{"bit_width":64,"date":1467804317,"note":"libraries","iterations":2,"flags":["rules:arithmetic","rules:polynomials","rules:fractions","rules:exponents","rules:trigonometry","setup:simplify","reduce:post-process","reduce:regimes","reduce:taylor","reduce:simplify","reduce:avg-error","generate:rr","generate:taylor","generate:simplify","precision:double"],"seed":"#(1065543365 620684644 906956026 369308393 342036037 1300431646)","points":256,"tests":[{"samplers":["default","default","default","default"],"bits":128,"start":34.47007589595272,"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":33618.39501953125,"target":false,"output":"(if (<= x.re 7.245203907458468e-303) (/ (cos (+ (* y.re (atan2 x.im x.re)) (* (log (- x.re)) y.im))) (/ (pow (exp y.im) (atan2 x.im x.re)) (pow (- x.re) y.re))) (if (<= x.re 1.9000291803962433e-198) (/ (cos (+ (* y.im (log x.re)) (* y.re (atan2 x.im x.re)))) (/ (pow (exp y.im) (atan2 x.im x.re)) (pow x.im y.re))) (* (- 1 (* (* (atan2 x.im x.re) y.re) (+ (* y.im (log x.re)) (* (atan2 x.im x.re) (* 1/2 y.re))))) (/ (pow x.re y.re) (pow (exp y.im) (atan2 x.im x.re))))))","end":4.182985123762641,"name":"powComplex, real part","status":"imp-start","end-est":16.162218502126557},{"samplers":["default","default","default","default"],"bits":128,"start":37.32692567054314,"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":62491.364990234375,"target":false,"output":"(if (<= x.re -1.3070982989098934e-194) (/ (sin (+ (* y.re (atan2 x.im x.re)) (* (log (- x.re)) y.im))) (/ (pow (exp y.im) (atan2 x.im x.re)) (pow (- x.re) y.re))) (if (<= x.re -1.493976508130172e-275) (/ (sin (+ (* y.re (atan2 x.im x.re)) (* (log (cube (cbrt (sqrt (+ (sqr x.re) (* x.im x.im)))))) y.im))) (/ (pow (exp y.im) (atan2 x.im x.re)) (pow (sqrt (+ (sqr x.re) (* x.im x.im))) y.re))) (if (<= x.re -1.7930759128224657e-307) (/ (sin (+ (* y.re (atan2 x.im x.re)) (* (log (- x.re)) y.im))) (/ (pow (exp y.im) (atan2 x.im x.re)) (pow (- x.re) y.re))) (if (<= x.re 5.252448876769321e-272) (/ (sin (+ (* y.im (log x.im)) (* y.re (atan2 x.im x.re)))) (/ (pow (exp y.im) (atan2 x.im x.re)) (pow x.im y.re))) (/ (sin (+ (* y.im (log x.re)) (* y.re (atan2 x.im x.re)))) (/ (pow (exp y.im) (atan2 x.im x.re)) (pow x.re y.re)))))))","end":3.8393830291845052,"name":"powComplex, imaginary part","status":"imp-start","end-est":18.0672273034938},{"samplers":["(uniform 0 1)","(uniform 0 1)"],"bits":128,"start":0.39370687743113586,"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":12268.720947265625,"target":false,"output":"(+ 0.5 (* (/ 1 6) (/ (pow (* -2 (log u1)) 0.5) (/ 1 (cos (* PI (* u2 2)))))))","end":0.415629453003976,"name":"normal distribution","status":"ex-start","end-est":0.37994008791597816},{"samplers":["default","default"],"bits":128,"start":0.0065,"link":"3-mathsquareoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(- (* re re) (* im im))","time":3215.08984375,"target":false,"output":"(* (+ re im) (- re im))","end":0.001375,"name":"math.square on complex, real part","status":"ex-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":0.007875,"link":"4-mathsquareoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(+ (* re im) (* im re))","time":2369.876953125,"target":false,"output":"(* re (+ im im))","end":0.007626542230170899,"name":"math.square on complex, imaginary part","status":"ex-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":29.970273744367113,"link":"5-mathsqrtoncompleximaginarypartimgreaterthan0branch","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* 0.5 (sqrt (* 2.0 (+ (sqrt (- (* re re) (* im im))) re))))","time":18181.140869140625,"target":false,"output":"(* 0.5 (sqrt (* 2.0 (+ (* (sqrt (+ re im)) (sqrt (- re im))) re))))","end":0.09862734775785399,"name":"math.sqrt on complex, imaginary part, im greater than 0 branch","status":"imp-start","end-est":0.0078125},{"samplers":["default","default"],"bits":128,"start":0.02403837319067736,"link":"6-mathsinoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))","time":8013.089111328125,"target":false,"output":"(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))","end":0.02403837319067736,"name":"math.sin on complex, real part","status":"ex-start","end-est":0.0078125},{"samplers":["default","default"],"bits":128,"start":31.236499600854447,"link":"7-mathlog10oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))","time":11482.2890625,"target":false,"output":"(if (<= re -2.2719880985124886e+96) (/ (log (- re)) (log 10)) (if (<= re -6.874181544003876e-236) (/ 1 (* (log 10) (/ 1 (log (sqrt (+ (sqr re) (* im im))))))) (if (<= re -4.877685844349987e-272) (/ (log im) (log 10)) (if (<= re 1.4120771415832492e+126) (cbrt (cube (/ (log (sqrt (+ (sqr re) (* im im)))) (log 10)))) (/ (log re) (log 10))))))","end":13.678202842187854,"name":"math.log10 on complex, real part","status":"imp-start","end-est":15.515202333183774},{"samplers":["default","default"],"bits":128,"start":0.8493635343791471,"link":"8-mathlog10oncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(/ (atan2 im re) (log 10))","time":4119.1201171875,"target":false,"output":"(/ 1 (cube (cbrt (/ (log 10) (atan2 im re)))))","end":0.8329709701790506,"name":"math.log10 on complex, imaginary part","status":"ex-start","end-est":0.7424898727075345},{"samplers":["default","default","default"],"bits":128,"start":31.027335994442637,"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":20187.8349609375,"target":false,"output":"(if (<= im -8.193549540332154e+140) (/ (log (- im)) (log base)) (if (<= im 5.11104370095671e-307) (cbrt (/ (cube (log (sqrt (+ (sqr im) (* re re))))) (cube (log base)))) (if (<= im 2.9099428310613175e-275) (/ (log (- re)) (log base)) (if (<= im 1.3135365250902935e+68) (* (+ (* (log base) (log (sqrt (+ (sqr re) (* im im))))) 0) (/ 1 (* (log base) (log base)))) (/ (log im) (log base))))))","end":13.745941642538638,"name":"math.log/2 on complex, real part","status":"imp-start","end-est":15.349583213293684},{"samplers":["default","default","default"],"bits":128,"start":31.173467938405857,"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":6696.986083984375,"target":false,"output":"(/ (atan2 im re) (log base))","end":0.30118872187554085,"name":"math.log/2 on complex, imaginary part","status":"imp-start","end-est":0.30078125},{"samplers":["default","default"],"bits":128,"start":30.906653542276363,"link":"11-mathlog1oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(log (sqrt (+ (* re re) (* im im))))","time":4237.760009765625,"target":false,"output":"(if (<= re -1.6264853133519774e+105) (log (- re)) (if (<= re -6.874181544003876e-236) (log (sqrt (+ (sqr re) (* im im)))) (if (<= re -4.877685844349987e-272) (log im) (if (<= re 1.4120771415832492e+126) (log (sqrt (+ (sqr re) (* im im)))) (log re)))))","end":13.301267967752471,"name":"math.log/1 on complex, real part","status":"imp-start","end-est":15.103194809402018},{"samplers":["default","default"],"bits":128,"start":0,"link":"12-mathlog1oncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(atan2 im re)","time":1140.8310546875,"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":0.008469360937770433,"link":"13-mathexponcomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (exp re) (cos im))","time":2297.48486328125,"target":false,"output":"(* (exp re) (cos im))","end":0.008469360937770433,"name":"math.exp on complex, real part","status":"ex-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":0.02735990164099428,"link":"14-mathexponcompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (exp re) (sin im))","time":3761.64794921875,"target":false,"output":"(* (exp re) (sin im))","end":0.02735990164099428,"name":"math.exp on complex, imaginary part","status":"ex-start","end-est":0.0078125},{"samplers":["default","default"],"bits":128,"start":7.076819318917616,"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":9191.509033203125,"target":false,"output":"(+ (* (sqr x.re) x.re) (* x.im (* x.re (- (- x.im) (+ x.im x.im)))))","end":0.2514011281273437,"name":"math.cube on complex, real part","status":"imp-start","end-est":0.21875},{"samplers":["default","default"],"bits":128,"start":7.1756100332722,"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":11777.9150390625,"target":false,"output":"(- (* 3 (* (* x.im x.re) x.re)) (pow x.im 3))","end":0.17648609062806486,"name":"math.cube on complex, imaginary part","status":"imp-start","end-est":0.140625},{"samplers":["default","default"],"bits":128,"start":0.011823120312590146,"link":"17-mathcosoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))","time":8282.6591796875,"target":false,"output":"(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))","end":0.011823120312590146,"name":"math.cos on complex, real part","status":"ex-start","end-est":0.015625},{"samplers":["default","default"],"bits":128,"start":0,"link":"18-mathargoncomplex","pinf":0,"ninf":0,"vars":["re","im"],"input":"(atan2 im re)","time":1172.347900390625,"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":30.238543782046204,"link":"19-mathabsoncomplex","pinf":0,"ninf":0,"vars":["re","im"],"input":"(sqrt (+ (* re re) (* im im)))","time":4555.956787109375,"target":false,"output":"(if (<= re -4.1802274413958103e+105) (- re) (if (<= re -6.874181544003876e-236) (sqrt (+ (sqr re) (* im im))) (if (<= re -4.877685844349987e-272) im (if (<= re 1.0894463226389134e+141) (sqrt (+ (sqr re) (* im im))) re))))","end":12.887984609630438,"name":"math.abs on complex","status":"imp-start","end-est":15.24379385000241},{"samplers":["default","default","default","default"],"bits":128,"start":0.009125,"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":3875.531005859375,"target":false,"output":"(- (* x.re y.re) (* x.im y.im))","end":0.009125,"name":"_multiplyComplex, real part","status":"ex-start","end-est":0.015625},{"samplers":["default","default","default","default"],"bits":128,"start":0.010424039677847347,"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":7097.341796875,"target":false,"output":"(+ (* x.re y.im) (* x.im y.re))","end":0.010424039677847347,"name":"_multiplyComplex, imaginary part","status":"ex-start","end-est":0.0078125},{"samplers":["default","default","default","default"],"bits":128,"start":25.349673509078844,"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":11011.593994140625,"target":false,"output":"(if (<= y.re -2.709243247914685e+149) (/ x.re y.re) (if (<= y.re 1.0663382734753051e+99) (* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im)))) (/ x.re y.re)))","end":12.988907810145916,"name":"_divideComplex, real part","status":"imp-start","end-est":16.55172594088989},{"samplers":["default","default","default","default"],"bits":128,"start":25.38528906565887,"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":11778.326171875,"target":false,"output":"(if (<= y.re -213268377032.2042) (- (/ x.im (+ (* (/ y.im y.re) y.im) y.re)) (/ (* y.im x.re) (+ (* y.re y.re) (* y.im y.im)))) (if (<= y.re 1.0222346456089473e+104) (- (/ (* x.im y.re) (+ (sqr y.re) (* y.im y.im))) (/ x.re (+ y.im (/ (sqr y.re) y.im)))) (- (/ x.im (+ (* (/ y.im y.re) y.im) y.re)) (/ (* y.im x.re) (+ (* y.re y.re) (* y.im y.im))))))","end":8.665952069844868,"name":"_divideComplex, imaginary part","status":"imp-start","end-est":8.079895822951276},{"samplers":["default","default"],"bits":128,"start":0.1331992568893477,"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":17817.89404296875,"target":false,"output":"(* (- a (/ 1.0 3.0)) (+ 1 (* 1 (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9)))))","end":0.1260048875021635,"name":"Octave 3.8, oct_fill_randg","status":"ex-start","end-est":0.11556625976844202},{"samplers":["default"],"bits":128,"start":45.400287308171265,"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":9207.64892578125,"target":false,"output":"(if (<= i 5327.726165563152) (/ (sqr (/ i 2)) (- (* (* i 2) (* i 2)) 1.0)) (+ (+ 1/16 (/ 0.00390625 (pow i 4))) (/ 0.015625 (* i i))))","end":0.004540241011860921,"name":"Octave 3.8, jcobi/4, as called","status":"imp-start","end-est":0.00390625},{"samplers":["default","default","default"],"bits":128,"start":52.83631416699893,"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":87130.4169921875,"target":false,"output":"(if (<= beta 4.205781944509689e+135) (/ (/ (* i (+ beta (+ i alpha))) (/ (sqr (+ (+ beta alpha) (* 2 i))) (+ (* alpha beta) (* i (+ beta (+ i alpha)))))) (- (sqr (+ (+ beta alpha) (* 2 i))) 1.0)) (/ (* (+ (* (/ i beta) (/ 1.0 beta)) i) i) (sqr (+ (+ beta alpha) (* i 2)))))","end":36.859459833445776,"name":"Octave 3.8, jcobi/4","status":"imp-start","end-est":37.73055621412597},{"samplers":["default","default"],"bits":128,"start":8.534534148417665,"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":36173.552001953125,"target":false,"output":"(if (<= alpha 2.2061842904913525e+200) (/ (/ (/ (+ (+ alpha 1.0) (+ beta (* beta alpha))) (+ alpha (+ 2 beta))) (+ (+ alpha 1.0) (+ 2 beta))) (+ alpha (+ 2 beta))) (/ (+ (* 0.25 (+ alpha beta)) 0.5) (* (+ (+ alpha beta) 2) (+ (+ alpha beta) (+ 2 1.0)))))","end":8.38707296445482,"name":"Octave 3.8, jcobi/3","status":"apx-start","end-est":1.0500227886491116},{"samplers":["default","default","default"],"bits":128,"start":24.546612926753227,"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":54555.93017578125,"target":false,"output":"(if (<= (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) -7.957594368202611e+34) (/ (+ (- (/ 8.0 (cube alpha)) (/ (/ 4.0 alpha) alpha)) (/ 2.0 alpha)) 2.0) (/ (cbrt (cube (+ (* (/ (+ alpha beta) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))) 2.0))","end":0.7643726334634443,"name":"Octave 3.8, jcobi/2","status":"imp-start","end-est":8.300252738303055},{"samplers":["default","default"],"bits":128,"start":16.30201031202049,"link":"29-Octave38jcobi1","pinf":0,"ninf":0,"vars":["alpha","beta"],"input":"(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)","time":21777.741943359375,"target":false,"output":"(if (<= (/ (- beta alpha) (+ (+ alpha beta) 2.0)) -0.7971908424412208) (+ (/ (+ 2.0 (/ (/ 8.0 alpha) alpha)) (* 2.0 alpha)) (- (/ (/ beta 2.0) (+ alpha (+ 2.0 beta))) (/ (/ 4.0 (* alpha alpha)) 2.0))) (/ (exp (log (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0))) 2.0))","end":0.01564624062518029,"name":"Octave 3.8, jcobi/1","status":"imp-start","end-est":4.153775403188892},{"samplers":["default"],"bits":128,"start":0.25975,"link":"30-JmatReallambertwestimator","pinf":0,"ninf":0,"vars":["x"],"input":"(- (log x) (log (log x)))","time":5815.613037109375,"target":false,"output":"(log (/ x (log x)))","end":0.0035,"name":"Jmat.Real.lambertw, estimator","status":"ex-start","end-est":0.00390625},{"samplers":["default"],"bits":128,"start":1.810437256626152,"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":38092.02099609375,"target":false,"output":"(* (+ (+ (+ (+ (/ -0.13857109526572012 (- (- 1 z) (- 1 6))) (/ 9.984369578019572e-06 (- (- 1 z) (- 1 7)))) (+ (/ -176.6150291621406 (- (+ 4 1) (+ 1 z))) (/ 12.507343278686905 (- (+ 1 5) (+ 1 z))))) (+ (+ (/ 771.3234287776531 (- (- 1 z) (- 1 3))) (/ -1259.1392167224028 (- (- 1 z) (- 1 2)))) (+ 0.9999999999998099 (/ 676.5203681218851 (- (- 1 z) 0))))) (/ 1.5056327351493116e-07 (- (+ 1 8) (+ 1 z)))) (/ (* (/ (* PI (* (sqrt PI) (sqrt 2))) (sin (* z PI))) (pow (+ (+ 0.5 7) (- 1 (+ 1 z))) (- (+ 1 0.5) (+ 1 z)))) (exp (+ (+ 0.5 7) (- 1 (+ 1 z))))))","end":0.6175813571750383,"name":"Jmat.Real.gamma, branch z less than 0.5","status":"imp-start","end-est":0.47819009999974793},{"samplers":["default"],"bits":128,"start":61.30663980435689,"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":249591.03393554688,"target":false,"output":"(+ (- (+ (+ (* (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (/ (* (log 6.5) (sqrt 2)) (exp (+ 0.5 6)))) (* (sqrt PI) 676.5203681218851)) (/ (* (* (* (sqrt PI) 676.5203681218851) (sqrt 2)) (pow (/ 1 (pow 6.5 1.0)) 0.5)) (* (exp (+ 0.5 6)) z))) (/ (* 2585.1948787825354 (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (* z (* (sqrt 2) (sqrt PI))))) (exp (+ 0.5 6)))) (* (* (sqrt PI) 1656.8104518737205) (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (+ (/ (sqrt 2) (exp (+ 0.5 6))) (/ (* z (* (log 6.5) (sqrt 2))) (exp (+ 0.5 6))))))) (/ (* (* (sqrt PI) 338.26018406094255) (* (* (* z (sqrt 2)) (* (log 6.5) (log 6.5))) (pow (/ 1 (pow 6.5 1.0)) 0.5))) (exp (+ 0.5 6))))","end":1.4663589013490559,"name":"Jmat.Real.gamma, branch z greater than 0.5","status":"imp-start","end-est":1.057806733932049},{"samplers":["default"],"bits":128,"start":0.19714961636251668,"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":17747.154052734375,"target":false,"output":"(fabs (* (sqrt (/ 1 PI)) (+ (* 1/21 (* (fabs x) (sqr (cube (fabs x))))) (+ (* 2/3 (pow (fabs x) 3)) (+ (* 2 (fabs x)) (* 1/5 (* (sqr (fabs x)) (cube (fabs x)))))))))","end":0.20885079096393466,"name":"Jmat.Real.erfi, branch x less than or equal to 0.5","status":"ex-start","end-est":0.17320253907376806},{"samplers":["default"],"bits":128,"start":1.5002555773082853,"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":81416.537109375,"target":false,"output":"(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (/ (/ (/ 15 (fabs x)) (* (cube (fabs x)) (cube (fabs x)))) 8) (+ (+ (/ (/ 1 2) (cube (fabs x))) (/ 1 (fabs x))) (/ (/ 3/4 (fabs x)) (sqr (* (fabs x) (fabs x)))))))","end":0.9965531946960509,"name":"Jmat.Real.erfi, branch x greater than or equal to 5","status":"apx-start","end-est":0.832219551930929},{"samplers":["default"],"bits":128,"start":13.82399788828162,"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":35699.263916015625,"target":false,"output":"(/ (- (sqr 1) (/ (sqr (* (* 1 (- (sqr 0.254829592) (sqr (* (/ 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)))))))))) 1)) (sqr (* (* (+ 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))))))) (+ 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)))))))","end":10.618970710883247,"name":"Jmat.Real.erf","status":"imp-start","end-est":11.637936614060786},{"samplers":["default"],"bits":128,"start":28.912571061384387,"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":37535.097900390625,"target":false,"output":"(if (<= x -4.0904756849807273e+24) (/ (+ (+ (+ 1 (/ 0.1049934947 (* x x))) (/ (* 0.0072644182 1) (sqr (cube x)))) (+ (+ (/ (/ (* 0.0424060604 1) (cube x)) x) (/ 0.0001789971 (pow x 10))) (/ (/ (* 1 0.0005064034) (sqr (cube x))) (* x x)))) (* (+ (+ (+ (+ 1 (/ (* 1 0.0694555761) (sqr (cube x)))) (* 0.2909738639 (/ (/ 1 x) (cube x)))) (+ (/ 0.7715471019 (* x x)) (/ (* (/ 1 (cube x)) (/ 1 (cube x))) (/ (pow x 6) 0.0003579942)))) (+ (/ (/ (* 0.0140005442 1) (sqr (cube x))) (* x x)) (/ (/ (* 0.0008327945 1) (sqr (cube x))) (pow x 4)))) x)) (if (<= x 2.6044556869853095e+29) (/ (+ (+ (+ x (* (cube x) 0.1049934947)) (* (* x 0.0424060604) (* (sqr x) (sqr x)))) (+ (* (* 0.0001789971 (cube x)) (sqr (* (sqr x) (sqr x)))) (* (+ (* x 0.0072644182) (* (cube x) 0.0005064034)) (cube (sqr x))))) (+ (+ (* (* (* (* x x) (* x x)) (* (cube x) (cube x))) (+ (* (* 2 0.0001789971) (* x x)) 0.0008327945)) (+ (+ 1 (* (* x 0.2909738639) (cube x))) (* (* 0.7715471019 x) x))) (* (* x x) (* (* (* x x) (* x x)) (+ 0.0694555761 (* 0.0140005442 (* x x))))))) (/ (+ (+ (+ 1 (/ 0.1049934947 (* x x))) (/ (* 0.0072644182 1) (sqr (cube x)))) (+ (+ (/ (/ (* 0.0424060604 1) (cube x)) x) (/ 0.0001789971 (pow x 10))) (/ (/ (* 1 0.0005064034) (sqr (cube x))) (* x x)))) (* (+ (+ (+ (+ 1 (/ (* 1 0.0694555761) (sqr (cube x)))) (* 0.2909738639 (/ (/ 1 x) (cube x)))) (+ (/ 0.7715471019 (* x x)) (/ (* (/ 1 (cube x)) (/ 1 (cube x))) (/ (pow x 6) 0.0003579942)))) (+ (/ (/ (* 0.0140005442 1) (sqr (cube x))) (* x x)) (/ (/ (* 0.0008327945 1) (sqr (cube x))) (pow x 4)))) x))))","end":0.2108393869751293,"name":"Jmat.Real.dawson","status":"imp-start","end-est":21.79739650771687},{"samplers":["default","default"],"bits":128,"start":38.05168230766155,"link":"37-mathsqrtoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))","time":12656.47802734375,"target":33.72040060758623,"output":"(if (<= re -742857814.634727) (/ (* 0.5 (sqrt (* (* im im) 2.0))) (sqrt (- (- re) re))) (if (<= re -4.877685844349987e-272) (* 0.5 (sqrt (* 2.0 (+ im re)))) (if (<= re 1.4120771415832492e+126) (* 0.5 (sqrt (* 2.0 (+ (sqr (sqrt (sqrt (+ (sqr re) (* im im))))) re)))) (* 0.5 (sqrt (* 2.0 (+ re re)))))))","end":15.9730095967543,"name":"math.sqrt on complex, real part","status":"gt-target","end-est":22.556972117434864},{"samplers":["default","default"],"bits":128,"start":58.91717458363983,"link":"38-mathsinoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (cos re)) (- (exp (- 0 im)) (exp im)))","time":15747.556884765625,"target":10.13008685200583,"output":"(* (- (+ (* 1/60 (pow im 5)) (+ (* 2 im) (* 1/3 (pow im 3))))) (* (cos re) 0.5))","end":0.21162015413640134,"name":"math.sin on complex, imaginary part","status":"gt-target","end-est":0.43940192705701736},{"samplers":["default"],"bits":128,"start":0.13275,"link":"39-mathcubeonreal","pinf":0,"ninf":0,"vars":["x"],"input":"(* (* x x) x)","time":1512.239013671875,"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":47.68670776089677,"link":"40-mathcosoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))","time":16677.72802734375,"target":12.292298687802464,"output":"(* (* 0.5 (sin re)) (- (+ (* 1/60 (pow im 5)) (+ (* 2 im) (* 1/3 (pow im 3))))))","end":2.7685671836143313,"name":"math.cos on complex, imaginary part","status":"gt-target","end-est":0.4399020825366849},{"samplers":["default","default"],"bits":128,"start":18.025631147156798,"link":"41-JmatReallambertwnewtonloopstep","pinf":0,"ninf":0,"vars":["wj","x"],"input":"(- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj)))))","time":10231.26806640625,"target":17.987954075581186,"output":"(+ (+ (pow wj 4) (- (sqr wj) (cube wj))) (/ x (* (exp wj) (+ 1 wj))))","end":0.029959962500721162,"name":"Jmat.Real.lambertw, newton loop step","status":"gt-target","end-est":0.8211027607219757},{"samplers":["default"],"bits":128,"start":0.12853441602772658,"link":"42-FastMathtest5","pinf":0,"ninf":0,"vars":["d1"],"input":"(* (* d1 (* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)) d1)","time":3389.3310546875,"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":0.0696462406251803,"link":"43-FastMathtest3","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))","time":9234.52490234375,"target":0.061625,"output":"(* d1 (+ (+ 3 d2) d3))","end":0.061625,"name":"FastMath test3","status":"eq-target","end-est":0.0703125},{"samplers":["default","default"],"bits":128,"start":0.18354024101186092,"link":"44-FastMathtest2","pinf":0,"ninf":0,"vars":["d1","d2"],"input":"(+ (+ (* d1 10) (* d1 d2)) (* d1 20))","time":4583.56396484375,"target":0.026125,"output":"(* d1 (+ d2 30))","end":0.026125,"name":"FastMath test2","status":"eq-target","end-est":0.01953125},{"samplers":["default"],"bits":128,"start":0.27475,"link":"45-FastMathtest1","pinf":0,"ninf":0,"vars":["d"],"input":"(+ (* d 10) (* d 20))","time":1029.76904296875,"target":0,"output":"(* d (+ 10 20))","end":0,"name":"FastMath test1","status":"eq-target","end-est":0},{"samplers":["default"],"bits":128,"start":0.1379174812503606,"link":"46-FastMathrepmul","pinf":0,"ninf":0,"vars":["d1"],"input":"(* (* (* d1 d1) d1) d1)","time":1617.8740234375,"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":0.021594360937770434,"link":"47-FastMathdist4","pinf":0,"ninf":0,"vars":["d1","d2","d3","d4"],"input":"(- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1))","time":8548.447998046875,"target":0.023125,"output":"(* d1 (- (+ d4 d2) (+ d3 d1)))","end":0.023125,"name":"FastMath dist4","status":"eq-target","end-est":0.01171875},{"samplers":["default","default","default"],"bits":128,"start":0.041858795589947914,"link":"48-FastMathdist3","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))","time":7653.3818359375,"target":0.022625,"output":"(* d1 (+ (+ d2 d3) (+ 5 32)))","end":0.0225,"name":"FastMath dist3","status":"eq-target","end-est":0.01171875},{"samplers":["default","default","default"],"bits":128,"start":0.010625,"link":"49-FastMathdist","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (* d1 d2) (* d1 d3))","time":3121.507080078125,"target":0.01225,"output":"(* d1 (+ d2 d3))","end":0.01225,"name":"FastMath dist","status":"eq-target","end-est":0.0078125}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}