##############ECHO OF PROBLEM################# ##############temp/sing6postode.ode################# diff ( y , x , 1 ) = neg ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=30; max_terms=20; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(2.0); x_end=c(3.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=1; array_given_rad_poles[1][1]=c(6.0); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(3.0); 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=false; glob_h=c(0.001); glob_display_interval=c(0.01); // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(c(1.0)/ ( c(x) - c(6.0) ) / ( c(x) - c(6.0) )); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = 0.0625 y[1] (numeric) = 0.0625 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.009999999999999 y[1] (closed_form) = 0.06281367579349373 y[1] (numeric) = 0.06281367579349374 absolute error = 1.387778780781446e-17 relative error = 2.20935769679187e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999998 y[1] (closed_form) = 0.06312971894649118 y[1] (numeric) = 0.06312971894649123 absolute error = 5.551115123125783e-17 relative error = 8.793188399636175e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999997 y[1] (closed_form) = 0.06344815334149689 y[1] (numeric) = 0.06344815334149698 absolute error = 8.326672684688674e-17 relative error = 1.312358555161099e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999996 y[1] (closed_form) = 0.06376900316294241 y[1] (numeric) = 0.06376900316294254 absolute error = 1.249000902703301e-16 relative error = 1.958633255583213e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999994 y[1] (closed_form) = 0.06409229290177838 y[1] (numeric) = 0.06409229290177855 absolute error = 1.665334536937735e-16 relative error = 2.598338211257108e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999993 y[1] (closed_form) = 0.06441804736014821 y[1] (numeric) = 0.06441804736014839 absolute error = 1.804112415015879e-16 relative error = 2.80063194857406e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999992 y[1] (closed_form) = 0.06474629165614514 y[1] (numeric) = 0.06474629165614536 absolute error = 2.220446049250313e-16 relative error = 3.42945671860663e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999991 y[1] (closed_form) = 0.06507705122865444 y[1] (numeric) = 0.06507705122865468 absolute error = 2.359223927328458e-16 relative error = 3.625277855690017e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.08999999999999 y[1] (closed_form) = 0.06541035184228222 y[1] (numeric) = 0.06541035184228249 absolute error = 2.636779683484747e-16 relative error = 4.031135147908336e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.099999999999989 y[1] (closed_form) = 0.06574621959237306 y[1] (numeric) = 0.06574621959237337 absolute error = 3.05311331771918e-16 relative error = 4.6437853562509e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999988 y[1] (closed_form) = 0.06608468091011782 y[1] (numeric) = 0.06608468091011814 absolute error = 3.191891195797325e-16 relative error = 4.8300016763925e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999987 y[1] (closed_form) = 0.06642576256775383 y[1] (numeric) = 0.06642576256775418 absolute error = 3.469446951953614e-16 relative error = 5.223044219349084e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999986 y[1] (closed_form) = 0.06676949168385932 y[1] (numeric) = 0.06676949168385972 absolute error = 4.024558464266192e-16 relative error = 6.027540966346878e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999985 y[1] (closed_form) = 0.06711589572874387 y[1] (numeric) = 0.0671158957287443 absolute error = 4.302114220422482e-16 relative error = 6.409978103860731e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999983 y[1] (closed_form) = 0.06746500252993701 y[1] (numeric) = 0.06746500252993749 absolute error = 4.85722573273506e-16 relative error = 7.199622842346605e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999982 y[1] (closed_form) = 0.06781684027777715 y[1] (numeric) = 0.06781684027777767 absolute error = 5.134781488891349e-16 relative error = 7.571543392259697e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999981 y[1] (closed_form) = 0.06817143753110255 y[1] (numeric) = 0.06817143753110309 absolute error = 5.412337245047638e-16 relative error = 7.939303381388008e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.17999999999998 y[1] (closed_form) = 0.0685288232230469 y[1] (numeric) = 0.0685288232230475 absolute error = 5.967448757360216e-16 relative error = 8.707939924690412e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.189999999999979 y[1] (closed_form) = 0.06888902666694147 y[1] (numeric) = 0.06888902666694213 absolute error = 6.661338147750939e-16 relative error = 9.669665068656848e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999978 y[1] (closed_form) = 0.06925207756232607 y[1] (numeric) = 0.06925207756232681 absolute error = 7.355227538141662e-16 relative error = 1.062094856507668e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999977 y[1] (closed_form) = 0.06961800600107126 y[1] (numeric) = 0.06961800600107207 absolute error = 8.049116928532385e-16 relative error = 1.156183204731334e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999976 y[1] (closed_form) = 0.06998684247361407 y[1] (numeric) = 0.0699868424736149 absolute error = 8.326672684688674e-16 relative error = 1.189748299879072e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999975 y[1] (closed_form) = 0.0703586178753095 y[1] (numeric) = 0.07035861787531039 absolute error = 8.881784197001252e-16 relative error = 1.262359106135608e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999974 y[1] (closed_form) = 0.07073336351290077 y[1] (numeric) = 0.07073336351290169 absolute error = 9.159339953157541e-16 relative error = 1.294910845217619e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999972 y[1] (closed_form) = 0.07111111111111007 y[1] (numeric) = 0.07111111111111104 absolute error = 9.71445146547012e-16 relative error = 1.366094737331756e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999971 y[1] (closed_form) = 0.0714918928193532 y[1] (numeric) = 0.07149189281935421 absolute error = 1.013078509970455e-15 relative error = 1.417053696606296e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.26999999999997 y[1] (closed_form) = 0.07187574121858016 y[1] (numeric) = 0.07187574121858126 absolute error = 1.096345236817342e-15 relative error = 1.525334164531624e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.279999999999969 y[1] (closed_form) = 0.07226268932824484 y[1] (numeric) = 0.07226268932824596 absolute error = 1.124100812432971e-15 relative error = 1.555575668277268e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999968 y[1] (closed_form) = 0.0726527706134061 y[1] (numeric) = 0.07265277061340726 absolute error = 1.165734175856414e-15 relative error = 1.604528176990555e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999967 y[1] (closed_form) = 0.07304601899196363 y[1] (numeric) = 0.07304601899196482 absolute error = 1.193489751472043e-15 relative error = 1.633887469765257e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999966 y[1] (closed_form) = 0.07344246884203123 y[1] (numeric) = 0.07344246884203247 absolute error = 1.235123114895487e-15 relative error = 1.681755984472875e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999965 y[1] (closed_form) = 0.07384215500945038 y[1] (numeric) = 0.07384215500945165 absolute error = 1.27675647831893e-15 relative error = 1.729034693198661e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999964 y[1] (closed_form) = 0.07424511281544745 y[1] (numeric) = 0.07424511281544877 absolute error = 1.318389841742373e-15 relative error = 1.775726093944421e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999963 y[1] (closed_form) = 0.07465137806443754 y[1] (numeric) = 0.0746513780644389 absolute error = 1.360023205165817e-15 relative error = 1.821832684711959e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999961 y[1] (closed_form) = 0.07506098705197814 y[1] (numeric) = 0.07506098705197954 absolute error = 1.40165656858926e-15 relative error = 1.867356963503081e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.35999999999996 y[1] (closed_form) = 0.07547397657287604 y[1] (numeric) = 0.07547397657287747 absolute error = 1.429412144204889e-15 relative error = 1.893913914585751e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.369999999999959 y[1] (closed_form) = 0.07589038392945059 y[1] (numeric) = 0.07589038392945209 absolute error = 1.498801083243961e-15 relative error = 1.97495519937978e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999958 y[1] (closed_form) = 0.07631024693995733 y[1] (numeric) = 0.07631024693995886 absolute error = 1.52655665885959e-15 relative error = 2.000460908036008e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999957 y[1] (closed_form) = 0.07673360394717475 y[1] (numeric) = 0.07673360394717633 absolute error = 1.582067810090848e-15 relative error = 2.061766590788543e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999956 y[1] (closed_form) = 0.07716049382715862 y[1] (numeric) = 0.07716049382716023 absolute error = 1.609823385706477e-15 relative error = 2.086331107875645e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999955 y[1] (closed_form) = 0.07759095599816691 y[1] (numeric) = 0.07759095599816855 absolute error = 1.637578961322106e-15 relative error = 2.110528141141596e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999954 y[1] (closed_form) = 0.07802503042975985 y[1] (numeric) = 0.07802503042976155 absolute error = 1.706967900361178e-15 relative error = 2.187718339818957e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999953 y[1] (closed_form) = 0.07846275765207836 y[1] (numeric) = 0.07846275765208009 absolute error = 1.734723475976807e-15 relative error = 2.210887722897739e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999952 y[1] (closed_form) = 0.07890417876530527 y[1] (numeric) = 0.07890417876530705 absolute error = 1.77635683940025e-15 relative error = 2.251283603982363e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.44999999999995 y[1] (closed_form) = 0.0793493354493134 y[1] (numeric) = 0.07934933544931524 absolute error = 1.845745778439323e-15 relative error = 2.326101117278222e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.459999999999949 y[1] (closed_form) = 0.07979826997350468 y[1] (numeric) = 0.07979826997350659 absolute error = 1.901256929670581e-15 relative error = 2.382579133986053e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999948 y[1] (closed_form) = 0.08025102520684466 y[1] (numeric) = 0.0802510252068466 absolute error = 1.942890293094024e-15 relative error = 2.421016165321603e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999947 y[1] (closed_form) = 0.08070764462809675 y[1] (numeric) = 0.08070764462809873 absolute error = 1.984523656517467e-15 relative error = 2.458904191371477e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999946 y[1] (closed_form) = 0.081168172336261 y[1] (numeric) = 0.08116817233626301 absolute error = 2.012279232133096e-15 relative error = 2.479148136780372e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999945 y[1] (closed_form) = 0.08163265306122192 y[1] (numeric) = 0.08163265306122398 absolute error = 2.067790383364354e-15 relative error = 2.533043219621414e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999944 y[1] (closed_form) = 0.08210113217461004 y[1] (numeric) = 0.08210113217461215 absolute error = 2.109423746787797e-15 relative error = 2.569299217825088e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999943 y[1] (closed_form) = 0.08257365570088247 y[1] (numeric) = 0.08257365570088462 absolute error = 2.151057110211241e-15 relative error = 2.605016202750307e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999942 y[1] (closed_form) = 0.08305027032862713 y[1] (numeric) = 0.08305027032862934 absolute error = 2.206568261442499e-15 relative error = 2.656906777920387e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999941 y[1] (closed_form) = 0.08353102342209609 y[1] (numeric) = 0.08353102342209837 absolute error = 2.275957200481571e-15 relative error = 2.724684922128611e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.549999999999939 y[1] (closed_form) = 0.08401596303297332 y[1] (numeric) = 0.08401596303297561 absolute error = 2.289834988289385e-15 relative error = 2.725476094811537e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999938 y[1] (closed_form) = 0.08450513791238205 y[1] (numeric) = 0.08450513791238441 absolute error = 2.359223927328458e-15 relative error = 2.791811226643504e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999937 y[1] (closed_form) = 0.08499859752313776 y[1] (numeric) = 0.08499859752314018 absolute error = 2.414735078559715e-15 relative error = 2.840911672574824e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999936 y[1] (closed_form) = 0.08549639205225221 y[1] (numeric) = 0.0854963920522547 absolute error = 2.498001805406602e-15 relative error = 2.921762831675887e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999935 y[1] (closed_form) = 0.08599857242369449 y[1] (numeric) = 0.08599857242369705 absolute error = 2.55351295663786e-15 relative error = 2.969250401108183e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999934 y[1] (closed_form) = 0.08650519031141532 y[1] (numeric) = 0.08650519031141794 absolute error = 2.622901895676932e-15 relative error = 3.032074591402652e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999933 y[1] (closed_form) = 0.08701629815264054 y[1] (numeric) = 0.08701629815264322 absolute error = 2.67841304690819e-15 relative error = 3.078059057637483e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999932 y[1] (closed_form) = 0.08753194916144039 y[1] (numeric) = 0.08753194916144313 absolute error = 2.747801985947262e-15 relative error = 3.139198900825718e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999931 y[1] (closed_form) = 0.08805219734258105 y[1] (numeric) = 0.08805219734258386 absolute error = 2.817190924986335e-15 relative error = 3.199455561597863e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63999999999993 y[1] (closed_form) = 0.08857709750566523 y[1] (numeric) = 0.0885770975056681 absolute error = 2.872702076217593e-15 relative error = 3.243165735966749e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999928 y[1] (closed_form) = 0.08910670527956849 y[1] (numeric) = 0.08910670527957142 absolute error = 2.92821322744885e-15 relative error = 3.286187294504612e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999927 y[1] (closed_form) = 0.08964107712717885 y[1] (numeric) = 0.08964107712718186 absolute error = 3.011479954295737e-15 relative error = 3.359486577814299e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999926 y[1] (closed_form) = 0.09018027036044654 y[1] (numeric) = 0.09018027036044961 absolute error = 3.066991105526995e-15 relative error = 3.40095576700798e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999925 y[1] (closed_form) = 0.09072434315575145 y[1] (numeric) = 0.09072434315575457 absolute error = 3.122502256758253e-15 relative error = 3.441746887489372e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999924 y[1] (closed_form) = 0.0912733545695963 y[1] (numeric) = 0.09127335456959948 absolute error = 3.178013407989511e-15 relative error = 3.481863269927548e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999923 y[1] (closed_form) = 0.09182736455463299 y[1] (numeric) = 0.09182736455463625 absolute error = 3.261280134836397e-15 relative error = 3.551534066837003e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999922 y[1] (closed_form) = 0.09238643397603057 y[1] (numeric) = 0.09238643397603388 absolute error = 3.316791286067655e-15 relative error = 3.590128055952661e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999921 y[1] (closed_form) = 0.09295062462819301 y[1] (numeric) = 0.09295062462819639 absolute error = 3.386180225106727e-15 relative error = 3.642988133378998e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72999999999992 y[1] (closed_form) = 0.09351999925183541 y[1] (numeric) = 0.09351999925183886 absolute error = 3.4555691641458e-15 relative error = 3.695005551529644e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999919 y[1] (closed_form) = 0.09409462155142742 y[1] (numeric) = 0.09409462155143092 absolute error = 3.497202527569243e-15 relative error = 3.716686958199674e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999917 y[1] (closed_form) = 0.09467455621301295 y[1] (numeric) = 0.0946745562130165 absolute error = 3.552713678800501e-15 relative error = 3.75255382323322e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999916 y[1] (closed_form) = 0.09525986892241545 y[1] (numeric) = 0.09525986892241908 absolute error = 3.635980405647388e-15 relative error = 3.816906790632599e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999915 y[1] (closed_form) = 0.09585062638383839 y[1] (numeric) = 0.09585062638384211 absolute error = 3.719247132494274e-15 relative error = 3.880253340860156e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999914 y[1] (closed_form) = 0.09644689633887067 y[1] (numeric) = 0.09644689633887445 absolute error = 3.774758283725532e-15 relative error = 3.91382037889819e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999913 y[1] (closed_form) = 0.09704874758590713 y[1] (numeric) = 0.09704874758591099 absolute error = 3.858025010572419e-15 relative error = 3.975347551144142e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999912 y[1] (closed_form) = 0.09765624999999463 y[1] (numeric) = 0.09765624999999854 absolute error = 3.913536161803677e-15 relative error = 4.007461029687186e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999911 y[1] (closed_form) = 0.09826947455311408 y[1] (numeric) = 0.09826947455311806 absolute error = 3.982925100842749e-15 relative error = 4.053064411868816e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.81999999999991 y[1] (closed_form) = 0.09888849333490993 y[1] (numeric) = 0.09888849333491398 absolute error = 4.052314039881821e-15 relative error = 4.097862049690326e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999909 y[1] (closed_form) = 0.09951337957387796 y[1] (numeric) = 0.09951337957388207 absolute error = 4.107825191113079e-15 relative error = 4.12791245629786e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999907 y[1] (closed_form) = 0.1001442076590231 y[1] (numeric) = 0.1001442076590273 absolute error = 4.149458554536523e-15 relative error = 4.143483334218232e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999906 y[1] (closed_form) = 0.1007810531619995 y[1] (numeric) = 0.1007810531620038 absolute error = 4.246603069191224e-15 relative error = 4.213691895405242e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999905 y[1] (closed_form) = 0.1014239928597448 y[1] (numeric) = 0.1014239928597491 absolute error = 4.329869796038111e-15 relative error = 4.269078424101993e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999904 y[1] (closed_form) = 0.1020731047576212 y[1] (numeric) = 0.1020731047576256 absolute error = 4.413136522884997e-15 relative error = 4.323505720105468e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999903 y[1] (closed_form) = 0.1027284681130771 y[1] (numeric) = 0.1027284681130816 absolute error = 4.496403249731884e-15 relative error = 4.376978779419277e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999902 y[1] (closed_form) = 0.1033901634598419 y[1] (numeric) = 0.1033901634598465 absolute error = 4.565792188770956e-15 relative error = 4.416079862901435e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999901 y[1] (closed_form) = 0.1040582726326676 y[1] (numeric) = 0.1040582726326723 absolute error = 4.635181127810029e-15 relative error = 4.454409063825723e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.9099999999999 y[1] (closed_form) = 0.1047328787926326 y[1] (numeric) = 0.1047328787926373 absolute error = 4.704570066849101e-15 relative error = 4.491970545528482e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999899 y[1] (closed_form) = 0.1054140664530206 y[1] (numeric) = 0.1054140664530253 absolute error = 4.746203430272544e-15 relative error = 4.502438422094042e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999898 y[1] (closed_form) = 0.1061019215057914 y[1] (numeric) = 0.1061019215057962 absolute error = 4.843347944927245e-15 relative error = 4.564807004614784e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999896 y[1] (closed_form) = 0.1067965312486578 y[1] (numeric) = 0.1067965312486627 absolute error = 4.926614671774132e-15 relative error = 4.613084914062739e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999895 y[1] (closed_form) = 0.1074979844127849 y[1] (numeric) = 0.1074979844127899 absolute error = 4.996003610813204e-15 relative error = 4.647532358959302e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999894 y[1] (closed_form) = 0.1082063711911282 y[1] (numeric) = 0.1082063711911333 absolute error = 5.079270337660091e-15 relative error = 4.694058475252277e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999893 y[1] (closed_form) = 0.108921783267428 y[1] (numeric) = 0.1089217832674331 absolute error = 5.148659276699163e-15 relative error = 4.726932595345069e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999892 y[1] (closed_form) = 0.1096443138458761 y[1] (numeric) = 0.1096443138458813 absolute error = 5.218048215738236e-15 relative error = 4.759068694682241e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999891 y[1] (closed_form) = 0.1103740576814745 y[1] (numeric) = 0.1103740576814798 absolute error = 5.301314942585122e-15 relative error = 4.803044351131895e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.99999999999989 y[1] (closed_form) = 0.111111111111103 y[1] (numeric) = 0.1111111111111083 absolute error = 5.35682609381638e-15 relative error = 4.821143484435096e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Finished! diff ( y , x , 1 ) = neg ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; Iterations = 1001 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.2 %