{"bit_width":32,"date":1469544028,"note":"hamming","iterations":2,"flags":["rules:arithmetic","rules:polynomials","rules:fractions","rules:exponents","rules:trigonometry","setup:simplify","reduce:post-process","reduce:regimes","reduce:taylor","reduce:simplify","reduce:avg-error","generate:rr","generate:taylor","generate:simplify"],"seed":"#(1065894488 2199264003 1058398788 1110142813 3223388056 148167450)","points":256,"tests":[{"samplers":["default","default"],"bits":128,"start":16.26605165262669,"link":"0-NMSEproblem346","pinf":0,"ninf":0,"vars":["x","n"],"input":"(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))","time":36540.513916015625,"target":false,"output":"(if (<= x 2.24202f-14) (cube (cube (cbrt (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))))) (if (<= x 0.9963511f0) (- (- (+ (/ 1 (* n x)) 1) (exp (/ (log x) n))) (/ (log x) n)) (* (+ (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n)))) (- (- (/ (/ 1/2 n) x) (* (/ (log x) (* x n)) (/ 1/4 n))) (/ 1/4 (* (sqr x) n))))))","end":8.30336680014742,"name":"NMSE problem 3.4.6","status":"imp-start","end-est":8.101695546904494},{"samplers":["default"],"bits":128,"start":15.193102929304374,"link":"1-NMSEproblem345","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- x (sin x)) (- x (tan x)))","time":6574.2939453125,"target":false,"output":"(if (<= x -0.024611041f0) (/ (- x (sin x)) (- x (tan x))) (if (<= x 0.2508728f0) (- (* 9/40 (sqr x)) (+ (* 27/2800 (pow x 4)) 1/2)) (/ (- x (sin x)) (- x (tan x)))))","end":0.07632020593211325,"name":"NMSE problem 3.4.5","status":"imp-start","end-est":0.07892044831941455},{"samplers":["default"],"bits":128,"start":20.204024656668267,"link":"2-NMSEproblem344","pinf":0,"ninf":0,"vars":["x"],"input":"(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))","time":7742.906005859375,"target":false,"output":"(if (<= x -0.0012153552f0) (sqrt (/ (* (+ (sqrt (exp (* 2 x))) 1) (- (sqrt (exp (* 2 x))) 1)) (- (exp x) 1))) (sqrt (+ (* 1/2 (sqr x)) (+ 2 x))))","end":3.4951489783544925,"name":"NMSE problem 3.4.4","status":"imp-start","end-est":0.40191925247550164},{"samplers":["default"],"bits":128,"start":14.997345987988528,"link":"3-NMSEproblem341","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sqr x))","time":6643.677001953125,"target":false,"output":"(sqr (/ (/ (sin x) (sqrt (+ 1 (cos x)))) x))","end":0.31949257716869806,"name":"NMSE problem 3.4.1","status":"imp-start","end-est":0.2410422987449989},{"samplers":["default"],"bits":128,"start":18.89122674147127,"link":"4-NMSEproblem336","pinf":0,"ninf":0,"vars":["N"],"input":"(- (log (+ N 1)) (log N))","time":5836.260986328125,"target":false,"output":"(if (<= N 314.9759f0) (log (+ 1 (/ 1 N))) (+ (/ 1 N) (- (/ 1/3 (cube N)) (/ 1/2 (* N N)))))","end":8.236424189638324,"name":"NMSE problem 3.3.6","status":"imp-start","end-est":0.11245911580066548},{"samplers":["default","default"],"bits":128,"start":18.265745591521,"link":"5-NMSEproblem335","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (cos (+ x eps)) (cos x))","time":14983.906982421875,"target":false,"output":"(if (<= eps -0.00030713418f0) (cbrt (cube (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))))) (if (<= eps 0.07828799f0) (- (* (- (* (sin x) (* eps 1/6)) (* 1/2 (cos x))) (* eps eps)) (* eps (sin x))) (- (* (cos x) (cos eps)) (cbrt (cube (+ (* (sin x) (sin eps)) (cos x)))))))","end":0.5966843374180975,"name":"NMSE problem 3.3.5","status":"imp-start","end-est":0.5580925800245978},{"samplers":["default"],"bits":128,"start":1.134707494601294,"link":"6-NMSEproblem334","pinf":0,"ninf":0,"vars":["x"],"input":"(- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3)))","time":193830.90502929688,"target":false,"output":"(if (<= x 19436852.0f0) (exp (log (- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3))))) (exp (+ (- (log (- (cbrt (/ 1 x)) (pow x -1/3))) (* (/ 1/9 (- (cbrt (/ 1 x)) (pow x -1/3))) (cbrt (/ 1 (pow x 7))))) (- (* (/ 1/3 (- (cbrt (/ 1 x)) (pow x -1/3))) (cbrt (/ 1 (pow x 4)))) (/ (* (cbrt (/ 1 (pow x 8))) 1/18) (sqr (- (cbrt (/ 1 x)) (pow x -1/3))))))))","end":13.195981066791362,"name":"NMSE problem 3.3.4","status":"uni-start","end-est":11.230484370009224},{"samplers":["default"],"bits":128,"start":5.612286319551642,"link":"7-NMSEproblem331","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (+ x 1)) (/ 1 x))","time":6553.248779296875,"target":false,"output":"(if (<= x -840391.9f0) (- (/ (/ 1 x) (* x x)) (/ (/ 1 x) x)) (if (<= x 15032.417f0) (/ (- x (+ 1 x)) (* (+ x 1) x)) (- (/ (/ 1 x) (* x x)) (/ (/ 1 x) x))))","end":0.10857332382517222,"name":"NMSE problem 3.3.1","status":"imp-start","end-est":0.04296875},{"samplers":["default","default","default"],"bits":128,"start":15.823467570813179,"link":"8-NMSEproblem321positive","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":14567.35302734375,"target":false,"output":"(if (<= b/2 -1.2459677f+19) (- (/ 1/2 (/ b/2 c)) (* (/ b/2 a) 2)) (if (<= b/2 -7.39763f-38) (/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a) (if (<= b/2 2.9183594f+10) (/ (* (/ a 1) (/ c (- (- b/2) (sqrt (- (sqr b/2) (* a c)))))) a) (- (/ (+ b/2 (- b/2)) a) (/ c (/ b/2 1/2))))))","end":2.5844654537233143,"name":"NMSE problem 3.2.1, positive","status":"imp-start","end-est":3.386132612619728},{"samplers":["default","default","default"],"bits":128,"start":16.943100439909852,"link":"9-NMSEproblem321negative","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":12817.31201171875,"target":false,"output":"(if (<= b/2 -0.15658416f0) (/ c (- (* (* a 1/2) (/ c b/2)) (- b/2 (- b/2)))) (if (<= b/2 3.574777f+11) (/ (pow (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) 1) a) (* -2 (/ b/2 a))))","end":3.9552924313634645,"name":"NMSE problem 3.2.1, negative","status":"imp-start","end-est":5.221377056245845},{"samplers":["default","default"],"bits":128,"start":14.083325252264485,"link":"10-NMSEsection35","pinf":0,"ninf":0,"vars":["a","x"],"input":"(- (exp (* a x)) 1)","time":6844.6220703125,"target":2.6494735348360416,"output":"(if (<= (* a x) -0.017917428f0) (- (exp (* a x)) 1) (+ (* a x) (* (* (* a x) (* a x)) (+ (* (* a x) 1/6) 1/2))))","end":0.11325731952036147,"name":"NMSE section 3.5","status":"gt-target","end-est":0.4275426608908786},{"samplers":["default"],"bits":128,"start":20.546963614470737,"link":"11-NMSEsection311","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (exp x) (- (exp x) 1))","time":5753.72802734375,"target":13.439168924576357,"output":"(if (<= x -0.024611041f0) (/ (exp x) (- (exp x) 1)) (if (<= x 0.2508728f0) (+ 1/2 (+ (/ 1 x) (* 1/12 x))) (/ 1 (- 1 (exp (- x))))))","end":0.028638349092998533,"name":"NMSE section 3.11","status":"gt-target","end-est":0.05523262247030779},{"samplers":["default"],"bits":128,"start":25.945793123110292,"link":"12-NMSEproblem343","pinf":0,"ninf":0,"vars":["eps"],"input":"(log (/ (- 1 eps) (+ 1 eps)))","time":6109.01806640625,"target":0.0670321985917836,"output":"(- (+ (* 2 eps) (+ (* 2/5 (pow eps 5)) (* 2/3 (pow eps 3)))))","end":0.07155343921696387,"name":"NMSE problem 3.4.3","status":"eq-target","end-est":0.3695983604978412},{"samplers":["default","default","default"],"bits":128,"start":29.598521431449125,"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":21378.10400390625,"target":6.361866081152963,"output":"(+ (/ 1 b) (/ 1 a))","end":0.056268439135617326,"name":"NMSE problem 3.4.2","status":"gt-target","end-est":1.8169518645435683},{"samplers":["default"],"bits":128,"start":14.371099599411002,"link":"14-NMSEproblem337","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (exp x) 2) (exp (- x)))","time":7308.763916015625,"target":2.5544844307735137,"output":"(* (+ x (+ (* 1/1920 (pow x 5)) (* (cube x) 1/24))) (+ x (+ (* 1/1920 (pow x 5)) (* (cube x) 1/24))))","end":0.09262490702624378,"name":"NMSE problem 3.3.7","status":"gt-target","end-est":1.5712500959708127},{"samplers":["default"],"bits":128,"start":4.040655241862123,"link":"15-NMSEproblem333","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))","time":17997.739013671875,"target":0.37943724786462363,"output":"(/ (/ 2 (+ 1 x)) (* (- x 1) x))","end":0.10713477500432696,"name":"NMSE problem 3.3.3","status":"eq-target","end-est":0.10841752930532607},{"samplers":["default","default"],"bits":128,"start":16.567758890655732,"link":"16-NMSEproblem332","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (tan (+ x eps)) (tan x))","time":16978.2099609375,"target":7.542053096428796,"output":"(if (<= eps -0.09829997f0) (log (exp (- (/ 1 (cotan (+ eps x))) (tan x)))) (if (<= eps 0.07828799f0) (+ (+ (+ (/ 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)))))) (log (exp (- (/ 1 (cotan (+ eps x))) (tan x))))))","end":7.332866184596898,"name":"NMSE problem 3.3.2","status":"eq-target","end-est":6.853642840317671},{"samplers":["default","default","default"],"bits":128,"start":16.169466741923717,"link":"17-NMSEp42positive","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":18696.285888671875,"target":10.15722609319962,"output":"(if (<= b -1.3221147f+12) (- (/ c b) (/ b a)) (if (<= b -5.8040364f-33) (/ (+ (- b) (sqr (sqrt (sqrt (- (sqr b) (* 4 (* a c))))))) (* 2 a)) (if (<= b 2.441097f+08) (* (/ c 2) (/ 4 (- (- b) (sqrt (- (sqr b) (* (* c a) 4)))))) (/ c (- b)))))","end":2.4936924257848654,"name":"NMSE p42, positive","status":"gt-target","end-est":3.4870208655599244},{"samplers":["default","default","default"],"bits":128,"start":16.276153904922957,"link":"18-NMSEp42negative","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":18431.411865234375,"target":9.86745840831355,"output":"(if (<= b -2.724577f+18) (* (/ c b) (/ -2 2)) (if (<= b -7.617411f-30) (/ 1 (* (+ (- b) (sqrt (- (sqr b) (* (* a c) 4)))) (/ (/ 2 c) 4))) (if (<= b 9.210374f+08) (/ (- (- b) (sqr (sqrt (sqrt (- (sqr b) (* 4 (* a c))))))) (* 2 a)) (- (/ c b) (/ b a)))))","end":2.7255626004906954,"name":"NMSE p42, negative","status":"gt-target","end-est":3.4940758062625434},{"samplers":["default"],"bits":128,"start":29.382097406665576,"link":"19-NMSEexample39","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 x) (cotan x))","time":6460.406982421875,"target":0.017469360937770434,"output":"(+ (* x 1/3) (+ (* 2/945 (pow x 5)) (* (cube x) 1/45)))","end":0.327125,"name":"NMSE example 3.9","status":"eq-target","end-est":0.3359375},{"samplers":["default"],"bits":128,"start":31.021608082262905,"link":"20-NMSEexample38","pinf":0,"ninf":0,"vars":["N"],"input":"(- (- (* (+ N 1) (log (+ N 1))) (* N (log N))) 1)","time":39472.657958984375,"target":0.00175,"output":"(- (- (/ (* (- (sqr N) 1) (log (+ N 1))) (- N 1)) (cube (cbrt (* N (log N))))) 1)","end":29.878263121676177,"name":"NMSE example 3.8","status":"lt-target","end-est":29.857394719012127},{"samplers":["default"],"bits":128,"start":26.339509602333997,"link":"21-NMSEexample37","pinf":0,"ninf":0,"vars":["x"],"input":"(- (exp x) 1)","time":4981.715087890625,"target":0.10173364687698322,"output":"(+ (* (+ 1/2 (* 1/6 x)) (sqr x)) x)","end":0.06492236875252402,"name":"NMSE example 3.7","status":"eq-target","end-est":1.0284229005182346},{"samplers":["default"],"bits":128,"start":8.303123270822958,"link":"22-NMSEexample36","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))","time":7488.7587890625,"target":0.2147712406251803,"output":"(/ (/ (/ 1 x) (+ (/ 1 (sqrt (+ 1 x))) (/ 1 (sqrt x)))) (+ 1 x))","end":0.3301882586243904,"name":"NMSE example 3.6","status":"eq-target","end-est":0.30306625976844204},{"samplers":["default"],"bits":128,"start":6.540673277531814,"link":"23-NMSEexample35","pinf":0,"ninf":0,"vars":["N"],"input":"(- (atan (+ N 1)) (atan N))","time":3270.695068359375,"target":0.5191592566793662,"output":"(atan2 (- 1 0) (+ 1 (* (+ N 1) N)))","end":0.5191592566793662,"name":"NMSE example 3.5","status":"eq-target","end-est":0.6506271047969931},{"samplers":["default"],"bits":128,"start":14.07333238681803,"link":"24-NMSEexample34","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sin x))","time":38727.14697265625,"target":0.01775,"output":"(/ (/ (sqr (sin x)) (+ 1 (cos x))) (sin x))","end":0.4165371940034867,"name":"NMSE example 3.4","status":"eq-target","end-est":0.457757036320205},{"samplers":["default","default"],"bits":128,"start":16.473848508581224,"link":"25-NMSEexample33","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (sin (+ x eps)) (sin x))","time":15891.6650390625,"target":7.39379707472343,"output":"(if (<= eps -0.00030713418f0) (+ (cbrt (* (cube (sin x)) (cube (cos eps)))) (- (* (cos x) (sin eps)) (sin x))) (if (<= eps 0.07828799f0) (- (* (- eps (* 1/6 (cube eps))) (cos x)) (* (* (sin x) 1/2) (sqr eps))) (+ (cbrt (* (cube (sin x)) (cube (cos eps)))) (- (* (cos x) (sin eps)) (sin x)))))","end":0.29209285627131953,"name":"NMSE example 3.3","status":"gt-target","end-est":0.24719291695820328},{"samplers":["default"],"bits":128,"start":27.401928625657185,"link":"26-NMSEexample310","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (log (- 1 x)) (log (+ 1 x)))","time":5080.06494140625,"target":0.6149472647170215,"output":"(- (+ (* 1/2 (sqr x)) (+ 1 x)))","end":0.024,"name":"NMSE example 3.10","status":"eq-target","end-est":0.673117336570851},{"samplers":["default"],"bits":128,"start":13.169451888019355,"link":"27-NMSEexample31","pinf":0,"ninf":0,"vars":["x"],"input":"(- (sqrt (+ x 1)) (sqrt x))","time":4674.1279296875,"target":0.1693468046888521,"output":"(/ 1 (+ (sqr (sqrt (sqrt (+ x 1)))) (sqrt x)))","end":0.2564004550737271,"name":"NMSE example 3.1","status":"eq-target","end-est":0.22398378907376806}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}