##############ECHO OF PROBLEM################# ##############temp/sqrt_sqrt_tonepostode.ode################# diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.5) x_end=c(1.5) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $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=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=c(-2.0) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(0.5) # 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=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(0.8) * (c(x) + c(2.0)) * sqrt(sqrt(c(0.1) * c(x) + c(0.2)))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.5 y[1] (closed_form) 1.4142135623730951 y[1] (numeric) 1.4142135623730951 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.51 y[1] (closed_form) 1.421288162189506 y[1] (numeric) 1.4212881621895062 absolute error 2.220446049250313e-16 relative error 1.562277171034548e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.52 y[1] (closed_form) 1.42836981194674 y[1] (numeric) 1.42836981194674 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] 0.53 y[1] (closed_form) 1.4354584906523087 y[1] (numeric) 1.4354584906523078 absolute error 8.881784197001252e-16 relative error 6.187419737205458e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.54 y[1] (closed_form) 1.4425541774590005 y[1] (numeric) 1.442554177459 absolute error 4.440892098500626e-16 relative error 3.078492418442872e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.55 y[1] (closed_form) 1.4496568516633104 y[1] (numeric) 1.4496568516633095 absolute error 8.881784197001252e-16 relative error 6.126818347949346e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.56 y[1] (closed_form) 1.4567664927038855 y[1] (numeric) 1.4567664927038848 absolute error 6.661338147750939e-16 relative error 4.572687648373155e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5700000000000001 y[1] (closed_form) 1.4638830801599996 y[1] (numeric) 1.4638830801599985 absolute error 1.1102230246251565e-15 relative error 7.584096296159195e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5800000000000001 y[1] (closed_form) 1.4710065937500454 y[1] (numeric) 1.4710065937500447 absolute error 6.661338147750939e-16 relative error 4.5284216780899344e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5900000000000001 y[1] (closed_form) 1.4781370133300544 y[1] (numeric) 1.4781370133300535 absolute error 8.881784197001252e-16 relative error 6.008769225656372e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6000000000000001 y[1] (closed_form) 1.4852743188922317 y[1] (numeric) 1.4852743188922308 absolute error 8.881784197001252e-16 relative error 5.979894814060738e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6100000000000001 y[1] (closed_form) 1.4924184905635163 y[1] (numeric) 1.4924184905635152 absolute error 1.1102230246251565e-15 relative error 7.43908650050263e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6200000000000001 y[1] (closed_form) 1.4995695086041594 y[1] (numeric) 1.499569508604159 absolute error 4.440892098500626e-16 relative error 2.9614446499611285e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6300000000000001 y[1] (closed_form) 1.506727353406328 y[1] (numeric) 1.5067273534063275 absolute error 4.440892098500626e-16 relative error 2.9473760388439866e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6400000000000001 y[1] (closed_form) 1.5138920054927205 y[1] (numeric) 1.5138920054927198 absolute error 6.661338147750939e-16 relative error 4.4001409107004956e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6500000000000001 y[1] (closed_form) 1.5210634455152092 y[1] (numeric) 1.5210634455152081 absolute error 1.1102230246251565e-15 relative error 7.298992214286667e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6600000000000001 y[1] (closed_form) 1.5282416542534973 y[1] (numeric) 1.528241654253497 absolute error 4.440892098500626e-16 relative error 2.9058834289331524e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6700000000000002 y[1] (closed_form) 1.5354266126137996 y[1] (numeric) 1.5354266126137992 absolute error 4.440892098500626e-16 relative error 2.8922854808024793e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6800000000000002 y[1] (closed_form) 1.542618301627535 y[1] (numeric) 1.5426183016275348 absolute error 2.220446049250313e-16 relative error 1.4394008206097633e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6900000000000002 y[1] (closed_form) 1.5498167024500447 y[1] (numeric) 1.5498167024500442 absolute error 4.440892098500626e-16 relative error 2.865430532191448e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7000000000000002 y[1] (closed_form) 1.5570217963593211 y[1] (numeric) 1.557021796359321 absolute error 2.220446049250313e-16 relative error 1.4260853987029803e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7100000000000002 y[1] (closed_form) 1.564233564754762 y[1] (numeric) 1.5642335647547618 absolute error 2.220446049250313e-16 relative error 1.41951055090576e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7200000000000002 y[1] (closed_form) 1.5714519891559355 y[1] (numeric) 1.571451989155935 absolute error 4.440892098500626e-16 relative error 2.8259801312071492e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7300000000000002 y[1] (closed_form) 1.5786770512013646 y[1] (numeric) 1.5786770512013644 absolute error 2.220446049250313e-16 relative error 1.4065232959208255e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7400000000000002 y[1] (closed_form) 1.5859087326473285 y[1] (numeric) 1.5859087326473287 absolute error 2.220446049250313e-16 relative error 1.4001096050109789e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7500000000000002 y[1] (closed_form) 1.5931470153666822 y[1] (numeric) 1.5931470153666822 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7600000000000002 y[1] (closed_form) 1.6003918813476865 y[1] (numeric) 1.6003918813476865 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7700000000000002 y[1] (closed_form) 1.6076433126928613 y[1] (numeric) 1.6076433126928609 absolute error 4.440892098500626e-16 relative error 2.7623615658015392e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7800000000000002 y[1] (closed_form) 1.6149012916178467 y[1] (numeric) 1.614901291617847 absolute error 2.220446049250313e-16 relative error 1.3749732325904683e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7900000000000003 y[1] (closed_form) 1.622165800450289 y[1] (numeric) 1.6221658004502892 absolute error 2.220446049250313e-16 relative error 1.3688157207074334e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8000000000000003 y[1] (closed_form) 1.6294368216287303 y[1] (numeric) 1.6294368216287303 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8100000000000003 y[1] (closed_form) 1.6367143377015232 y[1] (numeric) 1.6367143377015232 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8200000000000003 y[1] (closed_form) 1.6439983313257525 y[1] (numeric) 1.6439983313257527 absolute error 2.220446049250313e-16 relative error 1.3506376539078978e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8300000000000003 y[1] (closed_form) 1.651288785266178 y[1] (numeric) 1.6512887852661777 absolute error 2.220446049250313e-16 relative error 1.3446745772529367e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8400000000000003 y[1] (closed_form) 1.6585856823941834 y[1] (numeric) 1.6585856823941834 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8500000000000003 y[1] (closed_form) 1.6658890056867475 y[1] (numeric) 1.6658890056867472 absolute error 2.220446049250313e-16 relative error 1.3328895512669253e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8600000000000003 y[1] (closed_form) 1.6731987382254212 y[1] (numeric) 1.6731987382254214 absolute error 2.220446049250313e-16 relative error 1.3270665334144928e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8700000000000003 y[1] (closed_form) 1.6805148631953246 y[1] (numeric) 1.680514863195325 absolute error 4.440892098500626e-16 relative error 2.6425782929742918e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8800000000000003 y[1] (closed_form) 1.687837363884153 y[1] (numeric) 1.687837363884153 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8900000000000003 y[1] (closed_form) 1.695166223681196 y[1] (numeric) 1.6951662236811957 absolute error 2.220446049250313e-16 relative error 1.3098692141402085e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9000000000000004 y[1] (closed_form) 1.702501426076371 y[1] (numeric) 1.7025014260763707 absolute error 2.220446049250313e-16 relative error 1.3042256618648542e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9100000000000004 y[1] (closed_form) 1.70984295465927 y[1] (numeric) 1.7098429546592697 absolute error 2.220446049250313e-16 relative error 1.2986257265321738e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9200000000000004 y[1] (closed_form) 1.717190793118215 y[1] (numeric) 1.717190793118215 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9300000000000004 y[1] (closed_form) 1.7245449252393306 y[1] (numeric) 1.72454492523933 absolute error 6.661338147750939e-16 relative error 3.862664318139747e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9400000000000004 y[1] (closed_form) 1.7319053349056202 y[1] (numeric) 1.7319053349056197 absolute error 4.440892098500626e-16 relative error 2.5641656093995645e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9500000000000004 y[1] (closed_form) 1.7392720060960671 y[1] (numeric) 1.7392720060960665 absolute error 6.661338147750939e-16 relative error 3.829957662978108e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9600000000000004 y[1] (closed_form) 1.7466449228847327 y[1] (numeric) 1.7466449228847327 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9700000000000004 y[1] (closed_form) 1.7540240694398774 y[1] (numeric) 1.7540240694398772 absolute error 2.220446049250313e-16 relative error 1.2659153816283609e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9800000000000004 y[1] (closed_form) 1.7614094300230843 y[1] (numeric) 1.7614094300230843 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9900000000000004 y[1] (closed_form) 1.7688009889884004 y[1] (numeric) 1.7688009889884004 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0000000000000004 y[1] (closed_form) 1.7761987307814848 y[1] (numeric) 1.7761987307814846 absolute error 2.220446049250313e-16 relative error 1.2501112689532043e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0099999999999993 y[1] (closed_form) 1.7836026399387677 y[1] (numeric) 1.783602639938768 absolute error 4.440892098500626e-16 relative error 2.489843869401923e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0199999999999982 y[1] (closed_form) 1.791012701086623 y[1] (numeric) 1.7910127010866241 absolute error 1.1102230246251565e-15 relative error 6.198856233412384e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0299999999999971 y[1] (closed_form) 1.798428898940547 y[1] (numeric) 1.798428898940549 absolute error 1.9984014443252818e-15 relative error 1.111192911492102e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.039999999999996 y[1] (closed_form) 1.80585121830435 y[1] (numeric) 1.8058512183043525 absolute error 2.4424906541753444e-15 relative error 1.3525425735065722e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.049999999999995 y[1] (closed_form) 1.8132796440693562 y[1] (numeric) 1.8132796440693597 absolute error 3.552713678800501e-15 relative error 1.9592751125951608e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0599999999999938 y[1] (closed_form) 1.820714161213615 y[1] (numeric) 1.8207141612136197 absolute error 4.6629367034256575e-15 relative error 2.5610481879909865e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0699999999999927 y[1] (closed_form) 1.8281547548011228 y[1] (numeric) 1.8281547548011279 absolute error 5.10702591327572e-15 relative error 2.793541356312197e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0799999999999916 y[1] (closed_form) 1.8356014099810485 y[1] (numeric) 1.8356014099810547 absolute error 6.217248937900877e-15 relative error 3.3870364797579155e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0899999999999905 y[1] (closed_form) 1.843054111986978 y[1] (numeric) 1.843054111986985 absolute error 6.8833827526759706e-15 relative error 3.734769754131128e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0999999999999894 y[1] (closed_form) 1.8505128461361589 y[1] (numeric) 1.8505128461361664 absolute error 7.549516567451064e-15 relative error 4.0796888188127597e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1099999999999883 y[1] (closed_form) 1.857977597828759 y[1] (numeric) 1.857977597828767 absolute error 7.993605777301127e-15 relative error 4.3023154782073215e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1199999999999872 y[1] (closed_form) 1.865448352547133 y[1] (numeric) 1.865448352547142 absolute error 8.881784197001252e-15 relative error 4.761206165195529e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1299999999999861 y[1] (closed_form) 1.8729250958550985 y[1] (numeric) 1.872925095855108 absolute error 9.547918011776346e-15 relative error 5.097864315506526e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.139999999999985 y[1] (closed_form) 1.8804078133972182 y[1] (numeric) 1.8804078133972286 absolute error 1.0436096431476471e-14 relative error 5.549911225173125e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.149999999999984 y[1] (closed_form) 1.8878964908980949 y[1] (numeric) 1.887896490898106 absolute error 1.1102230246251565e-14 relative error 5.880740972705607e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1599999999999828 y[1] (closed_form) 1.8953911141616695 y[1] (numeric) 1.8953911141616815 absolute error 1.199040866595169e-14 relative error 6.326086777744045e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1699999999999817 y[1] (closed_form) 1.9028916690705326 y[1] (numeric) 1.9028916690705457 absolute error 1.3100631690576847e-14 relative error 6.884591437081571e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1799999999999806 y[1] (closed_form) 1.910398141585242 y[1] (numeric) 1.910398141585256 absolute error 1.3988810110276972e-14 relative error 7.322457976570845e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1899999999999795 y[1] (closed_form) 1.9179105177436453 y[1] (numeric) 1.9179105177436606 absolute error 1.532107773982716e-14 relative error 7.988421565074826e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1999999999999784 y[1] (closed_form) 1.9254287836602173 y[1] (numeric) 1.925428783660233 absolute error 1.5765166949677223e-14 relative error 8.18787331085174e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2099999999999773 y[1] (closed_form) 1.9329529255253983 y[1] (numeric) 1.9329529255254152 absolute error 1.687538997430238e-14 relative error 8.730367797092347e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2199999999999762 y[1] (closed_form) 1.9404829296049448 y[1] (numeric) 1.9404829296049626 absolute error 1.7763568394002505e-14 relative error 9.15419977315591e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2299999999999751 y[1] (closed_form) 1.9480187822392843 y[1] (numeric) 1.9480187822393034 absolute error 1.9095836023552692e-14 relative error 9.80269605080587e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.239999999999974 y[1] (closed_form) 1.9555604698428817 y[1] (numeric) 1.9555604698429014 absolute error 1.9761969838327786e-14 relative error 1.0105527363168447e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.249999999999973 y[1] (closed_form) 1.9631079789036072 y[1] (numeric) 1.963107978903628 absolute error 2.0872192862952943e-14 relative error 1.0632218445064866e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2599999999999718 y[1] (closed_form) 1.9706612959821193 y[1] (numeric) 1.9706612959821408 absolute error 2.1538326677728037e-14 relative error 1.0929491902866023e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2699999999999707 y[1] (closed_form) 1.9782204077112466 y[1] (numeric) 1.9782204077112686 absolute error 2.19824158875781e-14 relative error 1.111221772957606e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2799999999999696 y[1] (closed_form) 1.9857853007953825 y[1] (numeric) 1.9857853007954056 absolute error 2.3092638912203256e-14 relative error 1.1628970615782974e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2899999999999685 y[1] (closed_form) 1.9933559620098855 y[1] (numeric) 1.9933559620099093 absolute error 2.375877272697835e-14 relative error 1.191898144625537e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2999999999999674 y[1] (closed_form) 2.0009323782004844 y[1] (numeric) 2.000932378200509 absolute error 2.4424906541753444e-14 relative error 1.2206762611198137e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3099999999999663 y[1] (closed_form) 2.0085145362826915 y[1] (numeric) 2.008514536282717 absolute error 2.531308496145357e-14 relative error 1.260288860458157e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3199999999999652 y[1] (closed_form) 2.0161024232412257 y[1] (numeric) 2.0161024232412514 absolute error 2.5757174171303632e-14 relative error 1.277572700393595e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.329999999999964 y[1] (closed_form) 2.0236960261294343 y[1] (numeric) 2.023696026129461 absolute error 2.6645352591003757e-14 relative error 1.3166677330471537e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.339999999999963 y[1] (closed_form) 2.031295332068729 y[1] (numeric) 2.031295332068757 absolute error 2.7977620220553945e-14 relative error 1.3773290264031051e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.349999999999962 y[1] (closed_form) 2.0389003282480256 y[1] (numeric) 2.0389003282480553 absolute error 2.9753977059954195e-14 relative error 1.4593149379460357e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3599999999999608 y[1] (closed_form) 2.046511001923189 y[1] (numeric) 2.0465110019232187 absolute error 2.9753977059954195e-14 relative error 1.4538879601425637e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3699999999999597 y[1] (closed_form) 2.0541273404164824 y[1] (numeric) 2.054127340416513 absolute error 3.064215547965432e-14 relative error 1.4917359248741368e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3799999999999586 y[1] (closed_form) 2.06174933111603 y[1] (numeric) 2.061749331116061 absolute error 3.108624468950438e-14 relative error 1.5077606293039185e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3899999999999575 y[1] (closed_form) 2.069376961475278 y[1] (numeric) 2.0693769614753097 absolute error 3.1530333899354446e-14 relative error 1.5236631356365432e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3999999999999564 y[1] (closed_form) 2.077010219012465 y[1] (numeric) 2.077010219012498 absolute error 3.2862601528904634e-14 relative error 1.5822070218089481e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4099999999999553 y[1] (closed_form) 2.084649091310099 y[1] (numeric) 2.084649091310132 absolute error 3.3306690738754696e-14 relative error 1.5977120982900336e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4199999999999542 y[1] (closed_form) 2.0922935660144346 y[1] (numeric) 2.092293566014469 absolute error 3.419486915845482e-14 relative error 1.6343246336885649e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.429999999999953 y[1] (closed_form) 2.099943630834967 y[1] (numeric) 2.0999436308350017 absolute error 3.4638958368304884e-14 relative error 1.6495184851477156e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.439999999999952 y[1] (closed_form) 2.107599273543919 y[1] (numeric) 2.107599273543955 absolute error 3.597122599785507e-14 relative error 1.7067393431660096e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4499999999999509 y[1] (closed_form) 2.115260481975743 y[1] (numeric) 2.1152604819757794 absolute error 3.6415315207705135e-14 relative error 1.7215522872006612e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4599999999999498 y[1] (closed_form) 2.1229272440266223 y[1] (numeric) 2.1229272440266596 absolute error 3.730349362740526e-14 relative error 1.7571724953065543e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4699999999999487 y[1] (closed_form) 2.1305995476539814 y[1] (numeric) 2.1305995476540187 absolute error 3.730349362740526e-14 relative error 1.7508449050634787e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4799999999999476 y[1] (closed_form) 2.1382773808760005 y[1] (numeric) 2.1382773808760387 absolute error 3.8191672047105385e-14 relative error 1.786095311519368e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4899999999999465 y[1] (closed_form) 2.1459607317711358 y[1] (numeric) 2.145960731771175 absolute error 3.907985046680551e-14 relative error 1.821088796650606e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4999999999999454 y[1] (closed_form) 2.1536495884776423 y[1] (numeric) 2.1536495884776823 absolute error 3.9968028886505635e-14 relative error 1.855827851491754e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Finished! diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 1001 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.19999999999452%