##############ECHO OF PROBLEM################# ##############temp/sing4postode.ode################# diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ! #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(-1.0) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=c(0.1) $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 # 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(1.0) # 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) # ELIMINATED in preodein.rb #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=false $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(1.0))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] -2.0 y[1] (closed_form) 0.2 y[1] (numeric) 0.2 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -1.990000000000001 y[1] (closed_form) 0.20160883853148104 y[1] (numeric) 0.20160883853148126 absolute error 2.220446049250313e-16 relative error 1.1013634448886488e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] -1.9800000000000022 y[1] (closed_form) 0.20323550930818596 y[1] (numeric) 0.20323550930818637 absolute error 4.163336342344337e-16 relative error 2.0485280138871112e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] -1.9700000000000033 y[1] (closed_form) 0.20488024749533842 y[1] (numeric) 0.20488024749533906 absolute error 6.38378239159465e-16 relative error 3.1158603475134413e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] -1.9600000000000044 y[1] (closed_form) 0.2065432914738922 y[1] (numeric) 0.206543291473893 absolute error 8.049116928532385e-16 relative error 3.8970604521182535e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] -1.9500000000000055 y[1] (closed_form) 0.20822488287350244 y[1] (numeric) 0.20822488287350344 absolute error 9.992007221626409e-16 relative error 4.798661468186105e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] -1.9400000000000066 y[1] (closed_form) 0.20992526660508748 y[1] (numeric) 0.20992526660508862 absolute error 1.1379786002407855e-15 relative error 5.420874860107034e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] -1.9300000000000077 y[1] (closed_form) 0.21164469089292762 y[1] (numeric) 0.21164469089292898 absolute error 1.3600232051658168e-15 relative error 6.425973642088009e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] -1.9200000000000088 y[1] (closed_form) 0.21338340730624633 y[1] (numeric) 0.21338340730624786 absolute error 1.5265566588595902e-15 relative error 7.154055126079635e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] -1.91000000000001 y[1] (closed_form) 0.21514167079021362 y[1] (numeric) 0.21514167079021534 absolute error 1.7208456881689926e-15 relative error 7.998662843178359e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] -1.900000000000011 y[1] (closed_form) 0.2169197396963104 y[1] (numeric) 0.2169197396963123 absolute error 1.915134717478395e-15 relative error 8.828771047575481e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] -1.8900000000000121 y[1] (closed_form) 0.21871787581198796 y[1] (numeric) 0.21871787581199 absolute error 2.0539125955565396e-15 relative error 9.390693778144148e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] -1.8800000000000132 y[1] (closed_form) 0.220536344389553 y[1] (numeric) 0.22053634438955527 absolute error 2.275957200481571e-15 relative error 1.0320100329863747e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.8700000000000143 y[1] (closed_form) 0.22237541417420625 y[1] (numeric) 0.2223754141742087 absolute error 2.4424906541753444e-15 relative error 1.0983636222761238e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.8600000000000154 y[1] (closed_form) 0.22423535743115688 y[1] (numeric) 0.22423535743115955 absolute error 2.6645352591003757e-15 relative error 1.1882761441484188e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.8500000000000165 y[1] (closed_form) 0.2261164499717323 y[1] (numeric) 0.2261164499717352 absolute error 2.886579864025407e-15 relative error 1.276589944865254e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.8400000000000176 y[1] (closed_form) 0.22801897117839867 y[1] (numeric) 0.22801897117840172 absolute error 3.0531133177191805e-15 relative error 1.3389733766189435e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.8300000000000187 y[1] (closed_form) 0.22994320402860136 y[1] (numeric) 0.2299432040286046 absolute error 3.247402347028583e-15 relative error 1.4122628066992823e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.8200000000000198 y[1] (closed_form) 0.23188943511733218 y[1] (numeric) 0.2318894351173357 absolute error 3.524958103184872e-15 relative error 1.5201029324174695e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.810000000000021 y[1] (closed_form) 0.23385795467832424 y[1] (numeric) 0.23385795467832798 absolute error 3.747002708109903e-15 relative error 1.6022558280149042e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.800000000000022 y[1] (closed_form) 0.23584905660376917 y[1] (numeric) 0.2358490566037731 absolute error 3.913536161803677e-15 relative error 1.65933933260479e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.7900000000000231 y[1] (closed_form) 0.23786303846244863 y[1] (numeric) 0.2378630384624528 absolute error 4.163336342344337e-15 relative error 1.7503082316850173e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.7800000000000242 y[1] (closed_form) 0.2399002015161643 y[1] (numeric) 0.23990020151616867 absolute error 4.3576253716537394e-15 relative error 1.8164325599201822e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.7700000000000253 y[1] (closed_form) 0.24196085073434592 y[1] (numeric) 0.2419608507343505 absolute error 4.579669976578771e-15 relative error 1.892731804620281e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.7600000000000264 y[1] (closed_form) 0.24404529480671058 y[1] (numeric) 0.24404529480671538 absolute error 4.801714581503802e-15 relative error 1.9675505669170426e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.7500000000000275 y[1] (closed_form) 0.24615384615384034 y[1] (numeric) 0.2461538461538453 absolute error 4.9682480351975755e-15 relative error 2.0183507642990627e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.7400000000000286 y[1] (closed_form) 0.24828682093553864 y[1] (numeric) 0.24828682093554383 absolute error 5.190292640122607e-15 relative error 2.0904422637358327e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.7300000000000297 y[1] (closed_form) 0.2504445390568194 y[1] (numeric) 0.25044453905682484 absolute error 5.440092820663267e-15 relative error 2.172174662362692e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.7200000000000308 y[1] (closed_form) 0.25262732417137557 y[1] (numeric) 0.2526273241713813 absolute error 5.717648576819556e-15 relative error 2.263274012648314e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.710000000000032 y[1] (closed_form) 0.2548355036823659 y[1] (numeric) 0.25483550368237184 absolute error 5.9396931817445875e-15 relative error 2.3307950014484588e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.700000000000033 y[1] (closed_form) 0.25706940874035245 y[1] (numeric) 0.25706940874035866 absolute error 6.217248937900877e-15 relative error 2.4185098368435113e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.6900000000000341 y[1] (closed_form) 0.2593293742382122 y[1] (numeric) 0.2593293742382186 absolute error 6.439293542825908e-15 relative error 2.4830559830491728e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.6800000000000352 y[1] (closed_form) 0.2616157388028383 y[1] (numeric) 0.26161573880284494 absolute error 6.661338147750939e-15 relative error 2.546229893596398e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.6700000000000363 y[1] (closed_form) 0.2639288447834379 y[1] (numeric) 0.2639288447834449 absolute error 6.994405055138486e-15 relative error 2.650110131341506e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.6600000000000374 y[1] (closed_form) 0.2662690382362251 y[1] (numeric) 0.26626903823623227 absolute error 7.16093850883226e-15 relative error 2.689362066377132e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.6500000000000385 y[1] (closed_form) 0.2686366689052964 y[1] (numeric) 0.2686366689053038 absolute error 7.382983113757291e-15 relative error 2.7483154640962453e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.6400000000000396 y[1] (closed_form) 0.27103209019947005 y[1] (numeric) 0.27103209019947777 absolute error 7.716050021144838e-15 relative error 2.8469138158016997e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.6300000000000407 y[1] (closed_form) 0.2734556591648565 y[1] (numeric) 0.2734556591648645 absolute error 7.993605777301127e-15 relative error 2.9231816967013554e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.6200000000000419 y[1] (closed_form) 0.2759077364529198 y[1] (numeric) 0.27590773645292804 absolute error 8.215650382226158e-15 relative error 2.97768032453416e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.610000000000043 y[1] (closed_form) 0.2783886862837787 y[1] (numeric) 0.27838868628378727 absolute error 8.548717289613705e-15 relative error 3.0707847376022573e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.600000000000044 y[1] (closed_form) 0.28089887640448324 y[1] (numeric) 0.2808988764044922 absolute error 8.93729534823251e-15 relative error 3.1816771439708996e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.5900000000000452 y[1] (closed_form) 0.2834386780419941 y[1] (numeric) 0.28343867804200334 absolute error 9.270362255620057e-15 relative error 3.2706765074054455e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.5800000000000463 y[1] (closed_form) 0.2860084658505772 y[1] (numeric) 0.2860084658505868 absolute error 9.603429163007604e-15 relative error 3.3577429725541193e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.5700000000000474 y[1] (closed_form) 0.2886086178533167 y[1] (numeric) 0.2886086178533266 absolute error 9.880984919163893e-15 relative error 3.4236624646412444e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.5600000000000485 y[1] (closed_form) 0.2912395153774336 y[1] (numeric) 0.2912395153774437 absolute error 1.0103029524088925e-14 relative error 3.468976217391326e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.5500000000000496 y[1] (closed_form) 0.2939015429830874 y[1] (numeric) 0.2939015429830978 absolute error 1.0380585280245214e-14 relative error 3.531994141603593e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.5400000000000507 y[1] (closed_form) 0.2965950883853226 y[1] (numeric) 0.29659508838533327 absolute error 1.0658141036401503e-14 relative error 3.593498831833297e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.5300000000000518 y[1] (closed_form) 0.29932054236880856 y[1] (numeric) 0.2993205423688195 absolute error 1.0935696792557792e-14 relative error 3.653506941425806e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.5200000000000529 y[1] (closed_form) 0.3020782986950071 y[1] (numeric) 0.30207829869501834 absolute error 1.1268763699945339e-14 relative error 3.7304115352300865e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.510000000000054 y[1] (closed_form) 0.30486875400138724 y[1] (numeric) 0.30486875400139873 absolute error 1.149080830487037e-14 relative error 3.769100032080717e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.500000000000055 y[1] (closed_form) 0.30769230769229206 y[1] (numeric) 0.3076923076923038 absolute error 1.176836406102666e-14 relative error 3.824718319833859e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.4900000000000562 y[1] (closed_form) 0.3105493618210453 y[1] (numeric) 0.31054936182105736 absolute error 1.2045919817182948e-14 relative error 3.878906640331283e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.4800000000000573 y[1] (closed_form) 0.313440320962872 y[1] (numeric) 0.3134403209628844 absolute error 1.2378986724570495e-14 relative error 3.949391924607181e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.4700000000000584 y[1] (closed_form) 0.3163655920781884 y[1] (numeric) 0.3163655920782011 absolute error 1.2712053631958042e-14 relative error 4.018153032525836e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.4600000000000595 y[1] (closed_form) 0.31932558436580166 y[1] (numeric) 0.3193255843658147 absolute error 1.304512053934559e-14 relative error 4.085209948101691e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.4500000000000606 y[1] (closed_form) 0.3223207091055418 y[1] (numeric) 0.3223207091055551 absolute error 1.3322676295501878e-14 relative error 4.133360320679692e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.4400000000000617 y[1] (closed_form) 0.32535137948983023 y[1] (numeric) 0.3253513794898438 absolute error 1.354472090042691e-14 relative error 4.1631054159554555e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.4300000000000628 y[1] (closed_form) 0.32841801044367336 y[1] (numeric) 0.3284180104436872 absolute error 1.3822276656583199e-14 relative error 4.208745019163267e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.4200000000000639 y[1] (closed_form) 0.33152101843254866 y[1] (numeric) 0.3315210184325629 absolute error 1.4210854715202004e-14 relative error 4.286562216293791e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.410000000000065 y[1] (closed_form) 0.33466082125763486 y[1] (numeric) 0.33466082125764934 absolute error 1.4488410471358293e-14 relative error 4.329281932946837e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.400000000000066 y[1] (closed_form) 0.33783783783781673 y[1] (numeric) 0.3378378378378316 absolute error 1.4876988529977098e-14 relative error 4.403588604873496e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.3900000000000672 y[1] (closed_form) 0.34105248797787807 y[1] (numeric) 0.34105248797789334 absolute error 1.5265566588595902e-14 relative error 4.47601677944249e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.3800000000000683 y[1] (closed_form) 0.3443051921222749 y[1] (numeric) 0.34430519212229055 absolute error 1.5654144647214707e-14 relative error 4.5465897713373345e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.3700000000000694 y[1] (closed_form) 0.3475963710938628 y[1] (numeric) 0.3475963710938789 absolute error 1.609823385706477e-14 relative error 4.631300898339269e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.3600000000000705 y[1] (closed_form) 0.35092644581693316 y[1] (numeric) 0.35092644581694965 absolute error 1.6486811915683575e-14 relative error 4.698081923493507e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.3500000000000716 y[1] (closed_form) 0.35429583702389067 y[1] (numeric) 0.35429583702390754 absolute error 1.687538997430238e-14 relative error 4.763078820247173e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.3400000000000727 y[1] (closed_form) 0.3577049649448885 y[1] (numeric) 0.3577049649449057 absolute error 1.7208456881689926e-14 relative error 4.810796205845571e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.3300000000000738 y[1] (closed_form) 0.36115424897971365 y[1] (numeric) 0.3611542489797313 absolute error 1.765254609153999e-14 relative error 4.8878134872868535e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.320000000000075 y[1] (closed_form) 0.3646441073511989 y[1] (numeric) 0.36464410735121694 absolute error 1.8041124150158794e-14 relative error 4.947597886939905e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.310000000000076 y[1] (closed_form) 0.36817495673941564 y[1] (numeric) 0.368174956739434 absolute error 1.837419105754634e-14 relative error 4.990614033140527e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.300000000000077 y[1] (closed_form) 0.3717472118958831 y[1] (numeric) 0.37174721189590193 absolute error 1.8818280267396403e-14 relative error 5.062117391930009e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.2900000000000782 y[1] (closed_form) 0.3753612852370122 y[1] (numeric) 0.37536128523703144 absolute error 1.9262369477246466e-14 relative error 5.1316878524336206e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.2800000000000793 y[1] (closed_form) 0.3790175864159805 y[1] (numeric) 0.3790175864160002 absolute error 1.970645868709653e-14 relative error 5.199352060003949e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.2700000000000804 y[1] (closed_form) 0.38271652187221933 y[1] (numeric) 0.38271652187223937 absolute error 2.0039525594484076e-14 relative error 5.236127642583153e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.2600000000000815 y[1] (closed_form) 0.3864584943576753 y[1] (numeric) 0.3864584943576957 absolute error 2.0372592501871623e-14 relative error 5.271612035784719e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.2500000000000826 y[1] (closed_form) 0.39024390243899293 y[1] (numeric) 0.39024390243901375 absolute error 2.0816681711721685e-14 relative error 5.3342746886291116e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.2400000000000837 y[1] (closed_form) 0.3940731399747471 y[1] (numeric) 0.3940731399747684 absolute error 2.1316282072803006e-14 relative error 5.409219738794933e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.2300000000000848 y[1] (closed_form) 0.39794659556684187 y[1] (numeric) 0.39794659556686374 absolute error 2.1871393585115584e-14 relative error 5.496062494004152e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.220000000000086 y[1] (closed_form) 0.4018646519851775 y[1] (numeric) 0.4018646519851998 absolute error 2.225997164373439e-14 relative error 5.539171343827332e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.210000000000087 y[1] (closed_form) 0.4058276855646745 y[1] (numeric) 0.4058276855646972 absolute error 2.270406085358445e-14 relative error 5.594507634932223e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.200000000000088 y[1] (closed_form) 0.4098360655737349 y[1] (numeric) 0.4098360655737581 absolute error 2.3203661214665772e-14 relative error 5.6616933363789394e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.1900000000000892 y[1] (closed_form) 0.41389015355321057 y[1] (numeric) 0.41389015355323416 absolute error 2.3592239273284576e-14 relative error 5.700120930818788e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.1800000000000903 y[1] (closed_form) 0.41799030262494186 y[1] (numeric) 0.4179903026249659 absolute error 2.403632848313464e-14 relative error 5.750451226305643e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.1700000000000914 y[1] (closed_form) 0.42213685676892637 y[1] (numeric) 0.42213685676895085 absolute error 2.4480417692984702e-14 relative error 5.79916614729167e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.1600000000000925 y[1] (closed_form) 0.4263301500681738 y[1] (numeric) 0.42633015006819874 absolute error 2.4924506902834764e-14 relative error 5.846292339129457e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.1500000000000936 y[1] (closed_form) 0.4305705059203045 y[1] (numeric) 0.4305705059203299 absolute error 2.5424107263916085e-14 relative error 5.904748912045058e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.1400000000000947 y[1] (closed_form) 0.4348582362149531 y[1] (numeric) 0.434858236214979 absolute error 2.5868196473766147e-14 relative error 5.9486504611078215e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.1300000000000958 y[1] (closed_form) 0.43919364047604414 y[1] (numeric) 0.4391936404760705 absolute error 2.6367796834847468e-14 relative error 6.003683661326991e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.120000000000097 y[1] (closed_form) 0.4435770049680197 y[1] (numeric) 0.44357700496804664 absolute error 2.6922908347160046e-14 relative error 6.069500457784345e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.110000000000098 y[1] (closed_form) 0.4480086017651102 y[1] (numeric) 0.4480086017651376 absolute error 2.7422508708241367e-14 relative error 6.120978168767153e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.1000000000000991 y[1] (closed_form) 0.4524886877827608 y[1] (numeric) 0.4524886877827888 absolute error 2.7977620220553945e-14 relative error 6.183054068743032e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.0900000000001002 y[1] (closed_form) 0.4570175037703488 y[1] (numeric) 0.4570175037703772 absolute error 2.842170943040401e-14 relative error 6.218954240467322e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.0800000000001013 y[1] (closed_form) 0.4615952732643551 y[1] (numeric) 0.46159527326438415 absolute error 2.9032332093947844e-14 relative error 6.289564424833497e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.0700000000001024 y[1] (closed_form) 0.46622220150118787 y[1] (numeric) 0.4662222015012174 absolute error 2.9531932455029164e-14 relative error 6.334304192279852e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.0600000000001035 y[1] (closed_form) 0.47089847428889464 y[1] (numeric) 0.4708984742889248 absolute error 3.0142555118573e-14 relative error 6.401073004980824e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.0500000000001046 y[1] (closed_form) 0.47562425683704906 y[1] (numeric) 0.4756242568370796 absolute error 3.0531133177191805e-14 relative error 6.419170750505247e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.0400000000001057 y[1] (closed_form) 0.48039969254414594 y[1] (numeric) 0.4803996925441771 absolute error 3.114175584073564e-14 relative error 6.4824678958082165e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.0300000000001068 y[1] (closed_form) 0.4852249017419056 y[1] (numeric) 0.4852249017419372 absolute error 3.164135620181696e-14 relative error 6.520967099633154e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.020000000000108 y[1] (closed_form) 0.4900999803959479 y[1] (numeric) 0.49009998039598 absolute error 3.214095656289828e-14 relative error 6.558040777094473e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.010000000000109 y[1] (closed_form) 0.4950249987623835 y[1] (numeric) 0.4950249987624161 absolute error 3.26405569239796e-14 relative error 6.593718904213839e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] -1.0000000000001101 y[1] (closed_form) 0.49999999999994493 y[1] (numeric) 0.49999999999997813 absolute error 3.319566843629218e-14 relative error 6.639133687259167e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Finished! diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; Iterations 1001 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.19999999998899%