{"bit_width":64,"date":1469362879,"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":"#(1065385120 3968465003 4252011776 3360847114 2908152799 1991881914)","points":256,"tests":[{"samplers":["default"],"bits":128,"start":0.014625,"link":"0-arccos","pinf":0,"ninf":0,"vars":["x"],"input":"(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))","time":6121.629150390625,"target":false,"output":"(* 2 (atan (sqrt (sqr (/ (sqrt (- 1 x)) (sqrt (+ 1 x)))))))","end":0.01575,"name":"arccos","status":"ex-start","end-est":0.03515625},{"samplers":["default","default","default"],"bits":128,"start":11.580352314395903,"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":22336.10302734375,"target":false,"output":"(- (+ (- 3 4.5) (/ 2 (* r r))) (* (cbrt (cube (* (/ 0.125 (- 1 v)) (- 3 (* 2 v))))) (sqr (* w r))))","end":0.36956781465476646,"name":"Rosa's TurbineBenchmark","status":"imp-start","end-est":0.3405838867581883},{"samplers":["default","default"],"bits":128,"start":0.513448018959756,"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":41684.343994140625,"target":false,"output":"(+ (+ (+ (+ x1 x1) (+ (cube x1) (/ (* (* x1 (* x1 3)) (+ (* x1 (* x1 3)) (- (* x2 2) x1))) (+ (sqr x1) 1)))) (* (+ (* (- (/ (+ (* 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":0.4562542854374578,"name":"Rosa's FloatVsDoubleBenchmark","status":"ex-start","end-est":0.6042477189251009},{"samplers":["default","default","default"],"bits":128,"start":17.509177440207363,"link":"3-RosasDopplerBench","pinf":0,"ninf":0,"vars":["u","v","t1"],"input":"(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))","time":7416.18505859375,"target":false,"output":"(/ (* (/ (- t1) (+ t1 u)) v) (+ t1 u))","end":1.0163404451427056,"name":"Rosa's DopplerBench","status":"imp-start","end-est":0.5443065226161786},{"samplers":["default"],"bits":128,"start":0.14675284467733313,"link":"4-RosasBenchmark","pinf":0,"ninf":0,"vars":["x"],"input":"(- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x)))","time":4284.298828125,"target":false,"output":"(- (* x 0.954929658551372) (* 0.12900613773279798 (cube x)))","end":0.14675284467733313,"name":"Rosa's Benchmark","status":"ex-start","end-est":0.09765625},{"samplers":["default","default"],"bits":128,"start":0.002448120312590144,"link":"5-Radioactiveexchangebetweentwosurfaces","pinf":0,"ninf":0,"vars":["x","y"],"input":"(- (pow x 4) (pow y 4))","time":6516.56201171875,"target":false,"output":"(- (pow x 4) (pow y 4))","end":0.002448120312590144,"name":"Radioactive exchange between two surfaces","status":"ex-start","end-est":0.00390625},{"samplers":["default","default"],"bits":128,"start":14.435052680276002,"link":"6-NMSESection61mentionedB","pinf":0,"ninf":0,"vars":["a","b"],"input":"(* (* (/ PI 2) (/ 1 (- (sqr b) (sqr a)))) (- (/ 1 a) (/ 1 b)))","time":12515.383056640625,"target":false,"output":"(* (/ PI 2) (/ (/ 1 (+ a b)) (* a b)))","end":0.2911755656381608,"name":"NMSE Section 6.1 mentioned, B","status":"imp-start","end-est":0.252948779305326},{"samplers":["default","default"],"bits":128,"start":43.56064439639412,"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":36763.509033203125,"target":false,"output":"(if (<= x 46118455070.99842) 1 (/ (- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (pow E (- (* (+ 1 eps) x))))) 2))","end":0,"name":"NMSE Section 6.1 mentioned, A","status":"imp-start","end-est":1.045728971122166},{"samplers":["default"],"bits":128,"start":15.13463116010136,"link":"8-xx21","pinf":0,"ninf":0,"vars":["x"],"input":"(/ x (+ (sqr x) 1))","time":5008.913818359375,"target":0.4090913519773475,"output":"(if (<= x -3.2784791869173944e-06) (- (/ 1 (pow x 5)) (- (/ 1 (cube x)) (/ 1 x))) (if (<= x 501837.3637557024) (/ x (+ (sqr x) 1)) (- (/ 1 (pow x 5)) (- (/ 1 (cube x)) (/ 1 x)))))","end":0.008125,"name":"x / (x^2 + 1)","status":"eq-target","end-est":0.23348740809547358},{"samplers":["default","default","default"],"bits":128,"start":44.90400617439044,"link":"9-simplefmatest","pinf":0,"ninf":0,"vars":["x","y","z"],"input":"(- (fma x y z) (+ 1 (+ (* x y) z)))","time":8207.469970703125,"target":0,"output":"(cube (cbrt (- (fma x y z) (+ 1 (+ (* x y) z)))))","end":44.89843305407787,"name":"simple fma test","status":"eq-start","end-est":46.212787266826446},{"samplers":["default"],"bits":128,"start":42.17517702726594,"link":"10-ln1x","pinf":0,"ninf":0,"vars":["x"],"input":"(log (+ 1 x))","time":7685.819091796875,"target":7.111198611650797,"output":"(if (<= x 501837.3637557024) (+ (* (- (* 1/3 x) 1/2) (sqr x)) x) (log (+ 1 x)))","end":0.04716052656439302,"name":"ln(1 + x)","status":"gt-target","end-est":0.35289514136149974},{"samplers":["default","default","default"],"bits":128,"start":34.07437852601545,"link":"11-Thequadraticformular2","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))","time":22734.10400390625,"target":21.24254565743898,"output":"(if (<= b -2.6747491353258983e+90) (* (/ c b) (/ -2 2)) (if (<= b -1.6249307588497366e-76) (/ (/ (* c (* 4 a)) (+ (- b) (sqrt (- (sqr b) (* 4 (* a c)))))) (* 2 a)) (if (<= b -1.0745984396746834e-89) (* (/ c b) (/ -2 2)) (if (<= b 3.741572576046744e+123) (- (/ (- b) (* 2 a)) (/ (sqrt (- (sqr b) (* 4 (* a c)))) (* 2 a))) (- (+ (/ c b) (/ (- b) (* 2 a))) (/ (/ b 2) a))))))","end":7.331832795476095,"name":"The quadratic formula (r2)","status":"gt-target","end-est":6.812668225885582},{"samplers":["default","default","default"],"bits":128,"start":34.99921547988672,"link":"12-Thequadraticformular1","pinf":0,"ninf":0,"vars":["a","b","c"],"input":"(/ (+ (- b) (sqrt (- (sqr b) (* (* 4 a) c)))) (* 2 a))","time":25962.31591796875,"target":22.244219913565175,"output":"(if (<= b -1.9805160440224734e+152) (/ (- b) a) (if (<= b 1.2681432970921129e-148) (/ (+ (- b) (sqrt (- (sqr b) (* (* 4 a) c)))) (* 2 a)) (if (<= b 504667502.6761971) (* (* (/ 4 2) a) (/ (/ c (- (- b) (sqrt (- (sqr b) (* (* 4 a) c))))) a)) (* (/ c b) (/ -2 2)))))","end":6.628511697943477,"name":"The quadratic formula (r1)","status":"gt-target","end-est":7.273334217800368},{"samplers":["default"],"bits":128,"start":43.03428818406394,"link":"13-Kahansexpquotient","pinf":0,"ninf":0,"vars":["x"],"input":"(/ (- (exp x) 1) x)","time":7707.81201171875,"target":42.308523651176074,"output":"(if (<= x -3.2784791869173944e-06) (/ (/ (- (cube (exp x)) 1) (+ (+ (exp x) 1) (exp (+ x x)))) x) (/ (+ (* (+ 1/2 (* 1/6 x)) (sqr x)) x) x))","end":2.920463227921603,"name":"Kahan's exp quotient","status":"gt-target","end-est":0.12099157680731563},{"samplers":["(uniform -14 -13)","(uniform -3 -2)","(uniform 3 3.5)","(uniform 12.5 13.5)"],"bits":128,"start":3.6602412812178438,"link":"14-Expressionp6","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(* (+ a (+ b (+ c d))) 2)","time":7252.489990234375,"target":3.848451940312146,"output":"(* (+ a (+ (+ b c) d)) 2)","end":2.7584961692187497,"name":"Expression, p6","status":"gt-target","end-est":2.712449290374256},{"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":15894.18115234375,"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":14919.873046875,"target":false,"output":"#f","end":false,"name":"Expression 4, p15","status":"crash","end-est":false},{"samplers":["default"],"bits":128,"start":0.016625,"link":"17-Expression3p15","pinf":0,"ninf":0,"vars":["x"],"input":"(+ (* x (* x x)) (* x x))","time":9685.2470703125,"target":0.024219360937770436,"output":"(+ (sqr x) (pow x 3))","end":0.016,"name":"Expression 3, p15","status":"eq-target","end-est":0.015625},{"samplers":["default"],"bits":128,"start":0.00075,"link":"18-Expression2p15","pinf":0,"ninf":0,"vars":["x"],"input":"(+ x (* x x))","time":7310.02001953125,"target":0.02025,"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":0.39568665469173697,"link":"19-Expression1p15","pinf":0,"ninf":0,"vars":["a","b","c","d","e"],"input":"(+ (+ (+ (+ e d) c) b) a)","time":13498.51513671875,"target":0.19275,"output":"(+ (+ e d) (+ c (+ b a)))","end":0.271,"name":"Expression 1, p15","status":"eq-target","end-est":0.23828125},{"samplers":["default","default"],"bits":128,"start":0.006875,"link":"20-Differenceofsquares","pinf":0,"ninf":0,"vars":["a","b"],"input":"(- (sqr a) (sqr b))","time":11300.0087890625,"target":0.00075,"output":"(- (sqr a) (sqr b))","end":0.006875,"name":"Difference of squares","status":"eq-target","end-est":0.00390625},{"samplers":["default","default"],"bits":128,"start":51.871667943153746,"link":"21-CompoundInterest","pinf":0,"ninf":0,"vars":["i","n"],"input":"(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))","time":49695.02490234375,"target":51.40983450341315,"output":"(if (<= i -2.6993148136786055e-05) (* 100 (/ (/ (- (cube (pow (+ (/ i n) 1) n)) 1) (+ (sqr (pow (+ 1 (/ i n)) n)) (+ (sqr 1) (* (pow (+ 1 (/ i n)) n) 1)))) (/ i n))) (if (<= i 46118455070.99842) (* (+ (* 1/2 i) 1) (* 100 n)) (if (<= i 3.1880721816060146e+268) (* 100 (/ (/ (- (cube (pow (+ (/ i n) 1) n)) 1) (+ (sqr (pow (+ 1 (/ i n)) n)) (+ (sqr 1) (* (pow (+ 1 (/ i n)) n) 1)))) (/ i n))) (if (<= i 5.9681760581064156e+289) (* (+ (* 1/2 i) 1) (/ i (/ (/ i n) 100))) (* (/ 100 i) (/ (- (pow (+ 1 (/ i n)) n) 1) (/ 1 n)))))))","end":10.383095992170729,"name":"Compound Interest","status":"gt-target","end-est":15.200061633945621},{"samplers":["default","default","default","default"],"bits":128,"start":25.702699820466773,"link":"22-Complexdivisionrealpart","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(/ (+ (* a c) (* b d)) (+ (sqr c) (sqr d)))","time":14844.44287109375,"target":0.4878580637257004,"output":"(/ (+ (* a c) (* b d)) (+ (sqr c) (sqr d)))","end":25.702699820466773,"name":"Complex division, real part","status":"eq-start","end-est":25.33107522319774},{"samplers":["default","default","default","default"],"bits":128,"start":25.870368759955426,"link":"23-Complexdivisionimagpart","pinf":0,"ninf":0,"vars":["a","b","c","d"],"input":"(/ (- (* b c) (* a d)) (+ (sqr c) (sqr d)))","time":16713.181884765625,"target":0.45374883524815934,"output":"(if (<= c 1.5457874926092937e-19) (- (/ (* b c) (+ (sqr c) (sqr d))) (/ a (/ (+ (sqr c) (sqr d)) d))) (- (/ b (/ (+ (sqr c) (sqr d)) c)) (/ (* a d) (+ (sqr c) (sqr d)))))","end":23.508312135549943,"name":"Complex division, imag part","status":"lt-target","end-est":22.493324856338845},{"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":31022.47314453125,"target":false,"output":"#f","end":false,"name":"Area of a triangle","status":"crash","end-est":false}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}