##############ECHO OF PROBLEM################# ##############temp/exp_sqrtpostode.ode################# diff ( y , x , 1 ) = exp ( sqrt ( 0.1 * x + 0.2 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=16; 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 # ELIMINATED in preodein.rb $glob_max_h=c(0.01) # 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) # 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(c(20.0) * exp(sqrt(c(0.1) * x + c(0.2))) * sqrt( c(0.1) * x + c(0.2)) - c(20.0) * exp(sqrt(c(0.1) * x + c(0.2)))) 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) -13.836040790419254 y[1] (numeric) -13.836040790419254 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) -13.817211083627797 y[1] (numeric) -13.817211827509276 absolute error 7.43881479081665e-07 relative error 5.3837310190846e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 TOP MAIN SOLVE Loop x[1] 2.019999999999998 y[1] (closed_form) -13.798366503343264 y[1] (numeric) -13.798367990766014 absolute error 1.487422750301448e-06 relative error 1.0779701712815458e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0299999999999967 y[1] (closed_form) -13.779507056349988 y[1] (numeric) -13.779509286975541 absolute error 2.230625552712695e-06 relative error 1.6187992383114747e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0399999999999956 y[1] (closed_form) -13.760632749397818 y[1] (numeric) -13.760635722889422 absolute error 2.9734916040524695e-06 relative error 2.1608683686312266e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0499999999999945 y[1] (closed_form) -13.741743589202322 y[1] (numeric) -13.741747305224932 absolute error 3.7160226096233373e-06 relative error 2.7041856701090172e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0599999999999934 y[1] (closed_form) -13.722839582445001 y[1] (numeric) -13.722844040665276 absolute error 4.458220274727864e-06 relative error 3.248759302288326e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0699999999999923 y[1] (closed_form) -13.703920735773515 y[1] (numeric) -13.703925935859793 absolute error 5.200086278023264e-06 relative error 3.794597457389442e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.079999999999991 y[1] (closed_form) -13.684987055801876 y[1] (numeric) -13.68499299742418 absolute error 5.941622303495819e-06 relative error 4.341708383989164e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.08999999999999 y[1] (closed_form) -13.666038549110684 y[1] (numeric) -13.666045231940702 absolute error 6.6828300173682464e-06 relative error 4.890100370603104e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.099999999999989 y[1] (closed_form) -13.647075222247317 y[1] (numeric) -13.647082645958388 absolute error 7.423711071652406e-06 relative error 5.439781748656556e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.109999999999988 y[1] (closed_form) -13.628097081726136 y[1] (numeric) -13.628105245993252 absolute error 8.164267116583801e-06 relative error 5.990760901998002e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.119999999999987 y[1] (closed_form) -13.609104134028705 y[1] (numeric) -13.60911303852849 absolute error 8.904499784634368e-06 relative error 6.543046255608573e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1299999999999857 y[1] (closed_form) -13.590096385603974 y[1] (numeric) -13.590106030014681 absolute error 9.644410706499684e-06 relative error 7.096646287745269e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1399999999999846 y[1] (closed_form) -13.571073842868508 y[1] (numeric) -13.571084226870003 absolute error 1.0384001495111761e-05 relative error 7.651569518626171e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1499999999999835 y[1] (closed_form) -13.552036512206659 y[1] (numeric) -13.552047635480415 absolute error 1.112327375629718e-05 relative error 8.207824518682612e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1599999999999824 y[1] (closed_form) -13.532984399970768 y[1] (numeric) -13.532996262199859 absolute error 1.1862229090553456e-05 relative error 8.765419910318583e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1699999999999813 y[1] (closed_form) -13.513917512481392 y[1] (numeric) -13.513930113350465 absolute error 1.2600869073509102e-05 relative error 9.324364353912179e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.17999999999998 y[1] (closed_form) -13.49483585602745 y[1] (numeric) -13.494849195222741 absolute error 1.3339195291450778e-05 relative error 9.884666574505125e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 2.189999999999979 y[1] (closed_form) -13.475739436866458 y[1] (numeric) -13.475753514075762 absolute error 1.4077209304019789e-05 relative error 0.00010446335334673992% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.199999999999978 y[1] (closed_form) -13.456628261224697 y[1] (numeric) -13.456643076137368 absolute error 1.4814912670857439e-05 relative error 0.00011009379454693448% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.209999999999977 y[1] (closed_form) -13.437502335297403 y[1] (numeric) -13.43751788760435 absolute error 1.555230694805232e-05 relative error 0.00011573807810399247% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2199999999999758 y[1] (closed_form) -13.418361665248977 y[1] (numeric) -13.418377954642638 absolute error 1.6289393661494955e-05 relative error 0.00012139629313824064% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2299999999999747 y[1] (closed_form) -13.399206257213141 y[1] (numeric) -13.399223283387489 absolute error 1.7026174347734013e-05 relative error 0.00012706852944045384% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2399999999999736 y[1] (closed_form) -13.380036117293145 y[1] (numeric) -13.380053879943663 absolute error 1.7762650518449163e-05 relative error 0.00013275487721211508% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2499999999999725 y[1] (closed_form) -13.36085125156194 y[1] (numeric) -13.360869750385632 absolute error 1.8498823692425503e-05 relative error 0.00013845542730866727% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2599999999999714 y[1] (closed_form) -13.341651666062369 y[1] (numeric) -13.341670900757736 absolute error 1.923469536713185e-05 relative error 0.0001441702710321828% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2699999999999703 y[1] (closed_form) -13.322437366807325 y[1] (numeric) -13.322457337074374 absolute error 1.99702670489188e-05 relative error 0.00014989950036225694% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.279999999999969 y[1] (closed_form) -13.303208359779969 y[1] (numeric) -13.303229065320176 absolute error 2.070554020683346e-05 relative error 0.00015564320761473756% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.289999999999968 y[1] (closed_form) -13.283964650933871 y[1] (numeric) -13.283986091450185 absolute error 2.1440516313475655e-05 relative error 0.00016140148575273703% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.299999999999967 y[1] (closed_form) -13.2647062461932 y[1] (numeric) -13.264728421390046 absolute error 2.217519684677427e-05 relative error 0.00016717442840574225% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.309999999999966 y[1] (closed_form) -13.245433151452904 y[1] (numeric) -13.245456061036162 absolute error 2.2909583258012844e-05 relative error 0.00017296212963409106% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3199999999999648 y[1] (closed_form) -13.22614537257887 y[1] (numeric) -13.226169016255865 absolute error 2.3643676994922203e-05 relative error 0.00017876468410774843% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3299999999999637 y[1] (closed_form) -13.206842915408103 y[1] (numeric) -13.206867292887607 absolute error 2.437747950345681e-05 relative error 0.00018458218712525307% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3399999999999626 y[1] (closed_form) -13.18752578574891 y[1] (numeric) -13.187550896741115 absolute error 2.5110992204702143e-05 relative error 0.00019041473444426032% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3499999999999615 y[1] (closed_form) -13.168193989381034 y[1] (numeric) -13.16821983359757 absolute error 2.584421653573088e-05 relative error 0.0001962624225962339% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3599999999999604 y[1] (closed_form) -13.148847532055854 y[1] (numeric) -13.148874109209759 absolute error 2.6577153905193995e-05 relative error 0.00020212534855546077% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3699999999999593 y[1] (closed_form) -13.12948641949654 y[1] (numeric) -13.129513729302259 absolute error 2.730980571818975e-05 relative error 0.00020800360993280165% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.379999999999958 y[1] (closed_form) -13.110110657398216 y[1] (numeric) -13.110138699571591 absolute error 2.8042173374487334e-05 relative error 0.00021389730496792372% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.389999999999957 y[1] (closed_form) -13.09072025142812 y[1] (numeric) -13.090749025686387 absolute error 2.8774258266750508e-05 relative error 0.0002198065325214738% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.399999999999956 y[1] (closed_form) -13.07131520722577 y[1] (numeric) -13.071344713287553 absolute error 2.950606178409032e-05 relative error 0.00022573139210796088% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.409999999999955 y[1] (closed_form) -13.05189553040314 y[1] (numeric) -13.051925767988424 absolute error 3.0237585283643398e-05 relative error 0.00023167198368396254% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4199999999999537 y[1] (closed_form) -13.03246122654479 y[1] (numeric) -13.032492195374932 absolute error 3.096883014208629e-05 relative error 0.00023762840804780858% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4299999999999526 y[1] (closed_form) -13.01301230120804 y[1] (numeric) -13.013044001005758 absolute error 3.169979771833198e-05 relative error 0.0002436007665603235% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4399999999999515 y[1] (closed_form) -12.993548759923133 y[1] (numeric) -12.993581190412497 absolute error 3.243048936418802e-05 relative error 0.0002495891612321919% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4499999999999504 y[1] (closed_form) -12.97407060819338 y[1] (numeric) -12.9741037690998 absolute error 3.3160906420803826e-05 relative error 0.0002555936947025868% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4599999999999493 y[1] (closed_form) -12.95457785149532 y[1] (numeric) -12.95461174254554 absolute error 3.389105022044703e-05 relative error 0.0002616144702587515% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4699999999999482 y[1] (closed_form) -12.935070495278865 y[1] (numeric) -12.935105116200962 absolute error 3.462092209716161e-05 relative error 0.00026765159192443367% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.479999999999947 y[1] (closed_form) -12.915548544967468 y[1] (numeric) -12.915583895490837 absolute error 3.535052336900435e-05 relative error 0.00027370516432907255% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.489999999999946 y[1] (closed_form) -12.896012005958262 y[1] (numeric) -12.896048085813604 absolute error 3.607985534159752e-05 relative error 0.000279775292741103% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.499999999999945 y[1] (closed_form) -12.876460883622205 y[1] (numeric) -12.876497692541536 absolute error 3.6808919331221546e-05 relative error 0.000285862083253322% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.509999999999944 y[1] (closed_form) -12.856895183304243 y[1] (numeric) -12.856932721020872 absolute error 3.753771662928784e-05 relative error 0.00029196564251401626% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5199999999999427 y[1] (closed_form) -12.83731491032345 y[1] (numeric) -12.837353176571973 absolute error 3.826624852365512e-05 relative error 0.0002980860778984424% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5299999999999416 y[1] (closed_form) -12.817720069973166 y[1] (numeric) -12.817759064489469 absolute error 3.899451630218209e-05 relative error 0.0003042234975433016% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5399999999999405 y[1] (closed_form) -12.798110667521158 y[1] (numeric) -12.798150390042398 absolute error 3.972252124029296e-05 relative error 0.0003103780102566244% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5499999999999394 y[1] (closed_form) -12.778486708209755 y[1] (numeric) -12.77852715847436 absolute error 4.045026460453016e-05 relative error 0.00031654972555194823% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5599999999999383 y[1] (closed_form) -12.758848197255983 y[1] (numeric) -12.758889375003644 absolute error 4.1177747661436115e-05 relative error 0.00032273875372458875% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5699999999999372 y[1] (closed_form) -12.739195139851724 y[1] (numeric) -12.739237044823385 absolute error 4.190497166156604e-05 relative error 0.00032894520573341173% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.579999999999936 y[1] (closed_form) -12.719527541163842 y[1] (numeric) -12.719570173101694 absolute error 4.263193785192243e-05 relative error 0.00033516919330497073% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.589999999999935 y[1] (closed_form) -12.699845406334337 y[1] (numeric) -12.699888764981807 absolute error 4.335864747062601e-05 relative error 0.000341410828898751% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.599999999999934 y[1] (closed_form) -12.680148740480458 y[1] (numeric) -12.68019282558222 absolute error 4.4085101761126566e-05 relative error 0.0003476702258262008% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.609999999999933 y[1] (closed_form) -12.660437548694873 y[1] (numeric) -12.660482359996816 absolute error 4.4811301943781245e-05 relative error 0.0003539474980341474% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6199999999999317 y[1] (closed_form) -12.640711836045782 y[1] (numeric) -12.640757373295017 absolute error 4.5537249235394484e-05 relative error 0.0003602427602656218% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6299999999999306 y[1] (closed_form) -12.62097160757705 y[1] (numeric) -12.62101787052191 absolute error 4.626294485987614e-05 relative error 0.00036655612815182946% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6399999999999295 y[1] (closed_form) -12.60121686830837 y[1] (numeric) -12.601263856698381 absolute error 4.698839001093802e-05 relative error 0.0003728877179243872% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6499999999999284 y[1] (closed_form) -12.58144762323536 y[1] (numeric) -12.581495336821256 absolute error 4.7713585896502764e-05 relative error 0.0003792376467743309% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6599999999999273 y[1] (closed_form) -12.561663877329714 y[1] (numeric) -12.561712315863423 absolute error 4.8438533708505815e-05 relative error 0.0003856060326205974% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.669999999999926 y[1] (closed_form) -12.541865635539342 y[1] (numeric) -12.541914798773973 absolute error 4.9163234631777186e-05 relative error 0.00039199299418792575% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.679999999999925 y[1] (closed_form) -12.52205290278847 y[1] (numeric) -12.522102790478323 absolute error 4.9887689852923245e-05 relative error 0.00039839865108551027% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.689999999999924 y[1] (closed_form) -12.502225683977802 y[1] (numeric) -12.502276295878344 absolute error 5.061190054256315e-05 relative error 0.0004048231236732889% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.699999999999923 y[1] (closed_form) -12.482383983984626 y[1] (numeric) -12.482435319852495 absolute error 5.13358678695397e-05 relative error 0.0004112665331831289% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.709999999999922 y[1] (closed_form) -12.462527807662955 y[1] (numeric) -12.462579867255947 absolute error 5.205959299203755e-05 relative error 0.0004177290016558853% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7199999999999207 y[1] (closed_form) -12.442657159843645 y[1] (numeric) -12.44270994292071 absolute error 5.2783077064688655e-05 relative error 0.0004242106520063592% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7299999999999196 y[1] (closed_form) -12.422772045334519 y[1] (numeric) -12.422825551655757 absolute error 5.350632123857224e-05 relative error 0.0004307116080316954% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7399999999999185 y[1] (closed_form) -12.402872468920496 y[1] (numeric) -12.40292669824715 absolute error 5.42293266541094e-05 relative error 0.00043723199436258766% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7499999999999174 y[1] (closed_form) -12.382958435363722 y[1] (numeric) -12.38301338745817 absolute error 5.495209444816851e-05 relative error 0.0004437719365287881% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7599999999999163 y[1] (closed_form) -12.363029949403664 y[1] (numeric) -12.363085624029424 absolute error 5.56746257593943e-05 relative error 0.00045033156101089756% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.769999999999915 y[1] (closed_form) -12.343087015757273 y[1] (numeric) -12.343143412678975 absolute error 5.639692170156252e-05 relative error 0.0004569109950336233% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.779999999999914 y[1] (closed_form) -12.323129639119074 y[1] (numeric) -12.323186758102471 absolute error 5.711898339733068e-05 relative error 0.0004635103668471499% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.789999999999913 y[1] (closed_form) -12.303157824161293 y[1] (numeric) -12.303215664973246 absolute error 5.78408119533691e-05 relative error 0.00047012980553480066% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.799999999999912 y[1] (closed_form) -12.283171575533974 y[1] (numeric) -12.283230137942459 absolute error 5.8562408485229867e-05 relative error 0.0004767694412237667% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.809999999999911 y[1] (closed_form) -12.263170897865106 y[1] (numeric) -12.263230181639193 absolute error 5.92837740871488e-05 relative error 0.0004834294048488675% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8199999999999097 y[1] (closed_form) -12.243155795760739 y[1] (numeric) -12.243215800670589 absolute error 6.0004909849808996e-05 relative error 0.0004901098283057546% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8299999999999086 y[1] (closed_form) -12.223126273805082 y[1] (numeric) -12.223186999621959 absolute error 6.0725816876328054e-05 relative error 0.0004968108445911031% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8399999999999075 y[1] (closed_form) -12.203082336560652 y[1] (numeric) -12.203143783056891 absolute error 6.14464962396255e-05 relative error 0.0005035325874638304% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8499999999999064 y[1] (closed_form) -12.183023988568348 y[1] (numeric) -12.183086155517366 absolute error 6.216694901794995e-05 relative error 0.000510275191744536% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8599999999999053 y[1] (closed_form) -12.162951234347602 y[1] (numeric) -12.163014121523881 absolute error 6.288717627889184e-05 relative error 0.0005170387931943804% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.869999999999904 y[1] (closed_form) -12.142864078396464 y[1] (numeric) -12.142927685575566 absolute error 6.360717910247615e-05 relative error 0.0005238235287146182% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.879999999999903 y[1] (closed_form) -12.122762525191735 y[1] (numeric) -12.12282685215027 absolute error 6.432695853497705e-05 relative error 0.0005306295359766577% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.889999999999902 y[1] (closed_form) -12.10264657918906 y[1] (numeric) -12.102711625704698 absolute error 6.504651563865593e-05 relative error 0.0005374569538410366% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.899999999999901 y[1] (closed_form) -12.082516244823058 y[1] (numeric) -12.082582010674512 absolute error 6.57658514544579e-05 relative error 0.0005443059220602025% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9099999999998998 y[1] (closed_form) -12.062371526507409 y[1] (numeric) -12.062438011474445 absolute error 6.648496703576257e-05 relative error 0.0005511765815673969% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9199999999998987 y[1] (closed_form) -12.042212428634983 y[1] (numeric) -12.042279632498397 absolute error 6.720386341463325e-05 relative error 0.000558069074207911% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9299999999998976 y[1] (closed_form) -12.022038955577937 y[1] (numeric) -12.022106878119565 absolute error 6.792254162846234e-05 relative error 0.0005649835429700377% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9399999999998965 y[1] (closed_form) -12.00185111168782 y[1] (numeric) -12.001919752690531 absolute error 6.864100271108953e-05 relative error 0.0005719201319223543% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9499999999998954 y[1] (closed_form) -11.981648901295696 y[1] (numeric) -11.98171826054337 absolute error 6.93592476750382e-05 relative error 0.0005788789860762628% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9599999999998943 y[1] (closed_form) -11.961432328712235 y[1] (numeric) -11.961502405989771 absolute error 7.007727753638449e-05 relative error 0.0005858602516035719% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.969999999999893 y[1] (closed_form) -11.941201398227811 y[1] (numeric) -11.941272193321124 absolute error 7.079509331298084e-05 relative error 0.0005928640758331696% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.979999999999892 y[1] (closed_form) -11.92095611411263 y[1] (numeric) -11.921027626808641 absolute error 7.151269601024524e-05 relative error 0.0005998906071433724% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.989999999999891 y[1] (closed_form) -11.900696480616812 y[1] (numeric) -11.900768710703442 absolute error 7.223008663004293e-05 relative error 0.0006069399950472416% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 2.99999999999989 y[1] (closed_form) -11.880422501970507 y[1] (numeric) -11.880495449236674 absolute error 7.294726616713376e-05 relative error 0.0006140123901741256% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 Finished! diff ( y , x , 1 ) = exp ( 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 100.19999999998896%