{"bit_width":32,"date":1468938753,"note":"numerics","iterations":2,"flags":["rules:numerics","rules:arithmetic","rules:polynomials","rules:fractions","rules:exponents","rules:trigonometry","setup:simplify","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"],"bits":128,"start":0.051875,"link":"0-arccos","pinf":0,"ninf":0,"vars":["x"],"input":"(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))","time":6605.552978515625,"target":false,"output":"(* 2 (atan (sqrt (exp (- (log (- 1 x)) (log1p x))))))","end":0.04775,"name":"arccos","status":"ex-start","end-est":0.02734375},{"samplers":["default","default","default"],"bits":128,"start":6.022860951995282,"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":16337.109130859375,"target":false,"output":"(- (+ (/ 2 (* r r)) 3) (fma (log1p (expm1 (* (- 3 (* 2 v)) (/ 0.125 (- 1 v))))) (sqr (* w r)) 4.5))","end":0.6385990271230944,"name":"Rosa's TurbineBenchmark","status":"imp-start","end-est":0.669971257220265},{"samplers":["default","default"],"bits":128,"start":0.568596633487603,"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":25588.755126953125,"target":false,"output":"(+ (fma (+ (* (- (* (/ 4 (fma x1 x1 1)) (fma (* x1 3) x1 (- (* x2 2) x1))) 6) (sqr x1)) (/ (* (- (/ (fma (* x1 3) x1 (* x2 2)) (fma x1 x1 1)) (+ 3 (/ x1 (fma x1 x1 1)))) x1) (/ (/ (fma x1 x1 1) 2) (fma (* x1 3) x1 (- (* x2 2) x1))))) (fma x1 x1 1) (fma (/ (fma (* x1 3) x1 (- (* x2 2) x1)) (fma x1 x1 1)) (* x1 (* x1 3)) (cube x1))) (+ (+ x1 x1) (* (/ 3 (fma x1 x1 1)) (- (* x1 (* x1 3)) (fma x2 2 x1)))))","end":0.3143122115783841,"name":"Rosa's FloatVsDoubleBenchmark","status":"ex-start","end-est":0.33694928102870814},{"samplers":["default","default","default"],"bits":128,"start":8.520341802546978,"link":"3-RosasDopplerBench","pinf":0,"ninf":0,"vars":["u","v","t1"],"input":"(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))","time":6965.967041015625,"target":false,"output":"(* (* (/ (- t1) (+ t1 u)) v) (/ 1 (+ t1 u)))","end":0.5726992438477525,"name":"Rosa's DopplerBench","status":"imp-start","end-est":0.48275946774089146},{"samplers":["default"],"bits":128,"start":0.3876682512940026,"link":"4-RosasBenchmark","pinf":0,"ninf":0,"vars":["x"],"input":"(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))","time":3796.383056640625,"target":false,"output":"(- (* x 0.954929658551372) (* (cube (cbrt (* 0.12900613773279798 x))) (* x x)))","end":0.31542219310496844,"name":"Rosa's Benchmark","status":"ex-start","end-est":0.3472602447661041},{"samplers":["default","default"],"bits":128,"start":0.11892841410551688,"link":"5-Radioactiveexchangebetweentwosurfaces","pinf":0,"ninf":0,"vars":["x","y"],"input":"(- (pow x 4) (pow y 4))","time":6088.25,"target":false,"output":"(- (sqr (sqr (sqrt (sqrt (pow x 4))))) (pow y 4))","end":0.06202576232674948,"name":"Radioactive exchange between two surfaces","status":"ex-start","end-est":0.05859375},{"samplers":["default","default"],"bits":128,"start":7.208422399866562,"link":"6-NMSESection61mentionedB","pinf":0,"ninf":0,"vars":["a","b"],"input":"(* (* (/ PI 2) (/ 1 (- (sqr b) (sqr a)))) (- (/ 1 a) (/ 1 b)))","time":9300.157958984375,"target":false,"output":"(* (/ PI (+ a b)) (/ 1 (* 2 (* a b))))","end":0.29856240782629206,"name":"NMSE Section 6.1 mentioned, B","status":"imp-start","end-est":0.288105029305326},{"samplers":["default","default"],"bits":128,"start":24.85631405216837,"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":23609.52099609375,"target":false,"output":"1","end":0,"name":"NMSE Section 6.1 mentioned, A","status":"imp-start","end-est":9.814002717647128},{"samplers":["default"],"bits":128,"start":6.911457333196514,"link":"8-xx21","pinf":0,"ninf":0,"vars":["x"],"input":"(/ x (+ (sqr x) 1))","time":2576.70703125,"target":0.13889440323869057,"output":"(/ x (+ (sqr x) 1))","end":6.911457333196514,"name":"x / (x^2 + 1)","status":"eq-start","end-est":7.125972690190883},{"samplers":["default","default","default"],"bits":128,"start":19.86436833463951,"link":"9-simplefmatest","pinf":0,"ninf":0,"vars":["x","y","z"],"input":"(- (fma x y z) (+ 1 (+ (* x y) z)))","time":1050.489990234375,"target":0,"output":"(- 0 1)","end":0,"name":"simple fma test","status":"eq-target","end-est":0},{"samplers":["default"],"bits":128,"start":16.454135169623747,"link":"10-ln1x","pinf":0,"ninf":0,"vars":["x"],"input":"(log (+ 1 x))","time":1154.530029296875,"target":0.04025,"output":"(log1p x)","end":0.003375,"name":"ln(1 + x)","status":"eq-target","end-est":0},{"samplers":["default","default","default"],"bits":128,"start":15.94512973516033,"link":"11-Thequadraticformular2","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":13045.48681640625,"target":9.422105657755935,"output":"(* (/ c 2) (/ 4 (+ (- b) (sqrt (- (sqr b) (* (* c a) 4))))))","end":13.866281650000598,"name":"The quadratic formula (r2)","status":"lt-target","end-est":13.889188866521689},{"samplers":["default","default","default"],"bits":128,"start":15.946703872189707,"link":"12-Thequadraticformular1","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* (* 4 a) c)))) (* 2 a))","time":9945.251220703125,"target":9.439477743922927,"output":"(/ (/ (* (* 4 a) c) (- (- b) (sqrt (- (sqr b) (* (* 4 a) c))))) (* 2 a))","end":14.910083483253866,"name":"The quadratic formula (r1)","status":"lt-target","end-est":14.778920133221664},{"samplers":["default"],"bits":128,"start":16.842174785399393,"link":"13-Kahansexpquotient","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- (exp x) 1) x)","time":1737.9658203125,"target":15.604769557392963,"output":"(* (expm1 x) (/ 1 x))","end":0.19234382950874754,"name":"Kahan's exp quotient","status":"gt-target","end-est":0.25000000000524847},{"samplers":["(uniform -14 -13)","(uniform -3 -2)","(uniform 3 3.5)","(uniform 12.5 13.5)"],"bits":128,"start":4.093377145110761,"link":"14-Expressionp6","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(* (+ a (+ b (+ c d))) 2)","time":8740.239990234375,"target":4.2077266311574055,"output":"(* (+ a (+ (log (exp (+ b c))) d)) 2)","end":3.3850592113512734,"name":"Expression, p6","status":"eq-target","end-est":3.4650156767004825},{"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":14389.571044921875,"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":8149.31982421875,"target":false,"output":"#f","end":false,"name":"Expression 4, p15","status":"crash","end-est":false},{"samplers":["default"],"bits":128,"start":0.058625,"link":"17-Expression3p15","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (* x (* x x)) (* x x))","time":4653.032958984375,"target":0.0934080828133113,"output":"(* x (fma x x x))","end":0.053375,"name":"Expression 3, p15","status":"eq-target","end-est":0.046875},{"samplers":["default"],"bits":128,"start":0.004875,"link":"18-Expression2p15","pinf":0,"ninf":0,"vars":["x"],"input":"(+ x (* x x))","time":3693.279052734375,"target":0.0775,"output":"(fma x x x)","end":0,"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":0.4203189859449824,"link":"19-Expression1p15","pinf":0,"ninf":0,"vars":["a","b","c","d","e"],"input":"(+ (+ (+ (+ e d) c) b) a)","time":5675.391845703125,"target":0.272,"output":"(+ (+ (+ (log1p (expm1 (+ e d))) c) b) a)","end":0.274,"name":"Expression 1, p15","status":"eq-target","end-est":0.3046875},{"samplers":["default","default"],"bits":128,"start":0.03029055429154849,"link":"20-Differenceofsquares","pinf":0,"ninf":0,"vars":["a","b"],"input":"(- (sqr a) (sqr b))","time":2383.08203125,"target":0.00775,"output":"(* (+ a b) (- a b))","end":0.00775,"name":"Difference of squares","status":"eq-target","end-est":0},{"samplers":["default","default"],"bits":128,"start":22.60156954777393,"link":"21-CompoundInterest","pinf":0,"ninf":0,"vars":["i","n"],"input":"(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))","time":7761.5361328125,"target":20.579201136025674,"output":"(* 100 (/ (expm1 (* (expm1 (log1p (log1p (/ i n)))) n)) (/ i n)))","end":5.201756370261391,"name":"Compound Interest","status":"gt-target","end-est":6.137732291316323},{"samplers":["default","default","default","default"],"bits":128,"start":12.568175565112346,"link":"22-Complexdivisionrealpart","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(/ (+ (* a c) (* b d)) (+ (sqr c) (sqr d)))","time":4446.220947265625,"target":0.22453598053104068,"output":"(+ (/ (* c a) (sqr (hypot c d))) (/ (* b d) (sqr (hypot c d))))","end":8.044130989617296,"name":"Complex division, real part","status":"lt-target","end-est":9.176984984649085},{"samplers":["default","default","default","default"],"bits":128,"start":12.834682383536682,"link":"23-Complexdivisionimagpart","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(/ (- (* b c) (* a d)) (+ (sqr c) (sqr d)))","time":4917.159912109375,"target":0.23867570642042094,"output":"(/ (- (* b c) (* a d)) (sqr (hypot c d)))","end":8.206564429491927,"name":"Complex division, imag part","status":"lt-target","end-est":9.654478701087218},{"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":17901.623046875,"target":false,"output":"#f","end":false,"name":"Area of a triangle","status":"crash","end-est":false}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}