{"bit_width":32,"date":1469978164,"note":"hamming","iterations":2,"flags":["rules:arithmetic","rules:polynomials","rules:fractions","rules:exponents","rules:trigonometry","setup:simplify","reduce:post-process","reduce:taylor","reduce:simplify","reduce:avg-error","generate:rr","generate:taylor","generate:simplify"],"seed":"#(1065990927 2514927446 2806713580 2976231080 3799737104 4212629478)","points":256,"tests":[{"samplers":["default","default"],"bits":128,"start":14.58439662909991,"link":"0-NMSEproblem346","pinf":0,"ninf":0,"vars":["x","n"],"input":"(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))","time":12673.55810546875,"target":false,"output":"(- (pow (+ x 1) (/ 1 n)) (exp (/ (log x) n)))","end":14.670788204166893,"name":"NMSE problem 3.4.6","status":"apx-start","end-est":15.140889555320452},{"samplers":["default"],"bits":128,"start":14.672278760013935,"link":"1-NMSEproblem345","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- x (sin x)) (- x (tan x)))","time":4610.656982421875,"target":false,"output":"(/ (- x (sin x)) (- x (tan x)))","end":14.672278760013935,"name":"NMSE problem 3.4.5","status":"apx-start","end-est":14.704113075154751},{"samplers":["default"],"bits":128,"start":26.610532329588963,"link":"2-NMSEproblem344","pinf":0,"ninf":0,"vars":["x"],"input":"(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))","time":7731.5009765625,"target":false,"output":"(+ (+ (/ (* x 1/2) (sqrt 2)) (sqrt 2)) (exp (+ (log (/ (sqr x) (sqrt 2))) (log (- 1/4 (/ 1/8 2))))))","end":1.3185581122202312,"name":"NMSE problem 3.4.4","status":"imp-start","end-est":10.709429060975673},{"samplers":["default"],"bits":128,"start":14.577125305910076,"link":"3-NMSEproblem341","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sqr x))","time":7028.677001953125,"target":false,"output":"(/ (/ (sqr (sin x)) (+ 1 (cos x))) (sqr x))","end":7.427058985623789,"name":"NMSE problem 3.4.1","status":"imp-start","end-est":6.8301229638015775},{"samplers":["default"],"bits":128,"start":19.21499826052107,"link":"4-NMSEproblem336","pinf":0,"ninf":0,"vars":["N"],"input":"(- (log (+ N 1)) (log N))","time":3389.7041015625,"target":false,"output":"(log (/ (+ N 1) N))","end":16.748739856576123,"name":"NMSE problem 3.3.6","status":"imp-start","end-est":12.04308280293534},{"samplers":["default","default"],"bits":128,"start":18.380716849518997,"link":"5-NMSEproblem335","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (cos (+ x eps)) (cos x))","time":9295.918212890625,"target":false,"output":"(- (pow (* (cos x) (cos eps)) 1) (+ (* (sin x) (sin eps)) (cos x)))","end":8.954997705080663,"name":"NMSE problem 3.3.5","status":"imp-start","end-est":9.779683127639213},{"samplers":["default"],"bits":128,"start":18.88407782958603,"link":"6-NMSEproblem334","pinf":0,"ninf":0,"vars":["x"],"input":"(- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3)))","time":10254.662841796875,"target":false,"output":"(/ (- (cube (pow (+ x 1) (/ 1 3))) x) (+ (sqr (pow (+ x 1) (/ 1 3))) (+ (sqr (cbrt x)) (* (pow (+ x 1) (/ 1 3)) (cbrt x)))))","end":8.667455203036265,"name":"NMSE problem 3.3.4","status":"imp-start","end-est":12.494994762010647},{"samplers":["default"],"bits":128,"start":5.916025586960986,"link":"7-NMSEproblem331","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (+ x 1)) (/ 1 x))","time":3547.445068359375,"target":false,"output":"(/ (/ (- x (+ 1 x)) (+ x 1)) x)","end":4.97425135470773,"name":"NMSE problem 3.3.1","status":"apx-start","end-est":3.860228694295402},{"samplers":["default","default","default"],"bits":128,"start":15.89711683016068,"link":"8-NMSEproblem321positive","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":8517.049072265625,"target":false,"output":"(/ (* (/ a 1) (/ c (- (- b/2) (sqrt (- (sqr b/2) (* a c)))))) a)","end":13.570815398952906,"name":"NMSE problem 3.2.1, positive","status":"imp-start","end-est":12.064366427063417},{"samplers":["default","default","default"],"bits":128,"start":15.614467802466457,"link":"9-NMSEproblem321negative","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":9718.18896484375,"target":false,"output":"(/ (* (/ a 1) (/ c (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))))) a)","end":14.137584531347548,"name":"NMSE problem 3.2.1, negative","status":"imp-start","end-est":12.924651733788249},{"samplers":["default","default"],"bits":128,"start":22.591830604592513,"link":"10-NMSEsection35","pinf":0,"ninf":0,"vars":["a","x"],"input":"(- (exp (* a x)) 1)","time":4443.5048828125,"target":9.79706137612569,"output":"(+ (* (* 1/2 (* x a)) (* x a)) (* x a))","end":0.19689961668166842,"name":"NMSE section 3.5","status":"gt-target","end-est":11.225920434798006},{"samplers":["default"],"bits":128,"start":18.01655191525286,"link":"11-NMSEsection311","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (exp x) (- (exp x) 1))","time":5055.613037109375,"target":18.018577356172926,"output":"(/ (exp x) (+ (* 1/2 (sqr x)) (+ (* 1/6 (pow x 3)) x)))","end":5.258299235434264,"name":"NMSE section 3.11","status":"gt-target","end-est":7.6572852388314825},{"samplers":["default"],"bits":128,"start":25.76921723744424,"link":"12-NMSEproblem343","pinf":0,"ninf":0,"vars":["eps"],"input":"(log (/ (- 1 eps) (+ 1 eps)))","time":39081.88916015625,"target":0.1064594208475432,"output":"(- (+ (* 2 eps) (+ (* 2/5 (pow eps 5)) (* 2/3 (pow eps 3)))))","end":0.11215754116013335,"name":"NMSE problem 3.4.3","status":"eq-target","end-est":0.14736998197236317},{"samplers":["default","default","default"],"bits":128,"start":29.536568750684197,"link":"13-NMSEproblem342","pinf":0,"ninf":0,"vars":["a","b","eps"],"input":"(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))","time":7810.075927734375,"target":6.47255498719211,"output":"(+ (/ 1 b) (/ 1 a))","end":0.056127484975651606,"name":"NMSE problem 3.4.2","status":"gt-target","end-est":1.5220188656558726},{"samplers":["default"],"bits":128,"start":14.376567944515719,"link":"14-NMSEproblem337","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (exp x) 2) (exp (- x)))","time":6727.64599609375,"target":2.637620159876544,"output":"(* (+ x (+ (* 1/1920 (pow x 5)) (* (cube x) 1/24))) (+ x (+ (* 1/1920 (pow x 5)) (* (cube x) 1/24))))","end":0.0960519902262357,"name":"NMSE problem 3.3.7","status":"gt-target","end-est":1.5686434352393777},{"samplers":["default"],"bits":128,"start":4.320389877086724,"link":"15-NMSEproblem333","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))","time":12564.841064453125,"target":0.44019170801690904,"output":"(/ (/ 2 (+ 1 x)) (* x (- x 1)))","end":0.11066541406655657,"name":"NMSE problem 3.3.3","status":"eq-target","end-est":0.11328125},{"samplers":["default","default"],"bits":128,"start":22.452969319076605,"link":"16-NMSEproblem332","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (tan (+ x eps)) (tan x))","time":16776.199951171875,"target":8.707033540888892,"output":"(+ (+ (+ (/ eps (sqr (/ (cos x) (sin x)))) (* (/ (sqr eps) (cos x)) (sin x))) (/ (cube (sin x)) (/ (cube (cos x)) (sqr eps)))) (+ (+ (* 1/3 (cube eps)) eps) (+ (/ (* (* 4/3 eps) (sqr eps)) (sqr (/ (cos x) (sin x)))) (/ (cube eps) (/ (pow (cos x) 4) (pow (sin x) 4))))))","end":0.35120378743447567,"name":"NMSE problem 3.3.2","status":"gt-target","end-est":15.764434696047276},{"samplers":["default","default","default"],"bits":128,"start":15.958100033528916,"link":"17-NMSEp42positive","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":11931.62109375,"target":9.265608579978464,"output":"(/ 1 (* (/ 2 (* 4 c)) (- (- b) (sqrt (- (sqr b) (* (* a c) 4))))))","end":13.773432818601492,"name":"NMSE p42, positive","status":"lt-target","end-est":12.301002027285442},{"samplers":["default","default","default"],"bits":128,"start":15.678134718965588,"link":"18-NMSEp42negative","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":9961.442138671875,"target":9.45451799868958,"output":"(/ (- (- b) (sqrt (- (sqr b) (* (* 4 a) c)))) (* a 2))","end":15.696751002780301,"name":"NMSE p42, negative","status":"eq-start","end-est":13.638589772706762},{"samplers":["default"],"bits":128,"start":29.35376509932635,"link":"19-NMSEexample39","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 x) (cotan x))","time":5542.89599609375,"target":0.01902124062518029,"output":"(+ (* x 1/3) (+ (* 2/945 (pow x 5)) (* (cube x) 1/45)))","end":0.32075,"name":"NMSE example 3.9","status":"eq-target","end-est":0.28125},{"samplers":["default"],"bits":128,"start":31.021609728479014,"link":"20-NMSEexample38","pinf":0,"ninf":0,"vars":["N"],"input":"(- (- (* (+ N 1) (log (+ N 1))) (* N (log N))) 1)","time":39432.01708984375,"target":0.0015,"output":"(- (- (sqr (/ (* (sqrt (- (sqr N) 1)) (sqrt (log (+ N 1)))) (sqrt (- N 1)))) (* N (log N))) 1)","end":29.883957645697887,"name":"NMSE example 3.8","status":"lt-target","end-est":29.864764476800215},{"samplers":["default"],"bits":128,"start":26.232157416544652,"link":"21-NMSEexample37","pinf":0,"ninf":0,"vars":["x"],"input":"(- (exp x) 1)","time":3457.2900390625,"target":0.10556616562662262,"output":"(+ (* (+ 1/2 (* 1/6 x)) (sqr x)) x)","end":0.06774304531403245,"name":"NMSE example 3.7","status":"eq-target","end-est":1.084723402614991},{"samplers":["default"],"bits":128,"start":8.516994990009305,"link":"22-NMSEexample36","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))","time":9078.48681640625,"target":0.2203656015629507,"output":"(/ (/ (/ 1 x) (+ (/ 1 (sqrt (+ 1 x))) (/ 1 (sqrt x)))) (+ 1 x))","end":0.3178072917616197,"name":"NMSE example 3.6","status":"eq-target","end-est":0.31478500976844204},{"samplers":["default"],"bits":128,"start":6.859419372952644,"link":"23-NMSEexample35","pinf":0,"ninf":0,"vars":["N"],"input":"(- (atan (+ N 1)) (atan N))","time":3226.60791015625,"target":0.5984505490932377,"output":"(atan2 (- 1 0) (+ 1 (* (+ N 1) N)))","end":0.5984505490932377,"name":"NMSE example 3.5","status":"eq-target","end-est":0.5715607007850724},{"samplers":["default"],"bits":128,"start":13.576611110241748,"link":"24-NMSEexample34","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sin x))","time":37960.7919921875,"target":0.022375,"output":"(/ (/ (sqr (sin x)) (+ 1 (cos x))) (sin x))","end":0.42600416664841545,"name":"NMSE example 3.4","status":"eq-target","end-est":0.4574176925364244},{"samplers":["default","default"],"bits":128,"start":16.7446982448568,"link":"25-NMSEexample33","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (sin (+ x eps)) (sin x))","time":7773.680908203125,"target":7.733954916030829,"output":"(- (* (cos x) (sin eps)) (- (sin x) (* (cos eps) (sin x))))","end":0.4604234689178339,"name":"NMSE example 3.3","status":"gt-target","end-est":0.45955995324176596},{"samplers":["default"],"bits":128,"start":27.221683825113633,"link":"26-NMSEexample310","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (log (- 1 x)) (log (+ 1 x)))","time":5249.259033203125,"target":0.7111845611200958,"output":"(- (+ (* 1/2 (sqr x)) (+ 1 x)))","end":0.027375,"name":"NMSE example 3.10","status":"eq-target","end-est":0.5541925995509306},{"samplers":["default"],"bits":128,"start":13.21954543706752,"link":"27-NMSEexample31","pinf":0,"ninf":0,"vars":["x"],"input":"(- (sqrt (+ x 1)) (sqrt x))","time":3305.39501953125,"target":0.17107556406367186,"output":"(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))","end":0.17107556406367186,"name":"NMSE example 3.1","status":"eq-target","end-est":0.13509750976844204}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}