Initializing...
Initialized
Initializing(2)...
PI = 0.314159265358979323846264338327950271e1+/-0.313e-33
E = 0.271828182845904523536028747135266232e1+/-0.256e-32
LOG_E_10 = 0.230258509299404568401799145468436324e1+/-0.5e-32
Initialized(2)
##############ECHO OF PROBLEM#################
##############temp/sing1postode.ode#################
diff  (  y  ,  x  ,  1  )   =  neg ( 2.0 )   *  x  /   ( x  *   x  +  0.000001 )   /  (  x  *  x  +  0.000001 )  ; 
!
#BEGIN FIRST INPUT BLOCK
# Digits:=32; ELIMINATED in preodein.rb
max_terms=30 
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start=c(-2.0) 
x_end=c(-1.5) 
$array_y_init[0 + 1] = exact_soln_y(x_start)
$glob_look_poles=true 
$glob_max_h=c(0.001) 
$glob_min_h=c(0.001) 
#  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=2 
#  ELIMINATED in preodein.rb
$array_given_rad_poles[1][1]=c(0.0) 
#  ELIMINATED in preodein.rb
$array_given_rad_poles[1][2]=c(0.001) 
#  ELIMINATED in preodein.rb
$array_given_ord_poles[1][1]=c(1.0) 
#  ELIMINATED in preodein.rb
$array_given_ord_poles[1][2]=c(0.0) 
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE  BLOCK
$glob_desired_digits_correct=8 
$glob_max_minutes=(3.0) 
$glob_subiter_method=3 
$glob_max_iter=100000 
$glob_upper_ratio_limit=c(1.000001) 
$glob_lower_ratio_limit=c(0.999999) 
$glob_look_poles=true 
$glob_h=c(0.001) 
$glob_display_interval=c(0.01) 
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
def exact_soln_y (x)
x = c(x)
return(c(1.0) / (c(x) * c(x) + c(0.000001)))  
end


#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
 
TOP MAIN SOLVE Loop
x[1]                             -0.2e1+/-0.50e-32 
y[1] (closed_form)               0.249999937500015624996093750976562255e0+/-0.137e-32 
y[1] (numeric)                   0.249999937500015624996093750976562255e0+/-0.161e-32 
$glob_prec                        0.1e-15+/-0.50e-49%
absolute error                   0.0e0+/-0.298e-32 
relative error                   0.0e0+/-0.119200029800000000000000000000001306e-29%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   34 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.2000000249999984375001953124694824e1+/-0.504e-30 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.200000833350957876244776803004012256e1+/-0.518e-22 
Order of pole (three term test)                   0.20000500015340996160786401130292218e1+/-0.64e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.199e1+/-0.100e-31 
y[1] (closed_form)               0.2525188120201984747358716355971729e0+/-0.266e-32 
y[1] (numeric)                   0.252518812020198474735871509177610663e0+/-0.719e-32 
absolute error                   0.126419562237e-24+/-0.985e-32 
relative error                   0.500634234834305937e-22+/-0.39e-29%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   23 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.199000025125626554529874980661314824e1+/-0.995e-30 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.199000837538829622054272925910323598e1+/-0.517e-22 
Order of pole (three term test)                   0.20000505053403287303376081687093999e1+/-0.65e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.198e1+/-0.150e-31 
y[1] (closed_form)               0.255075947588014593405113405490917893e0+/-0.399e-32 
y[1] (numeric)                   0.255075947588014593405113149435954331e0+/-0.11e-31 
absolute error                   0.256054963562e-24+/-0.149e-31 
relative error                   0.1003838135203428362e-21+/-0.584e-29%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   22 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.198000025252523642197095202719073963e1+/-0.149e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.198000841769005827492260913945720986e1+/-0.531e-22 
Order of pole (three term test)                   0.20000510167995644286351587825887134e1+/-0.671e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.197e1+/-0.200e-31 
y[1] (closed_form)               0.257672123045653573744859763235393018e0+/-0.536e-32 
y[1] (numeric)                   0.257672123045653573744859374230522966e0+/-0.13e-31 
absolute error                   0.389004870052e-24+/-0.183e-31 
relative error                   0.1509689389189676852e-21+/-0.71e-29%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   22 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.197000025380709024922866477662325723e1+/-0.198e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.197000846042130778659611301951098754e1+/-0.535e-22 
Order of pole (three term test)                   0.20000515360675996103458128101566146e1+/-0.679e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.196e1+/-0.250e-31 
y[1] (closed_form)               0.260308137154275001490264085208224383e0+/-0.677e-32 
y[1] (numeric)                   0.260308137154275001490263559836726744e0+/-0.153e-31 
absolute error                   0.525371497639e-24+/-0.22e-31 
relative error                   0.2018267670701480039e-21+/-0.845e-29%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   22 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.196000025510202421504011259925714852e1+/-0.248e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.196000850358861911786317814819197798e1+/-0.524e-22 
Order of pole (three term test)                   0.20000520633042118491760837646437059e1+/-0.667e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.195e1+/-0.300e-31 
y[1] (closed_form)               0.262984809208465691396267877378598979e0+/-0.822e-32 
y[1] (numeric)                   0.262984809208465691396267212117840137e0+/-0.178e-31 
absolute error                   0.665260758842e-24+/-0.26e-31 
relative error                   0.2529654700757463842e-21+/-0.988e-29%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   22 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.195000025641023955225360327074920184e1+/-0.298e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.195000854719870150458735386751467483e1+/-0.53e-22 
Order of pole (three term test)                   0.20000525986732863210066071932989818e1+/-0.678e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.194e1+/-0.350e-31 
y[1] (closed_form)               0.265702979672924946082222849871705316e0+/-0.966e-32 
y[1] (numeric)                   0.265702979672924946082222041089288978e0+/-0.201e-31 
absolute error                   0.808782416338e-24+/-0.297e-31 
relative error                   0.3043934310912113138e-21+/-0.111e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   22 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.194000025773194164284697345570157633e1+/-0.347e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.194000859125840253278142584837400961e1+/-0.529e-22 
Order of pole (three term test)                   0.20000531423429431790403472681027877e1+/-0.68e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.193e1+/-0.400e-31 
y[1] (closed_form)               0.26846351084230158063261278621901629e0+/-0.112e-31 
y[1] (numeric)                   0.268463510842301580632611830168772541e0+/-0.222e-31 
absolute error                   0.956050243749e-24+/-0.334e-31 
relative error                   0.3561192508990893849e-21+/-0.124e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   22 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.193000025906734012541794827487344237e1+/-0.397e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.193000863577471172329034138344475859e1+/-0.539e-22 
Order of pole (three term test)                   0.2000053694485669561094315993129336e1+/-0.697e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.192e1+/-0.450e-31 
y[1] (closed_form)               0.271267287525149868394675457173541348e0+/-0.127e-31 
y[1] (numeric)                   0.271267287525149868394674349991347322e0+/-0.244e-31 
absolute error                   0.1107182194026e-23+/-0.371e-31 
relative error                   0.4081517547239640426e-21+/-0.136e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   22 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.192000026041664900603357303862324339e1+/-0.447e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.192000868075476422851319368869271315e1+/-0.535e-22 
Order of pole (three term test)                   0.20000542552784564225598712413984448e1+/-0.696e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.191e1+/-0.500e-31 
y[1] (closed_form)               0.274115217753017254730611899177133527e0+/-0.144e-31 
y[1] (numeric)                   0.274115217753017254730610636876557697e0+/-0.267e-31 
absolute error                   0.126230057583e-23+/-0.411e-31 
relative error                   0.460499999298599883000000000000000001e-21+/-0.149e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   22 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.191000026178008677256182443717323154e1+/-0.498e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.19100087262058446452711567200371152e1+/-0.54e-22 
Order of pole (three term test)                   0.2000054824902940397700378135553933e1+/-0.708e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.19e1+/-0.550e-31 
y[1] (closed_form)               0.277008233515724787887870391171636794e0+/-0.161e-31 
y[1] (numeric)                   0.277008233515724787887868969639398459e0+/-0.292e-31 
absolute error                   0.1421532238335e-23+/-0.453e-31 
relative error                   0.513173280192158833500000000000000001e-21+/-0.163e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   22 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.190000026315787651261369193999026406e1+/-0.549e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.190000877213539094810121947276459305e1+/-0.546e-22 
Order of pole (three term test)                   0.2000055403545550901581301615364566e1+/-0.72e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.189e1+/-0.600e-31 
y[1] (closed_form)               0.279947291523951870341852036098643347e0+/-0.178e-31 
y[1] (numeric)                   0.279947291523951870341850451089878467e0+/-0.312e-31 
absolute error                   0.158500876488e-23+/-0.490e-31 
relative error                   0.566181139403661288e-21+/-0.175e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   22 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.189000026455024603522945044962022769e1+/-0.597e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.189000881855099854743676416669510071e1+/-0.536e-22 
Order of pole (three term test)                   0.20000559913976626950648096943985692e1+/-0.71e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.188e1+/-0.650e-31 
y[1] (closed_form)               0.282933374000290289641724297837172409e0+/-0.196e-31 
y[1] (numeric)                   0.282933374000290289641722544970496426e0+/-0.335e-31 
absolute error                   0.1752866675983e-23+/-0.531e-31 
relative error                   0.6195333732460991183e-21+/-0.187e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   22 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.188000026595742799644853550901402856e1+/-0.648e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.188000886546042447732590443231452963e1+/-0.562e-22 
Order of pole (three term test)                   0.20000565886557541459786728636452394e1+/-0.748e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.187e1+/-0.700e-31 
y[1] (closed_form)               0.285967489499988704284164750446180775e0+/-0.214e-31 
y[1] (numeric)                   0.285967489499988704284162825198538581e0+/-0.364e-31 
absolute error                   0.1925247642194e-23+/-0.578e-31 
relative error                   0.673240040523584079400000000000000001e-21+/-0.202e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   22 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.187000026737966002890839647737047702e1+/-0.697e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.187000891287159171753751169435620115e1+/-0.567e-22 
Order of pole (three term test)                   0.20000571955215714308195396491362159e1+/-0.757e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.186e1+/-0.750e-31 
y[1] (closed_form)               0.289050673762668007090991128745771549e0+/-0.234e-31 
y[1] (numeric)                   0.289050673762668007090989026447064222e0+/-0.398e-31 
absolute error                   0.2102298707327e-23+/-0.632e-31 
relative error                   0.727311471016719652700000000000000002e-21+/-0.218e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   22 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.186000026881718487562395579156214603e1+/-0.749e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.186000896079259365511350194601005849e1+/-0.547e-22 
Order of pole (three term test)                   0.2000057812202298933207509260504673e1+/-0.736e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.185e1+/-0.800e-31 
y[1] (closed_form)               0.292183990596350446647057225111110267e0+/-0.254e-31 
y[1] (numeric)                   0.29218399059635044664705494093858763e0+/-0.428e-31 
absolute error                   0.2284172522637e-23+/-0.682e-31 
relative error                   0.7817582742897655137e-21+/-0.233e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   22 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.185000027027025052810585931753905395e1+/-0.799e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.185000900923169869064475180093528811e1+/-0.554e-22 
Order of pole (three term test)                   0.20000584389107361078084762672824587e1+/-0.744e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.184e1+/-0.850e-31 
y[1] (closed_form)               0.295368532795211249051497799061377876e0+/-0.273e-31 
y[1] (numeric)                   0.29536853279521124905149532803378534e0+/-0.458e-31 
absolute error                   0.2471027592536e-23+/-0.731e-31 
relative error                   0.836591348831747413600000000000000001e-21+/-0.247e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   22 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.184000027173911036898258040051735894e1+/-0.846e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.184000905819735499477751402618191101e1+/-0.555e-22 
Order of pole (three term test)                   0.200005907586548109162152141108843e1+/-0.75e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.183e1+/-0.900e-31 
y[1] (closed_form)               0.298605423092530952691644214027228634e0+/-0.294e-31 
y[1] (numeric)                   0.298605423092530952691641550998696126e0+/-0.496e-31 
absolute error                   0.2663028532508e-23+/-0.790e-31 
relative error                   0.8918218915544573708e-21+/-0.264e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   22 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.183000027322402331929865606976618133e1+/-0.898e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.183000910769819542069799380717823671e1+/-0.581e-22 
Order of pole (three term test)                   0.20000597232911213584317330357238844e1+/-0.79e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.182e1+/-0.950e-31 
y[1] (closed_form)               0.301895815150399966670702007395843679e0+/-0.315e-31 
y[1] (numeric)                   0.301895815150399966670699147049503822e0+/-0.532e-31 
absolute error                   0.2860346339857e-23+/-0.847e-31 
relative error                   0.947461407648866665700000000000000001e-21+/-0.28e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   22 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.182000027472525399066890652814782299e1+/-0.946e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.182000915774304257859544826062130183e1+/-0.562e-22 
Order of pole (three term test)                   0.20000603814184317268980466719254824e1+/-0.774e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.181e1+/-0.1e-30 
y[1] (closed_form)               0.305240894587804222153102117425561666e0+/-0.338e-31 
y[1] (numeric)                   0.305240894587804222153099054266883636e0+/-0.565e-31 
absolute error                   0.306315867803e-23+/-0.903e-31 
relative error                   0.1003521720825276103e-20+/-0.295e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.181000027624307284247643827244655426e1+/-0.995e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.181000920834091407836944139726294895e1+/-0.574e-22 
Order of pole (three term test)                   0.20000610504845800482276785736492383e1+/-0.796e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.18e1+/-0.1e-30 
y[1] (closed_form)               0.308641880048802454073316644038072827e0+/-0.344e-31 
y[1] (numeric)                   0.308641880048802454073313372387897539e0+/-0.595e-31 
absolute error                   0.3271650175288e-23+/-0.939e-31 
relative error                   0.10600149839583295288e-20+/-0.304e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.18000002777777563443105778668957041e1+/-0.999e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.180000925950102794712542328491504104e1+/-0.556e-22 
Order of pole (three term test)                   0.20000617307333409157333168955888126e1+/-0.77e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.179e1+/-0.1e-30 
y[1] (closed_form)               0.31210002431259189395090853877577517e0+/-0.35e-31 
y[1] (numeric)                   0.312100024312591893950905052763036678e0+/-0.625e-31 
absolute error                   0.3486012738492e-23+/-0.975e-31 
relative error                   0.11169536901414955692e-20+/-0.312e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.179000027932958714384964973366047661e1+/-0.993e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.179000931123280822829534694732828086e1+/-0.56e-22 
Order of pole (three term test)                   0.2000062422415317755829585454156807e1+/-0.784e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.178e1+/-0.1e-30 
y[1] (closed_form)               0.315616615447350256485842543289185933e0+/-0.356e-31 
y[1] (numeric)                   0.315616615447350256485838836843303031e0+/-0.658e-31 
absolute error                   0.3706445882902e-23+/-0.101e-30 
relative error                   0.11743506841832579702e-20+/-0.32e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.178000028089885424040272090701864234e1+/-0.996e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.178000936354589076952737676128655834e1+/-0.57e-22 
Order of pole (three term test)                   0.20000631257881736782581679881128895e1+/-0.799e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.177e1+/-0.1e-30 
y[1] (closed_form)               0.319192978009838165968219231951472453e0+/-0.362e-31 
y[1] (numeric)                   0.319192978009838165968215298794393589e0+/-0.691e-31 
absolute error                   0.3933157078864e-23+/-0.105e-30 
relative error                   0.12322191745530104464e-20+/-0.328e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.17700002824858531643341135644820638e1+/-0.991e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.177000941645012920681171392433183254e1+/-0.553e-22 
Order of pole (three term test)                   0.20000638411168714825969933248984324e1+/-0.784e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.176e1+/-0.1e-30 
y[1] (closed_form)               0.322830474292847916823373959396319926e0+/-0.368e-31 
y[1] (numeric)                   0.322830474292847916823369793034203534e0+/-0.724e-31 
absolute error                   0.4166362116392e-23+/-0.109e-30 
relative error                   0.12905727458097975592e-20+/-0.337e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.176000028409088616260465890511385495e1+/-0.994e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.176000946995560115264905637649974831e1+/-0.55e-22 
Order of pole (three term test)                   0.20000645686739232384727970165065712e1+/-0.779e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.175e1+/-0.1e-30 
y[1] (closed_form)               0.326530505622692041569945609813678428e0+/-0.374e-31 
y[1] (numeric)                   0.326530505622692041569941203528189786e0+/-0.754e-31 
absolute error                   0.4406285488642e-23+/-0.112e-30 
relative error                   0.13494253715251613642e-20+/-0.343e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.17500002857142623906743618722519732e1+/-0.997e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.175000952407261459642516665013502822e1+/-0.542e-22 
Order of pole (three term test)                   0.20000653087396498784274102116134803e1+/-0.768e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.174e1+/-0.1e-30 
y[1] (closed_form)               0.330294513709038938750515672309528237e0+/-0.381e-31 
y[1] (numeric)                   0.330294513709038938750511019148732849e0+/-0.787e-31 
absolute error                   0.4653160795388e-23+/-0.116e-30 
relative error                   0.14087914277277504188e-20+/-0.351e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.174000028735629811102239538196176721e1+/-0.991e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.174000957881171452553044548628288851e1+/-0.553e-22 
Order of pole (three term test)                   0.20000660616024512651602871759447822e1+/-0.797e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.173e1+/-0.1e-30 
y[1] (closed_form)               0.33412398204952318837141622793403457e0+/-0.387e-31 
y[1] (numeric)                   0.334123982049523188371411320702866909e0+/-0.831e-31 
absolute error                   0.4907231167661e-23+/-0.121e-30 
relative error                   0.14686857068923774561e-20+/-0.362e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.173000028901731689855217709880525988e1+/-0.994e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.173000963418368977615836954707819537e1+/-0.546e-22 
Order of pole (three term test)                   0.20000668275590872189622232672252939e1+/-0.789e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.172e1+/-0.1e-30 
y[1] (closed_form)               0.338020437391685576093301753210602619e0+/-0.394e-31 
y[1] (numeric)                   0.338020437391685576093296584460887815e0+/-0.868e-31 
absolute error                   0.5168749714804e-23+/-0.126e-30 
relative error                   0.15291234325025868404e-20+/-0.372e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.172000029069764985316173542109793451e1+/-0.997e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.172000969019958012313228433934646496e1+/-0.542e-22 
Order of pole (three term test)                   0.20000676069149700166526288855715977e1+/-0.788e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.171e1+/-0.1e-30 
y[1] (closed_form)               0.341985451254932712652538335714122049e0+/-0.401e-31 
y[1] (numeric)                   0.341985451254932712652532897734126804e0+/-0.914e-31 
absolute error                   0.5437979995245e-23+/-0.131e-30 
relative error                   0.15901202742075899745e-20+/-0.383e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.171000029239763581977268041157554804e1+/-0.991e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.171000974687068361854755782508279355e1+/-0.548e-22 
Order of pole (three term test)                   0.20000683999844689003257672024568494e1+/-0.8e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.17e1+/-0.1e-30 
y[1] (closed_form)               0.346020641515348956626658606692523635e0+/-0.408e-31 
y[1] (numeric)                   0.346020641515348956626652891496011222e0+/-0.955e-31 
absolute error                   0.5715196512413e-23+/-0.136e-30 
relative error                   0.16516923636070082413e-20+/-0.393e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.170000029411762161612489849234702343e1+/-0.994e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.170000980420856418947678368350871997e1+/-0.529e-22 
Order of pole (three term test)                   0.20000692070912271627971085533061618e1+/-0.772e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.169e1+/-0.1e-30 
y[1] (closed_form)               0.350127674056344646075191318514296238e0+/-0.416e-31 
y[1] (numeric)                   0.350127674056344646075185317829058953e0+/-0.994e-31 
absolute error                   0.6000685237285e-23+/-0.141e-30 
relative error                   0.17138563106894925785e-20+/-0.402e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.16900002958579622686586278807596796e1+/-0.997e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.16900098622250595054709471950645906e1+/-0.525e-22 
Order of pole (three term test)                   0.20000700285684924069233907863189781e1+/-0.777e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.168e1+/-0.1e-30 
y[1] (closed_form)               0.354308264488284974388827101464320626e0+/-0.423e-31 
y[1] (numeric)                   0.354308264488284974388820806720161458e0+/-0.1e-30 
absolute error                   0.6294744159168e-23+/-0.142e-30 
relative error                   0.17766292209579922368e-20+/-0.4e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.168000029761902125682088872976071738e1+/-0.999e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.168000992093228912710069245254034987e1+/-0.527e-22 
Order of pole (three term test)                   0.20000708647594606080605421290032976e1+/-0.784e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.167e1+/-0.1e-30 
y[1] (closed_form)               0.358564179940413804577502033955310711e0+/-0.431e-31 
y[1] (numeric)                   0.358564179940413804577495436271444289e0+/-0.1e-30 
absolute error                   0.6597683866422e-23+/-0.143e-30 
relative error                   0.18400287132748182222e-20+/-0.398e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.167000029940117076614938438893870694e1+/-0.993e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.167000998034266294732061456258133416e1+/-0.53e-22 
Order of pole (three term test)                   0.20000717160176346429417936623294932e1+/-0.792e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.166e1+/-0.1e-30 
y[1] (closed_form)               0.362897240928566944198379954137046691e0+/-0.439e-31 
y[1] (numeric)                   0.362897240928566944198373044308887738e0+/-0.1e-30 
absolute error                   0.6909828158953e-23+/-0.143e-30 
relative error                   0.19040729384639045753e-20+/-0.394e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.166000030120479195050400784746869562e1+/-0.996e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.166001004046888993800750542024488344e1+/-0.522e-22 
Order of pole (three term test)                   0.20000725827071979843322186221713959e1+/-0.788e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.165e1+/-0.1e-30 
y[1] (closed_form)               0.367309323302360586828067280783367939e0+/-0.447e-31 
y[1] (numeric)                   0.367309323302360586828060049268673557e0+/-0.1e-30 
absolute error                   0.7231514694382e-23+/-0.144e-30 
relative error                   0.19687805986969689382e-20+/-0.392e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.165000030303027520383403329957838108e1+/-0.998e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.165001010132398721462247801416016953e1+/-0.524e-22 
Order of pole (three term test)                   0.20000734652034042990830705638059188e1+/-0.791e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.164e1+/-0.1e-30 
y[1] (closed_form)               0.371802360275743502474902411175486624e0+/-0.455e-31 
y[1] (numeric)                   0.371802360275743502474894848079816604e0+/-0.1e-30 
absolute error                   0.756309567002e-23+/-0.145e-30 
relative error                   0.2034170967718146202e-20+/-0.389e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.16400003048780204418880034865002147e1+/-0.992e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.164001016292128943257877240728091052e1+/-0.516e-22 
Order of pole (three term test)                   0.20000743638929837278172292029792835e1+/-0.784e-19 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.163e1+/-0.1e-30 
y[1] (closed_form)               0.376378344545016920088479021235642577e0+/-0.463e-31 
y[1] (numeric)                   0.376378344545016920088471116297099776e0+/-0.1e-30 
absolute error                   0.7904938542801e-23+/-0.146e-30 
relative error                   0.21002639119306519701e-20+/-0.387e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   21 
h                                0.1e-2+/-0.5e-33 
Radius of convergence (given) for eq  1           0.163000030674843739429329943537553097e1+/-0.994e-29 
Order of pole (given)                             0.1e1+/-0.50e-33 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.163001022527445852956382451258265782e1+/-0.539e-22 
Order of pole (three term test)                   0.20000752791745666675842784612881184e1+/-0.825e-19 
NO COMPLEX POLE (six term test) for Equation 1
Finished!
Maximum Time Reached before Solution Completed!
diff  (  y  ,  x  ,  1  )   =  neg ( 2.0 )   *  x  /   ( x  *   x  +  0.000001 )   /  (  x  *  x  +  0.000001 )  ; 
Iterations                      380 
Total Elapsed Time              3 Minutes 0 Seconds
Elapsed Time(since restart)     3 Minutes 0 Seconds
Expected Time Remaining         56 Seconds
Optimized Time Remaining        56 Seconds
Expected Total Time             3 Minutes 56 Seconds
Time to Timeout                 0 Seconds
Percent Done                    0.762e2+/-0.225e-28%