{"bit_width":32,"date":1469200444,"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":"#(1065798049 1883600560 3605051291 3538956307 2647170081 378541646)","points":256,"tests":[{"samplers":["default","default"],"bits":128,"start":16.340096875223953,"link":"0-NMSEproblem346","pinf":0,"ninf":0,"vars":["x","n"],"input":"(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))","time":30849.60791015625,"target":false,"output":"(if (<= n 66058348.0f0) (cube (log (exp (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))))) (if (<= n 2.4911614f+20) (+ (- (/ (/ 1 n) x) (/ 1/2 (* (sqr x) n))) (/ (log x) (* x (* n n)))) (- (- (+ (/ 1 (* n x)) 1) (exp (/ (log x) n))) (/ (log x) n))))","end":12.96320227611983,"name":"NMSE problem 3.4.6","status":"imp-start","end-est":12.61444942872325},{"samplers":["default"],"bits":128,"start":14.893037293923728,"link":"1-NMSEproblem345","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- x (sin x)) (- x (tan x)))","time":5495.823974609375,"target":false,"output":"(if (<= x -0.020851452f0) (/ (- x (sin x)) (- x (tan x))) (if (<= x 5.3989635f0) (- (* 9/40 (sqr x)) (+ (* 27/2800 (pow x 4)) 1/2)) (/ (- x (sin x)) (- x (tan x)))))","end":0.09193987081110917,"name":"NMSE problem 3.4.5","status":"imp-start","end-est":0.17101017723407053},{"samplers":["default"],"bits":128,"start":18.68137992806583,"link":"2-NMSEproblem344","pinf":0,"ninf":0,"vars":["x"],"input":"(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))","time":8179.672119140625,"target":false,"output":"(if (<= x -0.0035937247f0) (sqrt (/ (* (+ (sqrt (exp (* 2 x))) 1) (- (sqrt (exp (* 2 x))) 1)) (- (exp x) 1))) (+ (+ (/ (* x 1/2) (sqrt 2)) (sqrt 2)) (* (- 1/4 (/ 1/8 2)) (/ (sqr x) (sqrt 2)))))","end":0.12264445604351165,"name":"NMSE problem 3.4.4","status":"imp-start","end-est":0.5057700956053106},{"samplers":["default"],"bits":128,"start":14.670250091013182,"link":"3-NMSEproblem341","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sqr x))","time":6846.73193359375,"target":false,"output":"(if (<= x -0.020851452f0) (* (/ 1 x) (/ (- 1 (cos x)) x)) (if (<= x 5.3989635f0) (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (sqr x))) (* (/ 1 x) (/ (- 1 (cos x)) x))))","end":0.2530815826739604,"name":"NMSE problem 3.4.1","status":"imp-start","end-est":0.2439570367844691},{"samplers":["default"],"bits":128,"start":19.008210232138083,"link":"4-NMSEproblem336","pinf":0,"ninf":0,"vars":["N"],"input":"(- (log (+ N 1)) (log N))","time":5951.364990234375,"target":false,"output":"(if (<= N 95.69362f0) (log (/ (+ N 1) N)) (+ (/ 1 N) (- (/ 1/3 (cube N)) (/ 1/2 (* N N)))))","end":8.338574881897337,"name":"NMSE problem 3.3.6","status":"imp-start","end-est":0.08094846691863104},{"samplers":["default","default"],"bits":128,"start":18.66410786108652,"link":"5-NMSEproblem335","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (cos (+ x eps)) (cos x))","time":14081.08984375,"target":false,"output":"(if (<= eps -0.0035937247f0) (- (cbrt (* (cube (cos x)) (cube (cos eps)))) (+ (* (sin x) (sin eps)) (cos x))) (if (<= eps 0.3662591f0) (- (* (- (* (sin x) (* eps 1/6)) (* 1/2 (cos x))) (* eps eps)) (* eps (sin x))) (/ (- (sqr (* (cos x) (cos eps))) (sqr (+ (* (sin x) (sin eps)) (cos x)))) (+ (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))))))","end":0.49921380039142804,"name":"NMSE problem 3.3.5","status":"imp-start","end-est":0.6674991883041899},{"samplers":["default"],"bits":128,"start":9.639646218225623,"link":"6-NMSEproblem334","pinf":0,"ninf":0,"vars":["x"],"input":"(- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3)))","time":19594.444091796875,"target":false,"output":"(if (<= x 1.3007283f+08) (- (sqr (sqrt (pow (+ x 1) (/ 1 3)))) (pow x (/ 1 3))) (- (- (cbrt (/ 1 x)) (* 1/9 (cbrt (/ 1 (pow x 7))))) (- (pow x -1/3) (* 1/3 (cbrt (/ 1 (pow x 4)))))))","end":12.92740087472709,"name":"NMSE problem 3.3.4","status":"uni-start","end-est":13.006482034610633},{"samplers":["default"],"bits":128,"start":5.52579695345213,"link":"7-NMSEproblem331","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (+ x 1)) (/ 1 x))","time":3356.138916015625,"target":false,"output":"(/ (/ -1 x) (+ 1 x))","end":0.09409436093777045,"name":"NMSE problem 3.3.1","status":"imp-start","end-est":0.1015625},{"samplers":["default","default","default"],"bits":128,"start":15.81302031910504,"link":"8-NMSEproblem321positive","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":13851.223876953125,"target":false,"output":"(if (<= b/2 -1.3809824f+19) (- (/ c (/ b/2 1/2)) (/ (* 2 b/2) a)) (if (<= b/2 1.7689368f-34) (/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a) (if (<= b/2 3.318237f+16) (/ (/ (* a c) (- (- b/2) (sqrt (- (sqr b/2) (* a c))))) a) (* -1/2 (/ c b/2)))))","end":3.448895212084971,"name":"NMSE problem 3.2.1, positive","status":"imp-start","end-est":4.24281358400417},{"samplers":["default","default","default"],"bits":128,"start":17.99065037636642,"link":"9-NMSEproblem321negative","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":15201.255859375,"target":false,"output":"(if (<= b/2 -1.4516784f-11) (/ c (/ b/2 -1/2)) (if (<= b/2 1.6024659f+18) (/ (pow (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) 1) a) (- (/ 1/2 (/ b/2 c)) (* (/ b/2 a) 2))))","end":2.313397611820907,"name":"NMSE problem 3.2.1, negative","status":"imp-start","end-est":4.838629627357251},{"samplers":["default","default"],"bits":128,"start":14.237431656268473,"link":"10-NMSEsection35","pinf":0,"ninf":0,"vars":["a","x"],"input":"(- (exp (* a x)) 1)","time":7743.51611328125,"target":2.820327248039763,"output":"(if (<= (* a x) -0.02085444f0) (- (exp (* a x)) 1) (+ (* a x) (* (* (* a x) (* a x)) (+ (* (* a x) 1/6) 1/2))))","end":0.118265871082856,"name":"NMSE section 3.5","status":"gt-target","end-est":0.5100437062150327},{"samplers":["default"],"bits":128,"start":20.846234689781674,"link":"11-NMSEsection311","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (exp x) (- (exp x) 1))","time":7116.51708984375,"target":13.629241892123247,"output":"(if (<= x 5.3989635f0) (cube (cbrt (/ (exp x) (+ x (* (sqr x) (+ 1/2 (* x 1/6))))))) (/ 1 (- 1 (exp (- x)))))","end":0.390876932459443,"name":"NMSE section 3.11","status":"gt-target","end-est":0.8517248735724402},{"samplers":["default"],"bits":128,"start":25.8487236136885,"link":"12-NMSEproblem343","pinf":0,"ninf":0,"vars":["eps"],"input":"(log (/ (- 1 eps) (+ 1 eps)))","time":5329.905029296875,"target":0.07877174947713132,"output":"(- (+ (* 2 eps) (+ (* 2/5 (pow eps 5)) (* 2/3 (pow eps 3)))))","end":0.08596986978972149,"name":"NMSE problem 3.4.3","status":"eq-target","end-est":0.10623578902471345},{"samplers":["default","default","default"],"bits":128,"start":29.597727736095525,"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":22854.271240234375,"target":6.707246378201662,"output":"(+ (/ 1 b) (/ 1 a))","end":0.058355235187904364,"name":"NMSE problem 3.4.2","status":"gt-target","end-est":2.516299147704742},{"samplers":["default"],"bits":128,"start":14.47213201147202,"link":"14-NMSEproblem337","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (exp x) 2) (exp (- x)))","time":6359.22705078125,"target":2.772111366078381,"output":"(* (+ x (+ (* 1/1920 (pow x 5)) (* (cube x) 1/24))) (+ x (+ (* 1/1920 (pow x 5)) (* (cube x) 1/24))))","end":0.0985135824277104,"name":"NMSE problem 3.3.7","status":"gt-target","end-est":1.0262425716799455},{"samplers":["default"],"bits":128,"start":4.060598800944528,"link":"15-NMSEproblem333","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))","time":7923.8720703125,"target":0.45035938285681704,"output":"(if (<= x -1.6975026f0) (+ (+ (/ 2 (pow x 7)) (/ (/ 2 x) (* x x))) (/ 2 (pow x 5))) (if (<= x 22.159796f0) (+ (- (sqr (sqrt (/ 1 (+ x 1)))) (/ 2 x)) (/ 1 (- x 1))) (+ (+ (/ 2 (pow x 7)) (/ (/ 2 x) (* x x))) (/ 2 (pow x 5)))))","end":0.10241170255902787,"name":"NMSE problem 3.3.3","status":"eq-target","end-est":0.16885948744137574},{"samplers":["default","default"],"bits":128,"start":17.03061389221692,"link":"16-NMSEproblem332","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (tan (+ x eps)) (tan x))","time":17163.6640625,"target":7.756492135799437,"output":"(if (<= (- (tan (+ x eps)) (tan x)) -1.2236342f-08) (- (tan (+ x eps)) (cube (cbrt (tan x)))) (if (<= (- (tan (+ x eps)) (tan x)) 1.9222349f-13) (+ (+ (+ (/ 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)))))) (- (tan (+ x eps)) (cube (cbrt (tan x))))))","end":7.613041290907292,"name":"NMSE problem 3.3.2","status":"eq-target","end-est":9.044125581298207},{"samplers":["default","default","default"],"bits":128,"start":15.994479455557707,"link":"17-NMSEp42positive","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":20233.814208984375,"target":9.754320753197268,"output":"(if (<= b -4.486354f+15) (- (/ c b) (/ b a)) (if (<= b 1.7689368f-34) (/ (+ (- (sqrt (- (sqr b) (* a (* 4 c))))) b) (- (* 2 a))) (if (<= b 3.318237f+16) (* (/ c 2) (/ 4 (- (- b) (sqrt (- (sqr b) (* (* c a) 4)))))) (/ c (- b)))))","end":2.5411312333698466,"name":"NMSE p42, positive","status":"gt-target","end-est":3.318316440229786},{"samplers":["default","default","default"],"bits":128,"start":18.127487996926774,"link":"18-NMSEp42negative","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":13149.166015625,"target":11.978300130238901,"output":"(if (<= b -1.4516784f-11) (* (/ c b) (/ -2 2)) (if (<= b 3.318237f+16) (/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a)) (- (/ c b) (/ b a))))","end":2.304956344250043,"name":"NMSE p42, negative","status":"gt-target","end-est":4.868744626521396},{"samplers":["default"],"bits":128,"start":29.36171201561421,"link":"19-NMSEexample39","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 x) (cotan x))","time":6619.676025390625,"target":0.017875,"output":"(+ (* x 1/3) (+ (* 2/945 (pow x 5)) (* (cube x) 1/45)))","end":0.32475,"name":"NMSE example 3.9","status":"eq-target","end-est":0.34765625},{"samplers":["default"],"bits":128,"start":31.02160228780084,"link":"20-NMSEexample38","pinf":0,"ninf":0,"vars":["N"],"input":"(- (- (* (+ N 1) (log (+ N 1))) (* N (log N))) 1)","time":37357.218017578125,"target":0.001375,"output":"(- (- (sqr (/ (* (sqrt (- (sqr N) 1)) (sqrt (log (+ N 1)))) (sqrt (- N 1)))) (* N (log N))) 1)","end":29.889983750460477,"name":"NMSE example 3.8","status":"lt-target","end-est":29.86729747020323},{"samplers":["default"],"bits":128,"start":26.327737217060097,"link":"21-NMSEexample37","pinf":0,"ninf":0,"vars":["x"],"input":"(- (exp x) 1)","time":4509.968994140625,"target":0.10030432343849159,"output":"(+ (* (+ 1/2 (* 1/6 x)) (sqr x)) x)","end":0.06870056406367188,"name":"NMSE example 3.7","status":"eq-target","end-est":0.7071385036829669},{"samplers":["default"],"bits":128,"start":8.430925327144358,"link":"22-NMSEexample36","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))","time":7306.321044921875,"target":0.21506372187554088,"output":"(/ (/ (/ 1 x) (+ (/ 1 (sqrt (+ 1 x))) (/ 1 (sqrt x)))) (+ 1 x))","end":0.3379023012014176,"name":"NMSE example 3.6","status":"eq-target","end-est":0.29525375976844204},{"samplers":["default"],"bits":128,"start":6.461012124589,"link":"23-NMSEexample35","pinf":0,"ninf":0,"vars":["N"],"input":"(- (atan (+ N 1)) (atan N))","time":3439.156982421875,"target":0.5043293483491635,"output":"(atan2 (- 1 0) (+ 1 (* (+ N 1) N)))","end":0.5043293483491635,"name":"NMSE example 3.5","status":"eq-target","end-est":0.6998654077277973},{"samplers":["default"],"bits":128,"start":13.66701830970949,"link":"24-NMSEexample34","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sin x))","time":36466.295166015625,"target":0.019125,"output":"(/ (/ (sqr (sin x)) (+ 1 (cos x))) (sin x))","end":0.4139748348334021,"name":"NMSE example 3.4","status":"eq-target","end-est":0.4764576599220341},{"samplers":["default","default"],"bits":128,"start":16.904646592035228,"link":"25-NMSEexample33","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (sin (+ x eps)) (sin x))","time":11148.633056640625,"target":7.647456870483766,"output":"(if (<= eps -0.0035937247f0) (+ (* (sin x) (cos eps)) (pow (- (* (cos x) (sin eps)) (sin x)) 1)) (if (<= eps 0.3662591f0) (- (* (- eps (* 1/6 (cube eps))) (cos x)) (* (* (sin x) 1/2) (sqr eps))) (+ (* (sin x) (cos eps)) (pow (- (* (cos x) (sin eps)) (sin x)) 1))))","end":0.2967474331002227,"name":"NMSE example 3.3","status":"gt-target","end-est":0.3833998982502433},{"samplers":["default"],"bits":128,"start":27.211237727103818,"link":"26-NMSEexample310","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (log (- 1 x)) (log (+ 1 x)))","time":5573.35302734375,"target":0.686393229626715,"output":"(- (+ (+ (* 1/2 (sqr x)) 1) x))","end":0.04,"name":"NMSE example 3.10","status":"eq-target","end-est":0.2641595673517995},{"samplers":["default"],"bits":128,"start":13.152704695652016,"link":"27-NMSEexample31","pinf":0,"ninf":0,"vars":["x"],"input":"(- (sqrt (+ x 1)) (sqrt x))","time":3833.428955078125,"target":0.17461804531403244,"output":"(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))","end":0.17461804531403244,"name":"NMSE example 3.1","status":"eq-target","end-est":0.16796875}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}