{"bit_width":32,"date":1470837094,"note":"hamming","iterations":3,"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":"#(1066118269 3146385405 2008244797 2413636924 657271294 3751684478)","points":256,"tests":[{"samplers":["default","default"],"bits":128,"start":28.286635292606267,"link":"0-NMSEproblem346","pinf":0,"ninf":0,"vars":["x","n"],"input":"(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))","time":11903.35107421875,"target":false,"output":"(fma (/ (log1p (/ 1 x)) n) (fma (/ (log1p (/ 1 x)) n) 1/2 1) (- 1 (pow x (/ 1 n))))","end":16.52545197060836,"name":"NMSE problem 3.4.6","status":"imp-start","end-est":12.78972720941719},{"samplers":["default"],"bits":128,"start":14.924547635326231,"link":"1-NMSEproblem345","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- x (sin x)) (- x (tan x)))","time":4066.804931640625,"target":false,"output":"(/ (- x (sin x)) (- x (tan x)))","end":14.924547635326231,"name":"NMSE problem 3.4.5","status":"apx-start","end-est":14.15662655387612},{"samplers":["default"],"bits":128,"start":16.965299574526846,"link":"2-NMSEproblem344","pinf":0,"ninf":0,"vars":["x"],"input":"(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))","time":2992.011962890625,"target":false,"output":"(sqrt (/ (expm1 (* x 2)) (expm1 x)))","end":0.17135325433397453,"name":"NMSE problem 3.4.4","status":"imp-start","end-est":0.15545329826958354},{"samplers":["default"],"bits":128,"start":14.774733773220435,"link":"3-NMSEproblem341","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sqr x))","time":8783.131103515625,"target":false,"output":"(/ (/ (sqr (sin x)) (+ 1 (cos x))) (sqr x))","end":7.400947927119017,"name":"NMSE problem 3.4.1","status":"imp-start","end-est":6.3829320466427335},{"samplers":["default"],"bits":128,"start":18.84675585744305,"link":"4-NMSEproblem336","pinf":0,"ninf":0,"vars":["N"],"input":"(- (log (+ N 1)) (log N))","time":1943.2109375,"target":false,"output":"(log1p (/ 1 N))","end":0.05058559633697832,"name":"NMSE problem 3.3.6","status":"imp-start","end-est":0.25332878328029584},{"samplers":["default","default"],"bits":128,"start":18.346667933272478,"link":"5-NMSEproblem335","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (cos (+ x eps)) (cos x))","time":5972.64697265625,"target":false,"output":"(/ (- (sqr (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (sqr (cos x))) (- (fma (cos eps) (cos x) (cos x)) (* (sin eps) (sin x))))","end":9.09346568705775,"name":"NMSE problem 3.3.5","status":"imp-start","end-est":10.698315707861795},{"samplers":["default"],"bits":128,"start":13.100260971430053,"link":"6-NMSEproblem334","pinf":0,"ninf":0,"vars":["x"],"input":"(- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3)))","time":10984.33984375,"target":false,"output":"(pow E (log (- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3)))))","end":13.100973804788675,"name":"NMSE problem 3.3.4","status":"apx-start","end-est":12.520626111189072},{"samplers":["default"],"bits":128,"start":5.682054927171172,"link":"7-NMSEproblem331","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (+ x 1)) (/ 1 x))","time":2349.196044921875,"target":false,"output":"(/ (- (- x x) 1) (fma x x x))","end":0.5254412561703456,"name":"NMSE problem 3.3.1","status":"imp-start","end-est":0.6233553868172976},{"samplers":["default","default","default"],"bits":128,"start":15.628854657875868,"link":"8-NMSEproblem321positive","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":8795.51416015625,"target":false,"output":"(/ (* (/ a 1) (/ c (- (- b/2) (sqrt (- (sqr b/2) (* a c)))))) a)","end":13.686527805987637,"name":"NMSE problem 3.2.1, positive","status":"imp-start","end-est":13.761716345082968},{"samplers":["default","default","default"],"bits":128,"start":15.633226839342028,"link":"9-NMSEproblem321negative","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":8746.779052734375,"target":false,"output":"(/ (/ (* a c) (+ (- b/2) (sqrt (- (sqr b/2) (* a c))))) a)","end":14.865607588295356,"name":"NMSE problem 3.2.1, negative","status":"apx-start","end-est":15.17735032239337},{"samplers":["default","default"],"bits":128,"start":12.125530341479074,"link":"10-NMSEsection35","pinf":0,"ninf":0,"vars":["a","x"],"input":"(- (exp (* a x)) 1)","time":1626.2529296875,"target":0.14169680673629925,"output":"(expm1 (* x a))","end":0.0622816068335203,"name":"NMSE section 3.5","status":"eq-target","end-est":0.05948757300974953},{"samplers":["default"],"bits":128,"start":18.15078219440019,"link":"11-NMSEsection311","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (exp x) (- (exp x) 1))","time":3807.364013671875,"target":18.111645747387755,"output":"(/ (exp x) (log1p (expm1 (expm1 x))))","end":1.8297344651005705,"name":"NMSE section 3.11","status":"gt-target","end-est":2.8519577143400743},{"samplers":["default"],"bits":128,"start":24.716131349960605,"link":"12-NMSEproblem343","pinf":0,"ninf":0,"vars":["eps"],"input":"(log (/ (- 1 eps) (+ 1 eps)))","time":5545.613037109375,"target":0.30070032888545917,"output":"(+ (log1p (- eps)) (- (log1p eps)))","end":0.024875,"name":"NMSE problem 3.4.3","status":"eq-target","end-est":0.01171875},{"samplers":["default","default","default"],"bits":128,"start":27.938587276026478,"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":15714.9990234375,"target":6.227924330900225,"output":"(* (/ (cube (expm1 (log1p (cbrt (expm1 (* eps (+ b a))))))) (expm1 (* a eps))) (/ eps (expm1 (* b eps))))","end":12.583375597973301,"name":"NMSE problem 3.4.2","status":"lt-target","end-est":12.621767958635044},{"samplers":["default"],"bits":128,"start":15.224962933064557,"link":"14-NMSEproblem337","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (exp x) 2) (exp (- x)))","time":5994.217041015625,"target":3.9732421107468854,"output":"(expm1 (log1p (fma (pow x 6) 1/360 (fma (pow x 4) 1/12 (sqr x)))))","end":0.6598078692544969,"name":"NMSE problem 3.3.7","status":"gt-target","end-est":1.4061499420937311},{"samplers":["default"],"bits":128,"start":4.0977667588149655,"link":"15-NMSEproblem333","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))","time":21230.44482421875,"target":0.41431727009056785,"output":"(* (- (+ (/ 1 (- x 1)) (/ 1 (+ 1 x))) (/ 2 x)) 1)","end":4.117387645201282,"name":"NMSE problem 3.3.3","status":"eq-start","end-est":5.264699944118257},{"samplers":["default","default"],"bits":128,"start":16.73016836030265,"link":"16-NMSEproblem332","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (tan (+ x eps)) (tan x))","time":5013.10302734375,"target":7.706624660628882,"output":"(- (/ 1 (cotan (+ x eps))) (tan x))","end":16.801551223269062,"name":"NMSE problem 3.3.2","status":"eq-start","end-est":16.800224133732662},{"samplers":["default","default","default"],"bits":128,"start":15.722292963242928,"link":"17-NMSEp42positive","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":14010.989990234375,"target":9.330810295188671,"output":"(/ 1 (* (/ 2 (* 4 c)) (- (- b) (sqrt (- (sqr b) (* (* a c) 4))))))","end":13.848847352789946,"name":"NMSE p42, positive","status":"lt-target","end-est":13.871849478497872},{"samplers":["default","default","default"],"bits":128,"start":15.735607370033756,"link":"18-NMSEp42negative","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":12877.302001953125,"target":9.45678040886443,"output":"(* (/ c 2) (/ 4 (+ (- b) (sqrt (- (sqr b) (* (* c a) 4))))))","end":13.89204742099544,"name":"NMSE p42, negative","status":"lt-target","end-est":14.174507780055874},{"samplers":["default"],"bits":128,"start":29.348660396646274,"link":"19-NMSEexample39","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 x) (cotan x))","time":5216.18896484375,"target":0.01864624062518029,"output":"(fma (cube x) 1/45 (fma 2/945 (pow x 5) (* x 1/3)))","end":0.320875,"name":"NMSE example 3.9","status":"eq-target","end-est":0.27734375},{"samplers":["default"],"bits":128,"start":31.021636762230838,"link":"20-NMSEexample38","pinf":0,"ninf":0,"vars":["N"],"input":"(- (- (* (+ N 1) (log (+ N 1))) (* N (log N))) 1)","time":20279.6240234375,"target":0.0025,"output":"(- (exp (log (- (fma N (log1p N) (log1p N)) (* N (log N))))) 1)","end":29.438278466935007,"name":"NMSE example 3.8","status":"lt-target","end-est":29.402759252066083},{"samplers":["default"],"bits":128,"start":25.089449446408366,"link":"21-NMSEexample37","pinf":0,"ninf":0,"vars":["x"],"input":"(- (exp x) 1)","time":1404.177001953125,"target":0.9373034245848706,"output":"(expm1 x)","end":0.004875,"name":"NMSE example 3.7","status":"eq-target","end-est":0.00390625},{"samplers":["default"],"bits":128,"start":8.363859673712932,"link":"22-NMSEexample36","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))","time":6706.52001953125,"target":0.22204248125036058,"output":"(sqr (/ (sqrt (/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))) (sqrt (* (sqrt x) (sqrt (+ x 1))))))","end":0.5893370038988984,"name":"NMSE example 3.6","status":"eq-target","end-est":0.5703952269894943},{"samplers":["default"],"bits":128,"start":6.615873892308521,"link":"23-NMSEexample35","pinf":0,"ninf":0,"vars":["N"],"input":"(- (atan (+ N 1)) (atan N))","time":2110.72509765625,"target":0.5430356171081161,"output":"(atan2 (- 1 0) (fma N (+ 1 N) 1))","end":0.5410143764829357,"name":"NMSE example 3.5","status":"eq-target","end-est":0.6663241368172976},{"samplers":["default"],"bits":128,"start":13.79299269270881,"link":"24-NMSEexample34","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sin x))","time":4798.587890625,"target":0.01825,"output":"(/ (/ (sqr (sin x)) (+ 1 (cos x))) (sin x))","end":0.4245405550849433,"name":"NMSE example 3.4","status":"eq-target","end-est":0.4540652282789831},{"samplers":["default","default"],"bits":128,"start":16.61077315094662,"link":"25-NMSEexample33","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (sin (+ x eps)) (sin x))","time":12801.8330078125,"target":7.61798659610945,"output":"(/ (/ (- (sqr (sqr (* (sin x) (cos eps)))) (sqr (sqr (- (* (cos x) (sin eps)) (sin 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":6.1662017477206,"name":"NMSE example 3.3","status":"gt-target","end-est":6.8364413314638925},{"samplers":["default"],"bits":128,"start":26.713842115663155,"link":"26-NMSEexample310","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (log (- 1 x)) (log (+ 1 x)))","time":4492.468017578125,"target":0.5139199155674425,"output":"(/ (log1p (- x)) (log1p x))","end":0.07876917344137623,"name":"NMSE example 3.10","status":"eq-target","end-est":0.049160009768442016},{"samplers":["default"],"bits":128,"start":13.151102188154525,"link":"27-NMSEexample31","pinf":0,"ninf":0,"vars":["x"],"input":"(- (sqrt (+ x 1)) (sqrt x))","time":5448.846923828125,"target":0.17433740625180283,"output":"(/ 1 (+ (sqr (sqrt (sqrt (+ x 1)))) (sqrt x)))","end":0.26244826130930177,"name":"NMSE example 3.1","status":"eq-target","end-est":0.2326901120835176}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}