{"bit_width":32,"date":1468596584,"note":"numerics","iterations":2,"flags":["rules:arithmetic","rules:polynomials","rules:fractions","rules:exponents","rules:trigonometry","setup:simplify","reduce:post-process","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"],"bits":128,"start":0.0535,"link":"0-arccos","pinf":0,"ninf":0,"vars":["x"],"input":"(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))","time":45304.56884765625,"target":false,"output":"(* 2 (atan (sqrt (/ (- (pow 1 3) (pow x 3)) (* (+ 1 x) (+ (+ 1 x) (* x x)))))))","end":0.0565,"name":"arccos","status":"ex-start","end-est":0.0625},{"samplers":["default","default","default"],"bits":128,"start":5.853435963408582,"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":17536.662841796875,"target":false,"output":"(- (+ (- 3 4.5) (/ 2 (* r r))) (* (* (/ 0.125 (- 1 v)) (- 3 (* 2 v))) (sqr (fabs (* r w)))))","end":0.42405464143854904,"name":"Rosa's TurbineBenchmark","status":"imp-start","end-est":0.31154252930532605},{"samplers":["default","default"],"bits":128,"start":0.562319133488163,"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":40278.012939453125,"target":false,"output":"(+ (+ (+ (+ x1 x1) (+ (cube x1) (/ (* (* x1 (* x1 3)) (+ (* x1 (* x1 3)) (- (* x2 2) x1))) (+ (sqr x1) 1)))) (* (+ (* (cube (cbrt (- (/ (+ (* 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":0.5794828085405621,"name":"Rosa's FloatVsDoubleBenchmark","status":"ex-start","end-est":0.6215465453685886},{"samplers":["default","default","default"],"bits":128,"start":8.861460826943441,"link":"3-RosasDopplerBench","pinf":0,"ninf":0,"vars":["u","v","t1"],"input":"(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))","time":6062.869873046875,"target":false,"output":"(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))","end":0.6317989334628639,"name":"Rosa's DopplerBench","status":"imp-start","end-est":0.3347429672072746},{"samplers":["default"],"bits":128,"start":0.3609610452007091,"link":"4-RosasBenchmark","pinf":0,"ninf":0,"vars":["x"],"input":"(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))","time":4750.112060546875,"target":false,"output":"(- (* x 0.954929658551372) (* (* (* 0.12900613773279798 x) x) x))","end":0.24322243955757988,"name":"Rosa's Benchmark","status":"ex-start","end-est":0.3004875488422101},{"samplers":["default","default"],"bits":128,"start":0.10949751186738838,"link":"5-Radioactiveexchangebetweentwosurfaces","pinf":0,"ninf":0,"vars":["x","y"],"input":"(- (pow x 4) (pow y 4))","time":6671.89306640625,"target":false,"output":"(- (pow x 4) (sqr (sqr (sqrt (sqrt (pow y 4))))))","end":0.056433641627478694,"name":"Radioactive exchange between two surfaces","status":"ex-start","end-est":0.07421875},{"samplers":["default","default"],"bits":128,"start":7.467761639034714,"link":"6-NMSESection61mentionedB","pinf":0,"ninf":0,"vars":["a","b"],"input":"(* (* (/ PI 2) (/ 1 (- (sqr b) (sqr a)))) (- (/ 1 a) (/ 1 b)))","time":9841.68896484375,"target":false,"output":"(/ (/ PI (+ a b)) (* 2 (* a b)))","end":0.26404774531980124,"name":"NMSE Section 6.1 mentioned, B","status":"imp-start","end-est":0.2910538086106521},{"samplers":["default","default"],"bits":128,"start":23.03267050362478,"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":22915.77685546875,"target":false,"output":"(/ (+ (* (cube x) 2/3) (- 2 (* x x))) 2)","end":0.21237096582793585,"name":"NMSE Section 6.1 mentioned, A","status":"imp-start","end-est":9.979607349124048},{"samplers":["default"],"bits":128,"start":7.134029249566671,"link":"8-xx21","pinf":0,"ninf":0,"vars":["x"],"input":"(/ x (+ (sqr x) 1))","time":2167.652099609375,"target":0.11756713694245507,"output":"(/ x (+ (sqr x) 1))","end":7.134029249566671,"name":"x / (x^2 + 1)","status":"eq-start","end-est":6.4400673275723825},{"samplers":["default","default","default"],"bits":128,"start":29.19366725919403,"link":"9-simplefmatest","pinf":0,"ninf":0,"vars":["x","y","z"],"input":"(- (fma x y z) (+ 1 (+ (* x y) z)))","time":6909.39990234375,"target":15.780249720317974,"output":"(- (- (fma (/ -1 x) (/ -1 y) (/ -1 z)) (/ (/ 1 x) y)) 1)","end":7.074195882781845,"name":"simple fma test","status":"gt-target","end-est":15.801643195959603},{"samplers":["default"],"bits":128,"start":26.528733779416264,"link":"10-ln1x","pinf":0,"ninf":0,"vars":["x"],"input":"(log (+ 1 x))","time":4011.802978515625,"target":8.318253166418797,"output":"(+ (* (- (* 1/3 x) 1/2) (sqr x)) x)","end":0.1263422937539664,"name":"ln(1 + x)","status":"gt-target","end-est":10.232987507309016},{"samplers":["default","default","default"],"bits":128,"start":15.838026402315622,"link":"11-Thequadraticformular2","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":11830.454833984375,"target":9.466974653593553,"output":"(* (/ c 2) (/ 4 (+ (- b) (sqrt (- (sqr b) (* (* c a) 4))))))","end":13.795966310964987,"name":"The quadratic formula (r2)","status":"lt-target","end-est":13.285373558610017},{"samplers":["default","default","default"],"bits":128,"start":15.83247866283046,"link":"12-Thequadraticformular1","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* (* 4 a) c)))) (* 2 a))","time":14290.549072265625,"target":9.593888703585556,"output":"(* (/ 1 2) (/ (+ (- b) (sqrt (- (sqr b) (* a (* c 4))))) a))","end":15.835375281393674,"name":"The quadratic formula (r1)","status":"eq-start","end-est":15.471249202200504},{"samplers":["default"],"bits":128,"start":27.27507003320973,"link":"13-Kahansexpquotient","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- (exp x) 1) x)","time":3564.516845703125,"target":26.09349321887693,"output":"(/ (+ (* (+ 1/2 (* 1/6 x)) (sqr x)) x) x)","end":3.197453384448777,"name":"Kahan's exp quotient","status":"gt-target","end-est":11.08506579588623},{"samplers":["(uniform -14 -13)","(uniform -3 -2)","(uniform 3 3.5)","(uniform 12.5 13.5)"],"bits":128,"start":4.106442964233359,"link":"14-Expressionp6","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(* (+ a (+ b (+ c d))) 2)","time":8949.428955078125,"target":4.211544703235781,"output":"(* (+ a (+ (cube (cbrt (+ b c))) d)) 2)","end":3.441289044736052,"name":"Expression, p6","status":"eq-target","end-est":3.4760737794462777},{"samplers":["default","default","default","default"],"bits":384,"start":false,"link":"15-Expressionp14","pinf":false,"ninf":false,"vars":["a","b","c","d"],"input":"(* a (+ (+ b c) d))","time":13713.467041015625,"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":7933.548095703125,"target":false,"output":"#f","end":false,"name":"Expression 4, p15","status":"crash","end-est":false},{"samplers":["default"],"bits":128,"start":0.057625,"link":"17-Expression3p15","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (* x (* x x)) (* x x))","time":5646.140869140625,"target":0.0841580828133113,"output":"(+ (sqr x) (pow x 3))","end":0.054875,"name":"Expression 3, p15","status":"eq-target","end-est":0.0546875},{"samplers":["default"],"bits":128,"start":0.004625,"link":"18-Expression2p15","pinf":0,"ninf":0,"vars":["x"],"input":"(+ x (* x x))","time":5042.36279296875,"target":0.068875,"output":"(+ x (sqr x))","end":0.004625,"name":"Expression 2, p15","status":"eq-target","end-est":0.00390625},{"samplers":["(uniform 1 2)","(uniform 2 4)","(uniform 4 8)","(uniform 8 16)","(uniform 16 32)"],"bits":128,"start":0.4344415421939006,"link":"19-Expression1p15","pinf":0,"ninf":0,"vars":["a","b","c","d","e"],"input":"(+ (+ (+ (+ e d) c) b) a)","time":13519.9130859375,"target":0.276125,"output":"(+ (+ (+ (pow (+ e d) 1) c) b) a)","end":0.262375,"name":"Expression 1, p15","status":"eq-target","end-est":0.27734375},{"samplers":["default","default"],"bits":128,"start":0.030147922317186965,"link":"20-Differenceofsquares","pinf":0,"ninf":0,"vars":["a","b"],"input":"(- (sqr a) (sqr b))","time":1952.5439453125,"target":0.00775,"output":"(* (+ a b) (- a b))","end":0.00775,"name":"Difference of squares","status":"eq-target","end-est":0.00390625},{"samplers":["default","default"],"bits":128,"start":29.652029132071455,"link":"21-CompoundInterest","pinf":0,"ninf":0,"vars":["i","n"],"input":"(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))","time":33644.510986328125,"target":28.553674982472064,"output":"(+ (* (* n i) (+ (* 50/3 i) 50)) (* 100 n))","end":0.2233578922370484,"name":"Compound Interest","status":"gt-target","end-est":14.51663649551627},{"samplers":["default","default","default","default"],"bits":128,"start":12.610969019814059,"link":"22-Complexdivisionrealpart","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(/ (+ (* a c) (* b d)) (+ (sqr c) (sqr d)))","time":5603.083984375,"target":0.2234278342041158,"output":"(/ (+ (* a c) (* b d)) (sqr (sqrt (+ (sqr c) (sqr d)))))","end":12.58487170014364,"name":"Complex division, real part","status":"eq-start","end-est":13.338511680940515},{"samplers":["default","default","default","default"],"bits":128,"start":12.604588894530508,"link":"23-Complexdivisionimagpart","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(/ (- (* b c) (* a d)) (+ (sqr c) (sqr d)))","time":7537.75390625,"target":0.2137157995042725,"output":"(/ (- (* b c) (* a d)) (+ (sqr (fabs c)) (sqr (fabs d))))","end":8.125345476183774,"name":"Complex division, imag part","status":"lt-target","end-est":8.22879104904973},{"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":17978.736083984375,"target":false,"output":"#f","end":false,"name":"Area of a triangle","status":"crash","end-est":false}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}