{"bit_width":64,"date":1468143828,"note":"numerics","iterations":2,"flags":["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":"#(1065639804 936413623 2655205282 2235462195 918319548 1069991914)","points":256,"tests":[{"samplers":["default"],"bits":128,"start":0.0135,"link":"0-arccos","pinf":0,"ninf":0,"vars":["x"],"input":"(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))","time":6977.927001953125,"target":false,"output":"(* 2 (atan (sqrt (cbrt (cube (/ (- 1 x) (+ 1 x)))))))","end":0.016073120312590145,"name":"arccos","status":"ex-start","end-est":0.0078125},{"samplers":["default","default","default"],"bits":128,"start":12.511853388810309,"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":14592.930908203125,"target":false,"output":"(- (+ 3 (- (/ (/ 2 r) r) 4.5)) (/ (* (sqr (* r w)) 0.125) (/ (- 1 v) (- 3 (* 2 v)))))","end":0.40014197527351497,"name":"Rosa's TurbineBenchmark","status":"imp-start","end-est":0.31773378907376804},{"samplers":["default","default"],"bits":128,"start":0.5252225546452101,"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":36776.136962890625,"target":false,"output":"(+ (+ (+ (/ (- (* 3 (sqr x1)) (+ (* x2 2) x1)) (/ (+ (sqr x1) 1) 3)) (+ (+ x1 x1) (cube x1))) (/ (+ (* (sqr x1) (- (* x2 6) (* 3 x1))) (* (pow x1 4) 9)) (+ (sqr x1) 1))) (* (+ (sqr x1) 1) (+ (* (/ (+ (- (* x2 2) x1) (* 3 (sqr x1))) (/ (+ (sqr x1) 1) (* 2 x1))) (- (/ (+ (- (* x2 2) x1) (* 3 (sqr x1))) (+ (sqr x1) 1)) 3)) (* (- (/ (+ (- (* x2 2) x1) (* 3 (sqr x1))) (/ (+ (sqr x1) 1) 4)) 6) (sqr x1)))))","end":0.5698570561224625,"name":"Rosa's FloatVsDoubleBenchmark","status":"ex-start","end-est":0.5554276367581883},{"samplers":["default","default","default"],"bits":128,"start":18.29811473702705,"link":"3-RosasDopplerBench","pinf":0,"ninf":0,"vars":["u","v","t1"],"input":"(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))","time":6848.305908203125,"target":false,"output":"(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))","end":1.1791854385212661,"name":"Rosa's DopplerBench","status":"imp-start","end-est":1.1785204687527457},{"samplers":["default"],"bits":128,"start":0.12375080969262983,"link":"4-RosasBenchmark","pinf":0,"ninf":0,"vars":["x"],"input":"(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))","time":3714.738037109375,"target":false,"output":"(- (* x 0.954929658551372) (* 0.12900613773279798 (pow x 3)))","end":0.10540644875485938,"name":"Rosa's Benchmark","status":"ex-start","end-est":0.08431625976844201},{"samplers":["default","default"],"bits":128,"start":0.0025731203125901442,"link":"5-Radioactiveexchangebetweentwosurfaces","pinf":0,"ninf":0,"vars":["x","y"],"input":"(- (pow x 4) (pow y 4))","time":4547.864013671875,"target":false,"output":"(- (pow x 4) (pow y 4))","end":0.0025731203125901442,"name":"Radioactive exchange between two surfaces","status":"ex-start","end-est":0.00390625},{"samplers":["default","default"],"bits":128,"start":14.692564282982865,"link":"6-NMSESection61mentionedB","pinf":0,"ninf":0,"vars":["a","b"],"input":"(* (* (/ PI 2) (/ 1 (- (sqr b) (sqr a)))) (- (/ 1 a) (/ 1 b)))","time":12382.98095703125,"target":false,"output":"(/ (/ 1 (/ (+ a b) PI)) (* 2 (* a b)))","end":0.28353383594786646,"name":"NMSE Section 6.1 mentioned, B","status":"imp-start","end-est":0.281913769536884},{"samplers":["default","default"],"bits":128,"start":43.75018664074974,"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":27070.445068359375,"target":false,"output":"(if (<= x 18073.65682704277) 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":1.0443955636384068},{"samplers":["default"],"bits":128,"start":15.230062728085569,"link":"8-xx21","pinf":0,"ninf":0,"vars":["x"],"input":"(/ x (+ (sqr x) 1))","time":3632.5830078125,"target":0.09209436093777043,"output":"(if (<= x -3991.8305494421847) (- (/ 1 (pow x 5)) (- (/ 1 (cube x)) (/ 1 x))) (if (<= x 36050.53017192879) (* x (/ 1 (+ (sqr x) 1))) (- (/ 1 (pow x 5)) (- (/ 1 (cube x)) (/ 1 x)))))","end":0.008625,"name":"x / (x^2 + 1)","status":"eq-target","end-est":0.01171875},{"samplers":["default","default","default"],"bits":128,"start":44.777184495126875,"link":"9-simplefmatest","pinf":0,"ninf":0,"vars":["x","y","z"],"input":"(- (fma x y z) (+ 1 (+ (* x y) z)))","time":7057.87109375,"target":0,"output":"(cube (cbrt (- (fma x y z) (+ 1 (+ (* x y) z)))))","end":44.77448637464231,"name":"simple fma test","status":"eq-start","end-est":42.60303095234554},{"samplers":["default"],"bits":128,"start":41.6037261134631,"link":"10-ln1x","pinf":0,"ninf":0,"vars":["x"],"input":"(log (+ 1 x))","time":5650.781982421875,"target":6.36851062525691,"output":"(if (<= x 0.00048645315118439684) (+ (* (- (* 1/3 x) 1/2) (sqr x)) x) (log (+ 1 x)))","end":0.05558014806848444,"name":"ln(1 + x)","status":"gt-target","end-est":0.300262290819862},{"samplers":["default","default","default"],"bits":128,"start":38.06156710364083,"link":"11-Thequadraticformular2","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":22351.218017578125,"target":25.910452465098658,"output":"(if (<= b -5.161999432096643e+18) (* (/ (/ c (/ 2 4)) (- (* (/ c b) a) b)) (/ 1 2)) (if (<= b -1.4884263778992505e-139) (/ (/ (* c (* 4 a)) (+ (- b) (sqrt (- (sqr b) (* 4 (* a c)))))) (* 2 a)) (if (<= b -3.31592532247251e-196) (* (/ (/ c (/ 2 4)) (- (* (/ c b) a) b)) (/ 1 2)) (if (<= b 2.4608343160951844e+34) (/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a)) (- (/ c b) (/ b a))))))","end":7.208846009912792,"name":"The quadratic formula (r2)","status":"gt-target","end-est":6.780642344340048},{"samplers":["default","default","default"],"bits":128,"start":34.88014543096501,"link":"12-Thequadraticformular1","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* (* 4 a) c)))) (* 2 a))","time":19850.533935546875,"target":22.43697561474639,"output":"(if (<= b -1.2339538201069979e+148) (/ (- b) a) (if (<= b 4.6117267249984834e-185) (/ (+ (- b) (sqrt (- (sqr b) (* (* 4 a) c)))) (* 2 a)) (if (<= b 2.4608343160951844e+34) (/ (/ (* (* 4 a) c) (- (- b) (sqrt (- (sqr b) (* (* 4 a) c))))) (* 2 a)) (* (/ c b) (/ -2 2)))))","end":7.150892493527147,"name":"The quadratic formula (r1)","status":"gt-target","end-est":6.716907778445224},{"samplers":["default"],"bits":128,"start":43.27680635866945,"link":"13-Kahansexpquotient","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- (exp x) 1) x)","time":6757.6259765625,"target":42.59663007417093,"output":"(if (<= x -6.349368961717618e-07) (/ (/ (- (cube (exp x)) 1) (+ (+ (exp x) 1) (exp (+ x x)))) x) (+ (* 1/6 (sqr x)) (+ 1 (* 1/2 x))))","end":0.10927602465548425,"name":"Kahan's exp quotient","status":"gt-target","end-est":0.16817600388637993},{"samplers":["(uniform -14 -13)","(uniform -3 -2)","(uniform 3 3.5)","(uniform 12.5 13.5)"],"bits":128,"start":3.7119587582324374,"link":"14-Expressionp6","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(* (+ a (+ b (+ c d))) 2)","time":5861.39697265625,"target":3.8397860238760075,"output":"(* (+ a (+ (+ b c) d)) 2)","end":2.769220822622857,"name":"Expression, p6","status":"gt-target","end-est":2.6498700877689108},{"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":13892.037841796875,"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":7740.240966796875,"target":false,"output":"#f","end":false,"name":"Expression 4, p15","status":"crash","end-est":false},{"samplers":["default"],"bits":128,"start":0.01275,"link":"17-Expression3p15","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (* x (* x x)) (* x x))","time":5912.7431640625,"target":0.02039624062518029,"output":"(+ (sqr x) (pow x 3))","end":0.01275,"name":"Expression 3, p15","status":"eq-target","end-est":0.01953125},{"samplers":["default"],"bits":128,"start":0.00075,"link":"18-Expression2p15","pinf":0,"ninf":0,"vars":["x"],"input":"(+ x (* x x))","time":3791.695068359375,"target":0.01775,"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":0.405082895316917,"link":"19-Expression1p15","pinf":0,"ninf":0,"vars":["a","b","c","d","e"],"input":"(+ (+ (+ (+ e d) c) b) a)","time":8182.303955078125,"target":0.1975,"output":"(+ (+ (+ e d) c) (+ b a))","end":0.34136560156295076,"name":"Expression 1, p15","status":"eq-target","end-est":0.296875},{"samplers":["default","default"],"bits":128,"start":0.006073120312590145,"link":"20-Differenceofsquares","pinf":0,"ninf":0,"vars":["a","b"],"input":"(- (sqr a) (sqr b))","time":3558.884033203125,"target":0.00075,"output":"(- (sqr a) (sqr b))","end":0.006073120312590145,"name":"Difference of squares","status":"eq-target","end-est":0.00390625},{"samplers":["default","default"],"bits":128,"start":51.96374147367467,"link":"21-CompoundInterest","pinf":0,"ninf":0,"vars":["i","n"],"input":"(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))","time":20770.203125,"target":51.260077234397436,"output":"(if (<= i -0.09197678863246804) (* 100 (/ (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (- (sqrt (pow (+ 1 (/ i n)) n)) 1)) (/ i n))) (if (<= i 18073.65682704277) (* (+ (* i 50) 100) n) (if (<= i 1.4768914403135694e+243) (* 100 (/ (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (- (sqrt (pow (+ 1 (/ i n)) n)) 1)) (/ i n))) (* (+ (* 1/2 i) 1) (cube (/ (cbrt (* i 100)) (cbrt (/ i n))))))))","end":10.688880486015291,"name":"Compound Interest","status":"gt-target","end-est":15.397845781964223},{"samplers":["default","default","default","default"],"bits":128,"start":26.19967890267938,"link":"22-Complexdivisionrealpart","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(/ (+ (* a c) (* b d)) (+ (sqr c) (sqr d)))","time":8049.306884765625,"target":0.5245993607910844,"output":"(* (+ (* a c) (* b d)) (/ 1 (+ (sqr c) (sqr d))))","end":26.394809145091433,"name":"Complex division, real part","status":"eq-start","end-est":26.812000421429946},{"samplers":["default","default","default","default"],"bits":128,"start":26.116436300874202,"link":"23-Complexdivisionimagpart","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(/ (- (* b c) (* a d)) (+ (sqr c) (sqr d)))","time":7604.430908203125,"target":0.39941488148878784,"output":"(/ 1 (/ (+ (sqr c) (sqr d)) (- (* b c) (* a d))))","end":26.31874175312164,"name":"Complex division, imag part","status":"eq-start","end-est":25.674501997662862},{"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":17609.001953125,"target":false,"output":"#f","end":false,"name":"Area of a triangle","status":"crash","end-est":false}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}