{"bit_width":64,"date":1470652128,"note":"libraries","iterations":2,"flags":["rules:numerics","rules:arithmetic","rules:polynomials","rules:fractions","rules:exponents","rules:trigonometry","setup:simplify","reduce:taylor","reduce:simplify","reduce:avg-error","generate:rr","generate:taylor","generate:simplify","precision:double"],"seed":"#(1066118269 3146385405 2008244797 2413636924 657271294 3751684478)","points":256,"tests":[{"samplers":["default","default","default","default"],"bits":128,"start":32.01483135608258,"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":11105.155029296875,"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":3.4698888892916835,"name":"powComplex, real part","status":"imp-start","end-est":2.715601464924832},{"samplers":["default","default","default","default"],"bits":128,"start":32.270121878634335,"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":15085.5380859375,"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":4.045578972865925,"name":"powComplex, imaginary part","status":"imp-start","end-est":3.4536253588533397},{"samplers":["(uniform 0 1)","(uniform 0 1)"],"bits":128,"start":0.42017089551525644,"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":5657.433837890625,"target":false,"output":"(+ (* (/ (pow (* -2 (log u1)) 0.5) 6) (cbrt (cube (cos (* PI (* u2 2)))))) 0.5)","end":0.4484051507130769,"name":"normal distribution","status":"ex-start","end-est":0.36726386722130433},{"samplers":["default","default"],"bits":128,"start":0.007698120312590145,"link":"3-mathsquareoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(- (* re re) (* im im))","time":2369.11083984375,"target":false,"output":"(* (+ re im) (- re im))","end":0.000625,"name":"math.square on complex, real part","status":"ex-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":0.007,"link":"4-mathsquareoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(+ (* re im) (* im re))","time":1041.446044921875,"target":false,"output":"(* im (+ re re))","end":0.007699671288691762,"name":"math.square on complex, imaginary part","status":"ex-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":30.034600280104854,"link":"5-mathsqrtoncompleximaginarypartimgreaterthan0branch","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* 0.5 (sqrt (* 2.0 (+ (sqrt (- (* re re) (* im im))) re))))","time":13943.005126953125,"target":false,"output":"(* 0.5 (sqrt (* 2.0 (fma (sqrt (+ re im)) (sqrt (- re im)) re))))","end":0.11812726534603094,"name":"math.sqrt on complex, imaginary part, im greater than 0 branch","status":"imp-start","end-est":0.7343739275807164},{"samplers":["default","default"],"bits":128,"start":0.021438232867308126,"link":"6-mathsinoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))","time":7641.721923828125,"target":false,"output":"(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))","end":0.021438232867308126,"name":"math.sin on complex, real part","status":"ex-start","end-est":0.015625},{"samplers":["default","default"],"bits":128,"start":30.16332673607504,"link":"7-mathlog10oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))","time":2011.43408203125,"target":false,"output":"(/ (log (hypot im re)) (log 10))","end":0.6027045140838662,"name":"math.log10 on complex, real part","status":"imp-start","end-est":0.556972509768442},{"samplers":["default","default"],"bits":128,"start":0.8445073312532456,"link":"8-mathlog10oncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(/ (atan2 im re) (log 10))","time":2357.3388671875,"target":false,"output":"(log1p (expm1 (/ (atan2 im re) (log 10))))","end":0.732040414066557,"name":"math.log10 on complex, imaginary part","status":"ex-start","end-est":0.744472509768442},{"samplers":["default","default","default"],"bits":128,"start":31.23059840637277,"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":5639.593017578125,"target":false,"output":"(/ (log (expm1 (log1p (hypot im re)))) (log base))","end":0.3532973687525242,"name":"math.log/2 on complex, real part","status":"imp-start","end-est":0.39385060090969964},{"samplers":["default","default","default"],"bits":128,"start":31.53174532425327,"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":4264.575927734375,"target":false,"output":"(/ (- (atan2 im re) 0) (log base))","end":0.31028308281331124,"name":"math.log/2 on complex, imaginary part","status":"imp-start","end-est":0.28125},{"samplers":["default","default"],"bits":128,"start":29.852196248287203,"link":"11-mathlog1oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(log (sqrt (+ (* re re) (* im im))))","time":1396.51708984375,"target":false,"output":"(log (hypot im re))","end":0.000125,"name":"math.log/1 on complex, real part","status":"imp-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":0,"link":"12-mathlog1oncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(atan2 im re)","time":776.18994140625,"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":0.009625,"link":"13-mathexponcomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (exp re) (cos im))","time":1859.52001953125,"target":false,"output":"(* (exp re) (cos im))","end":0.009625,"name":"math.exp on complex, real part","status":"ex-start","end-est":0.01171875},{"samplers":["default","default"],"bits":128,"start":0.022020011775584675,"link":"14-mathexponcompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (exp re) (sin im))","time":2189.633056640625,"target":false,"output":"(* (exp re) (sin im))","end":0.022020011775584675,"name":"math.exp on complex, imaginary part","status":"ex-start","end-est":0.01171875},{"samplers":["default","default"],"bits":128,"start":6.226465639393076,"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":26077.6748046875,"target":false,"output":"(+ (* (sqr x.re) (+ x.re x.im)) (* (- (- (+ x.re x.im)) (+ x.im x.im)) (* x.im x.re)))","end":0.2505970082014341,"name":"math.cube on complex, real part","status":"imp-start","end-est":0.232753759768442},{"samplers":["default","default"],"bits":128,"start":6.535102759580832,"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":6499.962890625,"target":false,"output":"(fma (* (- x.re x.im) (+ x.re x.im)) x.im (* (* (+ x.im x.im) x.re) x.re))","end":6.520414037705291,"name":"math.cube on complex, imaginary part","status":"apx-start","end-est":6.455363943856603},{"samplers":["default","default"],"bits":128,"start":0.009198120312590145,"link":"17-mathcosoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))","time":4742.364990234375,"target":false,"output":"(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))","end":0.009198120312590145,"name":"math.cos on complex, real part","status":"ex-start","end-est":0.0078125},{"samplers":["default","default"],"bits":128,"start":0,"link":"18-mathargoncomplex","pinf":0,"ninf":0,"vars":["re","im"],"input":"(atan2 im re)","time":952.635986328125,"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":28.729725032204577,"link":"19-mathabsoncomplex","pinf":0,"ninf":0,"vars":["re","im"],"input":"(sqrt (+ (* re re) (* im im)))","time":934.408935546875,"target":false,"output":"(hypot im re)","end":0.003625,"name":"math.abs on complex","status":"imp-start","end-est":0.01171875},{"samplers":["default","default","default","default"],"bits":128,"start":0.011448120312590146,"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":6179.995849609375,"target":false,"output":"(- (* x.re y.re) (* x.im y.im))","end":0.011448120312590146,"name":"_multiplyComplex, real part","status":"ex-start","end-est":0.01171875},{"samplers":["default","default","default","default"],"bits":128,"start":0.010049039677847345,"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":2351.906982421875,"target":false,"output":"(fma y.im x.re (* y.re x.im))","end":0.00554024101186092,"name":"_multiplyComplex, imaginary part","status":"ex-start","end-est":0},{"samplers":["default","default","default","default"],"bits":128,"start":25.128284645020447,"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":3071.573974609375,"target":false,"output":"(/ (fma y.re x.re (* y.im x.im)) (fma y.im y.im (* y.re y.re)))","end":25.12736503274437,"name":"_divideComplex, real part","status":"apx-start","end-est":25.962420619472002},{"samplers":["default","default","default","default"],"bits":128,"start":25.373879170831636,"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":4208.9140625,"target":false,"output":"(/ (- (* y.re x.im) (* y.im x.re)) (fma y.im y.im (* y.re y.re)))","end":25.372931050519043,"name":"_divideComplex, imaginary part","status":"apx-start","end-est":26.235737817807507},{"samplers":["default","default"],"bits":128,"start":0.1360749785305007,"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":13295.31494140625,"target":false,"output":"(+ (- a (/ 1.0 3.0)) (* rand (/ (- a (/ 1.0 3.0)) (sqrt (* (- a (/ 1.0 3.0)) 9)))))","end":0.11086693450061887,"name":"Octave 3.8, oct_fill_randg","status":"ex-start","end-est":0.13825123993272953},{"samplers":["default"],"bits":128,"start":45.594784760792216,"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":4745.64404296875,"target":false,"output":"(/ (sqr (/ i 2)) (- (* (* i 2) (* i 2)) 1.0))","end":15.506928070678628,"name":"Octave 3.8, jcobi/4, as called","status":"imp-start","end-est":16.232124403363965},{"samplers":["default","default","default"],"bits":128,"start":52.499198956571334,"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":46712.694091796875,"target":false,"output":"(/ (* (* (/ (+ (+ 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))","end":38.67810839107646,"name":"Octave 3.8, jcobi/4","status":"imp-start","end-est":40.56338373686884},{"samplers":["default","default"],"bits":128,"start":3.732476142868326,"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":29483.3427734375,"target":false,"output":"(* (/ 1 (+ (+ beta 1.0) (+ alpha 2))) (/ (/ (+ (+ alpha 1.0) (fma beta alpha beta)) (+ alpha (+ 2 beta))) (+ alpha (+ 2 beta))))","end":3.7837143006801957,"name":"Octave 3.8, jcobi/3","status":"apx-start","end-est":4.603628451407888},{"samplers":["default","default","default"],"bits":128,"start":23.38720532199308,"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":19520.010009765625,"target":false,"output":"(/ (+ (/ (/ (- beta alpha) (+ (+ alpha 2.0) (fma i 2 beta))) (/ (fma 2 i (+ alpha beta)) (+ alpha beta))) 1.0) 2.0)","end":12.205825415686558,"name":"Octave 3.8, jcobi/2","status":"imp-start","end-est":11.937404881025815},{"samplers":["default","default"],"bits":128,"start":16.143868587011657,"link":"29-Octave38jcobi1","pinf":0,"ninf":0,"vars":["alpha","beta"],"input":"(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)","time":9155.40380859375,"target":false,"output":"(/ (- (* beta (/ 1 (+ (+ alpha beta) 2.0))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)","end":15.624748085196671,"name":"Octave 3.8, jcobi/1","status":"apx-start","end-est":16.331753352013536},{"samplers":["default"],"bits":128,"start":0.263375,"link":"30-JmatReallambertwestimator","pinf":0,"ninf":0,"vars":["x"],"input":"(- (log x) (log (log x)))","time":4426.886962890625,"target":false,"output":"(log (/ x (log x)))","end":0.00325,"name":"Jmat.Real.lambertw, estimator","status":"ex-start","end-est":0},{"samplers":["default"],"bits":128,"start":1.818528232324072,"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":28318.373046875,"target":false,"output":"(* (* (/ (* PI (sqrt (* PI 2))) (sin (* z PI))) (/ (pow (+ (+ 0.5 7) (- 1 (+ 1 z))) (- (+ 1 0.5) (+ 1 z))) (exp (+ (+ 0.5 7) (cbrt (cube (- 1 (+ 1 z)))))))) (+ (+ (/ 1.5056327351493116e-07 (- (+ 1 8) (+ 1 z))) (+ (/ -0.13857109526572012 (- (- 1 z) (- 1 6))) (/ 9.984369578019572e-06 (fma z -1 7)))) (+ (+ (+ (/ -176.6150291621406 (- (- 1 z) (- 1 4))) (/ 12.507343278686905 (- (+ 1 5) (+ 1 z)))) (+ 0.9999999999998099 (/ 676.5203681218851 (- (- 1 z) 0)))) (+ (/ 771.3234287776531 (- (+ 1 3) (+ 1 z))) (/ -1259.1392167224028 (- (- 1 z) (- 1 2)))))))","end":0.5692610842353863,"name":"Jmat.Real.gamma, branch z less than 0.5","status":"imp-start","end-est":0.5727182727669767},{"samplers":["default"],"bits":128,"start":59.83491993580359,"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":92567.47192382812,"target":false,"output":"(* (+ (+ (+ (/ 1.5056327351493116e-07 (- (+ z 8) 1)) (/ 9.984369578019572e-06 (+ 7 (- z 1)))) (+ (/ -0.13857109526572012 (+ (- z 1) 6)) (/ 12.507343278686905 (- z (- 1 5))))) (+ (+ (/ -1259.1392167224028 (- z (- 1 2))) (/ 771.3234287776531 (+ (- z 1) 3))) (+ (+ (/ 676.5203681218851 (- z 0)) 0.9999999999998099) (/ -176.6150291621406 (- (+ z 4) 1))))) (/ (cube (cbrt (* (pow (+ (- z 1) (+ 0.5 7)) (+ 0.5 (- z 1))) (sqrt (* 2 PI))))) (exp (+ (- z 1) (+ 0.5 7)))))","end":0.9309073742235356,"name":"Jmat.Real.gamma, branch z greater than 0.5","status":"imp-start","end-est":0.6223995164107878},{"samplers":["default"],"bits":128,"start":0.21342354277368253,"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":12444.9580078125,"target":false,"output":"(fabs (+ (* (sqrt (/ 1 PI)) (fma (* 1/5 (* (fabs x) (cube (fabs x)))) (fabs x) (fma 2/3 (cube (fabs x)) (* 2 (fabs x))))) (* (sqrt (/ 1 PI)) (* 1/21 (* (cube (sqr (fabs x))) (fabs x))))))","end":0.23261572596321525,"name":"Jmat.Real.erfi, branch x less than or equal to 0.5","status":"ex-start","end-est":0.6217767759846262},{"samplers":["default"],"bits":128,"start":1.515357496899851,"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":94988.708984375,"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":0.9882489876370613,"name":"Jmat.Real.erfi, branch x greater than or equal to 5","status":"apx-start","end-est":0.9619368247750097},{"samplers":["default"],"bits":128,"start":14.066995138590388,"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":7417.218017578125,"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)) (/ (cube (log (exp (cbrt (/ 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":14.07854352964358,"name":"Jmat.Real.erf","status":"apx-start","end-est":14.01084796911424},{"samplers":["default"],"bits":128,"start":28.369230067033232,"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":12991.362060546875,"target":false,"output":"(/ (* x (+ (fma 0.0005064034 (pow x 8) (* 0.0072644182 (cube (sqr x)))) (fma 0.0001789971 (* (cube (sqr x)) (pow x 4)) (fma 0.0424060604 (pow x 4) (fma (* 0.1049934947 x) x 1))))) (fma 0.0003579942 (* (cube (sqr x)) (pow x 6)) (+ (fma (pow x 8) 0.0140005442 (* 0.0694555761 (cube (sqr x)))) (fma 0.0008327945 (* (cube (sqr x)) (pow x 4)) (fma 0.2909738639 (pow x 4) (fma (* 0.7715471019 x) x 1))))))","end":28.375178605852703,"name":"Jmat.Real.dawson","status":"apx-start","end-est":27.837904871146797},{"samplers":["default","default"],"bits":128,"start":36.70203403018071,"link":"37-mathsqrtoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))","time":2797.25390625,"target":31.817453730297263,"output":"(* 0.5 (sqrt (fma (hypot re im) 2.0 (* 2.0 re))))","end":13.000336522967952,"name":"math.sqrt on complex, real part","status":"gt-target","end-est":10.354882036424513},{"samplers":["default","default"],"bits":128,"start":59.00451210815145,"link":"38-mathsinoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (cos re)) (- (exp (- 0 im)) (exp im)))","time":11476.984130859375,"target":10.000905779326299,"output":"(* (- (+ (* 1/60 (pow im 5)) (+ (* 2 im) (* 1/3 (pow im 3))))) (* (cos re) 0.5))","end":0.20806023058027612,"name":"math.sin on complex, imaginary part","status":"gt-target","end-est":0.884599888564733},{"samplers":["default"],"bits":128,"start":0.121875,"link":"39-mathcubeonreal","pinf":0,"ninf":0,"vars":["x"],"input":"(* (* x x) x)","time":884.863037109375,"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":47.10468239698333,"link":"40-mathcosoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))","time":10006.802978515625,"target":12.15714876781439,"output":"(* (fma (cube im) 1/3 (fma (pow im 5) 1/60 (* im 2))) (* (sin re) (- 0.5)))","end":2.7212527134087776,"name":"math.cos on complex, imaginary part","status":"gt-target","end-est":0.9113916182183492},{"samplers":["default","default"],"bits":128,"start":28.219944172678876,"link":"41-JmatReallambertwnewtonloopstep","pinf":0,"ninf":0,"vars":["wj","x"],"input":"(- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj)))))","time":5451.52001953125,"target":28.162581201593305,"output":"(fma (- wj (* 2 x)) wj x)","end":0.0045,"name":"Jmat.Real.lambertw, newton loop step","status":"gt-target","end-est":3.0790576630190296},{"samplers":["default"],"bits":128,"start":0.12816901797735797,"link":"42-FastMathtest5","pinf":0,"ninf":0,"vars":["d1"],"input":"(* (* d1 (* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)) d1)","time":3603.77783203125,"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":0.07465360233631199,"link":"43-FastMathtest3","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))","time":3482.739013671875,"target":0.065625,"output":"(* d1 (+ (+ d3 3) d2))","end":0.0655,"name":"FastMath test3","status":"eq-target","end-est":0},{"samplers":["default","default"],"bits":128,"start":0.18854903967784734,"link":"44-FastMathtest2","pinf":0,"ninf":0,"vars":["d1","d2"],"input":"(+ (+ (* d1 10) (* d1 d2)) (* d1 20))","time":1958.880859375,"target":0.0265,"output":"(* d1 (+ d2 30))","end":0.0265,"name":"FastMath test2","status":"eq-target","end-est":0.0078125},{"samplers":["default"],"bits":128,"start":0.27525,"link":"45-FastMathtest1","pinf":0,"ninf":0,"vars":["d"],"input":"(+ (* d 10) (* d 20))","time":649.26611328125,"target":0,"output":"(* (+ 10 20) d)","end":0,"name":"FastMath test1","status":"eq-target","end-est":0},{"samplers":["default"],"bits":128,"start":0.13511560156295072,"link":"46-FastMathrepmul","pinf":0,"ninf":0,"vars":["d1"],"input":"(* (* (* d1 d1) d1) d1)","time":1001.18505859375,"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":0.02339624062518029,"link":"47-FastMathdist4","pinf":0,"ninf":0,"vars":["d1","d2","d3","d4"],"input":"(- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1))","time":5584.528076171875,"target":0.023073120312590144,"output":"(* d1 (+ (- d2 d3) (- d4 d1)))","end":0.023073120312590144,"name":"FastMath dist4","status":"eq-target","end-est":0.015625},{"samplers":["default","default","default"],"bits":128,"start":0.04594812031259015,"link":"48-FastMathdist3","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))","time":5279.4609375,"target":0.02375,"output":"(fma (+ d3 37) d1 (* d1 d2))","end":0.017698120312590146,"name":"FastMath dist3","status":"eq-target","end-est":0.01171875},{"samplers":["default","default","default"],"bits":128,"start":0.014323120312590145,"link":"49-FastMathdist","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (* d1 d2) (* d1 d3))","time":2246.819091796875,"target":0.011875,"output":"(* (+ d2 d3) d1)","end":0.011875,"name":"FastMath dist","status":"eq-target","end-est":0}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}