{"bit_width":32,"date":1468334290,"note":"hamming","iterations":3,"flags":["rules:numerics","rules:arithmetic","rules:polynomials","rules:fractions","rules:exponents","rules:trigonometry","setup:simplify","reduce:regimes","reduce:taylor","reduce:simplify","reduce:avg-error","generate:rr","generate:taylor","generate:simplify"],"seed":"#(1065639804 936413623 2655205282 2235462195 918319548 1069991914)","points":256,"tests":[{"samplers":["default","default"],"bits":128,"start":19.084746318346816,"link":"0-NMSEproblem346","pinf":0,"ninf":0,"vars":["x","n"],"input":"(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))","time":23815.89208984375,"target":false,"output":"(if (<= n -4522605.5f0) (fma (/ (log1p (/ 1 x)) n) (fma (/ (log1p (/ 1 x)) n) 1/2 1) (- 1 (pow x (/ 1 n)))) (if (<= n 2.4562411f+11) (- (pow E (/ (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":17.07517911779718,"name":"NMSE problem 3.4.6","status":"imp-start","end-est":2.7966230404030923},{"samplers":["default"],"bits":128,"start":15.031766657584182,"link":"1-NMSEproblem345","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- x (sin x)) (- x (tan x)))","time":7161.526123046875,"target":false,"output":"(if (<= x -0.121955805f0) (/ (- x (sin x)) (- x (tan x))) (if (<= x 0.43552306f0) (expm1 (log1p (- (* 9/40 (sqr x)) (+ (* 27/2800 (pow x 4)) 1/2)))) (/ (- x (sin x)) (- x (tan x)))))","end":0.031844865698866284,"name":"NMSE problem 3.4.5","status":"imp-start","end-est":0.1007901889458602},{"samplers":["default"],"bits":128,"start":16.89506788677117,"link":"2-NMSEproblem344","pinf":0,"ninf":0,"vars":["x"],"input":"(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))","time":4086.259033203125,"target":false,"output":"(sqrt (/ (expm1 (* x 2)) (expm1 x)))","end":0.18151330990251943,"name":"NMSE problem 3.4.4","status":"imp-start","end-est":0.03515625},{"samplers":["default"],"bits":128,"start":14.826754229893092,"link":"3-NMSEproblem341","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sqr x))","time":7051.43408203125,"target":false,"output":"(sqr (/ (/ (sin x) (sqrt (+ 1 (cos x)))) x))","end":0.33022495427914633,"name":"NMSE problem 3.4.1","status":"imp-start","end-est":0.3047273702825238},{"samplers":["default"],"bits":128,"start":18.801896445315663,"link":"4-NMSEproblem336","pinf":0,"ninf":0,"vars":["N"],"input":"(- (log (+ N 1)) (log N))","time":2377.822998046875,"target":false,"output":"(log1p (/ 1 N))","end":0.06956029851374132,"name":"NMSE problem 3.3.6","status":"imp-start","end-est":0.0234375},{"samplers":["default","default"],"bits":128,"start":17.521046021435566,"link":"5-NMSEproblem335","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (cos (+ x eps)) (cos x))","time":15002.087890625,"target":false,"output":"(if (<= eps -1.9234536f-05) (/ (- (cube (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))) (log1p (expm1 (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)))) (if (<= eps 5.083976f-14) (- (* (* eps 1/6) (cube x)) (* eps (fma 1/2 eps x))) (- (- (* (cos x) (cos eps)) (log1p (expm1 (* (sin x) (sin eps))))) (cos x))))","end":3.1891209958602698,"name":"NMSE problem 3.3.5","status":"imp-start","end-est":6.2396358463552755},{"samplers":["default"],"bits":128,"start":12.974098292858715,"link":"6-NMSEproblem334","pinf":0,"ninf":0,"vars":["x"],"input":"(- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3)))","time":10825.724853515625,"target":false,"output":"(exp (cube (cbrt (log (- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3)))))))","end":12.978866071861885,"name":"NMSE problem 3.3.4","status":"apx-start","end-est":12.565490553076591},{"samplers":["default"],"bits":128,"start":5.639885558829129,"link":"7-NMSEproblem331","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (+ x 1)) (/ 1 x))","time":2813.84912109375,"target":false,"output":"(/ (- (- x x) 1) (fma x x x))","end":0.49557940234921066,"name":"NMSE problem 3.3.1","status":"imp-start","end-est":0.6449476394623181},{"samplers":["default","default","default"],"bits":128,"start":17.709644546365297,"link":"8-NMSEproblem321positive","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":12125.13916015625,"target":false,"output":"(if (<= b/2 -1.3462214f+10) (- (/ 1/2 (/ b/2 c)) (* (/ b/2 a) 2)) (if (<= b/2 1.75507f-11) (/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a) (/ c (fma 1/2 (/ c (/ b/2 a)) (- (- b/2) b/2)))))","end":3.034843161957644,"name":"NMSE problem 3.2.1, positive","status":"imp-start","end-est":4.221287205447391},{"samplers":["default","default","default"],"bits":128,"start":16.58263419857319,"link":"9-NMSEproblem321negative","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":11697.39404296875,"target":false,"output":"(if (<= b/2 -0.002621575f0) (/ c (- (* (* 1/2 c) (/ a b/2)) (* 2 b/2))) (if (<= b/2 9.795369f+18) (/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a) (* -2 (/ b/2 a))))","end":3.8297616454203314,"name":"NMSE problem 3.2.1, negative","status":"imp-start","end-est":3.832409986899991},{"samplers":["default","default"],"bits":128,"start":12.380454177285642,"link":"10-NMSEsection35","pinf":0,"ninf":0,"vars":["a","x"],"input":"(- (exp (* a x)) 1)","time":2485.91796875,"target":0.1508600346460273,"output":"(expm1 (* x a))","end":0.07305470528017445,"name":"NMSE section 3.5","status":"eq-target","end-est":0.07439216452874396},{"samplers":["default"],"bits":128,"start":17.929085032068873,"link":"11-NMSEsection311","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (exp x) (- (exp x) 1))","time":2345.597900390625,"target":16.363337740805825,"output":"(/ (exp x) (expm1 x))","end":1.6088349578780463,"name":"NMSE section 3.11","status":"gt-target","end-est":1.240785968773609},{"samplers":["default"],"bits":128,"start":25.736015005862733,"link":"12-NMSEproblem343","pinf":0,"ninf":0,"vars":["eps"],"input":"(log (/ (- 1 eps) (+ 1 eps)))","time":6562.033935546875,"target":0.08926096985757483,"output":"(- (+ (* 2 eps) (+ (* 2/5 (pow eps 5)) (* 2/3 (pow eps 3)))))","end":0.09456284954498469,"name":"NMSE problem 3.4.3","status":"eq-target","end-est":0.5146223773508201},{"samplers":["default","default","default"],"bits":128,"start":28.056781690331565,"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":26240.44677734375,"target":6.284400082682007,"output":"(* (/ (expm1 (* eps (+ b a))) (expm1 (* a eps))) (/ eps (expm1 (* b eps))))","end":12.431452223995835,"name":"NMSE problem 3.4.2","status":"lt-target","end-est":12.739876108179924},{"samplers":["default"],"bits":128,"start":15.254002456458535,"link":"14-NMSEproblem337","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (exp x) 2) (exp (- x)))","time":5001.738037109375,"target":4.0939395307131266,"output":"(sqr (sqrt (fma (pow x 6) 1/360 (fma (pow x 4) 1/12 (sqr x)))))","end":0.3374488115531164,"name":"NMSE problem 3.3.7","status":"gt-target","end-est":1.4063091556525815},{"samplers":["default"],"bits":128,"start":3.980571522996354,"link":"15-NMSEproblem333","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))","time":14948.93603515625,"target":0.4335016254200322,"output":"(if (<= x -4.6474633f0) (+ (+ (/ 2 (pow x 5)) (/ 2 (pow x 7))) (/ 2 (cube x))) (if (<= x 19.416372f0) (/ (fma (- x 1) (- x (fma 2 x 2)) (+ (* x x) x)) (* (- x 1) (fma x x x))) (+ (+ (/ 2 (pow x 5)) (/ 2 (pow x 7))) (/ 2 (cube x)))))","end":0.46590964595635964,"name":"NMSE problem 3.3.3","status":"eq-target","end-est":0.3822307268908933},{"samplers":["default","default"],"bits":128,"start":16.628384121999098,"link":"16-NMSEproblem332","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (tan (+ x eps)) (tan x))","time":11524.39111328125,"target":11.687010599623093,"output":"(if (<= eps -2.8903562f-18) (- (tan (+ x eps)) (/ (sin x) (cos x))) (if (<= eps 8.7719215f-08) (+ eps (+ (* (pow eps 3) (sqr x)) (* (pow eps 4) (pow x 3)))) (/ (- (cos x) (* (cube (cbrt (cotan (+ eps x)))) (sin x))) (* (cotan (+ x eps)) (cos x)))))","end":12.669999500061339,"name":"NMSE problem 3.3.2","status":"eq-target","end-est":13.81180530658178},{"samplers":["default","default","default"],"bits":128,"start":15.95563821940551,"link":"17-NMSEp42positive","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":20126.802001953125,"target":9.81050801908691,"output":"(if (<= b -1.3462214f+10) (- (/ c b) (/ b a)) (if (<= b -1.4384158f-33) (/ (+ (- (sqrt (- (sqr b) (* a (* 4 c))))) b) (- (* 2 a))) (if (<= b 1.6720318f+16) (* (/ c 2) (/ 4 (- (- b) (sqrt (- (sqr b) (* (* c a) 4)))))) (* (/ c b) (/ -2 2)))))","end":2.4044592539656517,"name":"NMSE p42, positive","status":"gt-target","end-est":2.6476133103377033},{"samplers":["default","default","default"],"bits":128,"start":16.00359513147902,"link":"18-NMSEp42negative","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":19677.783935546875,"target":9.828316671183417,"output":"(if (<= b -1.3462214f+10) (/ (/ (* c 4) (- (fma (* a 2) (/ c b) (- b)) b)) 2) (if (<= b 2.0316441f-38) (* (/ c 2) (/ 4 (+ (- b) (sqrt (- (sqr b) (* (* c a) 4)))))) (if (<= b 1.6720318f+16) (/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a)) (- (/ c b) (/ b a)))))","end":2.727364478104296,"name":"NMSE p42, negative","status":"gt-target","end-est":2.4926661827777115},{"samplers":["default"],"bits":128,"start":29.301549382783474,"link":"19-NMSEexample39","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 x) (cotan x))","time":6201.18310546875,"target":0.0205,"output":"(fma (cube x) 1/45 (fma 2/945 (pow x 5) (* x 1/3)))","end":0.329,"name":"NMSE example 3.9","status":"eq-target","end-est":0.31640625},{"samplers":["default"],"bits":128,"start":31.021575423508832,"link":"20-NMSEexample38","pinf":0,"ninf":0,"vars":["N"],"input":"(- (- (* (+ N 1) (log (+ N 1))) (* N (log N))) 1)","time":19221.203857421875,"target":0.000875,"output":"(- (sqr (sqrt (fma N (log1p N) (log1p N)))) (fma N (log N) 1))","end":30.101235444980045,"name":"NMSE example 3.8","status":"eq-start","end-est":30.09244383246092},{"samplers":["default"],"bits":128,"start":25.10880713433818,"link":"21-NMSEexample37","pinf":0,"ninf":0,"vars":["x"],"input":"(- (exp x) 1)","time":2015.10400390625,"target":0.9273989806582178,"output":"(expm1 x)","end":0.003,"name":"NMSE example 3.7","status":"eq-target","end-est":0.0078125},{"samplers":["default"],"bits":128,"start":8.368720517735357,"link":"22-NMSEexample36","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))","time":7475.136962890625,"target":0.21608496250072112,"output":"(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))","end":2.950017025140893,"name":"NMSE example 3.6","status":"lt-target","end-est":2.7806879067672075},{"samplers":["default"],"bits":128,"start":6.5643844353113705,"link":"23-NMSEexample35","pinf":0,"ninf":0,"vars":["N"],"input":"(- (atan (+ N 1)) (atan N))","time":3002.383056640625,"target":0.513798763286981,"output":"(atan2 (- 1 0) (fma N (+ 1 N) 1))","end":0.5121006429743908,"name":"NMSE example 3.5","status":"eq-target","end-est":0.6823888992307603},{"samplers":["default"],"bits":128,"start":13.880469633258743,"link":"24-NMSEexample34","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sin x))","time":7169.23193359375,"target":0.0185,"output":"(/ (/ (sqr (sin x)) (+ 1 (cos x))) (sin x))","end":0.41267176419754675,"name":"NMSE example 3.4","status":"eq-target","end-est":0.4895619157156371},{"samplers":["default","default"],"bits":128,"start":16.75412287714829,"link":"25-NMSEexample33","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (sin (+ x eps)) (sin x))","time":13995.2158203125,"target":10.604993561199178,"output":"(if (<= eps -3.0143673f-27) (/ (/ (- (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)))) (if (<= eps 1.296251f-17) (- eps (* (* (* x eps) (+ eps x)) 1/2)) (/ (/ (- (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":2.1877295376077908,"name":"NMSE example 3.3","status":"gt-target","end-est":4.782379266826113},{"samplers":["default"],"bits":128,"start":26.572830754425816,"link":"26-NMSEexample310","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (log (- 1 x)) (log (+ 1 x)))","time":4874.73388671875,"target":0.4981549097422376,"output":"(/ (log1p (- x)) (log1p x))","end":0.08053101562950722,"name":"NMSE example 3.10","status":"eq-target","end-est":0.06640625},{"samplers":["default"],"bits":128,"start":13.011507050842821,"link":"27-NMSEexample31","pinf":0,"ninf":0,"vars":["x"],"input":"(- (sqrt (+ x 1)) (sqrt x))","time":4616.9091796875,"target":0.16970056406367184,"output":"(/ 1 (+ (sqr (sqrt (sqrt (+ x 1)))) (sqrt x)))","end":0.268624703513661,"name":"NMSE example 3.1","status":"eq-target","end-est":0.19524885231507558}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}