{"bit_width":64,"date":1468834353,"note":"hamming","iterations":2,"flags":["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","precision:double"],"seed":"#(1065767146 1567806045 1856802035 1672802504 2070886570 609046914)","points":256,"tests":[{"samplers":["default","default"],"bits":128,"start":30.697877516138306,"link":"0-NMSEproblem346","pinf":0,"ninf":0,"vars":["x","n"],"input":"(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))","time":35119.724853515625,"target":false,"output":"(if (<= n -164940.045680331) (- (/ 1 (* n x)) (+ (/ (log x) (* (sqr n) x)) (* 1/2 (/ 1 (* n (sqr x)))))) (if (<= n 1706414974795.34) (cube (* (cbrt (+ (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))) (cbrt (- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))))) (- (/ 1 (* n x)) (+ (/ (log x) (* (sqr n) x)) (* 1/2 (/ 1 (* n (sqr x))))))))","end":7.19228940206919,"name":"NMSE problem 3.4.6","status":"imp-start","end-est":21.957675971889707},{"samplers":["default"],"bits":128,"start":31.670859766169745,"link":"1-NMSEproblem345","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- x (sin x)) (- x (tan x)))","time":19777.300048828125,"target":false,"output":"(if (<= x -8.61646249982272e-12) (/ (- x (sin x)) (- x (tan x))) (if (<= x 8.584780819621077) (- (* 9/40 (sqr x)) (+ (* 27/2800 (pow x 4)) 1/2)) (cube (cbrt (- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))))))","end":0.26672625458861515,"name":"NMSE problem 3.4.5","status":"imp-start","end-est":0.5349518283778264},{"samplers":["default"],"bits":128,"start":45.3231135847982,"link":"2-NMSEproblem344","pinf":0,"ninf":0,"vars":["x"],"input":"(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))","time":6587.41796875,"target":false,"output":"(if (<= x -8.61646249982272e-12) (sqrt (/ (- (exp (* 2 x)) 1) (/ (- (sqr (exp x)) (sqr 1)) (+ (exp x) 1)))) (sqrt (+ (* 1/2 (sqr x)) (+ 2 x))))","end":7.62872077761838,"name":"NMSE problem 3.4.4","status":"imp-start","end-est":0.27444668224369734},{"samplers":["default"],"bits":128,"start":31.500430409264276,"link":"3-NMSEproblem341","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sqr x))","time":8748.8828125,"target":false,"output":"(if (<= x -8.61646249982272e-12) (* (/ 1 x) (/ (- 1 (cos x)) x)) (if (<= x 8.584780819621077) (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (sqr x))) (* (/ 1 x) (/ (- 1 (cos x)) x))))","end":0.49835787230239526,"name":"NMSE problem 3.4.1","status":"imp-start","end-est":0.7132595803889382},{"samplers":["default"],"bits":128,"start":29.383488587954993,"link":"4-NMSEproblem336","pinf":0,"ninf":0,"vars":["N"],"input":"(- (log (+ N 1)) (log N))","time":10871.77197265625,"target":false,"output":"(if (<= N 15879525.552212397) (- (log (+ N 1)) (log N)) (+ (/ 1 N) (- (/ 1/3 (cube N)) (/ 1/2 (* N N)))))","end":0.14759956358741877,"name":"NMSE problem 3.3.6","status":"imp-start","end-est":0.15066262166423156},{"samplers":["default","default"],"bits":128,"start":37.19748336246725,"link":"5-NMSEproblem335","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (cos (+ x eps)) (cos x))","time":21225.404052734375,"target":false,"output":"(if (<= eps -9.748260542427816e-17) (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)) (if (<= eps 0.00044197627601391903) (- (* (* eps 1/6) (cube x)) (* eps (+ (* eps 1/2) x))) (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))","end":3.906227183545969,"name":"NMSE problem 3.3.5","status":"imp-start","end-est":15.397151760675634},{"samplers":["default"],"bits":128,"start":29.714832933134883,"link":"6-NMSEproblem334","pinf":0,"ninf":0,"vars":["x"],"input":"(- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3)))","time":20304.10986328125,"target":false,"output":"(/ (- (cube (pow (+ x 1) (/ 1 3))) (pow (pow x (/ 1 3)) 3)) (+ (sqr (pow (+ x 1) (/ 1 3))) (+ (sqr (pow x (/ 1 3))) (* (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3))))))","end":29.65441603248017,"name":"NMSE problem 3.3.4","status":"apx-start","end-est":29.15852493071509},{"samplers":["default"],"bits":128,"start":14.063572097028864,"link":"7-NMSEproblem331","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (+ x 1)) (/ 1 x))","time":4163.840087890625,"target":false,"output":"(if (<= x -58516562547846.875) (- (/ (/ 1 x) (* x x)) (/ (/ 1 x) x)) (if (<= x 157093943.70564985) (/ (- x (+ 1 x)) (+ x (sqr x))) (- (/ (/ 1 x) (* x x)) (/ (/ 1 x) x))))","end":0.07363460194963134,"name":"NMSE problem 3.3.1","status":"imp-start","end-est":0.0703125},{"samplers":["default","default","default"],"bits":128,"start":35.159097653926565,"link":"8-NMSEproblem321positive","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":15072.54296875,"target":false,"output":"(if (<= b/2 -6.636085511448982e+62) (- (/ 1/2 (/ b/2 c)) (* (/ b/2 a) 2)) (if (<= b/2 3.186709671602115e-147) (/ 1 (/ a (+ (- b/2) (sqrt (- (sqr b/2) (* a c)))))) (if (<= b/2 8.495124006963825e+40) (/ (/ (* a c) (- (- b/2) (sqrt (- (sqr b/2) (* a c))))) a) (/ c (- (* (* 1/2 c) (/ a b/2)) (* 2 b/2))))))","end":7.216291108935923,"name":"NMSE problem 3.2.1, positive","status":"imp-start","end-est":10.332078062488135},{"samplers":["default","default","default"],"bits":128,"start":36.02112451795538,"link":"9-NMSEproblem321negative","pinf":0,"ninf":0,"vars":["a","b/2","c"],"input":"(/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a)","time":14811.68994140625,"target":false,"output":"(if (<= b/2 -2.496996520939034e+74) (/ c (- (* (* a 1/2) (/ c b/2)) (- b/2 (- b/2)))) (if (<= b/2 -9.074512816801552e-91) (/ (/ (* a c) (+ (- b/2) (sqrt (- (sqr b/2) (* a c))))) a) (if (<= b/2 -6.735949376426626e-136) (/ c (- (* (* a 1/2) (/ c b/2)) (- b/2 (- b/2)))) (if (<= b/2 2.7032921376893094e+83) (/ (- (- b/2) (sqrt (- (sqr b/2) (* a c)))) a) (- (/ 1/2 (/ b/2 c)) (* (/ b/2 a) 2))))))","end":7.3054018503194635,"name":"NMSE problem 3.2.1, negative","status":"imp-start","end-est":9.24144822476535},{"samplers":["default","default"],"bits":128,"start":33.61043941699916,"link":"10-NMSEsection35","pinf":0,"ninf":0,"vars":["a","x"],"input":"(- (exp (* a x)) 1)","time":8347.510009765625,"target":7.919035134533876,"output":"(if (<= (* a x) -7.260081363831148e-07) (log (exp (- (exp (* a x)) 1))) (+ (* (* 1/2 (* x a)) (* x a)) (* x a)))","end":0.1253134917417747,"name":"NMSE section 3.5","status":"gt-target","end-est":0.7459508788614166},{"samplers":["default"],"bits":128,"start":45.57578860326028,"link":"11-NMSEsection311","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (exp x) (- (exp x) 1))","time":4017.845947265625,"target":45.57419137623188,"output":"(if (<= x -8.61646249982272e-12) (/ 1 (- 1 (exp (- x)))) (+ 1/2 (+ (/ 1 x) (* 1/12 x))))","end":0.21119908842234894,"name":"NMSE section 3.11","status":"gt-target","end-est":0.7814165249861399},{"samplers":["default"],"bits":128,"start":59.35076276064805,"link":"12-NMSEproblem343","pinf":0,"ninf":0,"vars":["eps"],"input":"(log (/ (- 1 eps) (+ 1 eps)))","time":5943.509033203125,"target":0.062963379669456,"output":"(- (+ (* 2 eps) (+ (* 2/5 (pow eps 5)) (* 2/3 (pow eps 3)))))","end":0.08582898123240673,"name":"NMSE problem 3.4.3","status":"eq-target","end-est":0.28393701707793684},{"samplers":["default","default","default"],"bits":128,"start":62.020433327117736,"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":49323.35791015625,"target":14.56994117465894,"output":"(+ (/ 1 b) (/ 1 a))","end":0.015594360937770436,"name":"NMSE problem 3.4.2","status":"gt-target","end-est":3.267947769886195},{"samplers":["default"],"bits":128,"start":34.57905883708398,"link":"14-NMSEproblem337","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (exp x) 2) (exp (- x)))","time":5809.748046875,"target":8.51630132379576,"output":"(+ (sqr x) (+ (* 1/12 (pow x 4)) (* 1/360 (pow x 6))))","end":0.10672735777882134,"name":"NMSE problem 3.3.7","status":"gt-target","end-est":1.267502069487464},{"samplers":["default"],"bits":128,"start":9.484732195007844,"link":"15-NMSEproblem333","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))","time":8979.72705078125,"target":0.2619289489631605,"output":"(if (<= x -2.1401320122751497) (+ (+ (/ 2 (pow x 7)) (/ 2 (cube x))) (/ 2 (pow x 5))) (if (<= x 15879525.552212397) (/ (+ (+ x (sqr x)) (* (- (- x 2) (* x 2)) (- x 1))) (* (* (+ x 1) x) (- x 1))) (+ (+ (/ 2 (pow x 7)) (/ 2 (cube x))) (/ 2 (pow x 5)))))","end":0.2769352841088689,"name":"NMSE problem 3.3.3","status":"eq-target","end-est":0.2940199991561779},{"samplers":["default","default"],"bits":128,"start":36.7939064757676,"link":"16-NMSEproblem332","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (tan (+ x eps)) (tan x))","time":24539.994873046875,"target":26.719603348511637,"output":"(if (<= eps -1.5175483707585876e-61) (/ (cube (cbrt (- (cos x) (* (cotan (+ eps x)) (sin x))))) (* (cotan (+ x eps)) (cos x))) (if (<= eps 639.2159073015437) (+ (+ eps (* (* x x) (cube eps))) (* (pow eps 4) (cube x))) (/ (- (cos x) (* (cbrt (cube (cotan (+ eps x)))) (sin x))) (* (cotan (+ x eps)) (cos x)))))","end":24.565570547147185,"name":"NMSE problem 3.3.2","status":"gt-target","end-est":28.725334290424364},{"samplers":["default","default","default"],"bits":128,"start":34.723055686366145,"link":"17-NMSEp42positive","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":24409.8349609375,"target":22.260800326793266,"output":"(if (<= b -6.636085511448982e+62) (- (/ c b) (/ b a)) (if (<= b 1.2379375656305326e-258) (* (/ 1 2) (/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) a)) (if (<= b 2.7032921376893094e+83) (* (/ c 2) (/ 4 (- (- b) (sqrt (- (sqr b) (* (* c a) 4)))))) (* (/ (/ c (/ 2 4)) (- (* (/ c b) a) b)) (/ 1 2)))))","end":5.314385201413274,"name":"NMSE p42, positive","status":"gt-target","end-est":8.239447805029098},{"samplers":["default","default","default"],"bits":128,"start":36.0850891930089,"link":"18-NMSEp42negative","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":26208.390869140625,"target":23.794480144470437,"output":"(if (<= b -2.496996520939034e+74) (* (/ (/ c (/ 2 4)) (- (* (/ c b) a) b)) (/ 1 2)) (if (<= b -9.074512816801552e-91) (/ (/ (* c (* 4 a)) (+ (- b) (sqrt (- (sqr b) (* 4 (* a c)))))) (* 2 a)) (if (<= b -6.735949376426626e-136) (* (/ (/ c (/ 2 4)) (- (* (/ c b) a) b)) (/ 1 2)) (if (<= b 2.7032921376893094e+83) (* (/ 1 2) (/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) a)) (- (/ c b) (/ b a))))))","end":7.3258893353769565,"name":"NMSE p42, negative","status":"gt-target","end-est":9.254716824412421},{"samplers":["default"],"bits":128,"start":59.89183907293337,"link":"19-NMSEexample39","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 x) (cotan x))","time":6864.7080078125,"target":0.08272914777632703,"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":0.3046875},{"samplers":["default"],"bits":128,"start":63.32337907226415,"link":"20-NMSEexample38","pinf":0,"ninf":0,"vars":["N"],"input":"(- (- (* (+ N 1) (log (+ N 1))) (* N (log N))) 1)","time":21542.87109375,"target":60.773819432642284,"output":"(- (* (+ N 1) (log (+ N 1))) (+ (* (log N) (- N)) 1))","end":0.264,"name":"NMSE example 3.8","status":"gt-target","end-est":60.74514460060702},{"samplers":["default"],"bits":128,"start":59.24824549455067,"link":"21-NMSEexample37","pinf":0,"ninf":0,"vars":["x"],"input":"(- (exp x) 1)","time":4436.43505859375,"target":0.06183496250072115,"output":"(+ (* (+ 1/2 (* 1/6 x)) (sqr x)) x)","end":0.0620567671895733,"name":"NMSE example 3.7","status":"eq-target","end-est":0.5117463832515348},{"samplers":["default"],"bits":128,"start":19.735370607472543,"link":"22-NMSEexample36","pinf":0,"ninf":0,"vars":["x"],"input":"(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))","time":5901.55908203125,"target":0.6558452533471171,"output":"(/ (/ 1 (+ (sqrt (+ 1 x)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))","end":0.3859799082418204,"name":"NMSE example 3.6","status":"eq-target","end-est":0.43661889652663033},{"samplers":["default"],"bits":128,"start":14.576884729637724,"link":"23-NMSEexample35","pinf":0,"ninf":0,"vars":["N"],"input":"(- (atan (+ N 1)) (atan N))","time":3572.908203125,"target":0.4324989747304594,"output":"(atan2 (- 1 0) (+ 1 (* (+ N 1) N)))","end":0.4309989747304594,"name":"NMSE example 3.5","status":"eq-target","end-est":0.595525791504301},{"samplers":["default"],"bits":128,"start":30.65651606346277,"link":"24-NMSEexample34","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- 1 (cos x)) (sin x))","time":15316.272216796875,"target":0.08327405389745489,"output":"(if (<= x -8.61646249982272e-12) (/ (/ (sqr (sin x)) (+ 1 (cos x))) (sin x)) (if (<= x 8.584780819621077) (+ (* x 1/2) (+ (* 1/240 (pow x 5)) (* (cube x) 1/24))) (* (- 1 (cos x)) (/ 1 (sin x)))))","end":0.47540691326532675,"name":"NMSE example 3.4","status":"eq-target","end-est":0.6724175487649291},{"samplers":["default","default"],"bits":128,"start":36.46851257153738,"link":"25-NMSEexample33","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(- (sin (+ x eps)) (sin x))","time":24120.44091796875,"target":26.73857879474589,"output":"(if (<= eps -1.5175483707585876e-61) (/ (- (cube (+ (* (sin eps) (cos x)) (* (cos eps) (sin x)))) (cube (sin x))) (+ (sqr (+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))) (+ (sqr (sin x)) (* (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))))) (if (<= eps 2.331749649630336e-18) (- eps (* 1/2 (* (+ eps x) (* x eps)))) (/ (- (cube (+ (* (sin eps) (cos x)) (* (cos eps) (sin x)))) (cube (sin x))) (+ (sqr (+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))) (+ (sqr (sin x)) (* (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x)))))))","end":1.869657452958016,"name":"NMSE example 3.3","status":"gt-target","end-est":14.751198903214194},{"samplers":["default"],"bits":128,"start":61.28068203549304,"link":"26-NMSEexample310","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (log (- 1 x)) (log (+ 1 x)))","time":4590.93994140625,"target":0.3882103023851495,"output":"(- (+ (* 1/2 (sqr x)) (+ 1 x)))","end":0.007875,"name":"NMSE example 3.10","status":"eq-target","end-est":0.4201211079252832},{"samplers":["default"],"bits":128,"start":29.80696234990521,"link":"27-NMSEexample31","pinf":0,"ninf":0,"vars":["x"],"input":"(- (sqrt (+ x 1)) (sqrt x))","time":3467.9951171875,"target":0.165434210940655,"output":"(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))","end":0.165434210940655,"name":"NMSE example 3.1","status":"eq-target","end-est":0.14128876953688402}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}