{"bit_width":32,"date":1469034621,"note":"hamming","iterations":3,"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":"#(1065767146 1567806045 1856802035 1672802504 2070886570 609046914)","points":256,"tests":[{"samplers":["default","default"],"bits":128,"start":19.174307309488636,"link":"0-NMSEproblem346","pinf":0,"ninf":0,"vars":["x","n"],"input":"(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))","time":23500.256103515625,"target":false,"output":"(if (<= n -9.374609f+07) (fma (/ (log1p (/ 1 x)) n) (fma (/ (log1p (/ 1 x)) n) 1/2 1) (- 1 (pow x (/ 1 n)))) (if (<= n 1.082193f+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":17.21311357063368,"name":"NMSE problem 3.4.6","status":"imp-start","end-est":3.2559106018768884},{"samplers":["default"],"bits":128,"start":14.743467234030884,"link":"1-NMSEproblem345","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- x (sin x)) (- x (tan x)))","time":7162.64990234375,"target":false,"output":"(if (<= x -0.0019466438f0) (/ (- x (sin x)) (- x (tan x))) (if (<= x 0.52187485f0) (- (* 9/40 (sqr x)) (+ (* 27/2800 (pow x 4)) 1/2)) (/ (- x (sin x)) (- x (tan x)))))","end":0.16716463019947123,"name":"NMSE problem 3.4.5","status":"imp-start","end-est":0.10142712752553631},{"samplers":["default"],"bits":128,"start":16.582399409881287,"link":"2-NMSEproblem344","pinf":0,"ninf":0,"vars":["x"],"input":"(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))","time":4657.423828125,"target":false,"output":"(expm1 (log1p (sqrt (/ (expm1 (* x 2)) (expm1 x)))))","end":0.19891239542040942,"name":"NMSE problem 3.4.4","status":"imp-start","end-est":0.3864473446197439},{"samplers":["default"],"bits":128,"start":14.568143206394186,"link":"3-NMSEproblem341","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sqr x))","time":8880.532958984375,"target":false,"output":"(if (<= x -0.0019466438f0) (/ (/ (- 1 (cos x)) x) x) (if (<= x 0.52187485f0) (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (sqr x))) (/ (/ (- 1 (cos x)) x) x)))","end":0.3303904275221534,"name":"NMSE problem 3.4.1","status":"imp-start","end-est":0.22448742988170098},{"samplers":["default"],"bits":128,"start":19.07380371027815,"link":"4-NMSEproblem336","pinf":0,"ninf":0,"vars":["N"],"input":"(- (log (+ N 1)) (log N))","time":2570.238037109375,"target":false,"output":"(log1p (/ 1 N))","end":0.06431024623181456,"name":"NMSE problem 3.3.6","status":"imp-start","end-est":0.0390625},{"samplers":["default","default"],"bits":128,"start":18.586144059108534,"link":"5-NMSEproblem335","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (cos (+ x eps)) (cos x))","time":22112.876220703125,"target":false,"output":"(if (<= eps -0.00261488f0) (- (- (cbrt (* (cube (cos x)) (cube (cos eps)))) (* (sin x) (sin eps))) (cos x)) (if (<= eps 0.25760502f0) (- (* (cube eps) (* 1/6 (sin x))) (* eps (fma 1/2 eps (sin x)))) (/ (- (sqr (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (sqr (cos x))) (- (fma (cos eps) (cos x) (cos x)) (* (sin eps) (sin x))))))","end":0.5843542986901334,"name":"NMSE problem 3.3.5","status":"imp-start","end-est":0.7085915642529077},{"samplers":["default"],"bits":128,"start":9.710931131888001,"link":"6-NMSEproblem334","pinf":0,"ninf":0,"vars":["x"],"input":"(- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3)))","time":24954.379150390625,"target":false,"output":"(if (<= x 12708545.0f0) (exp (cube (cbrt (log (- (pow (+ x 1) (/ 1 3)) (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":12.874373313178147,"name":"NMSE problem 3.3.4","status":"uni-start","end-est":12.067057210391104},{"samplers":["default"],"bits":128,"start":5.779528156289481,"link":"7-NMSEproblem331","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (+ x 1)) (/ 1 x))","time":3124.093017578125,"target":false,"output":"(/ (- (- x x) 1) (fma x x x))","end":0.48584537254464466,"name":"NMSE problem 3.3.1","status":"imp-start","end-est":0.5547084111192894},{"samplers":["default","default","default"],"bits":128,"start":16.28178921840201,"link":"8-NMSEproblem321positive","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":15005.468994140625,"target":false,"output":"(if (<= b/2 -1.2816005f+19) (* -2 (/ b/2 a)) (if (<= b/2 1.9502276f-23) (/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a) (if (<= b/2 100403176.0f0) (cube (cbrt (/ c (- (- b/2) (sqrt (- (* b/2 b/2) (* c a))))))) (* -1/2 (/ c b/2)))))","end":2.5493976746540956,"name":"NMSE problem 3.2.1, positive","status":"imp-start","end-est":3.00251223561442},{"samplers":["default","default","default"],"bits":128,"start":17.72442999588378,"link":"9-NMSEproblem321negative","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":15282.2880859375,"target":false,"output":"(if (<= b/2 -2.0043302f-07) (/ c (- (* (* 1/2 c) (/ a b/2)) (* 2 b/2))) (if (<= b/2 100403176.0f0) (* (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) (/ 1 a)) (- (/ 1/2 (/ b/2 c)) (* (/ b/2 a) 2))))","end":3.3701136223216395,"name":"NMSE problem 3.2.1, negative","status":"imp-start","end-est":3.8799457619021784},{"samplers":["default","default"],"bits":128,"start":12.216348742536132,"link":"10-NMSEsection35","pinf":0,"ninf":0,"vars":["a","x"],"input":"(- (exp (* a x)) 1)","time":2809.327880859375,"target":0.1642619808996834,"output":"(expm1 (* x a))","end":0.06462681439460362,"name":"NMSE section 3.5","status":"eq-target","end-est":0.041347509768442016},{"samplers":["default"],"bits":128,"start":17.590275793452474,"link":"11-NMSEsection311","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (exp x) (- (exp x) 1))","time":4479.338134765625,"target":16.01138387574583,"output":"(/ (exp x) (expm1 x))","end":1.641164405809986,"name":"NMSE section 3.11","status":"gt-target","end-est":1.898789034408267},{"samplers":["default"],"bits":128,"start":25.84568746803947,"link":"12-NMSEproblem343","pinf":0,"ninf":0,"vars":["eps"],"input":"(log (/ (- 1 eps) (+ 1 eps)))","time":7732.718017578125,"target":0.09544408545525666,"output":"(- (+ (* 2 eps) (+ (* 2/5 (pow eps 5)) (* 2/3 (pow eps 3)))))","end":0.10256908545525667,"name":"NMSE problem 3.4.3","status":"eq-target","end-est":0.2928554731779874},{"samplers":["default","default","default"],"bits":128,"start":27.849610282649763,"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":33810.3720703125,"target":6.260820612776368,"output":"(* (/ (expm1 (* eps (+ b a))) (expm1 (* a eps))) (cube (cbrt (/ eps (expm1 (* b eps))))))","end":12.30912587662362,"name":"NMSE problem 3.4.2","status":"lt-target","end-est":12.59499640263569},{"samplers":["default"],"bits":128,"start":15.710936718443,"link":"14-NMSEproblem337","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (exp x) 2) (exp (- x)))","time":7215.301025390625,"target":4.277370597796448,"output":"(fma (pow x 6) 1/360 (fma (pow x 4) 1/12 (sqr x)))","end":0.3423961416111976,"name":"NMSE problem 3.3.7","status":"gt-target","end-est":1.4223992745641376},{"samplers":["default"],"bits":128,"start":4.220926183823653,"link":"15-NMSEproblem333","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))","time":10833.83984375,"target":0.3860017795062304,"output":"(if (<= x -0.0019466438f0) (/ (fma (- (/ 1 x) 1) (- (- (/ 1 x) (/ 2 x)) 2) (+ (/ 1 (sqr x)) (/ 1 x))) (* (- x 1) (fma x x x))) (if (<= x 0.52187485f0) (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))) (/ (fma (- (/ 1 x) 1) (- (- (/ 1 x) (/ 2 x)) 2) (+ (/ 1 (sqr x)) (/ 1 x))) (* (- x 1) (fma x x x)))))","end":0.20433314896764312,"name":"NMSE problem 3.3.3","status":"eq-target","end-est":0.13442274411883087},{"samplers":["default","default"],"bits":128,"start":16.973971046073206,"link":"16-NMSEproblem332","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (tan (+ x eps)) (tan x))","time":17345.632080078125,"target":7.71995787175171,"output":"(if (<= eps -0.003667146f0) (- (cube (cbrt (tan (+ x eps)))) (/ 1 (cotan x))) (if (<= eps 0.33526045f0) (+ (+ (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))) (- (cube (cbrt (tan (+ x eps)))) (/ 1 (cotan x)))))","end":7.66911141049333,"name":"NMSE problem 3.3.2","status":"eq-target","end-est":8.091891105005137},{"samplers":["default","default","default"],"bits":128,"start":16.88591374517988,"link":"17-NMSEp42positive","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":67425.90087890625,"target":10.60680593516889,"output":"(if (<= b -1.2816005f+19) (- (/ c b) (/ b a)) (if (<= b 3.5037975f0) (* (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (/ 1 (* 2 a))) (* (/ (/ c (/ 2 4)) (- (* (/ c b) a) b)) (/ 1 2))))","end":4.219138706353169,"name":"NMSE p42, positive","status":"gt-target","end-est":4.121827862451215},{"samplers":["default","default","default"],"bits":128,"start":16.382150391251898,"link":"18-NMSEp42negative","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":26242.055908203125,"target":9.96162623128845,"output":"(if (<= b -1.2816005f+19) (/ (/ (* c 4) (- (fma (* a 2) (/ c b) (- b)) b)) 2) (if (<= b 3.4383025f-30) (* (/ c 2) (/ 4 (+ (- b) (sqrt (- (sqr b) (* (* c a) 4)))))) (if (<= b 100403176.0f0) (/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a)) (- (/ c b) (/ b a)))))","end":2.6246517297641607,"name":"NMSE p42, negative","status":"gt-target","end-est":2.864297471182377},{"samplers":["default"],"bits":128,"start":29.308338496851682,"link":"19-NMSEexample39","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 x) (cotan x))","time":6107.950927734375,"target":0.019125,"output":"(fma (cube x) 1/45 (fma 2/945 (pow x 5) (* x 1/3)))","end":0.339125,"name":"NMSE example 3.9","status":"eq-target","end-est":0.3125},{"samplers":["default"],"bits":128,"start":31.02162470220658,"link":"20-NMSEexample38","pinf":0,"ninf":0,"vars":["N"],"input":"(- (- (* (+ N 1) (log (+ N 1))) (* N (log N))) 1)","time":28954.683837890625,"target":0.001625,"output":"(/ (- (sqr (fma N (log1p N) (log1p N))) (sqr (cube (cbrt (fma N (log N) 1))))) (+ (fma N (log1p N) (log1p N)) (fma N (log N) 1)))","end":30.07777644881346,"name":"NMSE example 3.8","status":"eq-start","end-est":30.003760453197906},{"samplers":["default"],"bits":128,"start":25.16142718243476,"link":"21-NMSEexample37","pinf":0,"ninf":0,"vars":["x"],"input":"(- (exp x) 1)","time":2009.09619140625,"target":0.9191154486467171,"output":"(expm1 x)","end":0.0035,"name":"NMSE example 3.7","status":"eq-target","end-est":0},{"samplers":["default"],"bits":128,"start":8.518333315247318,"link":"22-NMSEexample36","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))","time":13261.85986328125,"target":0.22041748125036056,"output":"(if (<= x 7.046752f+19) (/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (/ (- (/ 1/2 (* x x)) (+ (/ 1 x) (/ 3/8 (cube x)))) (/ (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (- (/ 1/2 (* x x)) (+ (/ 1 x) (/ 3/8 (cube x)))))))","end":0.4476354417594259,"name":"NMSE example 3.6","status":"eq-target","end-est":0.34509243997130434},{"samplers":["default"],"bits":128,"start":6.747015544049351,"link":"23-NMSEexample35","pinf":0,"ninf":0,"vars":["N"],"input":"(- (atan (+ N 1)) (atan N))","time":2945.906982421875,"target":0.505793492857235,"output":"(atan2 (- 1 0) (+ (fma N N N) 1))","end":0.5058453725446448,"name":"NMSE example 3.5","status":"eq-target","end-est":0.5586146611192893},{"samplers":["default"],"bits":128,"start":13.660293233431371,"link":"24-NMSEexample34","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sin x))","time":39651.31884765625,"target":0.01975,"output":"(/ (/ (sqr (sin x)) (+ 1 (cos x))) (sin x))","end":0.4195117387562053,"name":"NMSE example 3.4","status":"eq-target","end-est":0.39694457218038076},{"samplers":["default","default"],"bits":128,"start":16.82899242108417,"link":"25-NMSEexample33","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (sin (+ x eps)) (sin x))","time":11653.364013671875,"target":7.621073044211153,"output":"(if (<= eps -0.003667146f0) (+ (cube (* (cbrt (sin x)) (cbrt (cos eps)))) (- (* (cos x) (sin eps)) (sin x))) (if (<= eps 0.0023221506f0) (- (* (sin eps) (cos x)) (* eps (* (* 1/2 eps) (sin x)))) (+ (fma (cos eps) (sin x) (* (sin eps) (cos x))) (- (sin x)))))","end":0.37032179763772993,"name":"NMSE example 3.3","status":"gt-target","end-est":0.28349100466525945},{"samplers":["default"],"bits":128,"start":26.668642251956342,"link":"26-NMSEexample310","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (log (- 1 x)) (log (+ 1 x)))","time":7347.906005859375,"target":0.4726500812758443,"output":"(cbrt (cube (/ (log1p (- x)) (log1p x))))","end":0.08543421094065506,"name":"NMSE example 3.10","status":"eq-target","end-est":0.0703125},{"samplers":["default"],"bits":128,"start":13.233866382735291,"link":"27-NMSEexample31","pinf":0,"ninf":0,"vars":["x"],"input":"(- (sqrt (+ x 1)) (sqrt x))","time":4469.39306640625,"target":0.1763067671895733,"output":"(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))","end":0.1763067671895733,"name":"NMSE example 3.1","status":"eq-target","end-est":0.1640625}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}