{"bit_width":64,"date":1467808045,"note":"libraries","iterations":2,"flags":["rules:numerics","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":32.98166619060428,"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":17320.9951171875,"target":false,"output":"(* (exp (- (* (log (hypot x.im x.re)) y.re) (* y.im (atan2 x.im x.re)))) (cos (fma y.im (log (hypot x.im x.re)) (* y.re (atan2 x.im x.re)))))","end":3.4501238121234716,"name":"powComplex, real part","status":"imp-start","end-est":3.8999836982275293},{"samplers":["default","default","default","default"],"bits":128,"start":33.20410263723415,"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":22347.614013671875,"target":false,"output":"(* (exp (- (* (log (hypot x.im x.re)) y.re) (* 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":3.959632920496422,"name":"powComplex, imaginary part","status":"imp-start","end-est":4.6598738679885345},{"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":10969.241943359375,"target":false,"output":"(+ (* (/ (pow (* -2 (log u1)) 0.5) 6) (cos (* PI (* u2 2)))) 0.5)","end":0.37908852814696287,"name":"normal distribution","status":"ex-start","end-est":0.3682213379159782},{"samplers":["default","default"],"bits":128,"start":0.0065,"link":"3-mathsquareoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(- (* re re) (* im im))","time":3399.5869140625,"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":2123.94091796875,"target":false,"output":"(* im (+ re re))","end":0.007706334796223378,"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":17388.677978515625,"target":false,"output":"(* 0.5 (sqrt (* 2.0 (fma (sqrt (+ re im)) (sqrt (- re im)) re))))","end":0.09625234775785399,"name":"math.sqrt on complex, imaginary part, im greater than 0 branch","status":"imp-start","end-est":0.00390625},{"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":9657.056884765625,"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":31.09561313711413,"link":"7-mathlog10oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))","time":4697.802978515625,"target":false,"output":"(/ (log (hypot im re)) (log 10))","end":0.5977845890824238,"name":"math.log10 on complex, real part","status":"imp-start","end-est":0.5499001465266303},{"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":4063.31298828125,"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":30.900609823994632,"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":7794.743896484375,"target":false,"output":"(* (log (hypot im re)) (/ 1 (log base)))","end":0.4389206781359985,"name":"math.log/2 on complex, real part","status":"imp-start","end-est":0.39033129884221013},{"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":7162.39306640625,"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":30.802296138936892,"link":"11-mathlog1oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(log (sqrt (+ (* re re) (* im im))))","time":2171.64599609375,"target":false,"output":"(log (hypot im re))","end":0,"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":1189.05517578125,"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":2269.89794921875,"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":3671.385986328125,"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":28745.743896484375,"target":false,"output":"(fma x.im (* (- x.re) (fma 3 x.im x.re)) (* (+ x.re x.im) (sqr x.re)))","end":0.251148887888844,"name":"math.cube on complex, real part","status":"imp-start","end-est":0.228847509768442},{"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":7027.31103515625,"target":false,"output":"(fma (- x.re x.im) (* (+ x.re x.im) x.im) (* (* 2 x.im) (sqr x.re)))","end":7.15859819108407,"name":"math.cube on complex, imaginary part","status":"apx-start","end-est":6.208926949090554},{"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":7154.717041015625,"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":1133.308837890625,"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":29.636965174567518,"link":"19-mathabsoncomplex","pinf":0,"ninf":0,"vars":["re","im"],"input":"(sqrt (+ (* re re) (* im im)))","time":2124.346923828125,"target":false,"output":"(hypot im re)","end":0.003875,"name":"math.abs on complex","status":"imp-start","end-est":0.0078125},{"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":4773.162841796875,"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":3880.578857421875,"target":false,"output":"(fma y.im x.re (* y.re x.im))","end":0.00516524101186092,"name":"_multiplyComplex, imaginary part","status":"ex-start","end-est":0},{"samplers":["default","default","default","default"],"bits":128,"start":25.48609120450844,"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":7128.74609375,"target":false,"output":"(* (fma y.re x.re (* y.im x.im)) (/ 1 (fma y.im y.im (* y.re y.re))))","end":25.68694526157279,"name":"_divideComplex, real part","status":"apx-start","end-est":24.711191601839907},{"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":11486.89599609375,"target":false,"output":"(if (<= y.re -8.507570282412652e-145) (- (* (/ y.re 1) (/ x.im (fma y.im y.im (sqr y.re)))) (/ (* y.im x.re) (fma y.im y.im (sqr y.re)))) (- (/ (* y.re x.im) (fma y.im y.im (sqr y.re))) (/ y.im (/ (fma y.im y.im (sqr y.re)) x.re))))","end":25.682388912768204,"name":"_divideComplex, imaginary part","status":"apx-start","end-est":23.235151746902467},{"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":20111.1220703125,"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":10914.02001953125,"target":false,"output":"(if (<= i 5327.726165563152) (/ (sqr (/ i 2)) (- (* (* i 2) (* i 2)) 1.0)) (+ (/ 0.00390625 (pow i 4)) (fma (/ 0.015625 i) (/ 1 i) 1/16)))","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":53.13391308798889,"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":108569.16796875,"target":false,"output":"(if (<= alpha 2.069742248392879e+108) (/ (sqr (sqrt (* (* (/ (+ (+ beta alpha) i) (+ beta (fma i 2 alpha))) (fma i (+ (+ beta alpha) i) (* alpha beta))) (/ i (+ beta (fma i 2 alpha)))))) (- (sqr (+ beta (fma i 2 alpha))) 1.0)) (* (/ (fma (/ -1 i) (- (+ (/ 1 beta) (+ (/ 1 i) (/ 1 alpha)))) (/ 1 (* alpha beta))) (* (- (fma (/ -1 i) 2 (/ -1 alpha)) (/ 1 beta)) (- (fma (/ -1 i) 2 (/ -1 alpha)) (/ 1 beta)))) (/ (/ (+ (/ 1 beta) (+ (/ 1 i) (/ 1 alpha))) i) (- (fma (fma (/ -1 i) 2 (/ -1 alpha)) (fma (/ -1 i) 2 (/ -1 alpha)) (/ (/ 1 beta) beta)) (fma (/ (fma (/ -1 i) 2 (/ -1 alpha)) beta) 2 1.0)))))","end":28.582836648262905,"name":"Octave 3.8, jcobi/4","status":"imp-start","end-est":38.67057607821227},{"samplers":["default","default"],"bits":128,"start":3.4574330521018894,"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":33663.4638671875,"target":false,"output":"(if (<= alpha 2.2061842904913525e+200) (/ (/ (/ (+ (+ alpha 1.0) (fma beta alpha beta)) (+ alpha (+ 2 beta))) (+ (+ alpha 1.0) (+ 2 beta))) (+ alpha (+ 2 beta))) 0)","end":1.3886725547997174,"name":"Octave 3.8, jcobi/3","status":"imp-start","end-est":1.0500227886491116},{"samplers":["default","default","default"],"bits":128,"start":23.747252485775736,"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":38637.442138671875,"target":false,"output":"(/ (exp (log (fma (/ (- beta alpha) (+ (fma i 2 beta) (+ 2.0 alpha))) (/ (+ alpha beta) (fma 2 i (+ alpha beta))) 1.0))) 2.0)","end":12.36839301475413,"name":"Octave 3.8, jcobi/2","status":"imp-start","end-est":13.982129073556303},{"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":17633.591796875,"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))) (/ (fma (- beta alpha) (/ 1 (+ (+ alpha beta) 2.0)) 1.0) 2.0))","end":0.01414624062518029,"name":"Octave 3.8, jcobi/1","status":"imp-start","end-est":4.149869153188892},{"samplers":["default"],"bits":128,"start":0.25975,"link":"30-JmatReallambertwestimator","pinf":0,"ninf":0,"vars":["x"],"input":"(- (log x) (log (log x)))","time":5416.037841796875,"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":34427.22802734375,"target":false,"output":"(fma (* (/ (pow (+ (- 7 z) 0.5) (- 0.5 z)) (exp (+ (- 7 z) 0.5))) (* (/ PI (sin (* PI z))) (sqrt (* 2 PI)))) (+ (+ (/ 12.507343278686905 (- 5 z)) (+ (/ -176.6150291621406 (- (- 1 z) (- 1 4))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) (+ (/ -1259.1392167224028 (- (- 1 z) (- 1 2))) (/ 771.3234287776531 (- 3 z)))) (* (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (/ -0.13857109526572012 (- (- 1 z) (- 1 6)))) (* (/ (pow (+ (- 7 z) 0.5) (- 0.5 z)) (exp (+ (- 7 z) 0.5))) (* (/ PI (sin (* PI z))) (sqrt (* 2 PI))))))","end":0.5687209090661479,"name":"Jmat.Real.gamma, branch z less than 0.5","status":"imp-start","end-est":0.5019025583118237},{"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":235175.96313476562,"target":false,"output":"(- (fma (* (/ (sqrt 2) (* (exp (+ -1 7.5)) z)) (pow (/ 1 (pow 6.5 1.0)) 0.5)) (* (sqrt PI) 676.5203681218851) (fma (* 338.26018406094255 (sqrt PI)) (/ (* (* (* (sqrt 2) z) (sqr (log 6.5))) (pow (/ 1 (pow 6.5 1.0)) 0.5)) (exp (+ -1 7.5))) (/ (* (* (* (sqrt PI) 2585.1948787825354) (* (sqrt 2) z)) (pow (/ 1 (pow 6.5 1.0)) 0.5)) (exp (+ -1 7.5))))) (- (* (* (sqrt PI) 1656.8104518737205) (fma (pow (/ 1 (pow 6.5 1.0)) 0.5) (/ (* (sqrt 2) (* z (log 6.5))) (exp (+ -1 7.5))) (* (/ (sqrt 2) (exp (+ -1 7.5))) (pow (/ 1 (pow 6.5 1.0)) 0.5)))) (* (* (/ (* (sqrt 2) (log 6.5)) (exp (+ -1 7.5))) (pow (/ 1 (pow 6.5 1.0)) 0.5)) (* (sqrt PI) 676.5203681218851))))","end":1.6597794699259287,"name":"Jmat.Real.gamma, branch z greater than 0.5","status":"imp-start","end-est":0.98749423241962},{"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":12537.4580078125,"target":false,"output":"(fabs (fma (sqrt (/ 1 PI)) (fma (* (cube (fabs x)) (* 1/5 (fabs x))) (fabs x) (fma 2/3 (cube (fabs x)) (* 2 (fabs x)))) (* (sqrt (/ 1 PI)) (* (pow (fabs x) 7) 1/21))))","end":0.17345542690495297,"name":"Jmat.Real.erfi, branch x less than or equal to 0.5","status":"ex-start","end-est":0.15462875976844204},{"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":104559.0458984375,"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)))) (/ (* (cube (/ 1 (fabs x))) (/ (cube 1) (cube (fabs x)))) (fabs x))))","end":0.9968093035861321,"name":"Jmat.Real.erfi, branch x greater than or equal to 5","status":"apx-start","end-est":0.8969409140144468},{"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":7706.401123046875,"target":false,"output":"(- 1 (/ (fma (fma (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (/ (/ 1 (fma 0.3275911 (fabs x) 1)) (fma 0.3275911 (fabs x) 1)) (+ (/ 1.421413741 (fma 0.3275911 (fabs x) 1)) -0.284496736)) (/ (cbrt (cube (/ 1 (fma 0.3275911 (fabs x) 1)))) (fma 0.3275911 (fabs x) 1)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) (exp (* (fabs x) (fabs x)))))","end":13.830031175496396,"name":"Jmat.Real.erf","status":"apx-start","end-est":15.151295150108567},{"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":26175.359130859375,"target":false,"output":"(if (<= x -4.0904756849807273e+24) (cbrt (/ (cube (/ (+ (fma 0.0005064034 (/ 1 (pow x 8)) (* (/ 0.0072644182 (cube x)) (/ 1 (cube x)))) (fma 0.0001789971 (/ 1 (* (* (pow x 4) (cube x)) (cube x))) (fma 0.0424060604 (/ 1 (pow x 4)) (fma (/ 0.1049934947 x) (/ 1 x) 1)))) x)) (cube (fma 0.0003579942 (/ 1 (* (pow x 6) (sqr (cube x)))) (+ (fma (/ 1 (pow x 8)) 0.0140005442 (/ (* 0.0694555761 1) (sqr (cube x)))) (fma 0.0008327945 (/ 1 (* (* (pow x 4) (cube x)) (cube x))) (fma 0.2909738639 (/ 1 (pow x 4)) (fma (/ 0.7715471019 x) (/ 1 x) 1)))))))) (if (<= x 2.6044556869853095e+29) (/ (* 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))))) (cbrt (/ (cube (/ (+ (fma 0.0005064034 (/ 1 (pow x 8)) (* (/ 0.0072644182 (cube x)) (/ 1 (cube x)))) (fma 0.0001789971 (/ 1 (* (* (pow x 4) (cube x)) (cube x))) (fma 0.0424060604 (/ 1 (pow x 4)) (fma (/ 0.1049934947 x) (/ 1 x) 1)))) x)) (cube (fma 0.0003579942 (/ 1 (* (pow x 6) (sqr (cube x)))) (+ (fma (/ 1 (pow x 8)) 0.0140005442 (/ (* 0.0694555761 1) (sqr (cube x)))) (fma 0.0008327945 (/ 1 (* (* (pow x 4) (cube x)) (cube x))) (fma 0.2909738639 (/ 1 (pow x 4)) (fma (/ 0.7715471019 x) (/ 1 x) 1))))))))))","end":20.366919510019365,"name":"Jmat.Real.dawson","status":"imp-start","end-est":24.100152333029666},{"samplers":["default","default"],"bits":128,"start":37.301279876022534,"link":"37-mathsqrtoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))","time":5004.630859375,"target":32.5432812562869,"output":"(* 0.5 (sqrt (fma (hypot re im) 2.0 (* 2.0 re))))","end":12.88898148779604,"name":"math.sqrt on complex, real part","status":"gt-target","end-est":15.32796514425499},{"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":16134.79296875,"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":1232.629150390625,"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":11892.3330078125,"target":12.292298687802464,"output":"(* (fma (cube im) 1/3 (fma (pow im 5) 1/60 (* im 2))) (* (sin re) (- 0.5)))","end":2.7683171836143314,"name":"math.cos on complex, imaginary part","status":"gt-target","end-est":0.4399020825366849},{"samplers":["default","default"],"bits":128,"start":20.020608880635248,"link":"41-JmatReallambertwnewtonloopstep","pinf":0,"ninf":0,"vars":["wj","x"],"input":"(- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj)))))","time":7644.528076171875,"target":19.96466722932975,"output":"(fma wj (- wj (sqr wj)) (/ x (fma wj (exp wj) (exp wj))))","end":0.05995996250072116,"name":"Jmat.Real.lambertw, newton loop step","status":"gt-target","end-est":0.9560912980652254},{"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":3941.906982421875,"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":5088.39013671875,"target":0.061625,"output":"(fma d1 (+ d3 3) (* d1 d2))","end":0.0395,"name":"FastMath test3","status":"eq-target","end-est":0.05078125},{"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":3411.609130859375,"target":0.026125,"output":"(fma d1 (+ 20 10) (* d1 d2))","end":0.010198120312590144,"name":"FastMath test2","status":"eq-target","end-est":0.015625},{"samplers":["default"],"bits":128,"start":0.27475,"link":"45-FastMathtest1","pinf":0,"ninf":0,"vars":["d"],"input":"(+ (* d 10) (* d 20))","time":1040.116943359375,"target":0,"output":"(* (+ 10 20) d)","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":1329.55615234375,"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":12589.36083984375,"target":0.023125,"output":"(* d1 (+ (- d2 d3) (- d4 d1)))","end":0.023,"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":8249.737060546875,"target":0.022625,"output":"(fma (+ d3 37) d1 (* d1 d2))","end":0.016475919365257198,"name":"FastMath dist3","status":"eq-target","end-est":0.0078125},{"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":3150.39404296875,"target":0.01225,"output":"(* (+ d2 d3) d1)","end":0.01225,"name":"FastMath dist","status":"eq-target","end-est":0.0078125}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}