{"bit_width":32,"date":1471183246,"note":"numerics","iterations":3,"flags":["rules:numerics","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":"#(1066149172 3462179920 3756494053 4279790727 1233554805 3521179209)","points":256,"tests":[{"samplers":["default"],"bits":128,"start":0.054125,"link":"0-arccos","pinf":0,"ninf":0,"vars":["x"],"input":"(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))","time":76131.34106445312,"target":false,"output":"(* 2 (atan (sqrt (/ (- (pow 1 3) (pow x 3)) (fma (fma x x x) (+ 1 x) (+ 1 x))))))","end":0.056698120312590146,"name":"arccos","status":"ex-start","end-est":0.05859375},{"samplers":["default","default","default"],"bits":128,"start":5.928289922331584,"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":19839.35205078125,"target":false,"output":"(- (+ (/ 2 (* r r)) 3) (+ (sqr (* (* (sqrt (* (- 3 (* 2 v)) (/ 0.125 (- 1 v)))) w) r)) 4.5))","end":0.4605616979253223,"name":"Rosa's TurbineBenchmark","status":"imp-start","end-est":0.35859094383407},{"samplers":["default","default"],"bits":128,"start":0.5562157835197323,"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":35373.72998046875,"target":false,"output":"(+ (- (fma 9 (/ (* x1 x1) (fma x1 x1 1)) (* 2 x1)) (/ (fma x2 2 x1) (/ (fma x1 x1 1) 3))) (fma (fma (- (/ (fma (* 3 x1) x1 (- (* x2 2) x1)) (/ (fma x1 x1 1) 4)) 6) (* x1 x1) (/ (- (/ (fma (* 3 x1) x1 (* x2 2)) (fma x1 x1 1)) (+ (/ x1 (fma x1 x1 1)) 3)) (/ (/ (fma x1 x1 1) 2) (* x1 (fma (* 3 x1) x1 (- (* x2 2) x1)))))) (fma x1 x1 1) (fma (/ (fma (* 3 x1) x1 (- (* x2 2) x1)) (fma x1 x1 1)) (* (* 3 x1) x1) (cube x1))))","end":0.35338561908632365,"name":"Rosa's FloatVsDoubleBenchmark","status":"ex-start","end-est":0.3125763672213042},{"samplers":["default","default","default"],"bits":128,"start":8.548058222379655,"link":"3-RosasDopplerBench","pinf":0,"ninf":0,"vars":["u","v","t1"],"input":"(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))","time":7808.8291015625,"target":false,"output":"(/ (* (/ (- t1) (+ t1 u)) v) (+ t1 u))","end":0.49728064759033325,"name":"Rosa's DopplerBench","status":"imp-start","end-est":0.419406043248678},{"samplers":["default"],"bits":128,"start":0.3657349808724816,"link":"4-RosasBenchmark","pinf":0,"ninf":0,"vars":["x"],"input":"(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))","time":5839.4912109375,"target":false,"output":"(- (* x 0.954929658551372) (* (* (pow (* 0.12900613773279798 x) 1) x) x))","end":0.22679312431928925,"name":"Rosa's Benchmark","status":"ex-start","end-est":0.18587875976844204},{"samplers":["default","default"],"bits":128,"start":0.11513912365120053,"link":"5-Radioactiveexchangebetweentwosurfaces","pinf":0,"ninf":0,"vars":["x","y"],"input":"(- (pow x 4) (pow y 4))","time":6690.43798828125,"target":false,"output":"(- (pow x 4) (sqr (sqr (sqrt (sqrt (pow y 4))))))","end":0.05912212644251067,"name":"Radioactive exchange between two surfaces","status":"ex-start","end-est":0.0390625},{"samplers":["default","default"],"bits":128,"start":7.371145281382924,"link":"6-NMSESection61mentionedB","pinf":0,"ninf":0,"vars":["a","b"],"input":"(* (* (/ PI 2) (/ 1 (- (sqr b) (sqr a)))) (- (/ 1 a) (/ 1 b)))","time":13004.333984375,"target":false,"output":"(/ (* PI (/ 1 (+ a b))) (* 2 (* a b)))","end":0.29627237032701315,"name":"NMSE Section 6.1 mentioned, B","status":"imp-start","end-est":0.2754288086106521},{"samplers":["default","default"],"bits":128,"start":25.30875090762464,"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":24722.718994140625,"target":false,"output":"1","end":0,"name":"NMSE Section 6.1 mentioned, A","status":"imp-start","end-est":8.14029279602203},{"samplers":["default"],"bits":128,"start":6.988534210668103,"link":"8-xx21","pinf":0,"ninf":0,"vars":["x"],"input":"(/ x (+ (sqr x) 1))","time":2762.880859375,"target":0.12980015089556163,"output":"(/ x (+ (sqr x) 1))","end":6.988534210668103,"name":"x / (x^2 + 1)","status":"eq-start","end-est":6.305710843201668},{"samplers":["default","default","default"],"bits":128,"start":19.808568723185168,"link":"9-simplefmatest","pinf":0,"ninf":0,"vars":["x","y","z"],"input":"(- (fma x y z) (+ 1 (+ (* x y) z)))","time":990.9609375,"target":0,"output":"(- 0 1)","end":0,"name":"simple fma test","status":"eq-target","end-est":0},{"samplers":["default"],"bits":128,"start":16.462547453009655,"link":"10-ln1x","pinf":0,"ninf":0,"vars":["x"],"input":"(log (+ 1 x))","time":1089.389892578125,"target":0.03825,"output":"(log1p x)","end":0.00425,"name":"ln(1 + x)","status":"eq-target","end-est":0},{"samplers":["default","default","default"],"bits":128,"start":16.074915086938695,"link":"11-Thequadraticformular2","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":13844.327880859375,"target":9.41288534149792,"output":"(* (/ c 2) (/ 4 (+ (- b) (sqrt (- (sqr b) (* (* c a) 4))))))","end":13.891698914124333,"name":"The quadratic formula (r2)","status":"lt-target","end-est":14.116539842299016},{"samplers":["default","default","default"],"bits":128,"start":15.948430714242907,"link":"12-Thequadraticformular1","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* (* 4 a) c)))) (* 2 a))","time":13432.65185546875,"target":9.563879751586855,"output":"(/ (/ (* (* 4 a) c) (- (- b) (sqrt (- (sqr b) (* (* 4 a) c))))) (* 2 a))","end":15.144675420873343,"name":"The quadratic formula (r1)","status":"eq-start","end-est":14.383741573259663},{"samplers":["default"],"bits":128,"start":17.02777076844387,"link":"13-Kahansexpquotient","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- (exp x) 1) x)","time":1873.615966796875,"target":15.707978229196282,"output":"(* (expm1 x) (/ 1 x))","end":0.18323163876596138,"name":"Kahan's exp quotient","status":"gt-target","end-est":0.32639902223415096},{"samplers":["(uniform -14 -13)","(uniform -3 -2)","(uniform 3 3.5)","(uniform 12.5 13.5)"],"bits":128,"start":4.08053908901028,"link":"14-Expressionp6","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(* (+ a (+ b (+ c d))) 2)","time":14284.670166015625,"target":4.219699479543704,"output":"(* (+ a (+ (cbrt (/ (cube (- (sqr b) (sqr c))) (cube (- b c)))) d)) 2)","end":3.4054370741905338,"name":"Expression, p6","status":"eq-target","end-est":3.4076848660443293},{"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":14038.776123046875,"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":8025.176025390625,"target":false,"output":"#f","end":false,"name":"Expression 4, p15","status":"crash","end-est":false},{"samplers":["default"],"bits":128,"start":0.063,"link":"17-Expression3p15","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (* x (* x x)) (* x x))","time":4830.382080078125,"target":0.09017932343849161,"output":"(fma (sqr x) x (sqr x))","end":0.0615,"name":"Expression 3, p15","status":"eq-target","end-est":0.03125},{"samplers":["default"],"bits":128,"start":0.005375,"link":"18-Expression2p15","pinf":0,"ninf":0,"vars":["x"],"input":"(+ x (* x x))","time":3697.328125,"target":0.0755,"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":0.42106654219390055,"link":"19-Expression1p15","pinf":0,"ninf":0,"vars":["a","b","c","d","e"],"input":"(+ (+ (+ (+ e d) c) b) a)","time":11140.51806640625,"target":0.273875,"output":"(+ (+ (+ e d) c) (+ b a))","end":0.3553161656266226,"name":"Expression 1, p15","status":"eq-target","end-est":0.30078125},{"samplers":["default","default"],"bits":128,"start":0.03324386655643692,"link":"20-Differenceofsquares","pinf":0,"ninf":0,"vars":["a","b"],"input":"(- (sqr a) (sqr b))","time":3231.660888671875,"target":0.00825,"output":"(* (+ a b) (- a b))","end":0.00825,"name":"Difference of squares","status":"eq-target","end-est":0.0078125},{"samplers":["default","default"],"bits":128,"start":22.877710073242202,"link":"21-CompoundInterest","pinf":0,"ninf":0,"vars":["i","n"],"input":"(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))","time":10977.065185546875,"target":21.03539015402615,"output":"(* 100 (/ (expm1 (* (log1p (/ i n)) n)) (/ i n)))","end":5.439990144801789,"name":"Compound Interest","status":"gt-target","end-est":6.267052335897033},{"samplers":["default","default","default","default"],"bits":128,"start":12.398840391498398,"link":"22-Complexdivisionrealpart","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(/ (+ (* a c) (* b d)) (+ (sqr c) (sqr d)))","time":7530.52392578125,"target":0.2277721544653914,"output":"(cube (cbrt (/ (+ (* a c) (* b d)) (+ (sqr (fabs c)) (sqr (fabs d))))))","end":8.229473231228235,"name":"Complex division, real part","status":"lt-target","end-est":6.6894562748068855},{"samplers":["default","default","default","default"],"bits":128,"start":12.401391324053284,"link":"23-Complexdivisionimagpart","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(/ (- (* b c) (* a d)) (+ (sqr c) (sqr d)))","time":8366.56103515625,"target":0.24699220330766522,"output":"(- (* (/ b (hypot c d)) (/ c (hypot c d))) (* (/ a (hypot c d)) (/ d (hypot c d))))","end":0.041084962500721155,"name":"Complex division, imag part","status":"eq-target","end-est":0.053066259768442016},{"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":17163.906982421875,"target":false,"output":"#f","end":false,"name":"Area of a triangle","status":"crash","end-est":false}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}