{"bit_width":32,"date":1467905273,"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":"#(1065543365 620684644 906956026 369308393 342036037 1300431646)","points":256,"tests":[{"samplers":["default","default","default","default"],"bits":128,"start":16.2786314565146,"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":12322.118896484375,"target":false,"output":"(/ (pow (sqrt (+ (sqr x.im) (* x.re x.re))) y.re) (pow (exp y.im) (atan2 x.im x.re)))","end":9.329986407986786,"name":"powComplex, real part","status":"imp-start","end-est":12.63208129197499},{"samplers":["default","default","default","default"],"bits":128,"start":15.943892047824267,"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":14986.01318359375,"target":false,"output":"(/ (sin (+ (* y.re (atan2 x.im x.re)) (* (log (sqrt (+ (sqr x.re) (* x.im x.im)))) y.im))) (/ (exp (* y.im (atan2 x.im x.re))) (pow (sqrt (+ (sqr x.re) (* x.im x.im))) y.re)))","end":16.421660299312975,"name":"powComplex, imaginary part","status":"apx-start","end-est":17.89467921424667},{"samplers":["(uniform 0 1)","(uniform 0 1)"],"bits":128,"start":0.45095477359409547,"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":10209.0,"target":false,"output":"(+ 0.5 (/ (pow (* -2 (log u1)) 0.5) (/ 6 (log (exp (cos (* PI (* u2 2))))))))","end":0.44984599288051424,"name":"normal distribution","status":"ex-start","end-est":0.38864641092572777},{"samplers":["default","default"],"bits":128,"start":0.027942030901961016,"link":"3-mathsquareoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(- (* re re) (* im im))","time":3128.658935546875,"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":0.02525,"link":"4-mathsquareoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(+ (* re im) (* im re))","time":999.864990234375,"target":false,"output":"(* re (+ im im))","end":0.05748584879218341,"name":"math.square on complex, imaginary part","status":"ex-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":14.358033659937998,"link":"5-mathsqrtoncompleximaginarypartimgreaterthan0branch","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* 0.5 (sqrt (* 2.0 (+ (sqrt (- (* re re) (* im im))) re))))","time":11571.85498046875,"target":false,"output":"(* 0.5 (sqrt (* 2.0 (+ (* (sqrt (+ re im)) (sqrt (- re im))) re))))","end":0.48468538796881816,"name":"math.sqrt on complex, imaginary part, im greater than 0 branch","status":"imp-start","end-est":0.13677899083533873},{"samplers":["default","default"],"bits":128,"start":0.10397855080543654,"link":"6-mathsinoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))","time":7066.916015625,"target":false,"output":"(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))","end":0.10397855080543654,"name":"math.sin on complex, real part","status":"ex-start","end-est":0.11891996287584845},{"samplers":["default","default"],"bits":128,"start":15.020743683995809,"link":"7-mathlog10oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))","time":7045.65283203125,"target":false,"output":"(cbrt (cube (/ (log (sqrt (+ (sqr re) (* im im)))) (log 10))))","end":15.030919052961327,"name":"math.log10 on complex, real part","status":"apx-start","end-est":15.718227082772833},{"samplers":["default","default"],"bits":128,"start":0.4930212406251803,"link":"8-mathlog10oncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(/ (atan2 im re) (log 10))","time":3029.69091796875,"target":false,"output":"(cube (* (cbrt (atan2 im re)) (cbrt (/ 1 (log 10)))))","end":0.2548412937561237,"name":"math.log10 on complex, imaginary part","status":"ex-start","end-est":0.23577890629507225},{"samplers":["default","default","default"],"bits":128,"start":14.497519273862896,"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":11475.781005859375,"target":false,"output":"(cbrt (/ (cube (log (sqrt (+ (sqr im) (* re re))))) (cube (log base))))","end":14.50993651318637,"name":"math.log/2 on complex, real part","status":"apx-start","end-est":14.487364868970289},{"samplers":["default","default","default"],"bits":128,"start":14.827287285589087,"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":5846.10693359375,"target":false,"output":"(/ (- (atan2 im re) 0) (log base))","end":0.3827266921910158,"name":"math.log/2 on complex, imaginary part","status":"imp-start","end-est":0.387382519536884},{"samplers":["default","default"],"bits":128,"start":14.874273181981598,"link":"11-mathlog1oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(log (sqrt (+ (* re re) (* im im))))","time":2877.41015625,"target":false,"output":"(* 1/2 (log (+ (sqr re) (* im im))))","end":14.880307742974335,"name":"math.log/1 on complex, real part","status":"apx-start","end-est":15.55858467253556},{"samplers":["default","default"],"bits":128,"start":0.221875,"link":"12-mathlog1oncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(atan2 im re)","time":1407.1728515625,"target":false,"output":"(atan2 im re)","end":0.221875,"name":"math.log/1 on complex, imaginary part","status":"ex-start","end-est":0.25390625},{"samplers":["default","default"],"bits":128,"start":0.03541804061225982,"link":"13-mathexponcomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (exp re) (cos im))","time":2905.2158203125,"target":false,"output":"(* (exp re) (cos im))","end":0.03541804061225982,"name":"math.exp on complex, real part","status":"ex-start","end-est":0.046875},{"samplers":["default","default"],"bits":128,"start":0.08031245109044594,"link":"14-mathexponcompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (exp re) (sin im))","time":2991.368896484375,"target":false,"output":"(* (exp re) (sin im))","end":0.08031245109044594,"name":"math.exp on complex, imaginary part","status":"ex-start","end-est":0.16493717136321995},{"samplers":["default","default"],"bits":128,"start":3.3613995552007765,"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":8110.568115234375,"target":false,"output":"(+ (* (sqr x.re) x.re) (* x.im (* x.re (- (- x.im) (+ x.im x.im)))))","end":0.25460936478532203,"name":"math.cube on complex, real part","status":"imp-start","end-est":0.228847509768442},{"samplers":["default","default"],"bits":128,"start":3.1913428010414693,"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":13576.034912109375,"target":false,"output":"(+ (* x.im (* (+ x.im x.re) (- x.im))) (* (* x.re x.im) (+ (* 3 x.re) x.im)))","end":0.2654028182300593,"name":"math.cube on complex, imaginary part","status":"imp-start","end-est":0.2734375},{"samplers":["default","default"],"bits":128,"start":0.04095559767814785,"link":"17-mathcosoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))","time":8827.05615234375,"target":false,"output":"(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))","end":0.04095559767814785,"name":"math.cos on complex, real part","status":"ex-start","end-est":0.04296875},{"samplers":["default","default"],"bits":128,"start":0.221875,"link":"18-mathargoncomplex","pinf":0,"ninf":0,"vars":["re","im"],"input":"(atan2 im re)","time":1394.260986328125,"target":false,"output":"(atan2 im re)","end":0.221875,"name":"math.arg on complex","status":"ex-start","end-est":0.25390625},{"samplers":["default","default"],"bits":128,"start":13.742011932853645,"link":"19-mathabsoncomplex","pinf":0,"ninf":0,"vars":["re","im"],"input":"(sqrt (+ (* re re) (* im im)))","time":2394.43408203125,"target":false,"output":"(sqrt (+ (sqr re) (* im im)))","end":13.742011932853645,"name":"math.abs on complex","status":"apx-start","end-est":14.355353323433077},{"samplers":["default","default","default","default"],"bits":128,"start":0.048501989402604216,"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":3693.156005859375,"target":false,"output":"(- (* x.re y.re) (* x.im y.im))","end":0.048501989402604216,"name":"_multiplyComplex, real part","status":"ex-start","end-est":0.046875},{"samplers":["default","default","default","default"],"bits":128,"start":0.04814269090731548,"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":4084.419921875,"target":false,"output":"(+ (* x.re y.im) (* x.im y.re))","end":0.04814269090731548,"name":"_multiplyComplex, imaginary part","status":"ex-start","end-est":0.046875},{"samplers":["default","default","default","default"],"bits":128,"start":12.677489880215877,"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":7361.153076171875,"target":false,"output":"(/ (+ (* x.re y.re) (* x.im y.im)) (sqr (sqrt (+ (sqr y.re) (* y.im y.im)))))","end":12.65332471458259,"name":"_divideComplex, real part","status":"apx-start","end-est":11.785063479646913},{"samplers":["default","default","default","default"],"bits":128,"start":12.767949432894746,"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":9404.14306640625,"target":false,"output":"(cube (cbrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))))","end":12.95531674648407,"name":"_divideComplex, imaginary part","status":"apx-start","end-est":12.991393256939492},{"samplers":["default","default"],"bits":128,"start":0.12493893524781133,"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":17655.677001953125,"target":false,"output":"(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (* (sqrt 9) (sqrt (- a (/ 1.0 3.0))))) rand)))","end":0.09192340635885768,"name":"Octave 3.8, oct_fill_randg","status":"ex-start","end-est":0.0703125},{"samplers":["default"],"bits":128,"start":21.050044468019493,"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":7620.10400390625,"target":false,"output":"(/ (sqr (/ i 2)) (- (* (* i 2) (* i 2)) 1.0))","end":8.223216998934774,"name":"Octave 3.8, jcobi/4, as called","status":"imp-start","end-est":8.465887084069767},{"samplers":["default","default","default"],"bits":128,"start":26.56504541212159,"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":54132.8671875,"target":false,"output":"(* 1/16 (exp (/ (/ 0.25 i) i)))","end":0.00025,"name":"Octave 3.8, jcobi/4","status":"imp-start","end-est":8.80422337200534},{"samplers":["default","default"],"bits":128,"start":2.0007459284420217,"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":30858.85888671875,"target":false,"output":"(* (/ 1 (+ (+ beta 1.0) (+ alpha 2))) (/ (/ (+ (+ alpha 1.0) (+ beta (* beta alpha))) (+ alpha (+ 2 beta))) (+ alpha (+ 2 beta))))","end":2.028810679171331,"name":"Octave 3.8, jcobi/3","status":"apx-start","end-est":1.3644158733891645},{"samplers":["default","default","default"],"bits":128,"start":11.091789866953825,"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":39311.633056640625,"target":false,"output":"(/ (+ (* (/ (+ alpha beta) 1) (/ (cube (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0) 2.0)","end":4.7992771358154345,"name":"Octave 3.8, jcobi/2","status":"imp-start","end-est":4.649368185874918},{"samplers":["default","default"],"bits":128,"start":6.936902177530623,"link":"29-Octave38jcobi1","pinf":0,"ninf":0,"vars":["alpha","beta"],"input":"(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)","time":11016.4560546875,"target":false,"output":"(/ (+ (/ (- beta alpha) (pow (+ (+ alpha beta) 2.0) 1)) 1.0) 2.0)","end":6.591265264501229,"name":"Octave 3.8, jcobi/1","status":"apx-start","end-est":5.274416636094653},{"samplers":["default"],"bits":128,"start":0.27759436093777046,"link":"30-JmatReallambertwestimator","pinf":0,"ninf":0,"vars":["x"],"input":"(- (log x) (log (log x)))","time":5716.010009765625,"target":false,"output":"(log (/ x (log x)))","end":0.026,"name":"Jmat.Real.lambertw, estimator","status":"ex-start","end-est":0.015625},{"samplers":["default"],"bits":128,"start":1.9882045403957838,"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":578866.3449707031,"target":false,"output":"(* (+ (+ (/ (+ (- (* z 1259.1392167224028) 3777.417650167208) (* 771.3234287776531 (- 2 z))) (* (- 2 z) (- 3 z))) (+ (/ 676.5203681218851 (- 1 z)) (+ 0.9999999999998099 (/ 1.5056327351493116e-07 (- 8 z))))) (+ (+ (/ -176.6150291621406 (- 4 z)) (/ 12.507343278686905 (- 5 z))) (+ (/ -0.13857109526572012 (- (- 1 z) (- 1 6))) (/ 9.984369578019572e-06 (- 7 z))))) (/ (* (/ PI (sin (* z PI))) (sqrt (* PI 2))) (/ (exp (- (+ 0.5 7) z)) (pow (- (+ 0.5 7) z) (- 0.5 z)))))","end":0.9126018872786965,"name":"Jmat.Real.gamma, branch z less than 0.5","status":"imp-start","end-est":0.8807037819049043},{"samplers":["default"],"bits":128,"start":28.553250406761645,"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":86692.79296875,"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":0.14825,"name":"Jmat.Real.gamma, branch z greater than 0.5","status":"imp-start","end-est":1.544467792989955},{"samplers":["default"],"bits":128,"start":0.324875,"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":21795.08984375,"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":0.324875,"name":"Jmat.Real.erfi, branch x less than or equal to 0.5","status":"ex-start","end-est":0.32421875},{"samplers":["default"],"bits":128,"start":0.6942134197318649,"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":72229.76098632812,"target":false,"output":"(/ (+ (+ (+ (/ (cube (/ 1 (fabs x))) 2) (/ 1 (fabs x))) (* (* (cube (/ 1 (fabs x))) (* (/ 1 (fabs x)) (/ 3 4))) (/ 1 (fabs x)))) (* (/ 15 8) (/ (pow (sqr (cube (/ 1 (fabs x)))) 1) (fabs x)))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))","end":0.7246859775552734,"name":"Jmat.Real.erfi, branch x greater than or equal to 5","status":"ex-start","end-est":0.7354134979015365},{"samplers":["default"],"bits":128,"start":12.04936136910351,"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":25454.56298828125,"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":10.332738031175948,"name":"Jmat.Real.erf","status":"imp-start","end-est":11.438716007988885},{"samplers":["default"],"bits":128,"start":14.438461664152305,"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":32800.560791015625,"target":false,"output":"(* (+ (+ (+ 1 (* (cube x) (* 0.0424060604 x))) (* (sqr x) 0.1049934947)) (+ (* (pow x 10) 0.0001789971) (* (cube (sqr x)) (+ 0.0072644182 (* (* x 0.0005064034) x))))) (/ x (+ (+ (+ (* (* (cube x) (pow x 6)) (* 0.0003579942 (cube x))) (* (sqr x) 0.7715471019)) (+ (* 0.2909738639 (sqr (sqr x))) (* (cube (sqr x)) (* (pow x 4) 0.0008327945)))) (+ 1 (* (cube (sqr x)) (+ (* (* x 0.0140005442) x) 0.0694555761))))))","end":14.198330230485446,"name":"Jmat.Real.dawson","status":"apx-start","end-est":12.750311643002384},{"samplers":["default","default"],"bits":128,"start":17.980370285756297,"link":"37-mathsqrtoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))","time":4928.451904296875,"target":15.730676168898544,"output":"(* 0.5 (sqrt (* 2.0 (sqr (sqrt (+ re (sqrt (+ (sqr re) (* im im)))))))))","end":18.065455601629278,"name":"math.sqrt on complex, real part","status":"eq-start","end-est":18.21172088761328},{"samplers":["default","default"],"bits":128,"start":24.443742266309236,"link":"38-mathsinoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (cos re)) (- (exp (- 0 im)) (exp im)))","time":14944.955078125,"target":1.3817566900060774,"output":"(* (* (cos re) 0.5) (* (+ (+ (* (- 1/24) (cube im)) (- im)) (* (- 1/1920) (pow im 5))) (+ (sqrt (exp im)) (sqrt (exp (- im))))))","end":0.34066460376462315,"name":"math.sin on complex, imaginary part","status":"gt-target","end-est":1.079996439563025},{"samplers":["default"],"bits":128,"start":0.12775,"link":"39-mathcubeonreal","pinf":0,"ninf":0,"vars":["x"],"input":"(* (* x x) x)","time":1162.134033203125,"target":0.074125,"output":"(pow x 3)","end":0.074125,"name":"math.cube on real","status":"eq-target","end-est":0.0859375},{"samplers":["default","default"],"bits":128,"start":20.67002607341282,"link":"40-mathcosoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))","time":11682.5009765625,"target":6.045287641594692,"output":"(* (* 0.5 (sin re)) (- (+ (* 1/60 (pow im 5)) (+ (* 2 im) (* 1/3 (pow im 3))))))","end":1.6399889451047716,"name":"math.cos on complex, imaginary part","status":"gt-target","end-est":1.3761126826035384},{"samplers":["default","default"],"bits":128,"start":9.85954193324233,"link":"41-JmatReallambertwnewtonloopstep","pinf":0,"ninf":0,"vars":["wj","x"],"input":"(- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj)))))","time":8002.18603515625,"target":1.6678297333793481,"output":"(+ (- wj (/ wj (+ 1 wj))) (/ x (+ (exp wj) (* wj (exp wj)))))","end":1.5622068941476426,"name":"Jmat.Real.lambertw, newton loop step","status":"eq-target","end-est":1.6771877548754217},{"samplers":["default"],"bits":128,"start":0.12579157422627618,"link":"42-FastMathtest5","pinf":0,"ninf":0,"vars":["d1"],"input":"(* (* d1 (* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)) d1)","time":5178.875,"target":0.05748364687698316,"output":"(pow d1 (+ (+ 2 3) (+ 2 3)))","end":0.05748364687698316,"name":"FastMath test5","status":"eq-target","end-est":0.07878876953688403},{"samplers":["default","default","default"],"bits":128,"start":0.11472883213319658,"link":"43-FastMathtest3","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))","time":4188.08203125,"target":0.0777712406251803,"output":"(* d1 (+ 3 (+ d3 d2)))","end":0.07759436093777045,"name":"FastMath test3","status":"eq-target","end-est":0.08203125},{"samplers":["default","default"],"bits":128,"start":0.20787100167288164,"link":"44-FastMathtest2","pinf":0,"ninf":0,"vars":["d1","d2"],"input":"(+ (+ (* d1 10) (* d1 d2)) (* d1 20))","time":2321.1630859375,"target":0.035,"output":"(* d1 (+ d2 30))","end":0.035,"name":"FastMath test2","status":"eq-target","end-est":0.0390625},{"samplers":["default"],"bits":128,"start":0.27475,"link":"45-FastMathtest1","pinf":0,"ninf":0,"vars":["d"],"input":"(+ (* d 10) (* d 20))","time":624.258056640625,"target":0,"output":"(* d (+ 10 20))","end":0,"name":"FastMath test1","status":"eq-target","end-est":0},{"samplers":["default"],"bits":128,"start":0.13061560156295074,"link":"46-FastMathrepmul","pinf":0,"ninf":0,"vars":["d1"],"input":"(* (* (* d1 d1) d1) d1)","time":1241.572021484375,"target":0.065875,"output":"(pow d1 4)","end":0.065875,"name":"FastMath repmul","status":"eq-target","end-est":0.046875},{"samplers":["default","default","default","default"],"bits":128,"start":0.10182225645149934,"link":"47-FastMathdist4","pinf":0,"ninf":0,"vars":["d1","d2","d3","d4"],"input":"(- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1))","time":6439.93408203125,"target":0.09307592125684438,"output":"(* d1 (+ d4 (- d2 (+ d3 d1))))","end":0.09359716188202467,"name":"FastMath dist4","status":"eq-target","end-est":0.08203125},{"samplers":["default","default","default"],"bits":128,"start":0.0981356838705752,"link":"48-FastMathdist3","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))","time":5871.617919921875,"target":0.07691524101186092,"output":"(+ (* d1 (+ d2 d3)) (* d1 (+ 5 32)))","end":0.0994949925103147,"name":"FastMath dist3","status":"eq-target","end-est":0.07439216452874396},{"samplers":["default","default","default"],"bits":128,"start":0.05200392193050633,"link":"49-FastMathdist","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (* d1 d2) (* d1 d3))","time":1949.43212890625,"target":0.049,"output":"(* d1 (+ d2 d3))","end":0.049,"name":"FastMath dist","status":"eq-target","end-est":0.046875}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}