{"bit_width":32,"date":1470323081,"note":"hamming","iterations":2,"flags":["rules:numerics","rules:arithmetic","rules:polynomials","rules:fractions","rules:exponents","rules:trigonometry","setup:simplify","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":28.330075319317814,"link":"0-NMSEproblem346","pinf":0,"ninf":0,"vars":["x","n"],"input":"(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))","time":11640.776123046875,"target":false,"output":"(fma (/ (log1p (/ 1 x)) n) (fma (/ (log1p (/ 1 x)) n) 1/2 1) (- 1 (pow x (/ 1 n))))","end":16.165661755628093,"name":"NMSE problem 3.4.6","status":"imp-start","end-est":11.943088265433635},{"samplers":["default"],"bits":128,"start":29.90704252563894,"link":"1-NMSEproblem345","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- x (sin x)) (- x (tan x)))","time":4211.31689453125,"target":false,"output":"(- (* 9/40 (sqr x)) (+ (* 27/2800 (pow x 4)) 1/2))","end":0.275374484033183,"name":"NMSE problem 3.4.5","status":"imp-start","end-est":14.553953399082072},{"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":2540.718017578125,"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":14.89921435410269,"link":"3-NMSEproblem341","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sqr x))","time":5163.536865234375,"target":false,"output":"(sqr (/ (sqrt (/ (sqr (sin x)) (+ 1 (cos x)))) x))","end":7.1152288875776675,"name":"NMSE problem 3.4.1","status":"imp-start","end-est":8.657475283803088},{"samplers":["default"],"bits":128,"start":18.72935245103867,"link":"4-NMSEproblem336","pinf":0,"ninf":0,"vars":["N"],"input":"(- (log (+ N 1)) (log N))","time":2042.618896484375,"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":18.35281296191611,"link":"5-NMSEproblem335","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (cos (+ x eps)) (cos x))","time":6485.76416015625,"target":false,"output":"(/ (- (cube (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))) (cube (cos x))) (fma (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (- (fma (cos eps) (cos x) (cos x)) (* (sin eps) (sin x))) (* (cos x) (cos x))))","end":9.243848093832414,"name":"NMSE problem 3.3.5","status":"imp-start","end-est":8.89526828261407},{"samplers":["default"],"bits":128,"start":13.125160038583346,"link":"6-NMSEproblem334","pinf":0,"ninf":0,"vars":["x"],"input":"(- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3)))","time":7632.658203125,"target":false,"output":"(log (exp (- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3)))))","end":13.215894651750041,"name":"NMSE problem 3.3.4","status":"apx-start","end-est":13.89321823771732},{"samplers":["default"],"bits":128,"start":5.585848855405505,"link":"7-NMSEproblem331","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (+ x 1)) (/ 1 x))","time":1666.0,"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":15.823762817950064,"link":"8-NMSEproblem321positive","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":6191.52490234375,"target":false,"output":"(/ (/ (* a c) (- (- b/2) (sqrt (- (sqr b/2) (* a c))))) a)","end":14.680678699779898,"name":"NMSE problem 3.2.1, positive","status":"imp-start","end-est":15.457400191943437},{"samplers":["default","default","default"],"bits":128,"start":15.54944760487287,"link":"9-NMSEproblem321negative","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":6611.300048828125,"target":false,"output":"(/ (/ (* a c) (+ (- b/2) (sqrt (- (sqr b/2) (* a c))))) a)","end":14.919397084865556,"name":"NMSE problem 3.2.1, negative","status":"apx-start","end-est":13.349121358288413},{"samplers":["default","default"],"bits":128,"start":12.347168217964176,"link":"10-NMSEsection35","pinf":0,"ninf":0,"vars":["a","x"],"input":"(- (exp (* a x)) 1)","time":1773.5400390625,"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":2202.39306640625,"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":4883.3798828125,"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":14044.315185546875,"target":6.380279368973654,"output":"(* (cube (/ (cbrt (expm1 (* eps (+ b a)))) (cbrt (expm1 (* a eps))))) (/ eps (expm1 (* b eps))))","end":12.595511364778508,"name":"NMSE problem 3.4.2","status":"lt-target","end-est":12.891285537030596},{"samplers":["default"],"bits":128,"start":15.337557113053641,"link":"14-NMSEproblem337","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (exp x) 2) (exp (- x)))","time":4107.884033203125,"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":5469.552001953125,"target":0.3527256163321579,"output":"(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))","end":4.0488439056739844,"name":"NMSE problem 3.3.3","status":"eq-start","end-est":3.664540081427342},{"samplers":["default","default"],"bits":128,"start":16.723464992713605,"link":"16-NMSEproblem332","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (tan (+ x eps)) (tan x))","time":2621.43798828125,"target":7.484125223600749,"output":"(- (/ 1 (cotan (+ x eps))) (tan x))","end":16.805435384071558,"name":"NMSE problem 3.3.2","status":"eq-start","end-est":17.03812406460983},{"samplers":["default","default","default"],"bits":128,"start":15.878078383433941,"link":"17-NMSEp42positive","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":11043.324951171875,"target":9.29639108246347,"output":"(/ (* (/ c 1) (/ (* 4 a) (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))))) (* 2 a))","end":13.657191258321758,"name":"NMSE p42, positive","status":"lt-target","end-est":14.71272278206793},{"samplers":["default","default","default"],"bits":128,"start":15.624550432962764,"link":"18-NMSEp42negative","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":10832.965087890625,"target":9.285602690388735,"output":"(/ (* (/ c 1) (/ (* 4 a) (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))))) (* 2 a))","end":14.079585252684822,"name":"NMSE p42, negative","status":"lt-target","end-est":12.438669715089716},{"samplers":["default"],"bits":128,"start":29.38943911622077,"link":"19-NMSEexample39","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 x) (cotan x))","time":4771.202880859375,"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":19021.47998046875,"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":1709.092041015625,"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":6406.698974609375,"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":2243.927978515625,"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":4159.159912109375,"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":16.589060559141455,"link":"25-NMSEexample33","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (sin (+ x eps)) (sin x))","time":5691.3330078125,"target":7.429184591019201,"output":"(/ (- (sqr (* (sin x) (cos eps))) (sqr (- (* (cos x) (sin eps)) (sin x)))) (- (fma (cos eps) (sin x) (sin x)) (* (sin eps) (cos x))))","end":6.397907337820857,"name":"NMSE example 3.3","status":"gt-target","end-est":6.520749479293497},{"samplers":["default"],"bits":128,"start":26.847174445368367,"link":"26-NMSEexample310","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (log (- 1 x)) (log (+ 1 x)))","time":3900.98388671875,"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":3530.923095703125,"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"}