##############ECHO OF PROBLEM################# ##############temp/sin_sqrt_linpostode.ode################# diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #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_max_h=c(0.0001) $glob_upper_ratio_limit=c(1.001) $glob_lower_ratio_limit=c(0.999) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=c(-1.5) # 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) # 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(sin(sqrt(c(2.0)*c(x)+c(3.0)))-sqrt(c(2.0)*c(x)+c(3.0))*cos(sqrt(c(2.0)*c(x)+c(3.0)))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 2.0 y[1] (closed_form) 2.80289196959102 y[1] (numeric) 2.80289196959102 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] 2.009999999999999 y[1] (closed_form) 2.807633062296781 y[1] (numeric) 2.807634725094881 absolute error 1.662798100099394e-06 relative error 5.9224195726600537e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.019999999999998 y[1] (closed_form) 2.8123408902813747 y[1] (numeric) 2.812344216873596 absolute error 3.3265922212422083e-06 relative error 0.00011828552622258331% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0299999999999967 y[1] (closed_form) 2.8170154339090177 y[1] (numeric) 2.8170204252635203 absolute error 4.991354502603684e-06 relative error 0.00017718591252719747% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0399999999999956 y[1] (closed_form) 2.821656674099206 y[1] (numeric) 2.8216633311564765 absolute error 6.657057270320621e-06 relative error 0.00023592725973459685% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0499999999999945 y[1] (closed_form) 2.8262645923230667 y[1] (numeric) 2.826272915996097 absolute error 8.323673030385947e-06 relative error 0.000294511457030435% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0599999999999934 y[1] (closed_form) 2.8308391705997296 y[1] (numeric) 2.8308491617741973 absolute error 9.991174467760544e-06 relative error 0.0003529403779460864% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0699999999999923 y[1] (closed_form) 2.8353803914927247 y[1] (numeric) 2.8353920510271755 absolute error 1.1659534450814135e-05 relative error 0.00041121588079671436% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.079999999999991 y[1] (closed_form) 2.839888238106417 y[1] (numeric) 2.839901566832439 absolute error 1.3328726021999415e-05 relative error 0.0004693398086287633% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.08999999999999 y[1] (closed_form) 2.844362694082461 y[1] (numeric) 2.8443776928048625 absolute error 1.4998722401404763e-05 relative error 0.0005273139896191429% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.099999999999989 y[1] (closed_form) 2.848803743596285 y[1] (numeric) 2.84882041309327 absolute error 1.6669496984977883e-05 relative error 0.0005851402372820028% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.109999999999988 y[1] (closed_form) 2.8532113713536 y[1] (numeric) 2.8532297123769434 absolute error 1.834102334363763e-05 relative error 0.0006428203507031592% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.119999999999987 y[1] (closed_form) 2.857585562586939 y[1] (numeric) 2.8576055758621566 absolute error 2.0013275217500848e-05 relative error 0.0007003561145998744% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1299999999999857 y[1] (closed_form) 2.861926303052219 y[1] (numeric) 2.861947989278741 absolute error 2.1686226522099616e-05 relative error 0.0007577492997975332% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1399999999999846 y[1] (closed_form) 2.866233579025332 y[1] (numeric) 2.8662569388766697 absolute error 2.3359851337723114e-05 relative error 0.000815001663111723% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1499999999999835 y[1] (closed_form) 2.8705073772987566 y[1] (numeric) 2.8705324114226753 absolute error 2.503412391874349e-05 relative error 0.0008721149479260854% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1599999999999824 y[1] (closed_form) 2.874747685178202 y[1] (numeric) 2.8747743941968853 absolute error 2.670901868340181e-05 relative error 0.0009290908840838374% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1699999999999813 y[1] (closed_form) 2.8789544904792708 y[1] (numeric) 2.878982874989487 absolute error 2.8384510216028502e-05 relative error 0.0009859311882107322% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.17999999999998 y[1] (closed_form) 2.8831277815241507 y[1] (numeric) 2.8831578420974173 absolute error 3.0060573266599278e-05 relative error 0.0010426375639413356% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.189999999999979 y[1] (closed_form) 2.8872675471383284 y[1] (numeric) 2.88729928432108 absolute error 3.1737182751623294e-05 relative error 0.0010992117021880817% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.199999999999978 y[1] (closed_form) 2.891373776647332 y[1] (numeric) 2.8914071909610772 absolute error 3.341431374526138e-05 relative error 0.0011556552810687336% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.209999999999977 y[1] (closed_form) 2.8954464598734897 y[1] (numeric) 2.895481551814975 absolute error 3.50919414850992e-05 relative error 0.0012119699663392313% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2199999999999758 y[1] (closed_form) 2.89948558713272 y[1] (numeric) 2.899522357174089 absolute error 3.677004136903861e-05 relative error 0.0012681574115152002% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2299999999999747 y[1] (closed_form) 2.903491149231342 y[1] (numeric) 2.903529597820296 absolute error 3.844858895396541e-05 relative error 0.0013242192580522978% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2399999999999736 y[1] (closed_form) 2.9074631374629107 y[1] (numeric) 2.9075032650228647 absolute error 4.012755995397299e-05 relative error 0.0013801571355084765% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2499999999999725 y[1] (closed_form) 2.91140154360507 y[1] (numeric) 2.9114433505353117 absolute error 4.180693024169457e-05 relative error 0.0014359726618103923% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2599999999999714 y[1] (closed_form) 2.9153063599164413 y[1] (numeric) 2.9153498465922816 absolute error 4.348667584030963e-05 relative error 0.001491667443196469% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2699999999999703 y[1] (closed_form) 2.9191775791335166 y[1] (numeric) 2.9192227459064495 absolute error 4.516677293286975e-05 relative error 0.0015472430747524566% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.279999999999969 y[1] (closed_form) 2.9230151944675917 y[1] (numeric) 2.923062041665444 absolute error 4.684719785208458e-05 relative error 0.0016027011402729807% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.289999999999968 y[1] (closed_form) 2.9268191996017094 y[1] (numeric) 2.926867727528793 absolute error 4.8527927083430455e-05 relative error 0.001658043212578156% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.299999999999967 y[1] (closed_form) 2.9305895886876296 y[1] (numeric) 2.9306397976248943 absolute error 5.020893726470632e-05 relative error 0.0017132708537052703% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.309999999999966 y[1] (closed_form) 2.934326356342824 y[1] (numeric) 2.9343782465480057 absolute error 5.189020518159282e-05 relative error 0.0017683856149615816% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3199999999999648 y[1] (closed_form) 2.9380294976474834 y[1] (numeric) 2.938083069355255 absolute error 5.35717077716491e-05 relative error 0.0018233890372627173% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3299999999999637 y[1] (closed_form) 2.9416990081415553 y[1] (numeric) 2.941754261563673 absolute error 5.5253422117651496e-05 relative error 0.0018782826511050273% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3399999999999626 y[1] (closed_form) 2.9453348838218005 y[1] (numeric) 2.9453918191472495 absolute error 5.6935325448925767e-05 relative error 0.001933067976808388% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3499999999999615 y[1] (closed_form) 2.9489371211388637 y[1] (numeric) 2.9489957385340078 absolute error 5.861739514401165e-05 relative error 0.0019877465248012453% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3599999999999604 y[1] (closed_form) 2.9525057169943785 y[1] (numeric) 2.9525660166030985 absolute error 6.029960872000473e-05 relative error 0.0020423197954512052% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3699999999999593 y[1] (closed_form) 2.9560406687380762 y[1] (numeric) 2.9561026506819195 absolute error 6.198194384321454e-05 relative error 0.0020967892796168604% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.379999999999958 y[1] (closed_form) 2.9595419741649303 y[1] (numeric) 2.95960563854325 absolute error 6.366437831983873e-05 relative error 0.002151156458519308% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.389999999999957 y[1] (closed_form) 2.96300963151231 y[1] (numeric) 2.963074978402409 absolute error 6.534689009907169e-05 relative error 0.00220542280403317% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.399999999999956 y[1] (closed_form) 2.9664436394571614 y[1] (numeric) 2.966510668914429 absolute error 6.702945726777543e-05 relative error 0.0022595897786900597% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.409999999999955 y[1] (closed_form) 2.9698439971132 y[1] (numeric) 2.9699127091712576 absolute error 6.871205805758507e-05 relative error 0.002313658836099666% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4199999999999537 y[1] (closed_form) 2.973210704028132 y[1] (numeric) 2.9732810986989677 absolute error 7.039467083558293e-05 relative error 0.00236763142081426% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4299999999999526 y[1] (closed_form) 2.97654376018089 y[1] (numeric) 2.976615837454996 absolute error 7.20772741056308e-05 relative error 0.002421508968551181% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4399999999999515 y[1] (closed_form) 2.9798431659788855 y[1] (numeric) 2.979916925825396 absolute error 7.375984651059042e-05 relative error 0.002475292906442616% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4499999999999504 y[1] (closed_form) 2.983108922255287 y[1] (numeric) 2.9831843646221143 absolute error 7.544236682743843e-05 relative error 0.002528984653044535% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4599999999999493 y[1] (closed_form) 2.9863410302663085 y[1] (numeric) 2.986418155080279 absolute error 7.712481397037507e-05 relative error 0.0025825856186122665% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4699999999999482 y[1] (closed_form) 2.9895394916885256 y[1] (numeric) 2.9896182988555116 absolute error 7.880716698593915e-05 relative error 0.0026360972051059266% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.479999999999947 y[1] (closed_form) 2.9927043086162035 y[1] (numeric) 2.992784798021257 absolute error 8.048940505345215e-05 relative error 0.002689520806372937% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.489999999999946 y[1] (closed_form) 2.9958354835586456 y[1] (numeric) 2.99591765506613 absolute error 8.217150748457414e-05 relative error 0.0027428578082987903% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.499999999999945 y[1] (closed_form) 2.99893301943756 y[1] (numeric) 2.999016872891283 absolute error 8.385345372285968e-05 relative error 0.0027961095889559454% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.509999999999944 y[1] (closed_form) 3.0019969195844434 y[1] (numeric) 3.0020824548077853 absolute error 8.553522334198149e-05 relative error 0.00284927751870651% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5199999999999427 y[1] (closed_form) 3.005027187737983 y[1] (numeric) 3.005114404534027 absolute error 8.721679604395405e-05 relative error 0.002902362960303397% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5299999999999416 y[1] (closed_form) 3.008023828041478 y[1] (numeric) 3.00811272619314 absolute error 8.889815166179815e-05 relative error 0.002955367269137614% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5399999999999405 y[1] (closed_form) 3.010986845040275 y[1] (numeric) 3.0110774243104292 absolute error 9.057927015421186e-05 relative error 0.003008291793217724% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5499999999999394 y[1] (closed_form) 3.013916243679221 y[1] (numeric) 3.0140085038108286 absolute error 9.22601316077909e-05 relative error 0.0030611378733990586% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5599999999999383 y[1] (closed_form) 3.016812029300137 y[1] (numeric) 3.0169059700163707 absolute error 9.394071623392009e-05 relative error 0.003113906843434099% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5699999999999372 y[1] (closed_form) 3.019674207639305 y[1] (numeric) 3.0197698286436765 absolute error 9.562100437143783e-05 relative error 0.003166600030212915% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.579999999999936 y[1] (closed_form) 3.022502784824975 y[1] (numeric) 3.022600085801456 absolute error 9.7300976480863e-05 relative error 0.0032192187537222546% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.589999999999935 y[1] (closed_form) 3.025297767374884 y[1] (numeric) 3.0253967479880313 absolute error 9.898061314705942e-05 relative error 0.003271764327282964% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.599999999999934 y[1] (closed_form) 3.0280591621937942 y[1] (numeric) 3.0281598220888744 absolute error 0.00010065989508012407 relative error 0.003324238057726624% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.609999999999933 y[1] (closed_form) 3.030786976571049 y[1] (numeric) 3.0308893153741576 absolute error 0.00010233880310872578 relative error 0.003376641245321344% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6199999999999317 y[1] (closed_form) 3.0334812181781436 y[1] (numeric) 3.033585235496327 absolute error 0.0001040173181832138 relative error 0.0034289751840192637% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6299999999999306 y[1] (closed_form) 3.036141895066309 y[1] (numeric) 3.0362475904876858 absolute error 0.0001056954213769501 relative error 0.003481241161643459% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6399999999999295 y[1] (closed_form) 3.0387690156641187 y[1] (numeric) 3.0388763887579966 absolute error 0.00010737309387787164 relative error 0.0035334404597516075% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6499999999999284 y[1] (closed_form) 3.041362588775103 y[1] (numeric) 3.0414716390921006 absolute error 0.00010905031699781631 relative error 0.003585574354083704% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6599999999999273 y[1] (closed_form) 3.0439226235753827 y[1] (numeric) 3.0440333506475463 absolute error 0.00011072707216364108 relative error 0.003637644114408578% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.669999999999926 y[1] (closed_form) 3.0464491296113216 y[1] (numeric) 3.046561532952242 absolute error 0.00011240334092033066 relative error 0.003689651004764079% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.679999999999925 y[1] (closed_form) 3.048942116797189 y[1] (numeric) 3.0490561959021165 absolute error 0.00011407910492744477 relative error 0.0037415962834768746% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.689999999999924 y[1] (closed_form) 3.0514015954128375 y[1] (numeric) 3.0515173497588015 absolute error 0.00011575434596400314 relative error 0.0037934812034579875% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.699999999999923 y[1] (closed_form) 3.0538275761014013 y[1] (numeric) 3.0539450051473223 absolute error 0.00011742904592093595 relative error 0.00384530701208904% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.709999999999922 y[1] (closed_form) 3.0562200698670035 y[1] (numeric) 3.0563391730538054 absolute error 0.00011910318680197207 relative error 0.003897074951384474% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7199999999999207 y[1] (closed_form) 3.05857908807248 y[1] (numeric) 3.058699864823209 absolute error 0.0001207767507289681 relative error 0.003948786258297534% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7299999999999196 y[1] (closed_form) 3.06090464243712 y[1] (numeric) 3.0610270921570524 absolute error 0.00012244971993258247 relative error 0.00400044216454541% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7399999999999185 y[1] (closed_form) 3.0631967450344173 y[1] (numeric) 3.0633208671111745 absolute error 0.00012412207675716047 relative error 0.0040520438968984955% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7499999999999174 y[1] (closed_form) 3.065455408289843 y[1] (numeric) 3.0655812020935005 absolute error 0.0001257938036576256 relative error 0.004103592677206924% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7599999999999163 y[1] (closed_form) 3.0676806449786196 y[1] (numeric) 3.0678081098618195 absolute error 0.00012746488319992366 relative error 0.004155089722542225% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.769999999999915 y[1] (closed_form) 3.069872468223526 y[1] (numeric) 3.0700016035215842 absolute error 0.00012913529805835822 relative error 0.0042065362452364755% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.779999999999914 y[1] (closed_form) 3.0720308914927 y[1] (numeric) 3.0721616965237195 absolute error 0.0001308050310195874 relative error 0.004257933453137551% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.789999999999913 y[1] (closed_form) 3.0741559285974667 y[1] (numeric) 3.0742884026624426 absolute error 0.0001324740649759626 relative error 0.004309282549516014% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.799999999999912 y[1] (closed_form) 3.0762475936901765 y[1] (numeric) 3.076381736073106 absolute error 0.00013414238292952518 relative error 0.004360584733318293% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.809999999999911 y[1] (closed_form) 3.078305901262056 y[1] (numeric) 3.0784417112300417 absolute error 0.00013580996798578937 relative error 0.0044118411990864675% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8199999999999097 y[1] (closed_form) 3.080330866141069 y[1] (numeric) 3.0804683429444313 absolute error 0.00013747680336217982 relative error 0.004463053137353584% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8299999999999086 y[1] (closed_form) 3.082322503489803 y[1] (numeric) 3.0824616463621806 absolute error 0.00013914287237737355 relative error 0.004514221734417346% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8399999999999075 y[1] (closed_form) 3.0842808288033536 y[1] (numeric) 3.084421636961811 absolute error 0.00014080815845751715 relative error 0.004565348172661314% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8499999999999064 y[1] (closed_form) 3.0862058579072325 y[1] (numeric) 3.086348330552363 absolute error 0.00014247264513045366 relative error 0.004616433630485845% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8599999999999053 y[1] (closed_form) 3.088097606955285 y[1] (numeric) 3.0882417432713174 absolute error 0.00014413631603238386 relative error 0.004667479282641435% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.869999999999904 y[1] (closed_form) 3.089956092427622 y[1] (numeric) 3.0901018915825214 absolute error 0.00014579915489942863 relative error 0.004718486300071715% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.879999999999903 y[1] (closed_form) 3.091781331128562 y[1] (numeric) 3.0919287922741323 absolute error 0.00014746114557029344 relative error 0.004769455850115609% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.889999999999902 y[1] (closed_form) 3.093573340184588 y[1] (numeric) 3.0937224624565745 absolute error 0.00014912227198626837 relative error 0.004820389096622177% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.899999999999901 y[1] (closed_form) 3.0953321370423184 y[1] (numeric) 3.095482919560508 absolute error 0.00015078251818945176 relative error 0.004871287200007199% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9099999999998998 y[1] (closed_form) 3.0970577394664853 y[1] (numeric) 3.097210181334809 absolute error 0.00015244186832363837 relative error 0.00492215131739516% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9199999999998987 y[1] (closed_form) 3.098750165537933 y[1] (numeric) 3.098904265844563 absolute error 0.0001541003066298785 relative error 0.004972982602588331% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9299999999998976 y[1] (closed_form) 3.1004094336516186 y[1] (numeric) 3.100565191469073 absolute error 0.0001557578174544716 relative error 0.005023782206436594% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9399999999998965 y[1] (closed_form) 3.102035562514637 y[1] (numeric) 3.1021929768998717 absolute error 0.00015741438523475537 relative error 0.005074551276489842% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9499999999998954 y[1] (closed_form) 3.103628571144247 y[1] (numeric) 3.1037876411387577 absolute error 0.00015906999451065218 relative error 0.005125290957480978% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9599999999998943 y[1] (closed_form) 3.105188478865915 y[1] (numeric) 3.105349203495836 absolute error 0.00016072462992111625 relative error 0.005176002391320752% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.969999999999893 y[1] (closed_form) 3.1067153053113716 y[1] (numeric) 3.106877683587571 absolute error 0.00016237827619924872 relative error 0.005226686717049353% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.979999999999892 y[1] (closed_form) 3.108209070416675 y[1] (numeric) 3.1083731013348506 absolute error 0.00016403091817540627 relative error 0.0052773450710449435% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.989999999999891 y[1] (closed_form) 3.1096697944202933 y[1] (numeric) 3.1098354769610674 absolute error 0.0001656825407740925 relative error 0.005327978587031269% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 2.99999999999989 y[1] (closed_form) 3.1110974978611883 y[1] (numeric) 3.1112648309902062 absolute error 0.00016733312901795472 relative error 0.005378588396313282% Desired digits 8 Estimated correct digits 12 Correct digits 5 h 0.001 Finished! diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations 1001 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.19999999998896%