{"bit_width":64,"date":1470912020,"note":"numerics","iterations":2,"flags":["rules:numerics","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":"#(1066149172 3462179920 3756494053 4279790727 1233554805 3521179209)","points":256,"tests":[{"samplers":["default"],"bits":128,"start":0.0145,"link":"0-arccos","pinf":0,"ninf":0,"vars":["x"],"input":"(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))","time":4143.176025390625,"target":false,"output":"(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))","end":0.0145,"name":"arccos","status":"ex-start","end-est":0.0078125},{"samplers":["default","default","default"],"bits":128,"start":11.870811475275021,"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":15662.416015625,"target":false,"output":"(- (+ (/ 2 (* r r)) 3) (+ (* (* (* (- 3 (* 2 v)) (/ 0.125 (- 1 v))) (* w r)) (* w r)) 4.5))","end":0.35419942307341057,"name":"Rosa's TurbineBenchmark","status":"imp-start","end-est":0.32849506837909415},{"samplers":["default","default"],"bits":128,"start":0.5202239574757067,"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":38416.806884765625,"target":false,"output":"(+ (fma (/ 3 (fma x1 x1 1)) (- (* 3 (* x1 x1)) (fma x2 2 x1)) (+ x1 x1)) (fma (fma (- (* (fma (* 3 x1) x1 (- (* x2 2) x1)) (/ 4 (fma x1 x1 1))) 6) (* x1 x1) (/ (- (fma (fma (* 3 x1) x1 (* x2 2)) 3 (/ (* x1 x1) (fma x1 x1 1))) (fma (fma x1 x1 1) 9 (* (/ x1 (fma x1 x1 1)) (fma (* 3 x1) x1 (* x2 2))))) (/ (/ (/ (fma x1 x1 1) 2) (fma (* 3 x1) x1 (- (* x2 2) x1))) (/ (/ x1 (fma x1 x1 1)) (- 3 (/ x1 (fma x1 x1 1))))))) (fma x1 x1 1) (fma (/ (fma (* 3 x1) x1 (- (* x2 2) x1)) (fma x1 x1 1)) (* 3 (* x1 x1)) (cube x1))))","end":0.3395013100579263,"name":"Rosa's FloatVsDoubleBenchmark","status":"ex-start","end-est":0.2979088379159781},{"samplers":["default","default","default"],"bits":128,"start":17.95011065145471,"link":"3-RosasDopplerBench","pinf":0,"ninf":0,"vars":["u","v","t1"],"input":"(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))","time":7744.56787109375,"target":false,"output":"(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))","end":1.3439211414687824,"name":"Rosa's DopplerBench","status":"imp-start","end-est":1.0207078945622203},{"samplers":["default"],"bits":128,"start":0.1529470891004505,"link":"4-RosasBenchmark","pinf":0,"ninf":0,"vars":["x"],"input":"(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))","time":2863.974853515625,"target":false,"output":"(- (* x 0.954929658551372) (* 0.12900613773279798 (pow x 3)))","end":0.12922772816268008,"name":"Rosa's Benchmark","status":"ex-start","end-est":0.05859375},{"samplers":["default","default"],"bits":128,"start":0.0015,"link":"5-Radioactiveexchangebetweentwosurfaces","pinf":0,"ninf":0,"vars":["x","y"],"input":"(- (pow x 4) (pow y 4))","time":3693.3310546875,"target":false,"output":"(- (pow x 4) (pow y 4))","end":0.0015,"name":"Radioactive exchange between two surfaces","status":"ex-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":14.373603230206191,"link":"6-NMSESection61mentionedB","pinf":0,"ninf":0,"vars":["a","b"],"input":"(* (* (/ PI 2) (/ 1 (- (sqr b) (sqr a)))) (- (/ 1 a) (/ 1 b)))","time":14106.22998046875,"target":false,"output":"(/ (/ PI (+ a b)) (* 2 (* a b)))","end":0.23838477500432678,"name":"NMSE Section 6.1 mentioned, B","status":"imp-start","end-est":0.2780075195368841},{"samplers":["default","default"],"bits":128,"start":43.905313251597484,"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":30234.1318359375,"target":false,"output":"(if (<= x 1900404.342977934) 1 (/ (- (cube (* (cbrt (+ 1 (/ 1 eps))) (cbrt (exp (- (* (- 1 eps) x)))))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))) 2))","end":0,"name":"NMSE Section 6.1 mentioned, A","status":"imp-start","end-est":1.830808075385559},{"samplers":["default"],"bits":128,"start":15.068901192125324,"link":"8-xx21","pinf":0,"ninf":0,"vars":["x"],"input":"(/ x (+ (sqr x) 1))","time":3695.846923828125,"target":0.09457312031259014,"output":"(if (<= x -4.3616983017752945e+30) (- (/ 1 (pow x 5)) (- (/ 1 (cube x)) (/ 1 x))) (if (<= x 18533971.955403153) (/ x (+ (sqr x) 1)) (- (/ 1 (pow x 5)) (- (/ 1 (cube x)) (/ 1 x)))))","end":0.012875,"name":"x / (x^2 + 1)","status":"eq-target","end-est":0.0078125},{"samplers":["default","default","default"],"bits":128,"start":44.82608394101716,"link":"9-simplefmatest","pinf":0,"ninf":0,"vars":["x","y","z"],"input":"(- (fma x y z) (+ 1 (+ (* x y) z)))","time":3316.2900390625,"target":0,"output":"(- 0 1)","end":0,"name":"simple fma test","status":"eq-target","end-est":0},{"samplers":["default"],"bits":128,"start":39.151989359593735,"link":"10-ln1x","pinf":0,"ninf":0,"vars":["x"],"input":"(log (+ 1 x))","time":3158.8779296875,"target":0.18571846734780734,"output":"(log1p x)","end":0.000375,"name":"ln(1 + x)","status":"eq-target","end-est":0},{"samplers":["default","default","default"],"bits":128,"start":34.7094778494046,"link":"11-Thequadraticformular2","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":20884.84619140625,"target":22.149569716994208,"output":"(if (<= b -2.131991496773005e+35) (* (/ c b) (/ -2 2)) (if (<= b -1.066499756724946e-123) (/ (/ (* c (* 4 a)) (+ (- b) (sqrt (- (sqr b) (* 4 (* a c)))))) (* 2 a)) (if (<= b 7.918421860193221e+145) (/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a)) (- (/ c b) (/ b a)))))","end":6.840757582447251,"name":"The quadratic formula (r2)","status":"gt-target","end-est":7.596107709444518},{"samplers":["default","default","default"],"bits":128,"start":35.336165821482915,"link":"12-Thequadraticformular1","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* (* 4 a) c)))) (* 2 a))","time":22329.89111328125,"target":23.632360176341518,"output":"(if (<= b -431232863.47265303) (- (/ c b) (/ b a)) (if (<= b 1.4445095675228828e-303) (/ (+ (- b) (sqrt (- (sqr b) (* (* 4 a) c)))) (* 2 a)) (if (<= b 1.3336442321324732e+29) (/ (/ (* (* 4 a) c) (- (- b) (sqrt (- (sqr b) (* (* 4 a) c))))) (* 2 a)) (/ (* (/ 4 2) c) (- (fma (* a 2) (/ c b) (- b)) b)))))","end":6.450625385562198,"name":"The quadratic formula (r1)","status":"gt-target","end-est":8.498778503861143},{"samplers":["default"],"bits":128,"start":39.39444022388396,"link":"13-Kahansexpquotient","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- (exp x) 1) x)","time":4436.950927734375,"target":38.57668805532282,"output":"(/ (expm1 x) x)","end":0.011125,"name":"Kahan's exp quotient","status":"gt-target","end-est":0},{"samplers":["(uniform -14 -13)","(uniform -3 -2)","(uniform 3 3.5)","(uniform 12.5 13.5)"],"bits":128,"start":3.648216188898087,"link":"14-Expressionp6","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(* (+ a (+ b (+ c d))) 2)","time":6456.52099609375,"target":3.8310713870661095,"output":"(* (log1p (expm1 (+ a (+ (+ b c) d)))) 2)","end":2.7420749111641234,"name":"Expression, p6","status":"gt-target","end-est":2.7608718159223073},{"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":14919.453857421875,"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":8035.39208984375,"target":false,"output":"#f","end":false,"name":"Expression 4, p15","status":"crash","end-est":false},{"samplers":["default"],"bits":128,"start":0.018,"link":"17-Expression3p15","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (* x (* x x)) (* x x))","time":4918.660888671875,"target":0.02639624062518029,"output":"(fma (sqr x) x (sqr x))","end":0.017875,"name":"Expression 3, p15","status":"eq-target","end-est":0.01171875},{"samplers":["default"],"bits":128,"start":0.000875,"link":"18-Expression2p15","pinf":0,"ninf":0,"vars":["x"],"input":"(+ x (* x x))","time":3962.615966796875,"target":0.023125,"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":0.4064697375050483,"link":"19-Expression1p15","pinf":0,"ninf":0,"vars":["a","b","c","d","e"],"input":"(+ (+ (+ (+ e d) c) b) a)","time":6667.26220703125,"target":0.18675,"output":"(+ (log (exp (+ (+ d b) (+ c e)))) a)","end":0.3240424812503606,"name":"Expression 1, p15","status":"eq-target","end-est":0.3125},{"samplers":["default","default"],"bits":128,"start":0.005924039677847346,"link":"20-Differenceofsquares","pinf":0,"ninf":0,"vars":["a","b"],"input":"(- (sqr a) (sqr b))","time":2728.385986328125,"target":0.00025,"output":"(- (sqr a) (sqr b))","end":0.005924039677847346,"name":"Difference of squares","status":"eq-target","end-est":0},{"samplers":["default","default"],"bits":128,"start":53.76480853388061,"link":"21-CompoundInterest","pinf":0,"ninf":0,"vars":["i","n"],"input":"(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))","time":23727.447021484375,"target":51.40489611897848,"output":"(if (<= i -6.479751178580368e-13) (* 100 (/ (- (exp (* (log1p (/ i n)) n)) 1) (/ i n))) (if (<= i -1.9732740713568284e-223) (* 100 (/ (* (fma i (* 1/2 i) i) n) i)) (if (<= i 48071161730.91927) (* (* (fma i (* 1/2 i) i) (/ 100 i)) n) (if (<= i 3.211660408074495e+117) (* 100 (/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n))) (/ (expm1 (/ (- (log n) (log i)) n)) (/ (/ i 100) n))))))","end":4.658175557148936,"name":"Compound Interest","status":"gt-target","end-est":10.064310924677919},{"samplers":["default","default","default","default"],"bits":128,"start":25.540039274053324,"link":"22-Complexdivisionrealpart","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(/ (+ (* a c) (* b d)) (+ (sqr c) (sqr d)))","time":8505.748046875,"target":0.4577042590093747,"output":"(if (<= b -9.364561599243466e+17) (+ (/ (* b d) (fma c c (sqr d))) (/ (* c a) (fma c c (sqr d)))) (if (<= b -5.047869208437734e-09) (sqr (/ (sqrt (fma c a (* d b))) (hypot c d))) (+ (/ (* b d) (fma c c (sqr d))) (/ (* c a) (fma c c (sqr d))))))","end":25.427824375188642,"name":"Complex division, real part","status":"eq-start","end-est":25.405224272091775},{"samplers":["default","default","default","default"],"bits":128,"start":25.7616376234616,"link":"23-Complexdivisionimagpart","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(/ (- (* b c) (* a d)) (+ (sqr c) (sqr d)))","time":7725.610107421875,"target":0.41554367815687815,"output":"(/ (- (* b c) (* a d)) (+ (sqr c) (sqr d)))","end":25.7616376234616,"name":"Complex division, imag part","status":"eq-start","end-est":25.09769107892407},{"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":17371.8310546875,"target":false,"output":"#f","end":false,"name":"Area of a triangle","status":"crash","end-est":false}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}