##############ECHO OF PROBLEM################# ##############temp/tan_sqrtpostode.ode################# diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(1.4); x_end=c(2.1); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=c(0.0001); glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-2.0); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(0.5); 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(tan(sqrt(c(2.0)*c(x) + c(1.0)))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (closed_form) = -2.514161640922489 y[1] (numeric) = -2.514161640922489 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999999 y[1] (closed_form) = -2.477131584442638 y[1] (numeric) = -2.47708420282834 absolute error = 4.738161429829191e-05 relative error = 0.00191276130004022 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999998 y[1] (closed_form) = -2.441122841917847 y[1] (numeric) = -2.441030178933042 absolute error = 9.266298480525847e-05 relative error = 0.003795916502606587 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999997 y[1] (closed_form) = -2.40609157754059 y[1] (numeric) = -2.405955612058374 absolute error = 0.0001359654822157275 relative error = 0.0056508855890974 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999996 y[1] (closed_form) = -2.37199643510759 y[1] (numeric) = -2.371819033242745 absolute error = 0.0001774018648448283 relative error = 0.007479010601328398 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999994 y[1] (closed_form) = -2.338798364980749 y[1] (numeric) = -2.338581287980746 absolute error = 0.000217077000002952 relative error = 0.009281561132130293 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.459999999999993 y[1] (closed_form) = -2.306460465341871 y[1] (numeric) = -2.306205376825903 absolute error = 0.0002550885159684491 relative error = 0.01105973936260984 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999992 y[1] (closed_form) = -2.274947836382328 y[1] (numeric) = -2.27465630899026 absolute error = 0.0002915273920676142 relative error = 0.01281468468882379 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999991 y[1] (closed_form) = -2.244227446214415 y[1] (numeric) = -2.243900967720946 absolute error = 0.0003264784934691178 relative error = 0.01454747797598791 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.48999999999999 y[1] (closed_form) = -2.214268007419532 y[1] (numeric) = -2.213907986362986 absolute error = 0.0003600210565459783 relative error = 0.01625914547559852 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999989 y[1] (closed_form) = -2.185039863261551 y[1] (numeric) = -2.184647634131614 absolute error = 0.0003922291299369718 relative error = 0.01795066243558146 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999988 y[1] (closed_form) = -2.156514882693875 y[1] (numeric) = -2.156091710717991 absolute error = 0.0004231719758842623 relative error = 0.01962295643216913 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999987 y[1] (closed_form) = -2.128666363377349 y[1] (numeric) = -2.128213448941496 absolute error = 0.0004529144358529358 relative error = 0.02127691044708107 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999986 y[1] (closed_form) = -2.101468942004845 y[1] (numeric) = -2.100987424740807 absolute error = 0.0004815172640384446 relative error = 0.02291336571355973 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999984 y[1] (closed_form) = -2.074898511298209 y[1] (numeric) = -2.074389473866271 absolute error = 0.0005090374319380864 relative error = 0.02453312435120478 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.549999999999983 y[1] (closed_form) = -2.048932143105383 y[1] (numeric) = -2.048396614698585 absolute error = 0.0005355284067976029 relative error = 0.02613695180680559 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999982 y[1] (closed_form) = -2.023548017080985 y[1] (numeric) = -2.022986976674505 absolute error = 0.0005610404064801955 relative error = 0.02772557911867637 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999981 y[1] (closed_form) = -1.998725354483001 y[1] (numeric) = -1.998139733849983 absolute error = 0.0005856206330181468 relative error = 0.02929970501973374 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.57999999999998 y[1] (closed_form) = -1.974444356662424 y[1] (numeric) = -1.9738350431756 absolute error = 0.0006093134868239147 relative error = 0.03085999789094541 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999979 y[1] (closed_form) = -1.950686147862249 y[1] (numeric) = -1.950053987098845 absolute error = 0.0006321607634036663 relative error = 0.03240709757930303 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999978 y[1] (closed_form) = -1.927432721977594 y[1] (numeric) = -1.926778520143437 absolute error = 0.0006542018341568756 relative error = 0.03394161708978607 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999977 y[1] (closed_form) = -1.904666892960579 y[1] (numeric) = -1.90399141914784 absolute error = 0.0006754738127388027 relative error = 0.03546414416270232 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999976 y[1] (closed_form) = -1.882372248582089 y[1] (numeric) = -1.881676236873818 absolute error = 0.0006960117082714934 relative error = 0.03697524274466803 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999975 y[1] (closed_form) = -1.860533107288282 y[1] (numeric) = -1.859817258721693 absolute error = 0.0007158485665890169 relative error = 0.0384754543622372 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.639999999999973 y[1] (closed_form) = -1.839134477912795 y[1] (numeric) = -1.83839946231225 absolute error = 0.0007350156005452302 relative error = 0.03996529940428217 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999972 y[1] (closed_form) = -1.818162022026551 y[1] (numeric) = -1.817408479716169 absolute error = 0.0007535423103821604 relative error = 0.04144527832245944 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999971 y[1] (closed_form) = -1.797602018725817 y[1] (numeric) = -1.796830562130838 absolute error = 0.0007714565949794583 relative error = 0.04291587275398617 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.66999999999997 y[1] (closed_form) = -1.77744133167625 y[1] (numeric) = -1.776652546821471 absolute error = 0.0007887848547787346 relative error = 0.04437754657335757 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999969 y[1] (closed_form) = -1.757667378246064 y[1] (numeric) = -1.75686182615897 absolute error = 0.0008055520870944299 relative error = 0.04583074687875654 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999968 y[1] (closed_form) = -1.738268100575393 y[1] (numeric) = -1.737446318600975 absolute error = 0.0008217819744182897 relative error = 0.04727590491629383 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999967 y[1] (closed_form) = -1.719231938441632 y[1] (numeric) = -1.718394441475284 absolute error = 0.0008374969663478282 relative error = 0.04871343694946494 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999966 y[1] (closed_form) = -1.700547803791945 y[1] (numeric) = -1.699695085436344 absolute error = 0.0008527183556010787 relative error = 0.05014374507436108 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999965 y[1] (closed_form) = -1.682205056824688 y[1] (numeric) = -1.681337590476032 absolute error = 0.0008674663486558654 relative error = 0.0515672179878763 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.729999999999964 y[1] (closed_form) = -1.664193483510866 y[1] (numeric) = -1.663311723379479 absolute error = 0.0008817601313872991 relative error = 0.0529842317088692 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.739999999999962 y[1] (closed_form) = -1.646503274455525 y[1] (numeric) = -1.645607656525357 absolute error = 0.0008956179301682354 relative error = 0.05439515025953431 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999961 y[1] (closed_form) = -1.629125005006734 y[1] (numeric) = -1.628215947938018 absolute error = 0.0009090570687164679 relative error = 0.05580032630539056 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.75999999999996 y[1] (closed_form) = -1.612049616527122 y[1] (numeric) = -1.611127522506044 absolute error = 0.0009220940210779016 relative error = 0.05720010176016737 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.769999999999959 y[1] (closed_form) = -1.595268398749426 y[1] (numeric) = -1.594333654288401 absolute error = 0.0009347444610248168 relative error = 0.05859480835686259 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999958 y[1] (closed_form) = -1.578772973143534 y[1] (numeric) = -1.577825949835405 absolute error = 0.0009470233081292356 relative error = 0.05998476818637161 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999957 y[1] (closed_form) = -1.562555277228009 y[1] (numeric) = -1.561596332457219 absolute error = 0.00095894477079006 relative error = 0.06137029420752647 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999956 y[1] (closed_form) = -1.546607549764088 y[1] (numeric) = -1.545637027377672 absolute error = 0.0009705223864153734 relative error = 0.06275169072874449 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999955 y[1] (closed_form) = -1.530922316774773 y[1] (numeric) = -1.529940547715778 absolute error = 0.0009817690589943862 relative error = 0.06412925386460498 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.819999999999954 y[1] (closed_form) = -1.515492378335865 y[1] (numeric) = -1.514499681241621 absolute error = 0.0009926970942437663 relative error = 0.06550327196853534 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.829999999999953 y[1] (closed_form) = -1.500310796089632 y[1] (numeric) = -1.499307477857136 absolute error = 0.00100331823249622 relative error = 0.06687402604255333 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999951 y[1] (closed_form) = -1.485370881435411 y[1] (numeric) = -1.484357237755906 absolute error = 0.001013643679504961 relative error = 0.06824179012620814 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.84999999999995 y[1] (closed_form) = -1.4706661843547 y[1] (numeric) = -1.469642500219383 absolute error = 0.001023684135316616 relative error = 0.06960683166627572 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.859999999999949 y[1] (closed_form) = -1.456190482831306 y[1] (numeric) = -1.455157033009969 absolute error = 0.001033449821337351 relative error = 0.07096941186760056 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999948 y[1] (closed_form) = -1.441937772829909 y[1] (numeric) = -1.440894822324175 absolute error = 0.001042950505734108 relative error = 0.07232978602725976 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999947 y[1] (closed_form) = -1.427902258798918 y[1] (numeric) = -1.426850063271648 absolute error = 0.001052195527269539 relative error = 0.07368820385189356 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999946 y[1] (closed_form) = -1.414078344665924 y[1] (numeric) = -1.413017150848223 absolute error = 0.001061193817701422 relative error = 0.07504490976079048 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999945 y[1] (closed_form) = -1.400460625296164 y[1] (numeric) = -1.399390671373337 absolute error = 0.001069953922827604 relative error = 0.07640014317441694 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.909999999999944 y[1] (closed_form) = -1.387043878386449 y[1] (numeric) = -1.385965394364177 absolute error = 0.001078484022272619 relative error = 0.07775413878955446 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.919999999999943 y[1] (closed_form) = -1.37382305676887 y[1] (numeric) = -1.372736264820767 absolute error = 0.001086791948103683 relative error = 0.07910712684206483 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999942 y[1] (closed_form) = -1.36079328110032 y[1] (numeric) = -1.359698395897957 absolute error = 0.00109488520236245 relative error = 0.08045933335863771 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.93999999999994 y[1] (closed_form) = -1.347949832915417 y[1] (numeric) = -1.346847061941855 absolute error = 0.001102770973562484 relative error = 0.08181098039660364 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.949999999999939 y[1] (closed_form) = -1.335288148021956 y[1] (numeric) = -1.334177691869715 absolute error = 0.001110456152241701 relative error = 0.08316228627406658 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.959999999999938 y[1] (closed_form) = -1.322803810219309 y[1] (numeric) = -1.321685862873686 absolute error = 0.001117947345622428 relative error = 0.08451346579029601 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999937 y[1] (closed_form) = -1.310492545321511 y[1] (numeric) = -1.309367294430068 absolute error = 0.001125250891442997 relative error = 0.08586473043743507 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999936 y[1] (closed_form) = -1.298350215467915 y[1] (numeric) = -1.297217842596918 absolute error = 0.001132372870996434 relative error = 0.08721628860271237 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.989999999999935 y[1] (closed_form) = -1.286372813705393 y[1] (numeric) = -1.285233494583939 absolute error = 0.001139319121454152 relative error = 0.08856834576380283 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.999999999999934 y[1] (closed_form) = -1.274556458827097 y[1] (numeric) = -1.273410363579595 absolute error = 0.001146095247501089 relative error = 0.08992110467634964 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.009999999999933 y[1] (closed_form) = -1.262897390453665 y[1] (numeric) = -1.261744683821342 absolute error = 0.001152706632323364 relative error = 0.09127476555393639 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999932 y[1] (closed_form) = -1.25139196434375 y[1] (numeric) = -1.25023280589574 absolute error = 0.001159158448009734 relative error = 0.09262952624261218 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999931 y[1] (closed_form) = -1.240036647921414 y[1] (numeric) = -1.238871192256043 absolute error = 0.001165455665371073 relative error = 0.09398558238779836 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999929 y[1] (closed_form) = -1.228828016008843 y[1] (numeric) = -1.227656412945592 absolute error = 0.001171603063250037 relative error = 0.09534312759692212 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999928 y[1] (closed_form) = -1.217762746753406 y[1] (numeric) = -1.216585141516086 absolute error = 0.001177605237320467 relative error = 0.09670235359555869 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999927 y[1] (closed_form) = -1.206837617738849 y[1] (numeric) = -1.205654151130425 absolute error = 0.001183466608423833 relative error = 0.09806345037878386 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999926 y[1] (closed_form) = -1.196049502270946 y[1] (numeric) = -1.194860310840474 absolute error = 0.001189191430472025 relative error = 0.09942660635819006 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999925 y[1] (closed_form) = -1.185395365828569 y[1] (numeric) = -1.18420058203064 absolute error = 0.001194783797929366 relative error = 0.1007920085037818 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 3 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.089999999999924 y[1] (closed_form) = -1.174872262671616 y[1] (numeric) = -1.173672015018704 absolute error = 0.001200247652912489 relative error = 0.1021598424822091 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 3 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.099999999999923 y[1] (closed_form) = -1.164477332597786 y[1] (numeric) = -1.163271745805861 absolute error = 0.001205586791925395 relative error = 0.1035302927911786 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 3 h = 0.001 Finished! diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan ( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; Iterations = 701 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.3 %