{"bit_width":32,"date":1469029288,"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"],"seed":"#(1065767146 1567806045 1856802035 1672802504 2070886570 609046914)","points":256,"tests":[{"samplers":["default","default"],"bits":128,"start":14.844687861895803,"link":"0-NMSEproblem346","pinf":0,"ninf":0,"vars":["x","n"],"input":"(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))","time":31368.904052734375,"target":false,"output":"(if (<= x 0.6308159f0) (- (exp (/ (+ x (* (- (* 1/3 x) 1/2) (sqr x))) n)) (pow x (/ 1 n))) (* (+ (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n)))) (- (- (/ (/ 1/2 n) x) (* (/ 1/4 (* x n)) (/ (log x) n))) (/ 1/4 (* n (sqr x))))))","end":8.806154132222881,"name":"NMSE problem 3.4.6","status":"imp-start","end-est":9.595926948496912},{"samplers":["default"],"bits":128,"start":14.743467234030884,"link":"1-NMSEproblem345","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- x (sin x)) (- x (tan x)))","time":6570.39501953125,"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":19.762475417950647,"link":"2-NMSEproblem344","pinf":0,"ninf":0,"vars":["x"],"input":"(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))","time":7781.845947265625,"target":false,"output":"(if (<= x -0.00261488f0) (sqrt (/ (* (+ (sqrt (exp (* 2 x))) 1) (- (sqrt (exp (* 2 x))) 1)) (- (exp x) 1))) (sqrt (+ (* 1/2 (sqr x)) (+ 2 x))))","end":3.4788459737753903,"name":"NMSE problem 3.4.4","status":"imp-start","end-est":1.0212844036622997},{"samplers":["default"],"bits":128,"start":14.568143206394186,"link":"3-NMSEproblem341","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sqr x))","time":8339.510986328125,"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":19.073808301819966,"link":"4-NMSEproblem336","pinf":0,"ninf":0,"vars":["N"],"input":"(- (log (+ N 1)) (log N))","time":7225.799072265625,"target":false,"output":"(if (<= N 111.408356f0) (log (/ (+ N 1) N)) (+ (/ 1 N) (- (/ 1/3 (cube N)) (/ 1/2 (* N N)))))","end":8.526236308532177,"name":"NMSE problem 3.3.6","status":"imp-start","end-est":0.10239968406562798},{"samplers":["default","default"],"bits":128,"start":18.582232249658126,"link":"5-NMSEproblem335","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (cos (+ x eps)) (cos x))","time":22323.849853515625,"target":false,"output":"(if (<= eps -0.003667146f0) (- (* (cos x) (cos eps)) (log (exp (+ (* (sin eps) (sin x)) (cos x))))) (if (<= eps 0.25760502f0) (- (* (- (* (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":0.6324303308923617,"name":"NMSE problem 3.3.5","status":"imp-start","end-est":0.5785282753743705},{"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":23302.2861328125,"target":false,"output":"(if (<= x 12708545.0f0) (exp (log (- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3))))) (- (+ (cbrt (/ 1 x)) (* 1/3 (cbrt (/ 1 (pow x 4))))) (+ (pow x (* (log E) -1/3)) (* 1/9 (cbrt (/ 1 (pow x 7)))))))","end":12.874528034544582,"name":"NMSE problem 3.3.4","status":"uni-start","end-est":12.06341666128094},{"samplers":["default"],"bits":128,"start":5.779528156289481,"link":"7-NMSEproblem331","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (+ x 1)) (/ 1 x))","time":5177.843017578125,"target":false,"output":"(cube (cbrt (/ (- 1) (+ (* x x) x))))","end":0.9484040107537197,"name":"NMSE problem 3.3.1","status":"imp-start","end-est":1.0441762334778764},{"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":15007.16015625,"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":14879.910888671875,"target":false,"output":"(if (<= b/2 -2.0043302f-07) (/ c (- (* (* a 1/2) (/ c b/2)) (- b/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":3.376811973731257,"name":"NMSE problem 3.2.1, negative","status":"imp-start","end-est":3.879945761745627},{"samplers":["default","default"],"bits":128,"start":14.627659495925904,"link":"10-NMSEsection35","pinf":0,"ninf":0,"vars":["a","x"],"input":"(- (exp (* a x)) 1)","time":9888.101806640625,"target":3.9748363700910883,"output":"(if (<= (* a x) -0.0010577029f0) (- (exp (* a x)) 1) (+ (* (* 1/2 (* x a)) (* x a)) (* x a)))","end":0.1548198415242579,"name":"NMSE section 3.5","status":"gt-target","end-est":0.5828515262563495},{"samplers":["default"],"bits":128,"start":20.003379461347883,"link":"11-NMSEsection311","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (exp x) (- (exp x) 1))","time":4032.628173828125,"target":13.005534788167473,"output":"(if (<= x -0.00261488f0) (/ (exp x) (- (exp x) 1)) (if (<= x 0.25760502f0) (+ 1/2 (+ (/ 1 x) (* 1/12 x))) (/ 1 (- 1 (exp (- x))))))","end":0.05872329773392923,"name":"NMSE section 3.11","status":"gt-target","end-est":0.041022801503524595},{"samplers":["default"],"bits":128,"start":25.84568746803947,"link":"12-NMSEproblem343","pinf":0,"ninf":0,"vars":["eps"],"input":"(log (/ (- 1 eps) (+ 1 eps)))","time":10852.718994140625,"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":29.624057564981868,"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":33571.289794921875,"target":6.481852835235206,"output":"(if (<= (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) -1.0813295f-25) (+ (/ 1 b) (/ 1 a)) (if (<= (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) 8.0624277f-25) (+ (/ 1 b) (/ 1 a)) (+ (/ 1 b) (/ 1 a))))","end":0.05432844529780426,"name":"NMSE problem 3.4.2","status":"gt-target","end-est":2.863468253773461},{"samplers":["default"],"bits":128,"start":15.710936718443,"link":"14-NMSEproblem337","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (exp x) 2) (exp (- x)))","time":11328.453125,"target":4.277370597796448,"output":"(+ (sqr x) (+ (* 1/12 (pow x 4)) (* 1/360 (pow x 6))))","end":0.3373961416111976,"name":"NMSE problem 3.3.7","status":"gt-target","end-est":1.4162078347497697},{"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":14886.642822265625,"target":0.3860017795062304,"output":"(/ (/ 2 (* (+ x 1) x)) (- x 1))","end":0.10900733125324524,"name":"NMSE problem 3.3.3","status":"eq-target","end-est":0.10384750976844201},{"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":17789.740966796875,"target":7.71995787175171,"output":"(if (<= eps -0.003667146f0) (- (/ (sin (+ x eps)) (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (/ 1 (cotan x))) (if (<= eps 0.33526045f0) (+ (+ (+ (/ 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 eps))) (/ 1 (cotan x)))))","end":6.841133921590075,"name":"NMSE problem 3.3.2","status":"eq-target","end-est":7.120369187607355},{"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":60626.10009765625,"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":16.382095969066498,"link":"18-NMSEp42negative","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":20695.676025390625,"target":9.964204957269736,"output":"(if (<= b -1.2816005f+19) (* (/ c b) (/ -2 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":2.5064810704283893,"name":"NMSE p42, negative","status":"gt-target","end-est":2.8665824809508194},{"samplers":["default"],"bits":128,"start":29.308338496851682,"link":"19-NMSEexample39","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 x) (cotan x))","time":7132.93310546875,"target":0.019125,"output":"(+ (* x 1/3) (+ (* 2/945 (pow x 5)) (* (cube x) 1/45)))","end":0.3395,"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":44355.296142578125,"target":0.001625,"output":"(- (- (* (* (- (sqr N) 1) (log (+ N 1))) (/ 1 (- N 1))) (cube (cbrt (* N (log N))))) 1)","end":29.896813460408328,"name":"NMSE example 3.8","status":"lt-target","end-est":29.832368725848845},{"samplers":["default"],"bits":128,"start":26.294969088548637,"link":"21-NMSEexample37","pinf":0,"ninf":0,"vars":["x"],"input":"(- (exp x) 1)","time":6401.1298828125,"target":0.10341992500144233,"output":"(+ (* (+ 1/2 (* 1/6 x)) (sqr x)) x)","end":0.06772424843993387,"name":"NMSE example 3.7","status":"eq-target","end-est":0.8310253946881052},{"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":9359.126953125,"target":0.22041748125036056,"output":"(/ 1 (* (+ 1 x) (+ (sqrt x) (* (sqrt (/ 1 (+ 1 x))) x))))","end":0.20384436093777042,"name":"NMSE example 3.6","status":"eq-target","end-est":0.203125},{"samplers":["default"],"bits":128,"start":6.747015544049351,"link":"23-NMSEexample35","pinf":0,"ninf":0,"vars":["N"],"input":"(- (atan (+ N 1)) (atan N))","time":3448.905029296875,"target":0.505793492857235,"output":"(atan2 (- 1 0) (+ 1 (* (+ N 1) N)))","end":0.505793492857235,"name":"NMSE example 3.5","status":"eq-target","end-est":0.5664271611192893},{"samplers":["default"],"bits":128,"start":13.660293233431371,"link":"24-NMSEexample34","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sin x))","time":39706.240966796875,"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":18261.466064453125,"target":7.621073044211153,"output":"(if (<= eps -0.003667146f0) (+ (* (sin x) (cos eps)) (- (pow (* (cos x) (sin eps)) 1) (sin x))) (if (<= eps 3.458902f-08) (- (* (- eps (* 1/6 (cube eps))) (cos x)) (* (* (sin x) 1/2) (sqr eps))) (+ (* (sin x) (cos eps)) (- (pow (* (cos x) (sin eps)) 1) (sin x)))))","end":0.37542481735989863,"name":"NMSE example 3.3","status":"gt-target","end-est":0.2523294368151585},{"samplers":["default"],"bits":128,"start":27.228107522739943,"link":"26-NMSEexample310","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (log (- 1 x)) (log (+ 1 x)))","time":6202.373779296875,"target":0.6449684877688235,"output":"(- (+ (* 1/2 (sqr x)) (+ 1 x)))","end":0.026375,"name":"NMSE example 3.10","status":"eq-target","end-est":0.5004727135116326},{"samplers":["default"],"bits":128,"start":13.233866382735291,"link":"27-NMSEexample31","pinf":0,"ninf":0,"vars":["x"],"input":"(- (sqrt (+ x 1)) (sqrt x))","time":4248.10107421875,"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"}