{"bit_width":64,"date":1467976805,"note":"hamming","iterations":3,"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","precision:double"],"seed":"#(1065543365 620684644 906956026 369308393 342036037 1300431646)","points":256,"tests":[{"samplers":["default","default"],"bits":128,"start":30.728561415202932,"link":"0-NMSEproblem346","pinf":0,"ninf":0,"vars":["x","n"],"input":"(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))","time":133973.19995117188,"target":false,"output":"(if (<= n -3266859465.0066943) (+ (/ (log x) (* x (* n n))) (- (/ 1 (* n x)) (/ (/ 1/2 n) (sqr x)))) (if (<= n 147870895489.3786) (log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))) (+ (/ (log x) (* x (* n n))) (- (/ 1 (* n x)) (/ (/ 1/2 n) (sqr x))))))","end":7.222966948929668,"name":"NMSE problem 3.4.6","status":"imp-start","end-est":24.648489168968133},{"samplers":["default"],"bits":128,"start":31.24574903602734,"link":"1-NMSEproblem345","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- x (sin x)) (- x (tan x)))","time":19449.968017578125,"target":false,"output":"(if (<= x -1.6832923238537353e-08) (- (/ x (- x (tan x))) (/ (sin x) (- x (tan x)))) (if (<= x 0.05861471774619774) (- (* 9/40 (sqr x)) (+ (* 27/2800 (pow x 4)) 1/2)) (- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))))","end":0.1232778544906917,"name":"NMSE problem 3.4.5","status":"imp-start","end-est":0.32425757042271386},{"samplers":["default"],"bits":128,"start":42.981811243940044,"link":"2-NMSEproblem344","pinf":0,"ninf":0,"vars":["x"],"input":"(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))","time":15382.067138671875,"target":false,"output":"(if (<= x -3.6838407832643567e-13) (sqrt (/ (* (+ (sqrt (exp (* 2 x))) 1) (- (sqrt (exp (* 2 x))) 1)) (- (exp x) 1))) (+ (+ (/ (* x 1/2) (sqrt 2)) (sqrt 2)) (exp (+ (- (log (* x x)) (log (sqrt 2))) (log (- 1/4 (/ 1/8 2)))))))","end":0.9798554865036939,"name":"NMSE problem 3.4.4","status":"imp-start","end-est":0.6341184621498934},{"samplers":["default"],"bits":128,"start":31.049541806934123,"link":"3-NMSEproblem341","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sqr x))","time":46586.035888671875,"target":false,"output":"(* (/ (sin x) x) (/ (/ (sin x) (+ 1 (cos x))) x))","end":0.2845271873333425,"name":"NMSE problem 3.4.1","status":"imp-start","end-est":0.27098795440901735},{"samplers":["default"],"bits":128,"start":40.57427059699886,"link":"4-NMSEproblem336","pinf":0,"ninf":0,"vars":["N"],"input":"(- (log (+ N 1)) (log N))","time":6936.655029296875,"target":false,"output":"(if (<= N 24753.173418699997) (log (/ (+ N 1) N)) (+ (/ 1 N) (- (/ 1/3 (cube N)) (/ 1/2 (* N N)))))","end":19.16815554944082,"name":"NMSE problem 3.3.6","status":"imp-start","end-est":0.15171738530581833},{"samplers":["default","default"],"bits":128,"start":39.393490588358986,"link":"5-NMSEproblem335","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (cos (+ x eps)) (cos x))","time":34116.614013671875,"target":false,"output":"(if (<= eps -8.102966659834604e-08) (- (- (* (cos x) (cos eps)) (cbrt (* (cube (sin x)) (cube (sin eps))))) (cos x)) (if (<= eps 0.0009667373424041872) (- (* (- (* (sin x) (* eps 1/6)) (* 1/2 (cos x))) (* eps eps)) (* eps (sin x))) (log (exp (- (- (* (cos eps) (cos x)) (cos x)) (* (sin x) (sin eps)))))))","end":0.5964732064245656,"name":"NMSE problem 3.3.5","status":"imp-start","end-est":0.7214554987241759},{"samplers":["default"],"bits":128,"start":22.060499339919154,"link":"6-NMSEproblem334","pinf":0,"ninf":0,"vars":["x"],"input":"(- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3)))","time":41211.259033203125,"target":false,"output":"(if (<= x 7.172506652626118e+17) (/ (- (cube (pow (+ x 1) (/ 1 3))) (cube (pow x (/ 1 3)))) (+ (sqr (pow (+ x 1) (/ 1 3))) (+ (sqr (exp (/ (log x) 3))) (* (pow (+ x 1) (/ 1 3)) (exp (/ (log x) 3)))))) (- (- (pow x -1/3) (* 1/9 (cbrt (/ 1 (pow x 7))))) (- (cbrt (/ 1 x)) (* 1/3 (cbrt (/ 1 (pow x 4)))))))","end":29.138261486470903,"name":"NMSE problem 3.3.4","status":"uni-start","end-est":27.381032591068987},{"samplers":["default"],"bits":128,"start":13.957971295836575,"link":"7-NMSEproblem331","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (+ x 1)) (/ 1 x))","time":3877.659912109375,"target":false,"output":"(/ -1 (+ x (sqr x)))","end":0.3800280762104198,"name":"NMSE problem 3.3.1","status":"imp-start","end-est":0.6280999716396053},{"samplers":["default","default","default"],"bits":128,"start":37.08572242514225,"link":"8-NMSEproblem321positive","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":15672.3720703125,"target":false,"output":"(if (<= b/2 -4.191830935951668e+150) (- (/ 1/2 (/ b/2 c)) (* (/ b/2 a) 2)) (if (<= b/2 7.444658085812687e-61) (/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a) (/ c (+ (/ (* a 1/2) (/ b/2 c)) (- (- b/2) b/2)))))","end":7.689778286651884,"name":"NMSE problem 3.2.1, positive","status":"imp-start","end-est":10.130596694719587},{"samplers":["default","default","default"],"bits":128,"start":34.25018328787898,"link":"9-NMSEproblem321negative","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":97722.63696289062,"target":false,"output":"(if (<= b/2 -5.5367438047953165e+140) (/ c (- (* (* a 1/2) (/ c b/2)) (- b/2 (- b/2)))) (if (<= b/2 -5.4085235260168585e-306) (/ 1 (/ (+ (- b/2) (sqrt (- (sqr b/2) (* c a)))) c)) (if (<= b/2 3.4791896352684183e+99) (/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a) (/ (+ (/ (* 1/2 c) (/ b/2 a)) (- (- b/2) b/2)) a))))","end":6.324161871517689,"name":"NMSE problem 3.2.1, negative","status":"imp-start","end-est":7.753336163536166},{"samplers":["default","default"],"bits":128,"start":32.36386221954471,"link":"10-NMSEsection35","pinf":0,"ninf":0,"vars":["a","x"],"input":"(- (exp (* a x)) 1)","time":14536.246826171875,"target":5.919430750295891,"output":"(if (<= (* a x) -2.0523665265040743e-06) (log (exp (- (exp (* a x)) 1))) (+ (* 1/2 (sqr (* x a))) (+ (* x a) (cbrt (cube (* 1/6 (cube (* a x))))))))","end":3.721710540895825,"name":"NMSE section 3.5","status":"gt-target","end-est":0.07370897443253745},{"samplers":["default"],"bits":128,"start":45.768422635878245,"link":"11-NMSEsection311","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (exp x) (- (exp x) 1))","time":3618.60205078125,"target":30.110412893757392,"output":"(if (<= x -8.102966659834604e-08) (/ 1 (- 1 (exp (- x)))) (if (<= x 0.05861471774619774) (+ 1/2 (+ (/ 1 x) (* 1/12 x))) (/ 1 (- 1 (exp (- x))))))","end":0.05804097273226389,"name":"NMSE section 3.11","status":"gt-target","end-est":0.18654709668938427},{"samplers":["default"],"bits":128,"start":59.3835533315673,"link":"12-NMSEproblem343","pinf":0,"ninf":0,"vars":["eps"],"input":"(log (/ (- 1 eps) (+ 1 eps)))","time":5930.156982421875,"target":0.054742943846543386,"output":"(- (+ (* 2 eps) (+ (* 2/5 (pow eps 5)) (* 2/3 (pow eps 3)))))","end":0.06715102665985467,"name":"NMSE problem 3.4.3","status":"eq-target","end-est":0.09979825535520082},{"samplers":["default","default","default"],"bits":128,"start":62.00814815723609,"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":72014.2880859375,"target":14.4301000791675,"output":"(if (<= (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) 0.0) (+ (/ 1 b) (/ 1 a)) (if (<= (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) 4.8088960053893386e-148) (+ (/ 1 b) (/ 1 a)) (+ (/ 1 b) (/ 1 a))))","end":0.013,"name":"NMSE problem 3.4.2","status":"gt-target","end-est":2.636988362932},{"samplers":["default"],"bits":128,"start":34.85177271830734,"link":"14-NMSEproblem337","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (exp x) 2) (exp (- x)))","time":8640.366943359375,"target":8.567225233537041,"output":"(+ (sqr x) (+ (* 1/12 (pow x 4)) (* 1/360 (pow x 6))))","end":0.12431625269556966,"name":"NMSE problem 3.3.7","status":"gt-target","end-est":0.5112253853814265},{"samplers":["default"],"bits":128,"start":9.373514456292366,"link":"15-NMSEproblem333","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))","time":14462.0771484375,"target":0.22868914340139332,"output":"(/ (/ (/ 2 x) (+ 1 x)) (- x 1))","end":0.06783496250072114,"name":"NMSE problem 3.3.3","status":"eq-target","end-est":0.041347509768442016},{"samplers":["default","default"],"bits":128,"start":36.37981705968363,"link":"16-NMSEproblem332","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (tan (+ x eps)) (tan x))","time":40850.296875,"target":14.76854436509056,"output":"(if (<= eps -8.102966659834604e-08) (- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (tan x)) (if (<= eps 8.510050417588485e-09) (+ (+ (+ (/ 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)))))) (- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (tan x))))","end":0.4305094455128112,"name":"NMSE problem 3.3.2","status":"gt-target","end-est":0.38121787703690463},{"samplers":["default","default","default"],"bits":128,"start":34.27483852815191,"link":"17-NMSEp42positive","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":29159.779052734375,"target":21.921414254956968,"output":"(if (<= b -1.4230559129753548e+111) (- (/ c b) (/ b a)) (if (<= b -5.4085235260168585e-306) (/ 1 (/ (* 2 a) (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))))) (if (<= b 4.161458774616805e+86) (* (/ c 2) (/ 4 (- (- b) (sqrt (- (sqr b) (* (* c a) 4)))))) (* (/ (/ c (/ 2 4)) (- (* (/ c b) a) b)) (/ 1 2)))))","end":5.959649055948933,"name":"NMSE p42, positive","status":"gt-target","end-est":7.566540958946397},{"samplers":["default","default","default"],"bits":128,"start":34.39984087126731,"link":"18-NMSEp42negative","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":27805.26318359375,"target":21.655176886394713,"output":"(if (<= b -1.4230559129753548e+111) (* (/ (/ c (/ 2 4)) (- (* (/ c b) a) b)) (/ 1 2)) (if (<= b -5.4085235260168585e-306) (* (/ c 2) (/ 4 (+ (- b) (sqrt (- (sqr b) (* (* c a) 4)))))) (if (<= b 3.4791896352684183e+99) (/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a)) (- (/ c b) (/ b a)))))","end":5.872151786398915,"name":"NMSE p42, negative","status":"gt-target","end-est":7.720641814035476},{"samplers":["default"],"bits":128,"start":59.91541795664349,"link":"19-NMSEexample39","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 x) (cotan x))","time":7637.57421875,"target":0.09926528983625911,"output":"(+ (* x 1/3) (+ (* 2/945 (pow x 5)) (* (cube x) 1/45)))","end":0.331375,"name":"NMSE example 3.9","status":"eq-target","end-est":0.359375},{"samplers":["default"],"bits":128,"start":63.32613749492593,"link":"20-NMSEexample38","pinf":0,"ninf":0,"vars":["N"],"input":"(- (- (* (+ N 1) (log (+ N 1))) (* N (log N))) 1)","time":31650.51416015625,"target":60.76579176168329,"output":"(- (* (+ N 1) (log (+ N 1))) (+ (* (log N) (- N)) 1))","end":0.265,"name":"NMSE example 3.8","status":"gt-target","end-est":60.75868083652102},{"samplers":["default"],"bits":128,"start":59.314240425403135,"link":"21-NMSEexample37","pinf":0,"ninf":0,"vars":["x"],"input":"(- (exp x) 1)","time":6672.639892578125,"target":0.064261842188131,"output":"(+ (* (+ 1/2 (* 1/6 x)) (sqr x)) x)","end":0.06440112812734372,"name":"NMSE example 3.7","status":"eq-target","end-est":0.7172441164404613},{"samplers":["default"],"bits":128,"start":19.306133815258434,"link":"22-NMSEexample36","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))","time":11043.27490234375,"target":0.6934469979287559,"output":"(/ (sqr (sqrt (/ 1 (+ (sqrt (+ 1 x)) (sqrt x))))) (* (sqrt x) (sqrt (+ x 1))))","end":0.43336494607440706,"name":"NMSE example 3.6","status":"eq-target","end-est":0.35945136722130433},{"samplers":["default"],"bits":128,"start":14.452023100725867,"link":"23-NMSEexample35","pinf":0,"ninf":0,"vars":["N"],"input":"(- (atan (+ N 1)) (atan N))","time":4566.239013671875,"target":0.3782897148859687,"output":"(atan2 (- 1 0) (+ 1 (* (+ N 1) N)))","end":0.3767165945733785,"name":"NMSE example 3.5","status":"eq-target","end-est":0.6241937216396053},{"samplers":["default"],"bits":128,"start":30.234806576442164,"link":"24-NMSEexample34","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sin x))","time":47698.088134765625,"target":0.000375,"output":"(if (<= x -1.6832923238537353e-08) (/ (/ (sqr (sin x)) (+ 1 (cos x))) (sin x)) (if (<= x 5.881545813624529e-20) (+ (* x 1/2) (+ (* 1/240 (pow x 5)) (* (cube x) 1/24))) (/ (/ (sqr (sin x)) (+ 1 (cos x))) (sin x))))","end":0.5107855446001515,"name":"NMSE example 3.4","status":"eq-target","end-est":0.33682214472020305},{"samplers":["default","default"],"bits":128,"start":36.43035691512061,"link":"25-NMSEexample33","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (sin (+ x eps)) (sin x))","time":25374.863037109375,"target":14.676427577231411,"output":"(- (* (cos x) (sin eps)) (- (sin x) (* (cos eps) (sin x))))","end":0.4038842105638006,"name":"NMSE example 3.3","status":"gt-target","end-est":0.4600018364257265},{"samplers":["default"],"bits":128,"start":61.32684006595194,"link":"26-NMSEexample310","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (log (- 1 x)) (log (+ 1 x)))","time":5460.161865234375,"target":0.46633716028964006,"output":"(- (+ (* 1/2 (sqr x)) (+ 1 x)))","end":0.00575,"name":"NMSE example 3.10","status":"eq-target","end-est":0.29869442627741255},{"samplers":["default"],"bits":128,"start":29.731134132292325,"link":"27-NMSEexample31","pinf":0,"ninf":0,"vars":["x"],"input":"(- (sqrt (+ x 1)) (sqrt x))","time":4043.47998046875,"target":0.1614624062518029,"output":"(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))","end":0.1614624062518029,"name":"NMSE example 3.1","status":"eq-target","end-est":0.15462875976844204}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}