{"bit_width":32,"date":1467996705,"note":"hamming","iterations":3,"flags":["rules:numerics","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":"#(1065543365 620684644 906956026 369308393 342036037 1300431646)","points":256,"tests":[{"samplers":["default","default"],"bits":128,"start":19.25153018808365,"link":"0-NMSEproblem346","pinf":0,"ninf":0,"vars":["x","n"],"input":"(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))","time":21000.70703125,"target":false,"output":"(if (<= n -6.9678054f+08) (fma (/ (log1p (/ 1 x)) n) (fma (/ (log1p (/ 1 x)) n) 1/2 1) (- 1 (pow x (/ 1 n)))) (if (<= n 8.0860474f+08) (- (exp (/ (log1p x) n)) (pow x (/ 1 n))) (fma (/ (log1p (/ 1 x)) n) (fma (/ (log1p (/ 1 x)) n) 1/2 1) (- 1 (pow x (/ 1 n))))))","end":17.33924755132604,"name":"NMSE problem 3.4.6","status":"imp-start","end-est":2.562438196793106},{"samplers":["default"],"bits":128,"start":14.563735817971722,"link":"1-NMSEproblem345","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- x (sin x)) (- x (tan x)))","time":7947.0029296875,"target":false,"output":"(if (<= x -0.23566085f0) (/ (- x (sin x)) (- x (tan x))) (if (<= x 0.5589793f0) (- (* (sqr x) 9/40) (fma 27/2800 (pow x 4) 1/2)) (/ (- x (sin x)) (- x (tan x)))))","end":0.02861888715762928,"name":"NMSE problem 3.4.5","status":"imp-start","end-est":0.05057955949837765},{"samplers":["default"],"bits":128,"start":16.711888055838795,"link":"2-NMSEproblem344","pinf":0,"ninf":0,"vars":["x"],"input":"(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))","time":4992.31103515625,"target":false,"output":"(sqrt (cbrt (cube (/ (expm1 (* 2 x)) (expm1 x)))))","end":0.25792548148063627,"name":"NMSE problem 3.4.4","status":"imp-start","end-est":0.02734375},{"samplers":["default"],"bits":128,"start":14.421773388127752,"link":"3-NMSEproblem341","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sqr x))","time":10441.8798828125,"target":false,"output":"(if (<= x -0.23566085f0) (* (/ 1 x) (/ (- 1 (cos x)) x)) (if (<= x 0.5589793f0) (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (sqr x))) (sqr (/ (sqrt (/ (sqr (sin x)) (+ 1 (cos x)))) x))))","end":0.24558856729555878,"name":"NMSE problem 3.4.1","status":"imp-start","end-est":0.16150751565848603},{"samplers":["default"],"bits":128,"start":19.38850657724006,"link":"4-NMSEproblem336","pinf":0,"ninf":0,"vars":["N"],"input":"(- (log (+ N 1)) (log N))","time":2365.490966796875,"target":false,"output":"(log1p (/ 1 N))","end":0.053210543462337716,"name":"NMSE problem 3.3.6","status":"imp-start","end-est":0.04296875},{"samplers":["default","default"],"bits":128,"start":18.970932501546528,"link":"5-NMSEproblem335","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (cos (+ x eps)) (cos x))","time":25696.400146484375,"target":false,"output":"(if (<= eps -2.320036f-13) (cbrt (cube (- (/ (- (cube (* (cos eps) (cos x))) (cube (* (sin x) (sin eps)))) (+ (sqr (* (cos x) (cos eps))) (+ (sqr (* (sin x) (sin eps))) (* (* (cos x) (cos eps)) (* (sin x) (sin eps)))))) (cos x)))) (if (<= eps 0.18811941f0) (- (* 1/24 (pow eps 4)) (fma (* eps eps) 1/2 (* x eps))) (- (/ (- (cube (* (cos eps) (cos x))) (cube (* (sin x) (sin eps)))) (+ (cbrt (cube (sqr (* (cos x) (cos eps))))) (+ (sqr (* (sin x) (sin eps))) (* (* (cos x) (cos eps)) (* (sin x) (sin eps)))))) (cos x))))","end":1.4399381002681122,"name":"NMSE problem 3.3.5","status":"imp-start","end-est":7.113096928028165},{"samplers":["default"],"bits":128,"start":20.129437214446607,"link":"6-NMSEproblem334","pinf":0,"ninf":0,"vars":["x"],"input":"(- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3)))","time":14510.658935546875,"target":false,"output":"(if (<= x 7639594.5f0) (- (cbrt (+ 1 x)) (cbrt x)) (- (fma (cbrt (/ 1 (pow x 4))) 1/3 (cbrt (/ 1 x))) (fma 1/9 (cbrt (/ 1 (pow x 7))) (pow x -1/3))))","end":13.046496425991938,"name":"NMSE problem 3.3.4","status":"imp-start","end-est":11.315190208269538},{"samplers":["default"],"bits":128,"start":5.63586489556402,"link":"7-NMSEproblem331","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (+ x 1)) (/ 1 x))","time":3500.132080078125,"target":false,"output":"(/ (- (- x x) 1) (fma x x x))","end":0.5288627174849423,"name":"NMSE problem 3.3.1","status":"imp-start","end-est":0.5752220078476007},{"samplers":["default","default","default"],"bits":128,"start":17.566880541026745,"link":"8-NMSEproblem321positive","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":16630.77099609375,"target":false,"output":"(if (<= b/2 -3.840384f-10) (/ (- (/ (* 1/2 c) (/ b/2 a)) (- b/2 (- b/2))) a) (if (<= b/2 1.7973414f+17) (/ (* (/ a 1) (/ c (- (- b/2) (sqrt (- (sqr b/2) (* a c)))))) a) (/ (/ c (/ a a)) (fma c (* a (/ 1/2 b/2)) (- (- b/2) b/2)))))","end":3.5136643900091076,"name":"NMSE problem 3.2.1, positive","status":"imp-start","end-est":4.034183762339623},{"samplers":["default","default","default"],"bits":128,"start":17.925808417135634,"link":"9-NMSEproblem321negative","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":14442.018798828125,"target":false,"output":"(if (<= b/2 -1.3686002f-10) (/ c (- (* (* 1/2 c) (/ a b/2)) (* 2 b/2))) (if (<= b/2 1.7973414f+17) (/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a) (- (/ 1/2 (/ b/2 c)) (* (/ b/2 a) 2))))","end":3.348130125408938,"name":"NMSE problem 3.2.1, negative","status":"imp-start","end-est":4.172837632689729},{"samplers":["default","default"],"bits":128,"start":12.249816199565801,"link":"10-NMSEsection35","pinf":0,"ninf":0,"vars":["a","x"],"input":"(- (exp (* a x)) 1)","time":3137.06884765625,"target":0.14907652861488738,"output":"(expm1 (* x a))","end":0.06845322874971074,"name":"NMSE section 3.5","status":"eq-target","end-est":0.061747480164287515},{"samplers":["default"],"bits":128,"start":20.2898489352775,"link":"11-NMSEsection311","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (exp x) (- (exp x) 1))","time":7271.090087890625,"target":12.979246514277271,"output":"(if (<= x 255.52292f0) (/ (exp x) (expm1 x)) (fma (fma 1/2 (/ 1 x) 1) (/ (/ 1 (expm1 (/ 1 x))) x) (/ 1 (expm1 x))))","end":0.1895757500476197,"name":"NMSE section 3.11","status":"gt-target","end-est":0.17875200020584273},{"samplers":["default"],"bits":128,"start":25.90990583093843,"link":"12-NMSEproblem343","pinf":0,"ninf":0,"vars":["eps"],"input":"(log (/ (- 1 eps) (+ 1 eps)))","time":6808.27197265625,"target":0.11599414806839141,"output":"(- (+ (* 2 eps) (+ (* 2/5 (pow eps 5)) (* 2/3 (pow eps 3)))))","end":0.12218286994393229,"name":"NMSE problem 3.4.3","status":"eq-target","end-est":0.2575433131955973},{"samplers":["default","default","default"],"bits":128,"start":28.00347019772929,"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":31182.27685546875,"target":6.672010606725066,"output":"(if (<= b -2.0638378f+09) (* (cube (/ (cbrt (expm1 (* eps (+ b a)))) (cbrt (expm1 (* a eps))))) (/ eps (expm1 (* b eps)))) (if (<= b 8651331.0f0) (* (+ (* (* b 1/12) (sqr eps)) (- (/ 1 b) (* 1/2 eps))) (/ (expm1 (* eps (+ a b))) (expm1 (* a eps)))) (* (pow (/ (expm1 (* eps (+ b a))) (expm1 (* a eps))) 1) (/ eps (cube (cbrt (expm1 (* b eps))))))))","end":8.445913573308243,"name":"NMSE problem 3.4.2","status":"lt-target","end-est":8.476642644820819},{"samplers":["default"],"bits":128,"start":15.379029984115522,"link":"14-NMSEproblem337","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (exp x) 2) (exp (- x)))","time":6725.06005859375,"target":4.130247161087854,"output":"(fma (pow x 6) 1/360 (fma (pow x 4) 1/12 (sqr x)))","end":0.2979580291448698,"name":"NMSE problem 3.3.7","status":"gt-target","end-est":0.9766187826863146},{"samplers":["default"],"bits":128,"start":4.033527564625299,"link":"15-NMSEproblem333","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))","time":12242.5,"target":0.3729888055670145,"output":"(if (<= x -1.1296622f0) (/ (expm1 (log1p (fma (- (/ 1 x) 1) (- (/ 1 x) (fma 2 (/ 1 x) 2)) (+ (/ 1 (sqr x)) (/ 1 x))))) (* (- x 1) (fma x x x))) (if (<= x 1.859597f0) (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))) (/ (expm1 (log1p (fma (- (/ 1 x) 1) (- (/ 1 x) (fma 2 (/ 1 x) 2)) (+ (/ 1 (sqr x)) (/ 1 x))))) (* (- x 1) (fma x x x)))))","end":0.07235864687698315,"name":"NMSE problem 3.3.3","status":"eq-target","end-est":0.0390625},{"samplers":["default","default"],"bits":128,"start":17.245465665380003,"link":"16-NMSEproblem332","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (tan (+ x eps)) (tan x))","time":20774.826904296875,"target":8.129564051678269,"output":"(if (<= eps -0.027100457f0) (/ (- (* (cotan x) (sin (+ x eps))) (cos (+ (/ 1 eps) (/ 1 x)))) (* (cos (+ x eps)) (cotan x))) (if (<= eps 0.00019073929f0) (+ (+ (fma (/ eps (cos x)) (/ (sin x) (/ (cos x) (sin x))) (* (sin x) (/ (sqr eps) (cos x)))) (fma (/ (sqr eps) (cube (cos x))) (cube (sin x)) (* 1/3 (cube eps)))) (fma (/ (cube eps) (pow (cos x) 4)) (pow (sin x) 4) (fma (/ 4/3 (cos x)) (/ (* (sin x) (sin x)) (/ (cos x) (cube eps))) eps))) (/ (- (cos x) (* (cotan (+ eps x)) (sin x))) (* (cotan (+ x eps)) (cos x)))))","end":7.860472135665952,"name":"NMSE problem 3.3.2","status":"eq-target","end-est":7.314159310547167},{"samplers":["default","default","default"],"bits":128,"start":17.633225271946422,"link":"17-NMSEp42positive","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":19100.093017578125,"target":11.47464341161736,"output":"(if (<= b -3.840384f-10) (- (/ c b) (/ b a)) (if (<= b 1.7973414f+17) (* (/ c 2) (/ 4 (- (- b) (sqrt (- (sqr b) (* (* c a) 4)))))) (* (/ c b) (/ -2 2))))","end":2.601003281447741,"name":"NMSE p42, positive","status":"gt-target","end-est":4.257943437205194},{"samplers":["default","default","default"],"bits":128,"start":17.994203655694925,"link":"18-NMSEp42negative","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":27454.610107421875,"target":11.828613018184207,"output":"(if (<= b -1.3686002f-10) (/ (/ (* c 4) (- (fma (* a 2) (/ c b) (- b)) b)) 2) (if (<= b 1.7973414f+17) (* (/ 1 2) (/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) a)) (/ (fma (* 2 (/ c b)) a (- (- b) b)) (* a 2))))","end":3.6090301324590297,"name":"NMSE p42, negative","status":"gt-target","end-est":4.352773956101459},{"samplers":["default"],"bits":128,"start":29.417321132353212,"link":"19-NMSEexample39","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 x) (cotan x))","time":7999.471923828125,"target":0.016,"output":"(fma (log (exp (cube x))) 1/45 (fma 2/945 (pow x 5) (* x 1/3)))","end":0.3612474978404943,"name":"NMSE example 3.9","status":"eq-target","end-est":0.29525375976844204},{"samplers":["default"],"bits":128,"start":31.021645418221937,"link":"20-NMSEexample38","pinf":0,"ninf":0,"vars":["N"],"input":"(- (- (* (+ N 1) (log (+ N 1))) (* N (log N))) 1)","time":24281.216064453125,"target":0.00175,"output":"(- (exp (log (- (fma N (log1p N) (log1p N)) (* N (log N))))) 1)","end":29.453247630655103,"name":"NMSE example 3.8","status":"lt-target","end-est":29.430587957700695},{"samplers":["default"],"bits":128,"start":25.09811434812844,"link":"21-NMSEexample37","pinf":0,"ninf":0,"vars":["x"],"input":"(- (exp x) 1)","time":2172.239990234375,"target":0.977251882325564,"output":"(expm1 x)","end":0.00475,"name":"NMSE example 3.7","status":"eq-target","end-est":0.00390625},{"samplers":["default"],"bits":128,"start":8.526704664309117,"link":"22-NMSEexample36","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))","time":14516.70703125,"target":0.218761842188131,"output":"(if (<= x 1.1034064f+17) (/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (/ (- (+ (/ 1 (pow x 4)) (/ (/ 1 x) x)) (/ 1 (cube x))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ 1 x))))))","end":2.2884553381005404,"name":"NMSE example 3.6","status":"lt-target","end-est":2.3900641889612753},{"samplers":["default"],"bits":128,"start":6.5334771114007,"link":"23-NMSEexample35","pinf":0,"ninf":0,"vars":["N"],"input":"(- (atan (+ N 1)) (atan N))","time":3141.191162109375,"target":0.5426033190478932,"output":"(atan2 (- 1 0) (fma N (+ 1 N) 1))","end":0.541280198735303,"name":"NMSE example 3.5","status":"eq-target","end-est":0.5556907578476007},{"samplers":["default"],"bits":128,"start":13.505369220143699,"link":"24-NMSEexample34","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sin x))","time":9068.652099609375,"target":0.02125,"output":"(/ (/ (sqr (sin x)) (+ 1 (cos x))) (sin x))","end":0.4140032813892851,"name":"NMSE example 3.4","status":"eq-target","end-est":0.4364544948702002},{"samplers":["default","default"],"bits":128,"start":16.857546669076573,"link":"25-NMSEexample33","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (sin (+ x eps)) (sin x))","time":25028.909912109375,"target":7.817491441426268,"output":"(if (<= eps -5.9474005f-05) (+ (* (sin x) (cos eps)) (/ (- (sqr (* (cos x) (sin eps))) (sqr (sin x))) (fma (sin eps) (cos x) (sin x)))) (if (<= eps 0.00019073929f0) (/ (- (* (sin x) (* (cos x) (* 2 eps))) (fma (* (* eps 1/3) (sqr eps)) (* (cos x) (sin x)) (sqr eps))) (- (fma (cos eps) (sin x) (sin x)) (* (cos x) (sin eps)))) (+ (* (sin x) (cos eps)) (/ (- (sqr (* (cos x) (sin eps))) (sqr (sin x))) (fma (sin eps) (cos x) (sin x))))))","end":1.2576227928466155,"name":"NMSE example 3.3","status":"gt-target","end-est":1.5096413379766507},{"samplers":["default"],"bits":128,"start":26.84338510381886,"link":"26-NMSEexample310","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (log (- 1 x)) (log (+ 1 x)))","time":6018.31103515625,"target":0.5177114957919188,"output":"(/ (log1p (- x)) (log1p x))","end":0.07714417344137622,"name":"NMSE example 3.10","status":"eq-target","end-est":0.08041000976844202},{"samplers":["default"],"bits":128,"start":13.61717431018662,"link":"27-NMSEexample31","pinf":0,"ninf":0,"vars":["x"],"input":"(- (sqrt (+ x 1)) (sqrt x))","time":4649.091064453125,"target":0.17248364687698317,"output":"(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))","end":0.17248364687698317,"name":"NMSE example 3.1","status":"eq-target","end-est":0.2265625}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}