{"bit_width":64,"date":1471084893,"note":"libraries","iterations":3,"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","default","default","default"],"bits":128,"start":32.55470012745606,"link":"0-powComplexrealpart","pinf":0,"ninf":0,"vars":["x.re","x.im","y.re","y.im"],"input":"(* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))))","time":41155.82421875,"target":false,"output":"(if (<= y.re -3.4496838170280365e+48) (* (/ (pow (hypot x.im x.re) y.re) (+ (* (atan2 x.im x.re) y.im) (+ 1 (* 1/2 (* (sqr (atan2 x.im x.re)) (sqr y.im)))))) (cos (fma y.im (log (hypot x.im x.re)) (* y.re (atan2 x.im x.re))))) (* (/ (pow (hypot x.im x.re) y.re) (pow (exp y.im) (atan2 x.im x.re))) (- (* (cube (cbrt (cos (* y.im (log (hypot x.im x.re)))))) (cos (* y.re (atan2 x.im x.re)))) (* (sin (* y.im (log (hypot x.im x.re)))) (log (exp (sin (* y.re (atan2 x.im x.re)))))))))","end":1.7422235003533968,"name":"powComplex, real part","status":"imp-start","end-est":7.146271302291237},{"samplers":["default","default","default","default"],"bits":128,"start":32.65377814728883,"link":"1-powCompleximaginarypart","pinf":0,"ninf":0,"vars":["x.re","x.im","y.re","y.im"],"input":"(* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))))","time":24627.638916015625,"target":false,"output":"(* (/ (pow (hypot x.im x.re) y.re) (exp (* y.im (atan2 x.im x.re)))) (cube (cbrt (sin (fma y.im (log (hypot x.im x.re)) (* y.re (atan2 x.im x.re)))))))","end":4.34626660784953,"name":"powComplex, imaginary part","status":"imp-start","end-est":7.728712794985529},{"samplers":["(uniform 0 1)","(uniform 0 1)"],"bits":128,"start":0.3954071142757567,"link":"2-normaldistribution","pinf":0,"ninf":0,"vars":["u1","u2"],"input":"(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)","time":6918.241943359375,"target":false,"output":"(fma (* (pow (* -2 (log u1)) 0.5) (/ 1 6)) (log1p (expm1 (cos (* PI (* u2 2))))) 0.5)","end":0.4075389209033019,"name":"normal distribution","status":"ex-start","end-est":0.3991776367581883},{"samplers":["default","default"],"bits":128,"start":0.005924039677847346,"link":"3-mathsquareoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(- (* re re) (* im im))","time":2595.81591796875,"target":false,"output":"(- (sqr re) (sqr im))","end":0.005924039677847346,"name":"math.square on complex, real part","status":"ex-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":0.008,"link":"4-mathsquareoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(+ (* re im) (* im re))","time":2166.9970703125,"target":false,"output":"(* im (+ re re))","end":0.00760474281476955,"name":"math.square on complex, imaginary part","status":"ex-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":29.578996259730314,"link":"5-mathsqrtoncompleximaginarypartimgreaterthan0branch","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* 0.5 (sqrt (* 2.0 (+ (sqrt (- (* re re) (* im im))) re))))","time":17983.5009765625,"target":false,"output":"(* 0.5 (sqrt (* 2.0 (+ (* (sqrt (+ re im)) (sqrt (- re im))) re))))","end":0.14287862555755498,"name":"math.sqrt on complex, imaginary part, im greater than 0 branch","status":"imp-start","end-est":0.24219619548938517},{"samplers":["default","default"],"bits":128,"start":14.838015085588053,"link":"6-mathsinoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))","time":9285.50390625,"target":false,"output":"(* (fma 1/12 (pow im 4) (fma im im 2)) (* (sin re) 0.5))","end":2.981343253297186,"name":"math.sin on complex, real part","status":"imp-start","end-est":0.15734453969318848},{"samplers":["default","default"],"bits":128,"start":31.518183314735538,"link":"7-mathlog10oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))","time":5099.56201171875,"target":false,"output":"(/ (log (cube (expm1 (log1p (cbrt (hypot im re)))))) (log 10))","end":0.6115507883159139,"name":"math.log10 on complex, real part","status":"imp-start","end-est":0.5908775879159782},{"samplers":["default","default"],"bits":128,"start":0.845415414066557,"link":"8-mathlog10oncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(/ (atan2 im re) (log 10))","time":3984.22216796875,"target":false,"output":"(log1p (log1p (expm1 (expm1 (/ (atan2 im re) (log 10))))))","end":0.48794174570648297,"name":"math.log10 on complex, imaginary part","status":"ex-start","end-est":0.5332413086106521},{"samplers":["default","default","default"],"bits":128,"start":31.30955777101129,"link":"9-mathlog2oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im","base"],"input":"(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))","time":7480.195068359375,"target":false,"output":"(/ (/ 1 (log base)) (/ 1 (log (hypot im re))))","end":0.49111259689717696,"name":"math.log/2 on complex, real part","status":"imp-start","end-est":0.4746475586106522},{"samplers":["default","default","default"],"bits":128,"start":31.578107554455404,"link":"10-mathlog2oncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im","base"],"input":"(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0)))","time":5966.31396484375,"target":false,"output":"(/ (- (atan2 im re) 0) (log base))","end":0.3157193609377704,"name":"math.log/2 on complex, imaginary part","status":"imp-start","end-est":0.28125},{"samplers":["default","default"],"bits":128,"start":31.225921969033408,"link":"11-mathlog1oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(log (sqrt (+ (* re re) (* im im))))","time":2253.98583984375,"target":false,"output":"(log (hypot im re))","end":0.000125,"name":"math.log/1 on complex, real part","status":"imp-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":0,"link":"12-mathlog1oncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(atan2 im re)","time":1512.26611328125,"target":false,"output":"(atan2 im re)","end":0,"name":"math.log/1 on complex, imaginary part","status":"ex-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":0.008125,"link":"13-mathexponcomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (exp re) (cos im))","time":3160.56298828125,"target":false,"output":"(* (exp re) (cos im))","end":0.008125,"name":"math.exp on complex, real part","status":"ex-start","end-est":0.0078125},{"samplers":["default","default"],"bits":128,"start":0.014073120312590144,"link":"14-mathexponcompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (exp re) (sin im))","time":3092.615966796875,"target":false,"output":"(* (exp re) (sin im))","end":0.014073120312590144,"name":"math.exp on complex, imaginary part","status":"ex-start","end-est":0.01953125},{"samplers":["default","default"],"bits":128,"start":6.710148167252871,"link":"15-mathcubeoncomplexrealpart","pinf":0,"ninf":0,"vars":["x.re","x.im"],"input":"(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))","time":26298.617919921875,"target":false,"output":"(fma x.im (* (- x.re) (fma 3 x.im x.re)) (* (+ x.re x.im) (sqr x.re)))","end":0.23738928593921263,"name":"math.cube on complex, real part","status":"imp-start","end-est":0.2109375},{"samplers":["default","default"],"bits":128,"start":6.914626641778983,"link":"16-mathcubeoncompleximaginarypart","pinf":0,"ninf":0,"vars":["x.re","x.im"],"input":"(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))","time":15134.909912109375,"target":false,"output":"(fma (* (- x.re x.im) (+ x.re x.im)) x.im (* (* (+ x.im x.im) x.re) x.re))","end":6.907187919903444,"name":"math.cube on complex, imaginary part","status":"apx-start","end-est":7.345862259011346},{"samplers":["default","default"],"bits":128,"start":0.012823120312590145,"link":"17-mathcosoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))","time":8138.58203125,"target":false,"output":"(+ (/ 0.5 (/ (exp im) (cos re))) (* (* 0.5 (cos re)) (exp im)))","end":0.07175,"name":"math.cos on complex, real part","status":"ex-start","end-est":0.0625},{"samplers":["default","default"],"bits":128,"start":0,"link":"18-mathargoncomplex","pinf":0,"ninf":0,"vars":["re","im"],"input":"(atan2 im re)","time":1422.02001953125,"target":false,"output":"(atan2 im re)","end":0,"name":"math.arg on complex","status":"ex-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":30.064809477605888,"link":"19-mathabsoncomplex","pinf":0,"ninf":0,"vars":["re","im"],"input":"(sqrt (+ (* re re) (* im im)))","time":1864.328125,"target":false,"output":"(hypot im re)","end":0.003125,"name":"math.abs on complex","status":"imp-start","end-est":0},{"samplers":["default","default","default","default"],"bits":128,"start":0.009823120312590146,"link":"20-_multiplyComplexrealpart","pinf":0,"ninf":0,"vars":["x.re","x.im","y.re","y.im"],"input":"(- (* x.re y.re) (* x.im y.im))","time":4497.529052734375,"target":false,"output":"(- (* x.re y.re) (* x.im y.im))","end":0.009823120312590146,"name":"_multiplyComplex, real part","status":"ex-start","end-est":0.0078125},{"samplers":["default","default","default","default"],"bits":128,"start":0.01204024101186092,"link":"21-_multiplyCompleximaginarypart","pinf":0,"ninf":0,"vars":["x.re","x.im","y.re","y.im"],"input":"(+ (* x.re y.im) (* x.im y.re))","time":4341.416015625,"target":false,"output":"(fma y.im x.re (* y.re x.im))","end":0.006375,"name":"_multiplyComplex, imaginary part","status":"ex-start","end-est":0.0078125},{"samplers":["default","default","default","default"],"bits":128,"start":25.527005433343017,"link":"22-_divideComplexrealpart","pinf":0,"ninf":0,"vars":["x.re","x.im","y.re","y.im"],"input":"(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))","time":6247.818115234375,"target":false,"output":"(/ (fma y.re x.re (* y.im x.im)) (fma y.im y.im (* y.re y.re)))","end":25.526219635176172,"name":"_divideComplex, real part","status":"apx-start","end-est":26.040950894527285},{"samplers":["default","default","default","default"],"bits":128,"start":25.7616376234616,"link":"23-_divideCompleximaginarypart","pinf":0,"ninf":0,"vars":["x.re","x.im","y.re","y.im"],"input":"(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))","time":8142.439208984375,"target":false,"output":"(/ (- (* y.re x.im) (* y.im x.re)) (fma y.im y.im (* y.re y.re)))","end":25.7611376234616,"name":"_divideComplex, imaginary part","status":"apx-start","end-est":25.09769107892407},{"samplers":["default","default"],"bits":128,"start":0.14083760775026516,"link":"24-Octave38oct_fill_randg","pinf":0,"ninf":0,"vars":["a","rand"],"input":"(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))","time":24016.037109375,"target":false,"output":"(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt 1)) (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))))))","end":0.1368139233740031,"name":"Octave 3.8, oct_fill_randg","status":"ex-start","end-est":0.12337875976844201},{"samplers":["default"],"bits":128,"start":45.471851581883364,"link":"25-Octave38jcobi4ascalled","pinf":0,"ninf":0,"vars":["i"],"input":"(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0))","time":9391.491943359375,"target":false,"output":"(if (<= i 49809.97373367609) (/ (sqr (/ i 2)) (- (* (* i 2) (* i 2)) 1.0)) (+ (/ 0.00390625 (pow i 4)) (fma (/ 0.015625 i) (/ 1 i) 1/16)))","end":0.006573120312590144,"name":"Octave 3.8, jcobi/4, as called","status":"imp-start","end-est":0.00390625},{"samplers":["default","default","default"],"bits":128,"start":52.5048918172019,"link":"26-Octave38jcobi4","pinf":0,"ninf":0,"vars":["alpha","beta","i"],"input":"(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))","time":65459.921142578125,"target":false,"output":"(sqr (/ (sqrt (* (* (/ (+ (+ beta alpha) i) (+ beta (fma i 2 alpha))) (fma i (+ (+ beta alpha) i) (* alpha beta))) (/ i (+ beta (fma i 2 alpha))))) (sqrt (- (sqr (+ beta (fma i 2 alpha))) 1.0))))","end":38.648095650699766,"name":"Octave 3.8, jcobi/4","status":"imp-start","end-est":39.42666092620991},{"samplers":["default","default"],"bits":128,"start":3.5881222075334342,"link":"27-Octave38jcobi3","pinf":0,"ninf":0,"vars":["alpha","beta"],"input":"(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))","time":39891.35107421875,"target":false,"output":"(if (<= (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) 1.752335950282756e+129) (* (/ 1 (+ (+ beta 1.0) (+ alpha 2))) (/ (/ (+ (+ alpha 1.0) (fma beta alpha beta)) (+ alpha (+ 2 beta))) (+ alpha (+ 2 beta)))) 0)","end":0.25618922494593793,"name":"Octave 3.8, jcobi/3","status":"imp-start","end-est":1.066549408388707},{"samplers":["default","default","default"],"bits":128,"start":23.576219612398305,"link":"28-Octave38jcobi2","pinf":0,"ninf":0,"vars":["alpha","beta","i"],"input":"(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)","time":27744.140869140625,"target":false,"output":"(/ (fma (* (- beta alpha) (/ 1 (+ (fma i 2 beta) (+ 2.0 alpha)))) (/ (+ alpha beta) (fma 2 i (+ alpha beta))) 1.0) 2.0)","end":12.00078451674331,"name":"Octave 3.8, jcobi/2","status":"imp-start","end-est":11.2301855627219},{"samplers":["default","default"],"bits":128,"start":16.028000030397592,"link":"29-Octave38jcobi1","pinf":0,"ninf":0,"vars":["alpha","beta"],"input":"(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)","time":29547.3359375,"target":false,"output":"(if (<= (/ (- beta alpha) (+ (+ alpha beta) 2.0)) -0.9070372875212327) (+ (/ (+ 2.0 (/ 8.0 (* alpha alpha))) (* 2.0 alpha)) (- (/ (/ beta 2.0) (+ (+ alpha 2.0) beta)) (/ (/ 4.0 (* alpha alpha)) 2.0))) (/ (/ (- (* beta (+ (sqr (/ alpha (+ (+ alpha beta) 2.0))) (+ (sqr 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (+ alpha beta) 2.0) (+ (sqr (/ alpha (+ (+ alpha beta) 2.0))) (+ (sqr 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))) 2.0))","end":0.03214873482561022,"name":"Octave 3.8, jcobi/1","status":"imp-start","end-est":2.659677333167667},{"samplers":["default"],"bits":128,"start":0.26177124062518026,"link":"30-JmatReallambertwestimator","pinf":0,"ninf":0,"vars":["x"],"input":"(- (log x) (log (log x)))","time":4878.47802734375,"target":false,"output":"(log (/ x (log x)))","end":0.00525,"name":"Jmat.Real.lambertw, estimator","status":"ex-start","end-est":0},{"samplers":["default"],"bits":128,"start":1.8007309534504246,"link":"31-JmatRealgammabranchzlessthan05","pinf":0,"ninf":0,"vars":["z"],"input":"(* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- (- 1 z) 1) 7) 0.5) (+ (- (- 1 z) 1) 0.5))) (exp (- (+ (+ (- (- 1 z) 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1 z) 1) 1))) (/ -1259.1392167224028 (+ (- (- 1 z) 1) 2))) (/ 771.3234287776531 (+ (- (- 1 z) 1) 3))) (/ -176.6150291621406 (+ (- (- 1 z) 1) 4))) (/ 12.507343278686905 (+ (- (- 1 z) 1) 5))) (/ -0.13857109526572012 (+ (- (- 1 z) 1) 6))) (/ 9.984369578019572e-06 (+ (- (- 1 z) 1) 7))) (/ 1.5056327351493116e-07 (+ (- (- 1 z) 1) 8)))))","time":32973.734130859375,"target":false,"output":"(* (* (/ (expm1 (log1p (* PI (sqrt (* PI 2))))) (sin (* z PI))) (/ (pow (+ (+ 0.5 7) (- 1 (+ 1 z))) (- (+ 1 0.5) (+ 1 z))) (exp (+ (+ 0.5 7) (log (exp (- z))))))) (+ (+ (/ 1.5056327351493116e-07 (- (+ 1 8) (+ 1 z))) (+ (/ -0.13857109526572012 (- (- 1 z) (- 1 6))) (/ 9.984369578019572e-06 (fma z -1 7)))) (+ (+ (+ (/ -176.6150291621406 (- (- 1 z) (- 1 4))) (/ 12.507343278686905 (- (+ 1 5) (+ 1 z)))) (+ 0.9999999999998099 (/ 676.5203681218851 (- (- 1 z) 0)))) (+ (/ 771.3234287776531 (- (+ 1 3) (+ 1 z))) (/ -1259.1392167224028 (- (- 1 z) (- 1 2)))))))","end":0.6038033351084472,"name":"Jmat.Real.gamma, branch z less than 0.5","status":"imp-start","end-est":0.5107676390735161},{"samplers":["default"],"bits":128,"start":59.75667536335472,"link":"32-JmatRealgammabranchzgreaterthan05","pinf":0,"ninf":0,"vars":["z"],"input":"(* (* (* (sqrt (* PI 2)) (pow (+ (+ (- z 1) 7) 0.5) (+ (- z 1) 0.5))) (exp (- (+ (+ (- z 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1) 1))) (/ -1259.1392167224028 (+ (- z 1) 2))) (/ 771.3234287776531 (+ (- z 1) 3))) (/ -176.6150291621406 (+ (- z 1) 4))) (/ 12.507343278686905 (+ (- z 1) 5))) (/ -0.13857109526572012 (+ (- z 1) 6))) (/ 9.984369578019572e-06 (+ (- z 1) 7))) (/ 1.5056327351493116e-07 (+ (- z 1) 8))))","time":238261.4619140625,"target":false,"output":"(* (* (+ (+ (+ (/ 1.5056327351493116e-07 (- (+ z 8) 1)) (/ 9.984369578019572e-06 (+ 7 (- z 1)))) (+ (/ -0.13857109526572012 (+ (- z 1) 6)) (/ 12.507343278686905 (- z (- 1 5))))) (+ (+ (/ -1259.1392167224028 (- z (- 1 2))) (/ 771.3234287776531 (+ (- z 1) 3))) (+ (+ (/ 676.5203681218851 (- z 0)) 0.9999999999998099) (/ -176.6150291621406 (- (+ z 4) 1))))) (/ (pow (+ (- z 1) (+ 0.5 7)) (+ 0.5 (- z 1))) (exp (- z 1)))) (/ (sqrt (* 2 PI)) (exp (+ 0.5 7))))","end":0.8302385623726466,"name":"Jmat.Real.gamma, branch z greater than 0.5","status":"imp-start","end-est":0.3825187988422101},{"samplers":["default"],"bits":128,"start":0.21896743885377618,"link":"33-JmatRealerfibranchxlessthanorequalto05","pinf":0,"ninf":0,"vars":["x"],"input":"(fabs (* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))","time":13849.666015625,"target":false,"output":"(fabs (* (sqrt (/ 1 PI)) (+ (fma (* 1/5 (* (fabs x) (cube (fabs x)))) (fabs x) (fma 2/3 (cube (fabs x)) (* 2 (fabs x)))) (* 1/21 (pow (fabs x) 7)))))","end":0.19575445252211385,"name":"Jmat.Real.erfi, branch x less than or equal to 0.5","status":"ex-start","end-est":0.181972509768442},{"samplers":["default"],"bits":128,"start":1.4853218588035786,"link":"34-JmatRealerfibranchxgreaterthanorequalto5","pinf":0,"ninf":0,"vars":["x"],"input":"(* (* (/ 1 (sqrt PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1 (fabs x)) (* (/ 1 2) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 3 4) (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 15 8) (* (* (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))))))","time":108582.69311523438,"target":false,"output":"(fma (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (/ 1 (fabs x)) (fma (* (cube (/ 1 (fabs x))) (* (/ 1 (fabs x)) (/ 3 4))) (/ 1 (fabs x)) (/ (cube (/ 1 (fabs x))) 2))) (* (/ (* (/ 15 8) (exp (* (fabs x) (fabs x)))) (sqr (sqrt (sqrt PI)))) (/ (* (* (/ 1 (fabs x)) (/ 1 (* (fabs x) (fabs x)))) (/ (cube 1) (cube (fabs x)))) (fabs x))))","end":0.8477029275473357,"name":"Jmat.Real.erfi, branch x greater than or equal to 5","status":"apx-start","end-est":0.7438475478133107},{"samplers":["default"],"bits":128,"start":13.764320226584104,"link":"35-JmatRealerf","pinf":0,"ninf":0,"vars":["x"],"input":"(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))","time":14533.8408203125,"target":false,"output":"(/ (/ (- (pow 1 3) (pow (log1p (expm1 (cube (/ (fma (fma (+ -1.453152027 (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1 (sqr (fma 0.3275911 (fabs x) 1))) (+ (/ 1.421413741 (fma 0.3275911 (fabs x) 1)) -0.284496736)) (/ 1 (sqr (fma 0.3275911 (fabs x) 1))) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) (exp (* (fabs x) (fabs x))))))) 3)) (+ (sqr 1) (+ (sqr (log1p (expm1 (cube (/ (fma (fma (+ -1.453152027 (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1 (sqr (fma 0.3275911 (fabs x) 1))) (+ (/ 1.421413741 (fma 0.3275911 (fabs x) 1)) -0.284496736)) (/ 1 (sqr (fma 0.3275911 (fabs x) 1))) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) (exp (* (fabs x) (fabs x)))))))) (* 1 (log1p (expm1 (cube (/ (fma (fma (+ -1.453152027 (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1 (sqr (fma 0.3275911 (fabs x) 1))) (+ (/ 1.421413741 (fma 0.3275911 (fabs x) 1)) -0.284496736)) (/ 1 (sqr (fma 0.3275911 (fabs x) 1))) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) (exp (* (fabs x) (fabs x))))))))))) (fma (sqr (fma (fma (+ -1.453152027 (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1 (sqr (fma 0.3275911 (fabs x) 1))) (+ (/ 1.421413741 (fma 0.3275911 (fabs x) 1)) -0.284496736)) (/ 1 (sqr (fma 0.3275911 (fabs x) 1))) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))) (sqr (pow (exp (fabs x)) (- (fabs x)))) (fma (pow (exp (fabs x)) (- (fabs x))) (fma (fma (+ -1.453152027 (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (/ 1 (sqr (fma 0.3275911 (fabs x) 1))) (+ (/ 1.421413741 (fma 0.3275911 (fabs x) 1)) -0.284496736)) (/ 1 (sqr (fma 0.3275911 (fabs x) 1))) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))","end":12.845404794576696,"name":"Jmat.Real.erf","status":"apx-start","end-est":14.600857857875116},{"samplers":["default"],"bits":128,"start":28.940213065860863,"link":"36-JmatRealdawson","pinf":0,"ninf":0,"vars":["x"],"input":"(* (/ (+ (+ (+ (+ (+ 1 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x)","time":16713.573974609375,"target":false,"output":"(/ (* x (+ (fma 0.0001789971 (* (* (cube x) (sqr x)) (* (cube x) (sqr x))) (fma 0.0424060604 (* (sqr x) (sqr x)) (fma (* x 0.1049934947) x 1))) (fma 0.0005064034 (* (* (sqr x) (sqr x)) (* (sqr x) (sqr x))) (* (* (cube x) 0.0072644182) (cube x))))) (fma (* 0.0001789971 2) (* x (* (* (cube x) (cube x)) (* (* x x) (cube x)))) (+ (fma 0.0008327945 (* (cube (cube x)) x) (fma 0.2909738639 (* (* x x) (* x x)) (fma (* x 0.7715471019) x 1))) (fma (sqr (* (* x x) (* x x))) 0.0140005442 (* (* (cube x) (cube x)) 0.0694555761)))))","end":28.950035552690302,"name":"Jmat.Real.dawson","status":"apx-start","end-est":24.601548447431632},{"samplers":["default","default"],"bits":128,"start":37.55342384479879,"link":"37-mathsqrtoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))","time":4461.067138671875,"target":32.93917483118488,"output":"(* 0.5 (sqrt (fma (hypot re im) 2.0 (* 2.0 re))))","end":13.246204453618489,"name":"math.sqrt on complex, real part","status":"gt-target","end-est":11.697948877345658},{"samplers":["default","default"],"bits":128,"start":58.783552565896464,"link":"38-mathsinoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (cos re)) (- (exp (- 0 im)) (exp im)))","time":14169.638916015625,"target":10.262337541272766,"output":"(* (- (+ (* 1/60 (pow im 5)) (+ (* 2 im) (* 1/3 (pow im 3))))) (* (cos re) 0.5))","end":0.20861905531214006,"name":"math.sin on complex, imaginary part","status":"gt-target","end-est":0.24436924870546514},{"samplers":["default"],"bits":128,"start":0.1255,"link":"39-mathcubeonreal","pinf":0,"ninf":0,"vars":["x"],"input":"(* (* x x) x)","time":1259.285888671875,"target":0,"output":"(pow x 3)","end":0,"name":"math.cube on real","status":"eq-target","end-est":0},{"samplers":["default","default"],"bits":128,"start":46.877147882907906,"link":"40-mathcosoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))","time":11306.072998046875,"target":12.525081805440388,"output":"(* (fma (cube im) 1/3 (fma (pow im 5) 1/60 (* im 2))) (* (sin re) (- 0.5)))","end":2.84077341881578,"name":"math.cos on complex, imaginary part","status":"gt-target","end-est":0.23912146584887647},{"samplers":["default","default"],"bits":128,"start":18.35432198668395,"link":"41-JmatReallambertwnewtonloopstep","pinf":0,"ninf":0,"vars":["wj","x"],"input":"(- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj)))))","time":10887.22900390625,"target":18.304717813596024,"output":"(+ (fma wj (- wj (sqr wj)) (pow wj 4)) (/ x (fma wj (exp wj) (exp wj))))","end":0.028761842188131017,"name":"Jmat.Real.lambertw, newton loop step","status":"gt-target","end-est":1.196294175045096},{"samplers":["default"],"bits":128,"start":0.1338056566529068,"link":"42-FastMathtest5","pinf":0,"ninf":0,"vars":["d1"],"input":"(* (* d1 (* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)) d1)","time":4395.77294921875,"target":0,"output":"(pow d1 (+ (+ 2 3) (+ 2 3)))","end":0,"name":"FastMath test5","status":"eq-target","end-est":0},{"samplers":["default","default","default"],"bits":128,"start":0.07354469400057727,"link":"43-FastMathtest3","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))","time":4676.6201171875,"target":0.063,"output":"(fma d1 (+ d3 3) (* d1 d2))","end":0.041620723035582764,"name":"FastMath test3","status":"eq-target","end-est":0.0703125},{"samplers":["default","default"],"bits":128,"start":0.17444812031259016,"link":"44-FastMathtest2","pinf":0,"ninf":0,"vars":["d1","d2"],"input":"(+ (+ (* d1 10) (* d1 d2)) (* d1 20))","time":4073.81982421875,"target":0.027375,"output":"(fma d1 (+ 20 10) (* d1 d2))","end":0.0145,"name":"FastMath test2","status":"eq-target","end-est":0.01171875},{"samplers":["default"],"bits":128,"start":0.262,"link":"45-FastMathtest1","pinf":0,"ninf":0,"vars":["d"],"input":"(+ (* d 10) (* d 20))","time":1037.7177734375,"target":0,"output":"(* (+ 10 20) d)","end":0,"name":"FastMath test1","status":"eq-target","end-est":0},{"samplers":["default"],"bits":128,"start":0.13931372187554086,"link":"46-FastMathrepmul","pinf":0,"ninf":0,"vars":["d1"],"input":"(* (* (* d1 d1) d1) d1)","time":1383.217041015625,"target":0,"output":"(pow d1 4)","end":0,"name":"FastMath repmul","status":"eq-target","end-est":0},{"samplers":["default","default","default","default"],"bits":128,"start":0.02529248125036058,"link":"47-FastMathdist4","pinf":0,"ninf":0,"vars":["d1","d2","d3","d4"],"input":"(- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1))","time":11981.69384765625,"target":0.02525,"output":"(* d1 (+ (- d2 d3) (- d4 d1)))","end":0.02525,"name":"FastMath dist4","status":"eq-target","end-est":0.015625},{"samplers":["default","default","default"],"bits":128,"start":0.045375,"link":"48-FastMathdist3","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))","time":11554.2919921875,"target":0.02575,"output":"(fma (+ d3 37) d1 (* d1 d2))","end":0.0175,"name":"FastMath dist3","status":"eq-target","end-est":0.015625},{"samplers":["default","default","default"],"bits":128,"start":0.01375,"link":"49-FastMathdist","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (* d1 d2) (* d1 d3))","time":5215.298828125,"target":0.0125,"output":"(* (+ d2 d3) d1)","end":0.0125,"name":"FastMath dist","status":"eq-target","end-est":0.0234375}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}