589571222e-13 
relative error                   3.075857589537606e-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]                             8.500096000005856 
y[1] (closed_form)               1.8036592388801553 
y[1] (numeric)                   1.8036592388805297 
absolute error                   3.743672039036028e-13 
relative error                   2.075598293921847e-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]                             8.600064000005956 
y[1] (closed_form)               1.944413389065573 
y[1] (numeric)                   1.9444133890658057 
absolute error                   2.327027459614328e-13 
relative error                   1.1967760933453703e-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]                             8.700032000006056 
y[1] (closed_form)               2.085722587187912 
y[1] (numeric)                   2.085722587187998 
absolute error                   8.570921750106208e-14 
relative error                   4.109329688787618e-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]                             8.800000000006156 
y[1] (closed_form)               2.2261758211784866 
y[1] (numeric)                   2.2261758211784404 
absolute error                   4.618527782440651e-14 
relative error                   2.0746464580662403e-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]                             8.900096000006256 
y[1] (closed_form)               2.3645455308946595 
y[1] (numeric)                   2.3645455308944734 
absolute error                   1.8607337892717624e-13 
relative error                   7.869308351054367e-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]                             9.000064000006356 
y[1] (closed_form)               2.4990964635491126 
y[1] (numeric)                   2.4990964635487964 
absolute error                   3.161915174132446e-13 
relative error                   1.265223339815393e-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]                             9.100032000006456 
y[1] (closed_form)               2.6286637777069397 
y[1] (numeric)                   2.628663777706492 
absolute error                   4.476419235288631e-13 
relative error                   1.7029257500529576e-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]                             9.200000000006556 
y[1] (closed_form)               2.751953707311769 
y[1] (numeric)                   2.751953707311198 
absolute error                   5.710987238671805e-13 
relative error                   2.0752482948743176e-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]                             9.300096000006656 
y[1] (closed_form)               2.86787809921002 
y[1] (numeric)                   2.8678780992093413 
absolute error                   6.785683126508957e-13 
relative error                   2.3660988688389956e-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]                             9.400064000006756 
y[1] (closed_form)               2.9749831805740126 
y[1] (numeric)                   2.9749831805732314 
absolute error                   7.811529201262601e-13 
relative error                   2.6257389461124263e-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]                             9.500032000006856 
y[1] (closed_form)               3.0723527807886177 
y[1] (numeric)                   3.0723527807877407 
absolute error                   8.770761894538737e-13 
relative error                   2.8547378899266378e-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]                             9.600000000006956 
y[1] (closed_form)               3.159014637022744 
y[1] (numeric)                   3.1590146370217846 
absolute error                   9.592326932761353e-13 
relative error                   3.0364933483821304e-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]                             9.700096000007056 
y[1] (closed_form)               3.234191798568501 
y[1] (numeric)                   3.2341917985674606 
absolute error                   1.0405010186786967e-12 
relative error                   3.217190208506611e-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]                             9.800064000007156 
y[1] (closed_form)               3.296941491321772 
y[1] (numeric)                   3.2969414913206707 
absolute error                   1.1013412404281553e-12 
relative error                   3.3404937373839117e-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]                             9.900032000007256 
y[1] (closed_form)               3.346740858682571 
y[1] (numeric)                   3.346740858681419 
absolute error                   1.1519674103510624e-12 
relative error                   3.4420573895420425e-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  )   =  sin  (  x  )   -  cos  (  x  )  ; 
Iterations                      78125 
Total Elapsed Time              14 Seconds
Elapsed Time(since restart)     14 Seconds
Time to Timeout                 2 Minutes 46.0 Seconds
Percent Done                    100.00128000007356%