{"bit_width":64,"date":1469371478,"note":"numerics","iterations":2,"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","precision:double"],"seed":"#(1065385120 3968465003 4252011776 3360847114 2908152799 1991881914)","points":256,"tests":[{"samplers":["default"],"bits":128,"start":0.014625,"link":"0-arccos","pinf":0,"ninf":0,"vars":["x"],"input":"(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))","time":5974.575927734375,"target":false,"output":"(* 2 (atan (sqrt (sqr (/ (sqrt (- 1 x)) (sqrt (+ 1 x)))))))","end":0.01575,"name":"arccos","status":"ex-start","end-est":0.03515625},{"samplers":["default","default","default"],"bits":128,"start":11.580352314395903,"link":"1-RosasTurbineBenchmark","pinf":0,"ninf":0,"vars":["v","w","r"],"input":"(- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5)","time":79439.89013671875,"target":false,"output":"(- (- (/ (/ 2 r) r) (- 4.5 3)) (* (- 3 (* v 2)) (/ (sqr (* w r)) (/ (- 1 v) 0.125))))","end":0.3458998233554247,"name":"Rosa's TurbineBenchmark","status":"imp-start","end-est":0.320976269536884},{"samplers":["default","default"],"bits":128,"start":0.513448018959756,"link":"2-RosasFloatVsDoubleBenchmark","pinf":0,"ninf":0,"vars":["x1","x2"],"input":"(+ x1 (+ (+ (+ (+ (* (+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6))) (+ (* x1 x1) 1)) (* (* (* 3 x1) x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)))) (* (* x1 x1) x1)) x1) (* 3 (/ (- (- (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)))))","time":59798.1240234375,"target":false,"output":"(+ (+ (+ (+ x1 x1) (+ (cube x1) (/ (* (* x1 (* x1 3)) (+ (* x1 (* x1 3)) (- (* x2 2) x1))) (+ (sqr x1) 1)))) (* (+ (* (- (/ (+ (* x1 (* x1 3)) (- (* x2 2) x1)) (+ (sqr x1) 1)) 3) (/ (* (+ (* x1 (* x1 3)) (- (* x2 2) x1)) (* 2 x1)) (+ (sqr x1) 1))) (* (- (/ (+ (* x1 (* x1 3)) (- (* x2 2) x1)) (/ (+ (sqr x1) 1) 4)) 6) (sqr x1))) (+ (sqr x1) 1))) (* (/ 3 (+ (sqr x1) 1)) (- (* x1 (* x1 3)) (+ x1 (* x2 2)))))","end":0.4562542854374578,"name":"Rosa's FloatVsDoubleBenchmark","status":"ex-start","end-est":0.6042477189251009},{"samplers":["default","default","default"],"bits":128,"start":17.509177440207363,"link":"3-RosasDopplerBench","pinf":0,"ninf":0,"vars":["u","v","t1"],"input":"(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))","time":12151.533935546875,"target":false,"output":"(/ (* (/ (- t1) (+ t1 u)) v) (+ t1 u))","end":1.0163404451427056,"name":"Rosa's DopplerBench","status":"imp-start","end-est":0.5443065226161786},{"samplers":["default"],"bits":128,"start":0.14675284467733313,"link":"4-RosasBenchmark","pinf":0,"ninf":0,"vars":["x"],"input":"(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))","time":4775.56494140625,"target":false,"output":"(- (* x 0.954929658551372) (* 0.12900613773279798 (cube x)))","end":0.14675284467733313,"name":"Rosa's Benchmark","status":"ex-start","end-est":0.09765625},{"samplers":["default","default"],"bits":128,"start":0.002448120312590144,"link":"5-Radioactiveexchangebetweentwosurfaces","pinf":0,"ninf":0,"vars":["x","y"],"input":"(- (pow x 4) (pow y 4))","time":4837.150146484375,"target":false,"output":"(- (pow x 4) (pow y 4))","end":0.002448120312590144,"name":"Radioactive exchange between two surfaces","status":"ex-start","end-est":0.00390625},{"samplers":["default","default"],"bits":128,"start":14.435052680276002,"link":"6-NMSESection61mentionedB","pinf":0,"ninf":0,"vars":["a","b"],"input":"(* (* (/ PI 2) (/ 1 (- (sqr b) (sqr a)))) (- (/ 1 a) (/ 1 b)))","time":16940.617919921875,"target":false,"output":"(+ (* (/ (/ PI b) (+ a b)) (/ (- 1/2) (- b a))) (/ (/ (/ PI 2) (+ a b)) (* (- b a) a)))","end":0.2714039726155675,"name":"NMSE Section 6.1 mentioned, B","status":"imp-start","end-est":0.21388627930532603},{"samplers":["default","default"],"bits":128,"start":39.42807386222542,"link":"7-NMSESection61mentionedA","pinf":0,"ninf":0,"vars":["x","eps"],"input":"(/ (- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))) 2)","time":34687.138916015625,"target":false,"output":"(if (<= x 46118455070.99842) (/ (+ (* (cube x) 2/3) (- 2 (* x x))) 2) (/ (- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))) 2))","end":0.06406693897361637,"name":"NMSE Section 6.1 mentioned, A","status":"imp-start","end-est":0.8315055323351601},{"samplers":["default"],"bits":128,"start":15.13463116010136,"link":"8-xx21","pinf":0,"ninf":0,"vars":["x"],"input":"(/ x (+ (sqr x) 1))","time":6465.97607421875,"target":0.4090913519773475,"output":"(if (<= x -3.2784791869173944e-06) (- (/ 1 (pow x 5)) (- (/ 1 (cube x)) (/ 1 x))) (if (<= x 501837.3637557024) (/ x (+ (sqr x) 1)) (- (/ 1 (pow x 5)) (- (/ 1 (cube x)) (/ 1 x)))))","end":0.008125,"name":"x / (x^2 + 1)","status":"eq-target","end-est":0.23348740809547358},{"samplers":["default","default","default"],"bits":128,"start":45.97888688794463,"link":"9-simplefmatest","pinf":0,"ninf":0,"vars":["x","y","z"],"input":"(- (fma x y z) (+ 1 (+ (* x y) z)))","time":15214.447998046875,"target":1.900305213366796,"output":"(if (<= z -3.2784791869173944e-06) (- (- (fma (/ -1 x) (/ -1 y) (/ -1 z)) (/ (/ 1 x) y)) 1) (if (<= z 5.906184364389485e-18) (- (- (fma x y z) 1) (/ (- (sqr (* y x)) (* z z)) (- (* y x) z))) (- (- (fma (/ -1 x) (/ -1 y) (/ -1 z)) (/ (/ 1 x) y)) 1)))","end":22.118456409747452,"name":"simple fma test","status":"lt-target","end-est":21.89268938972614},{"samplers":["default"],"bits":128,"start":42.17517702726594,"link":"10-ln1x","pinf":0,"ninf":0,"vars":["x"],"input":"(log (+ 1 x))","time":5981.9189453125,"target":7.111198611650797,"output":"(if (<= x 501837.3637557024) (+ (* (- (* 1/3 x) 1/2) (sqr x)) x) (log (+ 1 x)))","end":0.04716052656439302,"name":"ln(1 + x)","status":"gt-target","end-est":0.35289514136149974},{"samplers":["default","default","default"],"bits":128,"start":33.482716486871865,"link":"11-Thequadraticformular2","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":37885.537841796875,"target":20.503764631690522,"output":"(if (<= b -1.3574531607557133e+150) (* (/ c b) (/ -2 2)) (if (<= b 4.531211813689417e-280) (/ (/ c (/ 2 4)) (+ (sqrt (- (* b b) (* 4 (* c a)))) (- b))) (if (<= b 3.741572576046744e+123) (- (/ (- b) (* 2 a)) (/ (sqrt (- (sqr b) (* 4 (* a c)))) (* 2 a))) (- (+ (/ c b) (/ (- b) (* 2 a))) (/ (/ b 2) a)))))","end":5.363305926606247,"name":"The quadratic formula (r2)","status":"gt-target","end-est":4.138840188265656},{"samplers":["default","default","default"],"bits":128,"start":34.996398401482935,"link":"12-Thequadraticformular1","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* (* 4 a) c)))) (* 2 a))","time":35438.0419921875,"target":22.2414028351614,"output":"(if (<= b -1.9805160440224734e+152) (- (/ c b) (/ b a)) (if (<= b 1.2681432970921129e-148) (/ (+ (- b) (sqrt (- (sqr b) (* (* 4 a) c)))) (* 2 a)) (if (<= b 504667502.6761971) (* (* (/ 4 2) a) (/ (/ c (- (- b) (sqrt (- (sqr b) (* (* 4 a) c))))) a)) (- (/ (+ b (- b)) (* a 2)) (* 1 (/ c b))))))","end":6.629261697943477,"name":"The quadratic formula (r1)","status":"gt-target","end-est":7.273334217800368},{"samplers":["default"],"bits":128,"start":43.03428818406394,"link":"13-Kahansexpquotient","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- (exp x) 1) x)","time":8737.52099609375,"target":42.308523651176074,"output":"(if (<= x -3.2784791869173944e-06) (/ (/ (- (cube (exp x)) 1) (+ (+ (exp x) 1) (exp (+ x x)))) x) (/ (+ (* (+ 1/2 (* 1/6 x)) (sqr x)) x) x))","end":2.920463227921603,"name":"Kahan's exp quotient","status":"gt-target","end-est":0.12099157680731563},{"samplers":["(uniform -14 -13)","(uniform -3 -2)","(uniform 3 3.5)","(uniform 12.5 13.5)"],"bits":128,"start":3.6602412812178438,"link":"14-Expressionp6","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(* (+ a (+ b (+ c d))) 2)","time":12147.341064453125,"target":3.848451940312146,"output":"(* (+ (+ a d) (+ c b)) 2)","end":0,"name":"Expression, p6","status":"gt-target","end-est":0},{"samplers":["default","default","default","default"],"bits":128,"start":false,"link":"15-Expressionp14","pinf":false,"ninf":false,"vars":["a","b","c","d"],"input":"(* a (+ (+ b c) d))","time":26562.553955078125,"target":false,"output":"#f","end":false,"name":"Expression, p14","status":"crash","end-est":false},{"samplers":["default","default"],"bits":384,"start":false,"link":"16-Expression4p15","pinf":false,"ninf":false,"vars":["a","b"],"input":"(* (+ a b) (+ a b))","time":16059.948974609375,"target":false,"output":"#f","end":false,"name":"Expression 4, p15","status":"crash","end-est":false},{"samplers":["default"],"bits":128,"start":0.016625,"link":"17-Expression3p15","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (* x (* x x)) (* x x))","time":9998.025146484375,"target":0.024219360937770436,"output":"(+ (sqr x) (pow x 3))","end":0.016,"name":"Expression 3, p15","status":"eq-target","end-est":0.015625},{"samplers":["default"],"bits":128,"start":0.00075,"link":"18-Expression2p15","pinf":0,"ninf":0,"vars":["x"],"input":"(+ x (* x x))","time":7865.64013671875,"target":0.02025,"output":"(+ x (sqr x))","end":0.00075,"name":"Expression 2, p15","status":"eq-target","end-est":0},{"samplers":["(uniform 1 2)","(uniform 2 4)","(uniform 4 8)","(uniform 8 16)","(uniform 16 32)"],"bits":128,"start":0.39568665469173697,"link":"19-Expression1p15","pinf":0,"ninf":0,"vars":["a","b","c","d","e"],"input":"(+ (+ (+ (+ e d) c) b) a)","time":13399.086181640625,"target":0.19275,"output":"(+ (+ (+ a b) e) (+ c d))","end":0.241,"name":"Expression 1, p15","status":"eq-target","end-est":0.21484375},{"samplers":["default","default"],"bits":128,"start":0.006875,"link":"20-Differenceofsquares","pinf":0,"ninf":0,"vars":["a","b"],"input":"(- (sqr a) (sqr b))","time":11842.089111328125,"target":0.00075,"output":"(- (sqr a) (sqr b))","end":0.006875,"name":"Difference of squares","status":"eq-target","end-est":0.00390625},{"samplers":["default","default"],"bits":128,"start":53.781139410314324,"link":"21-CompoundInterest","pinf":0,"ninf":0,"vars":["i","n"],"input":"(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))","time":68050.15600585938,"target":51.336935083411795,"output":"(if (<= i -2.6993148136786055e-05) (* (/ (- (cube (pow (+ 1 (/ i n)) n)) 1) (+ (sqr (pow (+ 1 (/ i n)) n)) (+ 1 (pow (+ 1 (/ i n)) n)))) (/ 100 (/ i n))) (if (<= i 46118455070.99842) (* (+ (* 1/2 i) 1) (* 100 n)) (* 100 (- (+ (+ (* (/ (pow n 4) i) (* (cube (log i)) 1/6)) (* (* 1/2 (/ (* n n) (/ i n))) (+ (* (log n) (log n)) (* (log i) (log i))))) (+ (+ (* (/ n (/ i n)) (+ (/ n i) (log i))) (/ (* (log i) (* 1/2 (log n))) (/ i (* (pow n 4) (log n))))) (* (/ (pow n 4) i) (- (/ (log i) i) (/ 1/2 (* i i)))))) (+ (+ (* (* (/ 1/6 i) (pow n 4)) (cube (log n))) (* (/ (pow n 4) i) (/ (log n) i))) (+ (+ (/ (* (log n) (cube n)) (/ i (log i))) (* (log n) (/ n (/ i n)))) (/ (* 1/2 (* (* (log n) (log i)) (* (pow n 4) (log i)))) i)))))))","end":6.629832769204628,"name":"Compound Interest","status":"gt-target","end-est":14.154531931375706},{"samplers":["default","default","default","default"],"bits":128,"start":27.021497440079067,"link":"22-Complexdivisionrealpart","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(/ (+ (* a c) (* b d)) (+ (sqr c) (sqr d)))","time":26089.8720703125,"target":7.862070841452749,"output":"(if (<= d -1.3574531607557133e+150) (- (+ (/ b d) (/ (/ a c) (* d d))) (/ b (* (cube d) (* c c)))) (if (<= d 1.1593976875307301e+138) (/ (+ (* a c) (* b d)) (+ (sqr c) (sqr d))) (- (+ (/ b d) (/ (/ a c) (* d d))) (/ b (* (cube d) (* c c))))))","end":19.202501614282742,"name":"Complex division, real part","status":"lt-target","end-est":19.0862139165212},{"samplers":["default","default","default","default"],"bits":128,"start":25.870368759955426,"link":"23-Complexdivisionimagpart","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(/ (- (* b c) (* a d)) (+ (sqr c) (sqr d)))","time":21168.867919921875,"target":0.45374883524815934,"output":"(if (<= d -2.0753310964069658e+55) (- (/ (* b c) (+ (sqr c) (* d d))) (/ a (+ d (/ (sqr c) d)))) (if (<= d 2.9373351910676443e+99) (- (/ b (+ (/ (* d d) c) c)) (/ (* a d) (+ (* d d) (* c c)))) (- (/ (* b c) (+ (sqr c) (* d d))) (/ a (+ d (/ (sqr c) d))))))","end":10.117608080448305,"name":"Complex division, imag part","status":"lt-target","end-est":11.383817371677688},{"samplers":["default","default","default"],"bits":384,"start":false,"link":"24-Areaofatriangle","pinf":false,"ninf":false,"vars":["a","b","c"],"input":"(sqrt (* (* (* (/ (+ (+ a b) c) 2) (- (/ (+ (+ a b) c) 2) a)) (- (/ (+ (+ a b) c) 2) b)) (- (/ (+ (+ a b) c) 2) c)))","time":35611.9580078125,"target":false,"output":"#f","end":false,"name":"Area of a triangle","status":"crash","end-est":false}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}