{"bit_width":32,"date":1470246488,"note":"hamming","iterations":2,"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":"#(1066021830 2830721961 259995540 547417586 81053319 3982124210)","points":256,"tests":[{"samplers":["default","default"],"bits":128,"start":19.032314758266033,"link":"0-NMSEproblem346","pinf":0,"ninf":0,"vars":["x","n"],"input":"(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))","time":23145.47998046875,"target":false,"output":"(if (<= n -2.1541062f+08) (fma (/ (log1p (/ 1 x)) n) (fma (/ (log1p (/ 1 x)) n) 1/2 1) (- 1 (pow x (/ 1 n)))) (if (<= n 1.4894959f+09) (cube (cbrt (- (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":17.086951728925367,"name":"NMSE problem 3.4.6","status":"imp-start","end-est":3.0623236718591484},{"samplers":["default"],"bits":128,"start":15.46861407222194,"link":"1-NMSEproblem345","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- x (sin x)) (- x (tan x)))","time":10456.95703125,"target":false,"output":"(if (<= x -0.22660221f0) (/ (- x (sin x)) (- x (cube (cbrt (tan x))))) (if (<= x 117.99512f0) (- (* 9/40 (sqr x)) (+ (* 27/2800 (pow x 4)) 1/2)) (cbrt (cube (/ (- x (sin x)) (- x (tan x)))))))","end":0.030062001325307623,"name":"NMSE problem 3.4.5","status":"imp-start","end-est":0.185965141920679},{"samplers":["default"],"bits":128,"start":17.216352375383625,"link":"2-NMSEproblem344","pinf":0,"ninf":0,"vars":["x"],"input":"(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))","time":3160.64892578125,"target":false,"output":"(sqrt (/ (expm1 (* x 2)) (expm1 x)))","end":0.17011421572393037,"name":"NMSE problem 3.4.4","status":"imp-start","end-est":0.2461292947452968},{"samplers":["default"],"bits":128,"start":15.20092151704827,"link":"3-NMSEproblem341","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sqr x))","time":8007.926025390625,"target":false,"output":"(if (<= x -0.22660221f0) (* (/ 1 x) (/ (- 1 (cos x)) x)) (if (<= x 117.99512f0) (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (sqr x))) (* (/ 1 x) (/ (- 1 (cos x)) x))))","end":0.1974661616545293,"name":"NMSE problem 3.4.1","status":"imp-start","end-est":0.261743590953634},{"samplers":["default"],"bits":128,"start":18.72935245103867,"link":"4-NMSEproblem336","pinf":0,"ninf":0,"vars":["N"],"input":"(- (log (+ N 1)) (log N))","time":4684.505126953125,"target":false,"output":"(log1p (/ 1 N))","end":0.06318533395494477,"name":"NMSE problem 3.3.6","status":"imp-start","end-est":0.15205448734709345},{"samplers":["default","default"],"bits":128,"start":18.354053764497618,"link":"5-NMSEproblem335","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (cos (+ x eps)) (cos x))","time":14166.807861328125,"target":false,"output":"(if (<= eps -0.005046406f0) (- (- (* (cos x) (cos eps)) (cbrt (* (cube (sin x)) (cube (sin eps))))) (cos x)) (if (<= eps 0.0018547908f0) (- (* (cube eps) (* 1/6 (sin x))) (* eps (fma 1/2 eps (sin x)))) (- (- (* (cos x) (cos eps)) (cbrt (* (cube (sin x)) (cube (sin eps))))) (cos x))))","end":0.5595127740637147,"name":"NMSE problem 3.3.5","status":"imp-start","end-est":0.9374344835132699},{"samplers":["default"],"bits":128,"start":9.624346364111437,"link":"6-NMSEproblem334","pinf":0,"ninf":0,"vars":["x"],"input":"(- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3)))","time":19252.489013671875,"target":false,"output":"(if (<= x 4.6312522f+08) (- (pow (+ x 1) (/ 1 3)) (cube (cbrt (pow x (/ 1 3))))) (- (fma (cbrt (/ 1 (pow x 4))) 1/3 (cbrt (/ 1 x))) (fma 1/9 (cbrt (/ 1 (pow x 7))) (pow x -1/3))))","end":12.946303691420997,"name":"NMSE problem 3.3.4","status":"uni-start","end-est":12.496391772411865},{"samplers":["default"],"bits":128,"start":5.585848855405505,"link":"7-NMSEproblem331","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (+ x 1)) (/ 1 x))","time":2995.77099609375,"target":false,"output":"(/ (- (- x x) 1) (fma x x x))","end":0.494214035041312,"name":"NMSE problem 3.3.1","status":"imp-start","end-est":0.750886943344335},{"samplers":["default","default","default"],"bits":128,"start":17.70371445146941,"link":"8-NMSEproblem321positive","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":14526.47998046875,"target":false,"output":"(if (<= b/2 -3.3743287f+13) (- (/ 1/2 (/ b/2 c)) (* (/ b/2 a) 2)) (if (<= b/2 3.0993998f-09) (/ (fma 1 (- b/2) (sqrt (- (sqr b/2) (* a c)))) a) (/ c (fma 1/2 (/ c (/ b/2 a)) (- (- b/2) b/2)))))","end":3.355582683225497,"name":"NMSE problem 3.2.1, positive","status":"imp-start","end-est":4.213028696680042},{"samplers":["default","default","default"],"bits":128,"start":16.99691967180018,"link":"9-NMSEproblem321negative","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":15072.216064453125,"target":false,"output":"(if (<= b/2 -0.00030340048f0) (/ c (- (/ (* 1/2 c) (/ b/2 a)) (* 2 b/2))) (if (<= b/2 5.979008f+15) (/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a) (/ (fma (* (/ c b/2) a) 1/2 (- (- b/2) b/2)) a)))","end":3.7331372961224556,"name":"NMSE problem 3.2.1, negative","status":"imp-start","end-est":4.770454020961301},{"samplers":["default","default"],"bits":128,"start":12.347168217964176,"link":"10-NMSEsection35","pinf":0,"ninf":0,"vars":["a","x"],"input":"(- (exp (* a x)) 1)","time":2632.509033203125,"target":0.1463157463363675,"output":"(expm1 (* x a))","end":0.057509951410791106,"name":"NMSE section 3.5","status":"eq-target","end-est":0.11349256062715135},{"samplers":["default"],"bits":128,"start":18.23842166904468,"link":"11-NMSEsection311","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (exp x) (- (exp x) 1))","time":2662.260009765625,"target":16.58740833191216,"output":"(/ (exp x) (expm1 x))","end":1.7123758844300918,"name":"NMSE section 3.11","status":"gt-target","end-est":1.5549731217067169},{"samplers":["default"],"bits":128,"start":25.866104137541992,"link":"12-NMSEproblem343","pinf":0,"ninf":0,"vars":["eps"],"input":"(log (/ (- 1 eps) (+ 1 eps)))","time":6609.450927734375,"target":0.07857664549430231,"output":"(- (+ (* 2 eps) (+ (* 2/5 (pow eps 5)) (* 2/3 (pow eps 3)))))","end":0.08536912674466289,"name":"NMSE problem 3.4.3","status":"eq-target","end-est":0.6231590407906936},{"samplers":["default","default","default"],"bits":128,"start":27.940687453617613,"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":29369.2490234375,"target":6.380279368973654,"output":"(/ (/ (expm1 (* eps (+ a b))) (/ (expm1 (* b eps)) eps)) (cube (cbrt (expm1 (* a eps)))))","end":12.608284805715297,"name":"NMSE problem 3.4.2","status":"lt-target","end-est":12.966440997802888},{"samplers":["default"],"bits":128,"start":15.337557113053641,"link":"14-NMSEproblem337","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (exp x) 2) (exp (- x)))","time":6124.0078125,"target":3.84576226480112,"output":"(fma (pow x 6) 1/360 (fma (pow x 4) 1/12 (sqr x)))","end":0.34705458864031125,"name":"NMSE problem 3.3.7","status":"gt-target","end-est":0.7442631170905049},{"samplers":["default"],"bits":128,"start":4.0488439056739844,"link":"15-NMSEproblem333","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))","time":9485.97607421875,"target":0.3527256163321579,"output":"(if (<= x -1.942274f0) (/ (fma (- (/ 1 x) 1) (- (/ 1 x) (fma 2 (/ 1 x) 2)) (+ (/ 1 (sqr x)) (/ 1 x))) (* (- x 1) (fma x x x))) (if (<= x 117.99512f0) (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))) (/ (fma (- (/ 1 x) 1) (- (/ 1 x) (fma 2 (/ 1 x) 2)) (+ (/ 1 (sqr x)) (/ 1 x))) (* (- x 1) (fma x x x)))))","end":0.15193872805286765,"name":"NMSE problem 3.3.3","status":"eq-target","end-est":0.12632509256732483},{"samplers":["default","default"],"bits":128,"start":16.738457156453794,"link":"16-NMSEproblem332","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (tan (+ x eps)) (tan x))","time":20684.4599609375,"target":7.493737885599128,"output":"(if (<= (- (tan (+ x eps)) (tan x)) -0.0050464487f0) (cbrt (cube (- (tan (+ x eps)) (tan x)))) (if (<= (- (tan (+ x eps)) (tan x)) 0.0006144298f0) (+ (+ (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))) (- (tan (+ x eps)) (log1p (log (exp (expm1 (tan x))))))))","end":7.353978557444865,"name":"NMSE problem 3.3.2","status":"eq-target","end-est":7.214998896353244},{"samplers":["default","default","default"],"bits":128,"start":16.24529021065273,"link":"17-NMSEp42positive","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":19629.0869140625,"target":9.783290876077452,"output":"(if (<= b -1.1084968f+11) (- (/ c b) (/ b a)) (if (<= b -1.9267308f-26) (/ (+ (- b) (cube (cbrt (sqrt (- (sqr b) (* 4 (* a c))))))) (* 2 a)) (if (<= b 5.979008f+15) (/ (* (/ c 1) (/ (* 4 a) (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))))) (* 2 a)) (* (/ c b) (/ -2 2)))))","end":2.6591959072471125,"name":"NMSE p42, positive","status":"gt-target","end-est":3.066080155024315},{"samplers":["default","default","default"],"bits":128,"start":16.016501515255882,"link":"18-NMSEp42negative","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":18727.0810546875,"target":9.768567527763798,"output":"(if (<= b -6.9499224f+11) (* (/ c b) (/ -2 2)) (if (<= b -1.9267308f-26) (/ (* (/ c 1) (/ (* 4 a) (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))))) (* 2 a)) (if (<= b 5.979008f+15) (/ (pow (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) 1) (* 2 a)) (/ (- b) a))))","end":2.5678362124248513,"name":"NMSE p42, negative","status":"gt-target","end-est":3.303149088999472},{"samplers":["default"],"bits":128,"start":29.38943911622077,"link":"19-NMSEexample39","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 x) (cotan x))","time":5680.27294921875,"target":0.018698120312590147,"output":"(fma (cube x) 1/45 (fma 2/945 (pow x 5) (* x 1/3)))","end":0.334375,"name":"NMSE example 3.9","status":"eq-target","end-est":0.3515625},{"samplers":["default"],"bits":128,"start":31.021571912084713,"link":"20-NMSEexample38","pinf":0,"ninf":0,"vars":["N"],"input":"(- (- (* (+ N 1) (log (+ N 1))) (* N (log N))) 1)","time":19942.339111328125,"target":0.001875,"output":"(- (fma N (log1p N) (log1p N)) (sqr (sqrt (fma N (log N) 1))))","end":30.08748734702748,"name":"NMSE example 3.8","status":"eq-start","end-est":30.00617503781676},{"samplers":["default"],"bits":128,"start":25.371206824882748,"link":"21-NMSEexample37","pinf":0,"ninf":0,"vars":["x"],"input":"(- (exp x) 1)","time":2187.058837890625,"target":0.8464869334228722,"output":"(expm1 x)","end":0.003375,"name":"NMSE example 3.7","status":"eq-target","end-est":0.00390625},{"samplers":["default"],"bits":128,"start":8.402625022228298,"link":"22-NMSEexample36","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))","time":7586.989013671875,"target":0.22293872187554084,"output":"(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))","end":2.990618109072632,"name":"NMSE example 3.6","status":"lt-target","end-est":2.8397396403237263},{"samplers":["default"],"bits":128,"start":6.495636338590191,"link":"23-NMSEexample35","pinf":0,"ninf":0,"vars":["N"],"input":"(- (atan (+ N 1)) (atan N))","time":2760.055908203125,"target":0.5055796366042627,"output":"(atan2 (- 1 0) (fma N (+ 1 N) 1))","end":0.5047352756664923,"name":"NMSE example 3.5","status":"eq-target","end-est":0.766511943344335},{"samplers":["default"],"bits":128,"start":13.95954979169528,"link":"24-NMSEexample34","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sin x))","time":36598.56494140625,"target":0.01875,"output":"(/ (/ (sqr (sin x)) (+ 1 (cos x))) (sin x))","end":0.3912360199961716,"name":"NMSE example 3.4","status":"eq-target","end-est":0.5169209119034307},{"samplers":["default","default"],"bits":128,"start":16.589107175344356,"link":"25-NMSEexample33","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (sin (+ x eps)) (sin x))","time":10468.403076171875,"target":7.3906508047878905,"output":"(if (<= eps -0.00018059072f0) (/ (- (sqr (* (sin x) (cos eps))) (sqr (- (* (cos x) (sin eps)) (sin x)))) (- (fma (cos eps) (sin x) (sin x)) (* (sin eps) (cos x)))) (if (<= eps 2.7825011f-09) (* (sin eps) (cos x)) (/ (- (sqr (* (sin x) (cos eps))) (sqr (- (* (cos x) (sin eps)) (sin x)))) (- (fma (cos eps) (sin x) (sin x)) (* (sin eps) (cos x))))))","end":0.40543136521350115,"name":"NMSE example 3.3","status":"gt-target","end-est":0.4813618378488116},{"samplers":["default"],"bits":128,"start":26.847174445368367,"link":"26-NMSEexample310","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (log (- 1 x)) (log (+ 1 x)))","time":5311.73095703125,"target":0.5111467217678726,"output":"(/ (log1p (- x)) (log1p x))","end":0.08011109062806492,"name":"NMSE example 3.10","status":"eq-target","end-est":0.09212875976844201},{"samplers":["default"],"bits":128,"start":13.146743244607297,"link":"27-NMSEexample31","pinf":0,"ninf":0,"vars":["x"],"input":"(- (sqrt (+ x 1)) (sqrt x))","time":3819.43798828125,"target":0.16821240625180284,"output":"(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))","end":0.16821240625180284,"name":"NMSE example 3.1","status":"eq-target","end-est":0.21322250976844204}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}