{"bit_width":32,"date":1468686986,"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":"#(1065670707 1252142602 108487242 4101615998 1494603059 839552182)","points":256,"tests":[{"samplers":["default","default"],"bits":128,"start":19.14350462481365,"link":"0-NMSEproblem346","pinf":0,"ninf":0,"vars":["x","n"],"input":"(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))","time":19959.510009765625,"target":false,"output":"(if (<= n -2.5270237f+10) (fma (/ (log1p (/ 1 x)) n) (fma (/ (log1p (/ 1 x)) n) 1/2 1) (- 1 (pow x (/ 1 n)))) (if (<= n 1.8224006f+09) (- (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":17.327293727539057,"name":"NMSE problem 3.4.6","status":"imp-start","end-est":3.5652659284304127},{"samplers":["default"],"bits":128,"start":14.569077457015345,"link":"1-NMSEproblem345","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- x (sin x)) (- x (tan x)))","time":6420.26904296875,"target":false,"output":"(if (<= x -0.01639637f0) (/ (- x (sin x)) (- x (tan x))) (if (<= x 4.281642f0) (- (* 9/40 (sqr x)) (+ (* 27/2800 (pow x 4)) 1/2)) (/ (- x (sin x)) (- x (tan x)))))","end":0.08551793743612326,"name":"NMSE problem 3.4.5","status":"imp-start","end-est":0.1549315682263262},{"samplers":["default"],"bits":128,"start":16.660638661710955,"link":"2-NMSEproblem344","pinf":0,"ninf":0,"vars":["x"],"input":"(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))","time":3467.260986328125,"target":false,"output":"(sqrt (/ (expm1 (* x 2)) (expm1 x)))","end":0.20073968659844219,"name":"NMSE problem 3.4.4","status":"imp-start","end-est":0.24825518643900868},{"samplers":["default"],"bits":128,"start":14.377034524128526,"link":"3-NMSEproblem341","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sqr x))","time":8890.913818359375,"target":false,"output":"(sqr (/ (/ (sin x) (sqrt (+ 1 (cos x)))) x))","end":0.3449815651421935,"name":"NMSE problem 3.4.1","status":"imp-start","end-est":0.3496158776568043},{"samplers":["default"],"bits":128,"start":19.1882667579293,"link":"4-NMSEproblem336","pinf":0,"ninf":0,"vars":["N"],"input":"(- (log (+ N 1)) (log N))","time":2586.579833984375,"target":false,"output":"(log1p (/ 1 N))","end":0.062255904107726426,"name":"NMSE problem 3.3.6","status":"imp-start","end-est":0.04296875},{"samplers":["default","default"],"bits":128,"start":18.653871134620314,"link":"5-NMSEproblem335","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (cos (+ x eps)) (cos x))","time":25832.567138671875,"target":false,"output":"(if (<= eps -0.008720061f0) (log (exp (- (* (cos eps) (cos x)) (fma (sin eps) (sin x) (cos x))))) (if (<= eps 0.019318156f0) (/ (- (fma (* (sin x) (sin x)) (* eps eps) (* (* (sin x) (* eps 4/3)) (* (cos x) (* eps eps)))) (* (fma (cos x) eps (* (sin x) 2)) (* eps (cos x)))) (- (fma (cos eps) (cos x) (cos x)) (* (sin eps) (sin x)))) (- (/ (- (sqr (* (cos x) (cos eps))) (sqr (* (sin x) (sin eps)))) (fma (sin x) (sin eps) (* (cos eps) (cos x)))) (cos x))))","end":0.6530625813245573,"name":"NMSE problem 3.3.5","status":"imp-start","end-est":0.7026880902749849},{"samplers":["default"],"bits":128,"start":13.063539649687343,"link":"6-NMSEproblem334","pinf":0,"ninf":0,"vars":["x"],"input":"(- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3)))","time":24944.4921875,"target":false,"output":"(if (<= x 0.03150794f0) (/ (* (+ (pow (+ x 1) (/ 1 3)) (cbrt x)) (- (pow (+ x 1) (/ 1 3)) (cbrt x))) (+ (pow x (/ 1 3)) (pow (+ x 1) (/ 1 3)))) (/ (- (+ (/ 1 x) 1) (/ 1 x)) (fma (pow x (/ 1 3)) (+ (pow (+ 1 x) (/ 1 3)) (pow x (/ 1 3))) (sqr (pow (+ 1 x) (/ 1 3))))))","end":1.68046371139121,"name":"NMSE problem 3.3.4","status":"imp-start","end-est":1.6558071692269554},{"samplers":["default"],"bits":128,"start":5.954478919247316,"link":"7-NMSEproblem331","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (+ x 1)) (/ 1 x))","time":4543.64111328125,"target":false,"output":"(cube (/ (cbrt (- 1)) (cbrt (fma x x x))))","end":1.0292580555510327,"name":"NMSE problem 3.3.1","status":"imp-start","end-est":0.9726861706619345},{"samplers":["default","default","default"],"bits":128,"start":17.03385931951042,"link":"8-NMSEproblem321positive","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":16615.60595703125,"target":false,"output":"(if (<= b/2 -1.6844219f+10) (- (/ 1/2 (/ b/2 c)) (* (/ b/2 a) 2)) (if (<= b/2 0.0037315278f0) (/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a) (/ c (fma 1/2 (/ c (/ b/2 a)) (- (- b/2) b/2)))))","end":3.734211309134784,"name":"NMSE problem 3.2.1, positive","status":"imp-start","end-est":4.2364388520988845},{"samplers":["default","default","default"],"bits":128,"start":17.645728638338042,"link":"9-NMSEproblem321negative","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":14415.817138671875,"target":false,"output":"(if (<= b/2 -1.4598629f-09) (/ c (- (* (* 1/2 c) (/ a b/2)) (* 2 b/2))) (if (<= b/2 2.2299319f+17) (/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a) (/ (fma (/ (* 1/2 c) b/2) a (- (- b/2) b/2)) a)))","end":3.412585870350289,"name":"NMSE problem 3.2.1, negative","status":"imp-start","end-est":3.817714829537428},{"samplers":["default","default"],"bits":128,"start":12.212113605972839,"link":"10-NMSEsection35","pinf":0,"ninf":0,"vars":["a","x"],"input":"(- (exp (* a x)) 1)","time":3224.9951171875,"target":0.15503260155357926,"output":"(expm1 (* x a))","end":0.06610665266266337,"name":"NMSE section 3.5","status":"eq-target","end-est":0.0546875},{"samplers":["default"],"bits":128,"start":17.7692216734353,"link":"11-NMSEsection311","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (exp x) (- (exp x) 1))","time":3000.947998046875,"target":16.042955996249013,"output":"(/ (exp x) (expm1 x))","end":1.7956939347002838,"name":"NMSE section 3.11","status":"gt-target","end-est":2.1722704762093},{"samplers":["default"],"bits":128,"start":24.701507036424022,"link":"12-NMSEproblem343","pinf":0,"ninf":0,"vars":["eps"],"input":"(log (/ (- 1 eps) (+ 1 eps)))","time":6979.701904296875,"target":0.28704591166953425,"output":"(+ (log1p (- eps)) (- (log1p eps)))","end":0.024625,"name":"NMSE problem 3.4.3","status":"eq-target","end-est":0.0234375},{"samplers":["default","default","default"],"bits":128,"start":28.07038909571422,"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":30341.48681640625,"target":6.217741397611786,"output":"(* (/ (cube (cbrt (expm1 (* eps (+ b a))))) (expm1 (* a eps))) (/ eps (expm1 (* b eps))))","end":12.325567910617021,"name":"NMSE problem 3.4.2","status":"lt-target","end-est":12.582756119287177},{"samplers":["default"],"bits":128,"start":14.679953814064174,"link":"14-NMSEproblem337","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (exp x) 2) (exp (- x)))","time":6442.614013671875,"target":2.720509876555737,"output":"(* (fma 1/1920 (pow x 5) (fma (cube x) 1/24 x)) (fma 1/1920 (pow x 5) (fma (cube x) 1/24 x)))","end":0.15022764723805618,"name":"NMSE problem 3.3.7","status":"gt-target","end-est":1.7432832958353668},{"samplers":["default"],"bits":128,"start":4.7271196378632805,"link":"15-NMSEproblem333","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))","time":10535.656005859375,"target":0.7969074385572402,"output":"(if (<= x -0.01639637f0) (+ (/ (/ 2 x) (* x x)) (+ (/ 2 (pow x 7)) (/ 2 (pow x 5)))) (if (<= x 17.42791f0) (+ (/ (- x (fma 2 x 2)) (fma x x x)) (/ 1 (- x 1))) (+ (/ (/ 2 x) (* x x)) (+ (/ 2 (pow x 7)) (/ 2 (pow x 5))))))","end":0.11279236853587687,"name":"NMSE problem 3.3.3","status":"eq-target","end-est":0.2346783369223789},{"samplers":["default","default"],"bits":128,"start":16.83798575141395,"link":"16-NMSEproblem332","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (tan (+ x eps)) (tan x))","time":18754.694091796875,"target":7.760894689978921,"output":"(if (<= (- (tan (+ x eps)) (tan x)) -0.0013098668f0) (- (tan (+ x eps)) (cube (/ (cbrt (sin x)) (cbrt (cos x))))) (if (<= (- (tan (+ x eps)) (tan x)) 0.012468386f0) (+ (+ (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))) (- (tan (+ x eps)) (cube (/ (cbrt (sin x)) (cbrt (cos x)))))))","end":7.5630282527037584,"name":"NMSE problem 3.3.2","status":"eq-target","end-est":7.944257997744237},{"samplers":["default","default","default"],"bits":128,"start":16.203501728387113,"link":"17-NMSEp42positive","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":17991.1669921875,"target":10.08428867462757,"output":"(if (<= b -1.6844219f+10) (- (/ c b) (/ b a)) (if (<= b 3.426723f-06) (* (/ 1 2) (/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) a)) (if (<= b 2.2299319f+17) (/ (/ (* c (* 4 a)) (- (- b) (sqrt (- (sqr b) (* 4 (* a c)))))) (* 2 a)) (* (/ c b) (/ -2 2)))))","end":3.7699440855682167,"name":"NMSE p42, positive","status":"gt-target","end-est":3.444549926647703},{"samplers":["default","default","default"],"bits":128,"start":15.96621602225329,"link":"18-NMSEp42negative","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":22384.614013671875,"target":9.636570393518086,"output":"(if (<= b -2.3005939f+20) (/ (/ (/ 4 2) 2) (- (/ a b) (/ b c))) (if (<= b 1.0894418f-30) (* (/ c 2) (/ 4 (+ (- b) (sqrt (- (sqr b) (* (* c a) 4)))))) (if (<= b 2.2299319f+17) (* (/ 1 2) (/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) a)) (- (/ c b) (/ b a)))))","end":3.0823312934602867,"name":"NMSE p42, negative","status":"gt-target","end-est":2.7505963155524014},{"samplers":["default"],"bits":128,"start":29.31607894503014,"link":"19-NMSEexample39","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 x) (cotan x))","time":6078.983154296875,"target":0.01802124062518029,"output":"(fma (cube x) 1/45 (fma 2/945 (pow x 5) (* x 1/3)))","end":0.3225,"name":"NMSE example 3.9","status":"eq-target","end-est":0.28515625},{"samplers":["default"],"bits":128,"start":31.021609593234782,"link":"20-NMSEexample38","pinf":0,"ninf":0,"vars":["N"],"input":"(- (- (* (+ N 1) (log (+ N 1))) (* N (log N))) 1)","time":28904.028076171875,"target":0.001375,"output":"(- (expm1 (log1p (cube (cbrt (- (fma N (log1p N) (log1p N)) (* N (log N))))))) 1)","end":29.438728607281156,"name":"NMSE example 3.8","status":"lt-target","end-est":29.41739826300403},{"samplers":["default"],"bits":128,"start":25.131736264882985,"link":"21-NMSEexample37","pinf":0,"ninf":0,"vars":["x"],"input":"(- (exp x) 1)","time":2348.743896484375,"target":0.9445048355905326,"output":"(expm1 x)","end":0.004,"name":"NMSE example 3.7","status":"eq-target","end-est":0.0078125},{"samplers":["default"],"bits":128,"start":8.345573248557992,"link":"22-NMSEexample36","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))","time":8892.9521484375,"target":0.21656372187554088,"output":"(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))","end":2.959451154673079,"name":"NMSE example 3.6","status":"lt-target","end-est":2.7061915483838708},{"samplers":["default"],"bits":128,"start":6.889623952194282,"link":"23-NMSEexample35","pinf":0,"ninf":0,"vars":["N"],"input":"(- (atan (+ N 1)) (atan N))","time":2900.23291015625,"target":0.5994049004416014,"output":"(atan2 (- 1 0) (fma N (+ 1 N) 1))","end":0.5987586598164211,"name":"NMSE example 3.5","status":"eq-target","end-est":0.5743896373771156},{"samplers":["default"],"bits":128,"start":13.441710630796573,"link":"24-NMSEexample34","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sin x))","time":37750.451171875,"target":0.0205,"output":"(cube (cbrt (/ (sin x) (+ (cos x) 1))))","end":0.9953701146557916,"name":"NMSE example 3.4","status":"eq-target","end-est":1.0159550421893868},{"samplers":["default","default"],"bits":128,"start":16.695231656538926,"link":"25-NMSEexample33","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (sin (+ x eps)) (sin x))","time":21425.81787109375,"target":7.662017165416587,"output":"(if (<= eps -0.1735093f0) (+ (expm1 (log1p (* (sin x) (cos eps)))) (- (* (cos x) (sin eps)) (sin x))) (if (<= eps 0.058325335f0) (- (* (sin eps) (cos x)) (* eps (* (* 1/2 eps) (sin x)))) (+ (expm1 (log1p (* (sin x) (cos eps)))) (- (* (cos x) (sin eps)) (sin x)))))","end":0.26728477611597296,"name":"NMSE example 3.3","status":"gt-target","end-est":0.33852119466523584},{"samplers":["default"],"bits":128,"start":26.67245750924076,"link":"26-NMSEexample310","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (log (- 1 x)) (log (+ 1 x)))","time":6016.56982421875,"target":0.4783493096428078,"output":"(/ (log1p (- x)) (log1p x))","end":0.08229981250360577,"name":"NMSE example 3.10","status":"eq-target","end-est":0.08107377930532605},{"samplers":["default"],"bits":128,"start":13.106320113187243,"link":"27-NMSEexample31","pinf":0,"ninf":0,"vars":["x"],"input":"(- (sqrt (+ x 1)) (sqrt x))","time":5015.399169921875,"target":0.1654199250014423,"output":"(/ 1 (+ (sqr (sqrt (sqrt (+ x 1)))) (sqrt x)))","end":0.25161021406186607,"name":"NMSE example 3.1","status":"eq-target","end-est":0.25228500976844204}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}