{"bit_width":32,"date":1471016118,"note":"libraries","iterations":2,"flags":["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","default","default","default"],"bits":128,"start":15.81712593986379,"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":14179.9990234375,"target":false,"output":"(/ (cos (+ (* y.re (atan2 x.im x.re)) (* (log (sqrt (+ (sqr x.re) (* x.im x.im)))) y.im))) (/ (exp (cube (cbrt (* y.im (atan2 x.im x.re))))) (pow (sqrt (+ (sqr x.re) (* x.im x.im))) y.re)))","end":16.186736175709388,"name":"powComplex, real part","status":"apx-start","end-est":16.023323085061502},{"samplers":["default","default","default","default"],"bits":128,"start":16.065004734945756,"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":16121.2939453125,"target":false,"output":"(/ (sin (+ (* y.re (atan2 x.im x.re)) (* (log (sqrt (+ (sqr x.re) (* x.im x.im)))) y.im))) (/ (exp (cube (cbrt (* y.im (atan2 x.im x.re))))) (pow (sqrt (+ (sqr x.re) (* x.im x.im))) y.re)))","end":16.43028197516309,"name":"powComplex, imaginary part","status":"apx-start","end-est":16.360478863239685},{"samplers":["(uniform 0 1)","(uniform 0 1)"],"bits":128,"start":0.4589199270909162,"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":10298.218994140625,"target":false,"output":"(+ 0.5 (/ (pow (* -2 (log u1)) 0.5) (/ 6 (log (exp (cos (* PI (* u2 2))))))))","end":0.4588904018469576,"name":"normal distribution","status":"ex-start","end-est":0.4607214543313229},{"samplers":["default","default"],"bits":128,"start":0.03324386655643692,"link":"3-mathsquareoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(- (* re re) (* im im))","time":3200.0380859375,"target":false,"output":"(* (+ (fabs im) re) (- re (fabs im)))","end":0,"name":"math.square on complex, real part","status":"ex-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":0.027625,"link":"4-mathsquareoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(+ (* re im) (* im re))","time":1015.7861328125,"target":false,"output":"(* re (+ im im))","end":0.06397894716226976,"name":"math.square on complex, imaginary part","status":"ex-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":13.946513622731226,"link":"5-mathsqrtoncompleximaginarypartimgreaterthan0branch","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* 0.5 (sqrt (* 2.0 (+ (sqrt (- (* re re) (* im im))) re))))","time":11663.28515625,"target":false,"output":"(* 0.5 (sqrt (* 2.0 (+ (* (sqrt (+ re im)) (sqrt (- re im))) re))))","end":0.5239580134669466,"name":"math.sqrt on complex, imaginary part, im greater than 0 branch","status":"imp-start","end-est":0.570508608305831},{"samplers":["default","default"],"bits":128,"start":0.11637260697692725,"link":"6-mathsinoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))","time":11087.412841796875,"target":false,"output":"(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))","end":0.11637260697692725,"name":"math.sin on complex, real part","status":"ex-start","end-est":0.14419556275762696},{"samplers":["default","default"],"bits":128,"start":14.595963348364302,"link":"7-mathlog10oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))","time":7782.861083984375,"target":false,"output":"(cbrt (cube (/ (log (sqrt (+ (sqr re) (* im im)))) (log 10))))","end":14.60930953912625,"name":"math.log10 on complex, real part","status":"apx-start","end-est":14.051329465560038},{"samplers":["default","default"],"bits":128,"start":0.513636842188131,"link":"8-mathlog10oncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(/ (atan2 im re) (log 10))","time":3084.4931640625,"target":false,"output":"(cube (* (cbrt (atan2 im re)) (cbrt (/ 1 (log 10)))))","end":0.256369458609385,"name":"math.log10 on complex, imaginary part","status":"ex-start","end-est":0.26894384768442015},{"samplers":["default","default","default"],"bits":128,"start":14.667965144931426,"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":15152.51806640625,"target":false,"output":"(/ (+ (+ (* (log base) (log (cbrt (sqrt (+ (sqr re) (* im im)))))) (* (log (cbrt (sqrt (+ (sqr im) (* re re))))) (+ (log base) (log base)))) 0) (* (log base) (log base)))","end":14.685277808614764,"name":"math.log/2 on complex, real part","status":"apx-start","end-est":13.949987464849727},{"samplers":["default","default","default"],"bits":128,"start":14.988254286150992,"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":6484.5908203125,"target":false,"output":"(/ (- (atan2 im re) 0) (log base))","end":0.3887785718784256,"name":"math.log/2 on complex, imaginary part","status":"imp-start","end-est":0.4186325195368841},{"samplers":["default","default"],"bits":128,"start":14.446852300988096,"link":"11-mathlog1oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(log (sqrt (+ (* re re) (* im im))))","time":3903.14599609375,"target":false,"output":"(log (sqrt (exp (log (+ (sqr re) (* im im))))))","end":14.448550421300688,"name":"math.log/1 on complex, real part","status":"apx-start","end-est":13.882961140545854},{"samplers":["default","default"],"bits":128,"start":0.223625,"link":"12-mathlog1oncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(atan2 im re)","time":1089.676025390625,"target":false,"output":"(atan2 im re)","end":0.223625,"name":"math.log/1 on complex, imaginary part","status":"ex-start","end-est":0.234375},{"samplers":["default","default"],"bits":128,"start":0.030698120312590144,"link":"13-mathexponcomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (exp re) (cos im))","time":2583.757080078125,"target":false,"output":"(* (exp re) (cos im))","end":0.030698120312590144,"name":"math.exp on complex, real part","status":"ex-start","end-est":0.01953125},{"samplers":["default","default"],"bits":128,"start":0.0674111191253458,"link":"14-mathexponcompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (exp re) (sin im))","time":2784.126953125,"target":false,"output":"(* (exp re) (sin im))","end":0.0674111191253458,"name":"math.exp on complex, imaginary part","status":"ex-start","end-est":0.0390625},{"samplers":["default","default"],"bits":128,"start":3.207551671517373,"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":8487.6259765625,"target":false,"output":"(+ (* (sqr x.re) x.re) (* x.im (* x.re (- (- x.im) (+ x.im x.im)))))","end":0.25760986647430095,"name":"math.cube on complex, real part","status":"imp-start","end-est":0.2109375},{"samplers":["default","default"],"bits":128,"start":3.341367910537465,"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":16375.192138671875,"target":false,"output":"(+ (* (* x.re x.im) (+ (+ x.re x.re) (+ x.im x.re))) (* x.im (* (+ x.re x.im) (- x.im))))","end":0.26815450145148256,"name":"math.cube on complex, imaginary part","status":"imp-start","end-est":0.26009750976844204},{"samplers":["default","default"],"bits":128,"start":0.032875,"link":"17-mathcosoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))","time":8409.35595703125,"target":false,"output":"(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))","end":0.032875,"name":"math.cos on complex, real part","status":"ex-start","end-est":0.03515625},{"samplers":["default","default"],"bits":128,"start":0.223625,"link":"18-mathargoncomplex","pinf":0,"ninf":0,"vars":["re","im"],"input":"(atan2 im re)","time":1099.552001953125,"target":false,"output":"(atan2 im re)","end":0.223625,"name":"math.arg on complex","status":"ex-start","end-est":0.234375},{"samplers":["default","default"],"bits":128,"start":13.391739109788745,"link":"19-mathabsoncomplex","pinf":0,"ninf":0,"vars":["re","im"],"input":"(sqrt (+ (* re re) (* im im)))","time":2516.586181640625,"target":false,"output":"(sqrt (+ (sqr re) (* im im)))","end":13.391739109788745,"name":"math.abs on complex","status":"apx-start","end-est":12.864979514806102},{"samplers":["default","default","default","default"],"bits":128,"start":0.04351840061561778,"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":3452.72509765625,"target":false,"output":"(- (* x.re y.re) (* x.im y.im))","end":0.04351840061561778,"name":"_multiplyComplex, real part","status":"ex-start","end-est":0.04296875},{"samplers":["default","default","default","default"],"bits":128,"start":0.049064446870979606,"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":3676.114990234375,"target":false,"output":"(+ (* x.re y.im) (* x.im y.re))","end":0.049064446870979606,"name":"_multiplyComplex, imaginary part","status":"ex-start","end-est":0.037441259768442016},{"samplers":["default","default","default","default"],"bits":128,"start":12.398840391498398,"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":10248.011962890625,"target":false,"output":"(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))","end":12.398840391498398,"name":"_divideComplex, real part","status":"apx-start","end-est":10.757899739321005},{"samplers":["default","default","default","default"],"bits":128,"start":12.401391324053284,"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":7017.568115234375,"target":false,"output":"(/ (- (* x.im y.re) (* x.re y.im)) (sqr (sqrt (+ (sqr y.re) (* y.im y.im)))))","end":12.373937188355209,"name":"_divideComplex, imaginary part","status":"apx-start","end-est":11.844346189411594},{"samplers":["default","default"],"bits":128,"start":0.1443122693882707,"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":17044.65087890625,"target":false,"output":"(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (* (sqrt 9) (sqrt (- a (/ 1.0 3.0))))) rand)))","end":0.09970844960164414,"name":"Octave 3.8, oct_fill_randg","status":"ex-start","end-est":0.1015625},{"samplers":["default"],"bits":128,"start":20.92869011749475,"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":7475.52001953125,"target":false,"output":"(/ (sqr (/ i 2)) (- (* (* i 2) (* i 2)) 1.0))","end":7.624580403610162,"name":"Octave 3.8, jcobi/4, as called","status":"imp-start","end-est":7.9881264268549},{"samplers":["default","default","default"],"bits":128,"start":25.50714740478685,"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":59575.090087890625,"target":false,"output":"(/ (/ (* i (+ beta (+ i alpha))) (/ 1 (/ (+ (* alpha beta) (* i (+ beta (+ i alpha)))) (sqr (+ (+ beta alpha) (* 2 i)))))) (- (sqr (+ (+ beta alpha) (* 2 i))) 1.0))","end":18.9909647611832,"name":"Octave 3.8, jcobi/4","status":"imp-start","end-est":17.804829966389157},{"samplers":["default","default"],"bits":128,"start":1.9954355071018153,"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":30548.447021484375,"target":false,"output":"(* (/ 1 (+ (+ beta 1.0) (+ alpha 2))) (/ (/ (+ (+ alpha 1.0) (+ beta (* beta alpha))) (+ alpha (+ 2 beta))) (+ alpha (+ 2 beta))))","end":2.018211085607185,"name":"Octave 3.8, jcobi/3","status":"apx-start","end-est":1.4251143570388909},{"samplers":["default","default","default"],"bits":128,"start":10.950241882758437,"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":28284.43310546875,"target":false,"output":"(/ (+ (/ (pow (* (/ (+ alpha beta) 1) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) 1) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)","end":4.7419492332243784,"name":"Octave 3.8, jcobi/2","status":"imp-start","end-est":4.759232255270121},{"samplers":["default","default"],"bits":128,"start":6.801951553673824,"link":"29-Octave38jcobi1","pinf":0,"ninf":0,"vars":["alpha","beta"],"input":"(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)","time":10909.611083984375,"target":false,"output":"(/ (+ (/ (- beta alpha) (pow (+ (+ alpha beta) 2.0) 1)) 1.0) 2.0)","end":6.457121595047489,"name":"Octave 3.8, jcobi/1","status":"apx-start","end-est":6.1250174410005265},{"samplers":["default"],"bits":128,"start":0.2783443609377705,"link":"30-JmatReallambertwestimator","pinf":0,"ninf":0,"vars":["x"],"input":"(- (log x) (log (log x)))","time":5496.929931640625,"target":false,"output":"(log (/ x (log x)))","end":0.02675,"name":"Jmat.Real.lambertw, estimator","status":"ex-start","end-est":0.03125},{"samplers":["default"],"bits":128,"start":false,"link":"31-JmatRealgammabranchzlessthan05","pinf":false,"ninf":false,"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":600000,"target":false,"output":"#f","end":false,"name":"Jmat.Real.gamma, branch z less than 0.5","status":"timeout","end-est":false},{"samplers":["default"],"bits":128,"start":28.412556459684215,"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":94522.72094726562,"target":false,"output":"(- (+ (* 2585.1948787825354 (* (/ (* z (sqrt 2)) (exp 6.5)) (* (sqrt PI) (pow (/ 1 (pow 6.5 1.0)) 0.5)))) (+ (* 338.26018406094255 (* (/ (* z (* (sqrt 2) (sqr (log 6.5)))) (exp 6.5)) (* (sqrt PI) (pow (/ 1 (pow 6.5 1.0)) 0.5)))) (+ (* 676.5203681218851 (* (/ (sqrt 2) (* (exp 6.5) z)) (* (sqrt PI) (pow (/ 1 (pow 6.5 1.0)) 0.5)))) (* 676.5203681218851 (* (/ (* (sqrt 2) (log 6.5)) (exp 6.5)) (* (sqrt PI) (pow (/ 1 (pow 6.5 1.0)) 0.5))))))) (+ (* 1656.8104518737205 (* (/ (sqrt 2) (exp 6.5)) (* (sqrt PI) (pow (/ 1 (pow 6.5 1.0)) 0.5)))) (* 1656.8104518737205 (* (/ (* z (* (sqrt 2) (log 6.5))) (exp 6.5)) (* (sqrt PI) (pow (/ 1 (pow 6.5 1.0)) 0.5))))))","end":0.14325,"name":"Jmat.Real.gamma, branch z greater than 0.5","status":"imp-start","end-est":1.2707708463948013},{"samplers":["default"],"bits":128,"start":0.33175,"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":21150.1259765625,"target":false,"output":"(fabs (/ (+ (+ (* (* (fabs x) 1/21) (* (cube (fabs x)) (cube (fabs x)))) (* (fabs x) 2)) (* (cube (fabs x)) (+ 2/3 (* (fabs x) (* 1/5 (fabs x)))))) (sqrt PI)))","end":0.33175,"name":"Jmat.Real.erfi, branch x less than or equal to 0.5","status":"ex-start","end-est":0.3359375},{"samplers":["default"],"bits":128,"start":0.673050692904732,"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":70574.90893554688,"target":false,"output":"(/ (+ (+ (/ (/ (/ 3 4) (fabs x)) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (/ 1 (fabs x))) (+ (/ (/ 15 (cube (fabs x))) (* (* 8 (fabs x)) (cube (fabs x)))) (/ (/ 1 2) (cube (fabs x))))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))","end":0.673050692904732,"name":"Jmat.Real.erfi, branch x greater than or equal to 5","status":"ex-start","end-est":0.7124191870596437},{"samplers":["default"],"bits":128,"start":12.022236645357317,"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":27459.92578125,"target":false,"output":"(- 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)))) (/ (pow (- (sqr -1.453152027) (sqr (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))) 1) (- -1.453152027 (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911)))))))))))) (exp (- (* (fabs x) (fabs x))))))","end":10.366817345074127,"name":"Jmat.Real.erf","status":"imp-start","end-est":11.535506811064232},{"samplers":["default"],"bits":128,"start":14.344459541406541,"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":29634.333984375,"target":false,"output":"(* (/ x (+ (+ (* (* (* (* x x) (* x x)) (* (cube x) (cube x))) (+ (pow (* (* 2 0.0001789971) (* x x)) 1) 0.0008327945)) (+ (+ 1 (* (* x 0.2909738639) (cube x))) (* (* 0.7715471019 x) x))) (* (* x x) (* (* (* x x) (* x x)) (+ 0.0694555761 (* 0.0140005442 (* x x))))))) (+ (+ (+ (* (* x 0.0424060604) (cube x)) (+ (* (* x x) 0.1049934947) 1)) (* (* (* x x) 0.0001789971) (* (* (* x x) (* x x)) (* (* x x) (* x x))))) (* (* x x) (* (* (* x x) (* x x)) (+ 0.0072644182 (* (* 0.0005064034 x) x))))))","end":14.110335254065383,"name":"Jmat.Real.dawson","status":"apx-start","end-est":12.9977970209243},{"samplers":["default","default"],"bits":128,"start":17.666812348668802,"link":"37-mathsqrtoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))","time":5598.2998046875,"target":15.321334505650116,"output":"(* 0.5 (sqrt (* 2.0 (+ (sqr (sqrt (sqrt (+ (sqr re) (* im im))))) re))))","end":17.989539539957978,"name":"math.sqrt on complex, real part","status":"eq-start","end-est":17.260336319812545},{"samplers":["default","default"],"bits":128,"start":25.105128867694297,"link":"38-mathsinoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (cos re)) (- (exp (- 0 im)) (exp im)))","time":12461.8310546875,"target":4.779675932378213,"output":"(* (- (+ (* 1/60 (pow im 5)) (+ (* 2 im) (* 1/3 (pow im 3))))) (* (cos re) 0.5))","end":0.4454925466611044,"name":"math.sin on complex, imaginary part","status":"gt-target","end-est":1.5414138770628005},{"samplers":["default"],"bits":128,"start":0.132125,"link":"39-mathcubeonreal","pinf":0,"ninf":0,"vars":["x"],"input":"(* (* x x) x)","time":1433.991943359375,"target":0.072375,"output":"(pow x 3)","end":0.072375,"name":"math.cube on real","status":"eq-target","end-est":0.07421875},{"samplers":["default","default"],"bits":128,"start":20.435692703605294,"link":"40-mathcosoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))","time":12195.43603515625,"target":5.714232579751755,"output":"(+ (* (* 0.5 (sin re)) (- (* 1/60 (pow im 5)))) (* (+ (* 2 im) (* 1/3 (cube im))) (* (sin re) (- 0.5))))","end":1.4937162000295165,"name":"math.cos on complex, imaginary part","status":"gt-target","end-est":1.6662276032260843},{"samplers":["default","default"],"bits":128,"start":3.0338776421881293,"link":"41-JmatReallambertwnewtonloopstep","pinf":0,"ninf":0,"vars":["wj","x"],"input":"(- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj)))))","time":6921.833984375,"target":2.3914998869841573,"output":"(- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj)))))","end":3.0338776421881293,"name":"Jmat.Real.lambertw, newton loop step","status":"eq-target","end-est":2.5236420272571904},{"samplers":["default"],"bits":128,"start":0.12734813790326746,"link":"42-FastMathtest5","pinf":0,"ninf":0,"vars":["d1"],"input":"(* (* d1 (* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)) d1)","time":5595.358154296875,"target":0.05859924843993386,"output":"(pow d1 (+ (+ 2 3) (+ 2 3)))","end":0.05859924843993386,"name":"FastMath test5","status":"eq-target","end-est":0.045253759768442016},{"samplers":["default","default","default"],"bits":128,"start":0.11466994950937849,"link":"43-FastMathtest3","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))","time":4353.949951171875,"target":0.07694812031259013,"output":"(* d1 (+ (+ 3 d2) d3))","end":0.07694812031259013,"name":"FastMath test3","status":"eq-target","end-est":0.0546875},{"samplers":["default","default"],"bits":128,"start":0.20449863580352212,"link":"44-FastMathtest2","pinf":0,"ninf":0,"vars":["d1","d2"],"input":"(+ (+ (* d1 10) (* d1 d2)) (* d1 20))","time":3378.06689453125,"target":0.03675,"output":"(* d1 (+ 30 d2))","end":0.03675,"name":"FastMath test2","status":"eq-target","end-est":0.02734375},{"samplers":["default"],"bits":128,"start":0.26475,"link":"45-FastMathtest1","pinf":0,"ninf":0,"vars":["d"],"input":"(+ (* d 10) (* d 20))","time":638.684814453125,"target":0,"output":"(* d (+ 10 20))","end":0,"name":"FastMath test1","status":"eq-target","end-est":0},{"samplers":["default"],"bits":128,"start":0.140511842188131,"link":"46-FastMathrepmul","pinf":0,"ninf":0,"vars":["d1"],"input":"(* (* (* d1 d1) d1) d1)","time":1759.64208984375,"target":0.06425,"output":"(pow d1 4)","end":0.06425,"name":"FastMath repmul","status":"eq-target","end-est":0.07421875},{"samplers":["default","default","default","default"],"bits":128,"start":0.09870358504721016,"link":"47-FastMathdist4","pinf":0,"ninf":0,"vars":["d1","d2","d3","d4"],"input":"(- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1))","time":10382.06201171875,"target":0.08425960194963135,"output":"(+ (* d1 (+ d4 d2)) (* d1 (- (+ d3 d1))))","end":0.09560708992026984,"name":"FastMath dist4","status":"eq-target","end-est":0.09110128162065376},{"samplers":["default","default","default"],"bits":128,"start":0.09441460794984513,"link":"48-FastMathdist3","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))","time":6902.199951171875,"target":0.07899060156295074,"output":"(+ (* d1 d2) (* d1 (+ 32 (+ d3 5))))","end":0.09241895706344525,"name":"FastMath dist3","status":"eq-target","end-est":0.109375},{"samplers":["default","default","default"],"bits":128,"start":0.05782887309009203,"link":"49-FastMathdist","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (* d1 d2) (* d1 d3))","time":2398.5859375,"target":0.048875,"output":"(* d1 (+ d2 d3))","end":0.048875,"name":"FastMath dist","status":"eq-target","end-est":0.046875}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}