##############ECHO OF PROBLEM################# ##############temp/tanpostode.ode################# diff ( y , x , 1 ) = tan ( x ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.1) x_end=c(1.5) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true # 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(1.570796327) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(0.0) # 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(neg(ln(cos(c(x))))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 0.005008355623235254 y[1] (numeric) 0.005008355623235254 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] 0.11000000000000001 y[1] (closed_form) 0.006062240346532338 y[1] (numeric) 0.006062240346532249 absolute error 8.933825901280557e-17 relative error 1.4736838842740363e-12% Desired digits 8 Estimated correct digits 13 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 0.12000000000000002 y[1] (closed_form) 0.007217346646627739 y[1] (numeric) 0.007217346646627682 absolute error 5.637851296924623e-17 relative error 7.811529046562943e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.13000000000000003 y[1] (closed_form) 0.008473908649082243 y[1] (numeric) 0.00847390864908224 absolute error 3.469446951953614e-18 relative error 4.0942699474691276e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.14000000000000004 y[1] (closed_form) 0.009832181658295606 y[1] (numeric) 0.009832181658295499 absolute error 1.0755285551056204e-16 relative error 1.093885968022342e-12% Desired digits 8 Estimated correct digits 13 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 0.15000000000000005 y[1] (closed_form) 0.011292442366641833 y[1] (numeric) 0.011292442366641736 absolute error 9.71445146547012e-17 relative error 8.602613278919059e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.16000000000000006 y[1] (closed_form) 0.012854989082009669 y[1] (numeric) 0.0128549890820096 absolute error 6.938893903907228e-17 relative error 5.397821701473156e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.17000000000000007 y[1] (closed_form) 0.014520141974147178 y[1] (numeric) 0.014520141974147067 absolute error 1.1102230246251565e-16 relative error 7.646089319249677e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.18000000000000008 y[1] (closed_form) 0.016288243340248813 y[1] (numeric) 0.016288243340248795 absolute error 1.734723475976807e-17 relative error 1.0650156924474756e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.19000000000000009 y[1] (closed_form) 0.01815965789025992 y[1] (numeric) 0.018159657890259855 absolute error 6.591949208711867e-17 relative error 3.629996362567773e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2000000000000001 y[1] (closed_form) 0.020134773052408354 y[1] (numeric) 0.020134773052408298 absolute error 5.551115123125783e-17 relative error 2.756979236208379e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2100000000000001 y[1] (closed_form) 0.02221399929951903 y[1] (numeric) 0.02221399929951901 absolute error 2.0816681711721685e-17 relative error 9.370974326163953e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2200000000000001 y[1] (closed_form) 0.024397770496703126 y[1] (numeric) 0.024397770496703105 absolute error 2.0816681711721685e-17 relative error 8.532206545075357e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.23000000000000012 y[1] (closed_form) 0.026686544271060854 y[1] (numeric) 0.026686544271060746 absolute error 1.0755285551056204e-16 relative error 4.0302279087964716e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.24000000000000013 y[1] (closed_form) 0.029080802404080987 y[1] (numeric) 0.029080802404080893 absolute error 9.367506770274758e-17 relative error 3.221199552925744e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2500000000000001 y[1] (closed_form) 0.03158105124746966 y[1] (numeric) 0.031581051247469565 absolute error 9.71445146547012e-17 relative error 3.0760380296866973e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y[1] (closed_form) 0.034187822163188435 y[1] (numeric) 0.034187822163188386 absolute error 4.85722573273506e-17 relative error 1.4207473379117588e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y[1] (closed_form) 0.036901671988538005 y[1] (numeric) 0.03690167198853799 absolute error 1.3877787807814457e-17 relative error 3.760747700571677e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y[1] (closed_form) 0.03972318352717689 y[1] (numeric) 0.0397231835271768 absolute error 9.020562075079397e-17 relative error 2.2708557759243838e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y[1] (closed_form) 0.042652966067024164 y[1] (numeric) 0.04265296606702404 absolute error 1.249000902703301e-16 relative error 2.928286161249939e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y[1] (closed_form) 0.04569165592605806 y[1] (numeric) 0.045691655926058 absolute error 6.245004513516506e-17 relative error 1.3667713255178752e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y[1] (closed_form) 0.04883991702708585 y[1] (numeric) 0.048839917027085816 absolute error 3.469446951953614e-17 relative error 7.103711806122671e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y[1] (closed_form) 0.05209844150263039 y[1] (numeric) 0.05209844150263034 absolute error 4.85722573273506e-17 relative error 9.323168971359391e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3300000000000002 y[1] (closed_form) 0.05546795033115276 y[1] (numeric) 0.05546795033115269 absolute error 6.938893903907228e-17 relative error 1.250973555446144e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3400000000000002 y[1] (closed_form) 0.058949194005906855 y[1] (numeric) 0.05894919400590681 absolute error 4.163336342344337e-17 relative error 7.062583997208105e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3500000000000002 y[1] (closed_form) 0.06254295323780479 y[1] (numeric) 0.06254295323780475 absolute error 4.163336342344337e-17 relative error 6.656763275175439e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3600000000000002 y[1] (closed_form) 0.0662500396937582 y[1] (numeric) 0.06625003969375816 absolute error 4.163336342344337e-17 relative error 6.284277506231576e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3700000000000002 y[1] (closed_form) 0.07007129677205522 y[1] (numeric) 0.07007129677205519 absolute error 2.7755575615628914e-17 relative error 3.961047803342206e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3800000000000002 y[1] (closed_form) 0.07400760041643002 y[1] (numeric) 0.07400760041642994 absolute error 8.326672684688674e-17 relative error 1.1251104802527978e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y[1] (closed_form) 0.07805985997058702 y[1] (numeric) 0.07805985997058701 absolute error 1.3877787807814457e-17 relative error 1.7778391881619582e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y[1] (closed_form) 0.08222901907505553 y[1] (numeric) 0.08222901907505546 absolute error 6.938893903907228e-17 relative error 8.43849772496212e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y[1] (closed_form) 0.08651605660836616 y[1] (numeric) 0.08651605660836607 absolute error 8.326672684688674e-17 relative error 9.624424657241578e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.42000000000000026 y[1] (closed_form) 0.09092198767467256 y[1] (numeric) 0.09092198767467245 absolute error 1.1102230246251565e-16 relative error 1.2210721004006634e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.43000000000000027 y[1] (closed_form) 0.09544786464007339 y[1] (numeric) 0.09544786464007325 absolute error 1.3877787807814457e-16 relative error 1.4539652469069408e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4400000000000003 y[1] (closed_form) 0.10009477822003766 y[1] (numeric) 0.10009477822003751 absolute error 1.5265566588595902e-16 relative error 1.5251111856242603e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4500000000000003 y[1] (closed_form) 0.10486385862049037 y[1] (numeric) 0.10486385862049023 absolute error 1.3877787807814457e-16 relative error 1.3234099899031125e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4600000000000003 y[1] (closed_form) 0.10975627673528227 y[1] (numeric) 0.10975627673528211 absolute error 1.5265566588595902e-16 relative error 1.390860463079888e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4700000000000003 y[1] (closed_form) 0.11477324540294474 y[1] (numeric) 0.11477324540294469 absolute error 5.551115123125783e-17 relative error 4.8365933224568006e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4800000000000003 y[1] (closed_form) 0.11991602072582375 y[1] (numeric) 0.11991602072582362 absolute error 1.249000902703301e-16 relative error 1.0415629997921791e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4900000000000003 y[1] (closed_form) 0.12518590345488673 y[1] (numeric) 0.12518590345488662 absolute error 1.1102230246251565e-16 relative error 8.868594578024896e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5000000000000003 y[1] (closed_form) 0.1305842404437229 y[1] (numeric) 0.13058424044372277 absolute error 1.3877787807814457e-16 relative error 1.0627459914502686e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5100000000000003 y[1] (closed_form) 0.13611242617548622 y[1] (numeric) 0.13611242617548605 absolute error 1.6653345369377348e-16 relative error 1.223499267282667e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5200000000000004 y[1] (closed_form) 0.1417719043667884 y[1] (numeric) 0.14177190436678835 absolute error 5.551115123125783e-17 relative error 3.915525539365042e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5300000000000004 y[1] (closed_form) 0.1475641696528218 y[1] (numeric) 0.14756416965282165 absolute error 1.3877787807814457e-16 relative error 9.404578252610443e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5400000000000004 y[1] (closed_form) 0.15349076935828165 y[1] (numeric) 0.1534907693582815 absolute error 1.6653345369377348e-16 relative error 1.0849737374437631e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5500000000000004 y[1] (closed_form) 0.159553305358981 y[1] (numeric) 0.15955330535898085 absolute error 1.3877787807814457e-16 relative error 8.697900539628839e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5600000000000004 y[1] (closed_form) 0.1657534360393848 y[1] (numeric) 0.1657534360393846 absolute error 1.942890293094024e-16 relative error 1.172156873195903e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5700000000000004 y[1] (closed_form) 0.17209287835166318 y[1] (numeric) 0.17209287835166293 absolute error 2.498001805406602e-16 relative error 1.451542811842603e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5800000000000004 y[1] (closed_form) 0.17857340998225993 y[1] (numeric) 0.17857340998225973 absolute error 1.942890293094024e-16 relative error 1.0880064917207086e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5900000000000004 y[1] (closed_form) 0.18519687163240187 y[1] (numeric) 0.18519687163240156 absolute error 3.0531133177191805e-16 relative error 1.6485771551148656e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6000000000000004 y[1] (closed_form) 0.19196516941943795 y[1] (numeric) 0.19196516941943773 absolute error 2.220446049250313e-16 relative error 1.1566921520011306e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6100000000000004 y[1] (closed_form) 0.19888027740640507 y[1] (numeric) 0.19888027740640474 absolute error 3.3306690738754696e-16 relative error 1.6747105933834558e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6200000000000004 y[1] (closed_form) 0.20594424026775485 y[1] (numeric) 0.2059442402677545 absolute error 3.3306690738754696e-16 relative error 1.6172674067238577e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6300000000000004 y[1] (closed_form) 0.21315917609977578 y[1] (numeric) 0.21315917609977547 absolute error 3.0531133177191805e-16 relative error 1.4323161562090462e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6400000000000005 y[1] (closed_form) 0.22052727938487904 y[1] (numeric) 0.22052727938487865 absolute error 3.885780586188048e-16 relative error 1.762040776554597e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6500000000000005 y[1] (closed_form) 0.22805082411961658 y[1] (numeric) 0.22805082411961616 absolute error 4.163336342344337e-16 relative error 1.8256177579786318e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6600000000000005 y[1] (closed_form) 0.23573216711705908 y[1] (numeric) 0.23573216711705858 absolute error 4.996003610813204e-16 relative error 2.1193559079836167e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6700000000000005 y[1] (closed_form) 0.2435737514949815 y[1] (numeric) 0.24357375149498106 absolute error 4.440892098500626e-16 relative error 1.8232227697950962e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6800000000000005 y[1] (closed_form) 0.2515781103622067 y[1] (numeric) 0.2515781103622062 absolute error 4.996003610813204e-16 relative error 1.985865782845839e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6900000000000005 y[1] (closed_form) 0.259747870716431 y[1] (numeric) 0.25974787071643063 absolute error 3.885780586188048e-16 relative error 1.4959816900405655e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7000000000000005 y[1] (closed_form) 0.26808575756793157 y[1] (numeric) 0.2680857575679311 absolute error 4.440892098500626e-16 relative error 1.6565192193678273e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7100000000000005 y[1] (closed_form) 0.2765945983047113 y[1] (numeric) 0.27659459830471095 absolute error 3.3306690738754696e-16 relative error 1.2041699636542533e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7200000000000005 y[1] (closed_form) 0.28527732731592603 y[1] (numeric) 0.2852773273159257 absolute error 3.3306690738754696e-16 relative error 1.1675197272817166e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7300000000000005 y[1] (closed_form) 0.29413699089182177 y[1] (numeric) 0.2941369908918214 absolute error 3.885780586188048e-16 relative error 1.3210785132486675e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7400000000000005 y[1] (closed_form) 0.3031767524199507 y[1] (numeric) 0.30317675241995024 absolute error 4.440892098500626e-16 relative error 1.4647864861185813e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7500000000000006 y[1] (closed_form) 0.3123998978991059 y[1] (numeric) 0.3123998978991054 absolute error 4.996003610813204e-16 relative error 1.599233432664801e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7600000000000006 y[1] (closed_form) 0.32180984179426003 y[1] (numeric) 0.3218098417942596 absolute error 4.440892098500626e-16 relative error 1.3799739851771792e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7700000000000006 y[1] (closed_form) 0.3314101332578185 y[1] (numeric) 0.3314101332578181 absolute error 3.885780586188048e-16 relative error 1.172499026505363e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7800000000000006 y[1] (closed_form) 0.3412044627447259 y[1] (numeric) 0.3412044627447255 absolute error 3.885780586188048e-16 relative error 1.1388422516311627e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7900000000000006 y[1] (closed_form) 0.351196669051421 y[1] (numeric) 0.3511966690514206 absolute error 3.885780586188048e-16 relative error 1.1064400458818433e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8000000000000006 y[1] (closed_form) 0.36139074681134437 y[1] (numeric) 0.3613907468113441 absolute error 2.7755575615628914e-16 relative error 7.680212031028582e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8100000000000006 y[1] (closed_form) 0.37179085448269517 y[1] (numeric) 0.371790854482695 absolute error 1.6653345369377348e-16 relative error 4.4792240499160716e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8200000000000006 y[1] (closed_form) 0.3824013228674413 y[1] (numeric) 0.38240132286744116 absolute error 1.1102230246251565e-16 relative error 2.9032928450668915e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8300000000000006 y[1] (closed_form) 0.3932266642042512 y[1] (numeric) 0.39322666420425095 absolute error 2.220446049250313e-16 relative error 5.646733172949231e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8400000000000006 y[1] (closed_form) 0.4042715818820776 y[1] (numeric) 0.40427158188207746 absolute error 1.6653345369377348e-16 relative error 4.1193460326466824e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8500000000000006 y[1] (closed_form) 0.41554098082563534 y[1] (numeric) 0.41554098082563506 absolute error 2.7755575615628914e-16 relative error 6.679383477528874e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8600000000000007 y[1] (closed_form) 0.4270399786090209 y[1] (numeric) 0.42703997860902065 absolute error 2.220446049250313e-16 relative error 5.1996210202212856e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8700000000000007 y[1] (closed_form) 0.43877391735931565 y[1] (numeric) 0.4387739173593153 absolute error 3.3306690738754696e-16 relative error 7.590854747977093e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8800000000000007 y[1] (closed_form) 0.4507483765182265 y[1] (numeric) 0.4507483765182262 absolute error 3.3306690738754696e-16 relative error 7.389198158855244e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8900000000000007 y[1] (closed_form) 0.4629691865367751 y[1] (numeric) 0.46296918653677477 absolute error 3.3306690738754696e-16 relative error 7.194148489212476e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9000000000000007 y[1] (closed_form) 0.4754424435858151 y[1] (numeric) 0.4754424435858149 absolute error 2.220446049250313e-16 relative error 4.6702730881651565e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9100000000000007 y[1] (closed_form) 0.48817452537386696 y[1] (numeric) 0.4881745253738667 absolute error 2.7755575615628914e-16 relative error 5.685584595872223e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9200000000000007 y[1] (closed_form) 0.5011721081735231 y[1] (numeric) 0.5011721081735228 absolute error 3.3306690738754696e-16 relative error 6.64575905074565e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9300000000000007 y[1] (closed_form) 0.5144421851686615 y[1] (numeric) 0.5144421851686614 absolute error 1.1102230246251565e-16 relative error 2.1581103895302956e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9400000000000007 y[1] (closed_form) 0.5279920862470625 y[1] (numeric) 0.5279920862470624 absolute error 1.1102230246251565e-16 relative error 2.1027266384171742e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9500000000000007 y[1] (closed_form) 0.5418294993769632 y[1] (numeric) 0.5418294993769632 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] 0.9600000000000007 y[1] (closed_form) 0.5559624937218419 y[1] (numeric) 0.5559624937218417 absolute error 2.220446049250313e-16 relative error 3.993877418575006e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9700000000000008 y[1] (closed_form) 0.5703995446655491 y[1] (numeric) 0.570399544665549 absolute error 1.1102230246251565e-16 relative error 1.9463953556907733e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9800000000000008 y[1] (closed_form) 0.5851495609401413 y[1] (numeric) 0.5851495609401413 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] 0.9900000000000008 y[1] (closed_form) 0.6002219140717494 y[1] (numeric) 0.6002219140717494 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] 1.0000000000000007 y[1] (closed_form) 0.6156264703860153 y[1] (numeric) 0.6156264703860154 absolute error 1.1102230246251565e-16 relative error 1.8034036514528286e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0099999999999996 y[1] (closed_form) 0.6313736258445025 y[1] (numeric) 0.6313736258445044 absolute error 1.887379141862766e-15 relative error 2.9893221138882324e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0199999999999985 y[1] (closed_form) 0.6474743440177003 y[1] (numeric) 0.6474743440177039 absolute error 3.552713678800501e-15 relative error 5.487033905861417e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0299999999999974 y[1] (closed_form) 0.6639401975394141 y[1] (numeric) 0.6639401975394195 absolute error 5.329070518200751e-15 relative error 8.026431503846996e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0399999999999963 y[1] (closed_form) 0.680783413432427 y[1] (numeric) 0.6807834134324343 absolute error 7.327471962526033e-15 relative error 1.0763293902214529e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0499999999999952 y[1] (closed_form) 0.6980169227472175 y[1] (numeric) 0.6980169227472266 absolute error 9.103828801926284e-15 relative error 1.3042418464721346e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.059999999999994 y[1] (closed_form) 0.7156544150154879 y[1] (numeric) 0.7156544150154989 absolute error 1.099120794378905e-14 relative error 1.5358261911304191e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.069999999999993 y[1] (closed_form) 0.7337103980897286 y[1] (numeric) 0.7337103980897416 absolute error 1.2989609388114332e-14 relative error 1.77040006819227e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0799999999999919 y[1] (closed_form) 0.7522002640207033 y[1] (numeric) 0.7522002640207183 absolute error 1.4988010832439613e-14 relative error 1.9925559122147675e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0899999999999908 y[1] (closed_form) 0.7711403617187078 y[1] (numeric) 0.7711403617187248 absolute error 1.6986412276764895e-14 relative error 2.2027652966971922e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0999999999999897 y[1] (closed_form) 0.7905480772542113 y[1] (numeric) 0.7905480772542303 absolute error 1.8984813721090177e-14 relative error 2.4014749092844047e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1099999999999886 y[1] (closed_form) 0.8104419227821106 y[1] (numeric) 0.8104419227821319 absolute error 2.1316282072803006e-14 relative error 2.630204765275197e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1199999999999875 y[1] (closed_form) 0.8308416352250318 y[1] (numeric) 0.8308416352250554 absolute error 2.353672812205332e-14 relative error 2.8328777861112416e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1299999999999863 y[1] (closed_form) 0.8517682860294555 y[1] (numeric) 0.8517682860294814 absolute error 2.5868196473766147e-14 relative error 3.0369992517978747e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1399999999999852 y[1] (closed_form) 0.8732444035195404 y[1] (numeric) 0.8732444035195686 absolute error 2.8199664825478976e-14 relative error 3.229298087891835e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1499999999999841 y[1] (closed_form) 0.8952941096242921 y[1] (numeric) 0.8952941096243227 absolute error 3.0531133177191805e-14 relative error 3.4101791633594146e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.159999999999983 y[1] (closed_form) 0.9179432730527655 y[1] (numeric) 0.9179432730527985 absolute error 3.3084646133829665e-14 relative error 3.6042146726345566e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.169999999999982 y[1] (closed_form) 0.9412196813500059 y[1] (numeric) 0.9412196813500414 absolute error 3.552713678800501e-14 relative error 3.77458498711458e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1799999999999808 y[1] (closed_form) 0.9651532346968531 y[1] (numeric) 0.9651532346968912 absolute error 3.808064974464287e-14 relative error 3.945554796446773e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1899999999999797 y[1] (closed_form) 0.9897761648364393 y[1] (numeric) 0.9897761648364799 absolute error 4.063416270128073e-14 relative error 4.105389091481662e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1999999999999786 y[1] (closed_form) 1.0151232831406047 y[1] (numeric) 1.0151232831406483 absolute error 4.3520742565306136e-14 relative error 4.287237155142473e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2099999999999775 y[1] (closed_form) 1.0412322625978032 y[1] (numeric) 1.0412322625978498 absolute error 4.6629367034256575e-14 relative error 4.478286805858234e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2199999999999764 y[1] (closed_form) 1.068143959445243 y[1] (numeric) 1.0681439594452928 absolute error 4.973799150320701e-14 relative error 4.656487645077279e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2299999999999753 y[1] (closed_form) 1.0959027813270712 y[1] (numeric) 1.0959027813271238 absolute error 5.262457136723242e-14 relative error 4.801937933172072e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2399999999999742 y[1] (closed_form) 1.1245571102957586 y[1] (numeric) 1.1245571102958145 absolute error 5.595524044110789e-14 relative error 4.975758005424167e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2499999999999731 y[1] (closed_form) 1.1541597907618726 y[1] (numeric) 1.1541597907619316 absolute error 5.906386491005833e-14 relative error 5.117477266390443e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.259999999999972 y[1] (closed_form) 1.1847686947387062 y[1] (numeric) 1.1847686947387688 absolute error 6.261657858885883e-14 relative error 5.285131086508709e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.269999999999971 y[1] (closed_form) 1.216447379556299 y[1] (numeric) 1.2164473795563648 absolute error 6.59472476627343e-14 relative error 5.421298838819371e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2799999999999698 y[1] (closed_form) 1.2492658568128756 y[1] (numeric) 1.2492658568129456 absolute error 6.994405055138486e-14 relative error 5.5988123080403375e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2899999999999687 y[1] (closed_form) 1.2833014959319478 y[1] (numeric) 1.283301495932021 absolute error 7.327471962526033e-14 relative error 5.7098600646489095e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2999999999999676 y[1] (closed_form) 1.318640091629052 y[1] (numeric) 1.3186400916291292 absolute error 7.72715225139109e-14 relative error 5.859940328255106e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3099999999999665 y[1] (closed_form) 1.3553771323160788 y[1] (numeric) 1.3553771323161603 absolute error 8.149037000748649e-14 relative error 6.012376043871651e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3199999999999654 y[1] (closed_form) 1.3936193166131492 y[1] (numeric) 1.3936193166132347 absolute error 8.548717289613705e-14 relative error 6.134183982458905e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3299999999999643 y[1] (closed_form) 1.4334863785845537 y[1] (numeric) 1.4334863785846437 absolute error 8.992806499463768e-14 relative error 6.273381201112913e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3399999999999632 y[1] (closed_form) 1.4751133003291814 y[1] (numeric) 1.4751133003292765 absolute error 9.50350909079134e-14 relative error 6.4425621331395824e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3499999999999621 y[1] (closed_form) 1.5186530149602182 y[1] (numeric) 1.5186530149603183 absolute error 1.0014211682118912e-13 relative error 6.594140717773664e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.359999999999961 y[1] (closed_form) 1.564279736472824 y[1] (numeric) 1.5642797364729288 absolute error 1.0480505352461478e-13 relative error 6.69989203855135e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.36999999999996 y[1] (closed_form) 1.6121930994905003 y[1] (numeric) 1.6121930994906104 absolute error 1.1013412404281553e-13 relative error 6.831323374205056e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3799999999999588 y[1] (closed_form) 1.6626233574001665 y[1] (numeric) 1.6626233574002822 absolute error 1.156852391659413e-13 relative error 6.957994343760308e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3899999999999577 y[1] (closed_form) 1.7158379811675877 y[1] (numeric) 1.7158379811677094 absolute error 1.2168044349891716e-13 relative error 7.091604500800038e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3999999999999566 y[1] (closed_form) 1.7721501376694475 y[1] (numeric) 1.7721501376695754 absolute error 1.2789769243681803e-13 relative error 7.217091245159179e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4099999999999555 y[1] (closed_form) 1.8319297289556065 y[1] (numeric) 1.831929728955741 absolute error 1.3455903058456897e-13 relative error 7.345206994445243e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4199999999999544 y[1] (closed_form) 1.8956179807142446 y[1] (numeric) 1.8956179807143863 absolute error 1.4166445794216997e-13 relative error 7.473259875325334e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4299999999999533 y[1] (closed_form) 1.9637470439240394 y[1] (numeric) 1.9637470439241886 absolute error 1.4921397450962104e-13 relative error 7.598431527690836e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4399999999999522 y[1] (closed_form) 2.036966830539076 y[1] (numeric) 2.0369668305392334 absolute error 1.5765166949677223e-13 relative error 7.739530518278017e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.449999999999951 y[1] (closed_form) 2.116082544013316 y[1] (numeric) 2.1160825440134823 absolute error 1.6608936448392342e-13 relative error 7.848907640857995e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.45999999999995 y[1] (closed_form) 2.202108465746448 y[1] (numeric) 2.202108465746623 absolute error 1.7497114868092467e-13 relative error 7.94561900117916e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.469999999999949 y[1] (closed_form) 2.2963472549521304 y[1] (numeric) 2.296347254952316 absolute error 1.8562928971732617e-13 relative error 8.08367677480015e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4799999999999478 y[1] (closed_form) 2.400510821257009 y[1] (numeric) 2.400510821257207 absolute error 1.9761969838327786e-13 relative error 8.232401896851097e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4899999999999467 y[1] (closed_form) 2.5169120195345895 y[1] (numeric) 2.5169120195348 absolute error 2.1049828546892968e-13 relative error 8.363354929976997e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4999999999999456 y[1] (closed_form) 2.648783653977668 y[1] (numeric) 2.6487836539778926 absolute error 2.2470914018413168e-13 relative error 8.483484102096707e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Finished! diff ( y , x , 1 ) = tan ( x ) ; Iterations 1401 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.14285714285325%