{"bit_width":64,"date":1469968745,"note":"libraries","iterations":2,"flags":["rules:numerics","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","precision:double"],"seed":"#(1065990927 2514927446 2806713580 2976231080 3799737104 4212629478)","points":256,"tests":[{"samplers":["default","default","default","default"],"bits":128,"start":32.52905048333607,"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":15702.1748046875,"target":false,"output":"(* (/ (pow (hypot x.im x.re) y.re) (exp (* y.im (atan2 x.im x.re)))) (cos (cube (cbrt (fma y.im (log (hypot x.im x.re)) (* y.re (atan2 x.im x.re)))))))","end":3.8629113900688945,"name":"powComplex, real part","status":"imp-start","end-est":8.330934622468645},{"samplers":["default","default","default","default"],"bits":128,"start":32.11449513042455,"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":34101.505859375,"target":false,"output":"(* (/ (pow (hypot x.im x.re) y.re) (pow (exp 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":1.8911271212500826,"name":"powComplex, imaginary part","status":"imp-start","end-est":9.578389231588972},{"samplers":["(uniform 0 1)","(uniform 0 1)"],"bits":128,"start":0.4055289659082226,"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":9225.322021484375,"target":false,"output":"(fma (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)) (cos (* PI (* u2 2))) 0.5)","end":0.3830641161673309,"name":"normal distribution","status":"ex-start","end-est":0.3461113769897463},{"samplers":["default","default"],"bits":128,"start":0.00725,"link":"3-mathsquareoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(- (* re re) (* im im))","time":2546.76513671875,"target":false,"output":"(- (sqr re) (sqr im))","end":0.00725,"name":"math.square on complex, real part","status":"ex-start","end-est":0.0078125},{"samplers":["default","default"],"bits":128,"start":0.00875,"link":"4-mathsquareoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(+ (* re im) (* im re))","time":964.219970703125,"target":false,"output":"(* im (+ re re))","end":0.007503337554497499,"name":"math.square on complex, imaginary part","status":"ex-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":29.82146856231123,"link":"5-mathsqrtoncompleximaginarypartimgreaterthan0branch","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* 0.5 (sqrt (* 2.0 (+ (sqrt (- (* re re) (* im im))) re))))","time":14790.9150390625,"target":false,"output":"(* 0.5 (sqrt (* 2.0 (fma (sqrt (+ re im)) (sqrt (- re im)) re))))","end":0.08825263159559747,"name":"math.sqrt on complex, imaginary part, im greater than 0 branch","status":"imp-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":0.032050295710572156,"link":"6-mathsinoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))","time":10583.842041015625,"target":false,"output":"(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))","end":0.032050295710572156,"name":"math.sin on complex, real part","status":"ex-start","end-est":0.01953125},{"samplers":["default","default"],"bits":128,"start":30.644025308422453,"link":"7-mathlog10oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))","time":4456.77197265625,"target":false,"output":"(log (exp (/ (log (hypot im re)) (log 10))))","end":0.5902468222795307,"name":"math.log10 on complex, real part","status":"imp-start","end-est":0.5885925781475362},{"samplers":["default","default"],"bits":128,"start":0.8422810156295079,"link":"8-mathlog10oncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(/ (atan2 im re) (log 10))","time":2673.29296875,"target":false,"output":"(/ (atan2 im re) (log 10))","end":0.8422810156295079,"name":"math.log10 on complex, imaginary part","status":"ex-start","end-est":0.8600387695368841},{"samplers":["default","default","default"],"bits":128,"start":30.899194763529174,"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":6580.067138671875,"target":false,"output":"(* (log (hypot im re)) (/ 1 (log base)))","end":0.4419088359478673,"name":"math.log/2 on complex, real part","status":"imp-start","end-est":0.41310502930532605},{"samplers":["default","default","default"],"bits":128,"start":31.22156716433313,"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":5410.93896484375,"target":false,"output":"(- (/ (atan2 im re) (log base)) 0)","end":0.31368872187554087,"name":"math.log/2 on complex, imaginary part","status":"imp-start","end-est":0.34212875976844204},{"samplers":["default","default"],"bits":128,"start":30.346094432433414,"link":"11-mathlog1oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(log (sqrt (+ (* re re) (* im im))))","time":1355.137939453125,"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":1371.739013671875,"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":0.00725,"link":"13-mathexponcomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (exp re) (cos im))","time":2106.406005859375,"target":false,"output":"(* (exp re) (cos im))","end":0.00725,"name":"math.exp on complex, real part","status":"ex-start","end-est":0.00390625},{"samplers":["default","default"],"bits":128,"start":0.029184124220474755,"link":"14-mathexponcompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (exp re) (sin im))","time":2842.47607421875,"target":false,"output":"(* (exp re) (sin im))","end":0.029184124220474755,"name":"math.exp on complex, imaginary part","status":"ex-start","end-est":0.015625},{"samplers":["default","default"],"bits":128,"start":6.986041399970436,"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":25683.223876953125,"target":false,"output":"(fma x.im (* (- x.re) (fma 3 x.im x.re)) (* (+ x.re x.im) (sqr x.re)))","end":0.25268832561706,"name":"math.cube on complex, real part","status":"imp-start","end-est":0.23046875},{"samplers":["default","default"],"bits":128,"start":6.957472569314011,"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":6136.3828125,"target":false,"output":"(fma (* (- x.re x.im) (+ x.re x.im)) x.im (* (* (+ x.im x.im) x.re) x.re))","end":6.940253208376242,"name":"math.cube on complex, imaginary part","status":"apx-start","end-est":6.482811544275851},{"samplers":["default","default"],"bits":128,"start":0.010323120312590145,"link":"17-mathcosoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))","time":4591.322998046875,"target":false,"output":"(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))","end":0.010323120312590145,"name":"math.cos on complex, real part","status":"ex-start","end-est":0.00390625},{"samplers":["default","default"],"bits":128,"start":0,"link":"18-mathargoncomplex","pinf":0,"ninf":0,"vars":["re","im"],"input":"(atan2 im re)","time":866.51513671875,"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":29.196338386371547,"link":"19-mathabsoncomplex","pinf":0,"ninf":0,"vars":["re","im"],"input":"(sqrt (+ (* re re) (* im im)))","time":848.5830078125,"target":false,"output":"(hypot im re)","end":0.0035,"name":"math.abs on complex","status":"imp-start","end-est":0.0078125},{"samplers":["default","default","default","default"],"bits":128,"start":0.01014624062518029,"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":5293.885986328125,"target":false,"output":"(- (* x.re y.re) (* x.im y.im))","end":0.01014624062518029,"name":"_multiplyComplex, real part","status":"ex-start","end-est":0.0078125},{"samplers":["default","default","default","default"],"bits":128,"start":0.01164624062518029,"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":2466.623046875,"target":false,"output":"(fma y.im x.re (* y.re x.im))","end":0.006719360937770434,"name":"_multiplyComplex, imaginary part","status":"ex-start","end-est":0.01171875},{"samplers":["default","default","default","default"],"bits":128,"start":25.58735883659281,"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":4759.037109375,"target":false,"output":"(/ (fma y.re x.re (* y.im x.im)) (fma y.im y.im (* y.re y.re)))","end":25.587600044930532,"name":"_divideComplex, real part","status":"apx-start","end-est":24.846461240700357},{"samplers":["default","default","default","default"],"bits":128,"start":25.54227690309802,"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":6599.7109375,"target":false,"output":"(* (- (* y.re x.im) (* y.im x.re)) (/ 1 (fma y.im y.im (* y.re y.re))))","end":25.71853110260256,"name":"_divideComplex, imaginary part","status":"apx-start","end-est":23.823219551014606},{"samplers":["default","default"],"bits":128,"start":0.12940216645737784,"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":16502.237060546875,"target":false,"output":"(fma (sqrt (- a 0.3333333333333333)) (* rand 1/3) (- a 0.3333333333333333))","end":0.1226560156295073,"name":"Octave 3.8, oct_fill_randg","status":"ex-start","end-est":0.10775375976844202},{"samplers":["default"],"bits":128,"start":45.73192161384937,"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":5427.755859375,"target":false,"output":"(/ (sqr (/ i 2)) (- (* (* i 2) (* i 2)) 1.0))","end":15.489928162626798,"name":"Octave 3.8, jcobi/4, as called","status":"imp-start","end-est":13.563883829677344},{"samplers":["default","default","default"],"bits":128,"start":52.43489526224103,"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":55142.0458984375,"target":false,"output":"(/ 1 (/ (- (sqr (+ beta (fma i 2 alpha))) 1.0) (* (* (/ (+ (+ beta alpha) i) (+ beta (fma i 2 alpha))) (fma i (+ (+ beta alpha) i) (* alpha beta))) (/ i (+ beta (fma i 2 alpha))))))","end":39.41243417439005,"name":"Octave 3.8, jcobi/4","status":"imp-start","end-est":41.72324215971639},{"samplers":["default","default"],"bits":128,"start":3.3231444298134467,"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":33137.295166015625,"target":false,"output":"(/ (/ (/ (+ (+ alpha 1.0) (fma beta alpha beta)) (+ alpha (+ 2 beta))) (+ (+ alpha 1.0) (+ 2 beta))) (+ alpha (+ 2 beta)))","end":3.3188895423112825,"name":"Octave 3.8, jcobi/3","status":"apx-start","end-est":4.066462398492752},{"samplers":["default","default","default"],"bits":128,"start":23.37984993334118,"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":24174.473876953125,"target":false,"output":"(/ (fma (* (- beta alpha) (/ 1 (+ (fma i 2 beta) (+ 2.0 alpha)))) (/ (+ alpha beta) (fma 2 i (+ alpha beta))) 1.0) 2.0)","end":12.370620323696036,"name":"Octave 3.8, jcobi/2","status":"imp-start","end-est":12.545046525783974},{"samplers":["default","default"],"bits":128,"start":16.490046558494694,"link":"29-Octave38jcobi1","pinf":0,"ninf":0,"vars":["alpha","beta"],"input":"(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)","time":12384.573974609375,"target":false,"output":"(/ (fma (- beta alpha) (/ 1 (+ (+ alpha beta) 2.0)) 1.0) 2.0)","end":16.709882737441138,"name":"Octave 3.8, jcobi/1","status":"apx-start","end-est":17.071386985074145},{"samplers":["default"],"bits":128,"start":0.261,"link":"30-JmatReallambertwestimator","pinf":0,"ninf":0,"vars":["x"],"input":"(- (log x) (log (log x)))","time":5373.885986328125,"target":false,"output":"(log (/ x (log x)))","end":0.00375,"name":"Jmat.Real.lambertw, estimator","status":"ex-start","end-est":0.01171875},{"samplers":["default"],"bits":128,"start":1.813011044174038,"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":38208.619873046875,"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) (log (exp (- 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":0.5953022997268657,"name":"Jmat.Real.gamma, branch z less than 0.5","status":"imp-start","end-est":0.4658775879159783},{"samplers":["default"],"bits":128,"start":59.99276712271079,"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":245210.05590820312,"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))))) (/ (pow (+ (- z 1) (+ 0.5 7)) (+ 0.5 (- z 1))) 1)) (/ (sqrt (* 2 PI)) (exp (+ (- z 1) (+ 0.5 7)))))","end":0.8875808144769447,"name":"Jmat.Real.gamma, branch z greater than 0.5","status":"imp-start","end-est":0.644124140141048},{"samplers":["default"],"bits":128,"start":0.16967067813599754,"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":13083.833984375,"target":false,"output":"(fabs (* (fma (* (* 1/21 (cube (fabs x))) (cube (fabs x))) (fabs x) (fma (* (cube (fabs x)) (* (fabs x) 1/5)) (fabs x) (fma 2/3 (cube (fabs x)) (* 2 (fabs x))))) (sqrt (/ 1 PI))))","end":0.18216433398777596,"name":"Jmat.Real.erfi, branch x less than or equal to 0.5","status":"ex-start","end-est":0.16701127930532605},{"samplers":["default"],"bits":128,"start":1.5280281064329546,"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":85464.25415039062,"target":false,"output":"(fma (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (/ 1 (fabs x)) (fma (/ (/ (/ 3 4) (fabs x)) (cube (fabs x))) (/ 1 (fabs x)) (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))))) (* (/ (/ 15 8) (sqr (cube (fabs x)))) (/ (exp (* (fabs x) (fabs x))) (* (sqrt PI) (fabs x)))))","end":0.9021102405076455,"name":"Jmat.Real.erfi, branch x greater than or equal to 5","status":"apx-start","end-est":0.9753128899329561},{"samplers":["default"],"bits":128,"start":13.780717295586696,"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":8950.5771484375,"target":false,"output":"(log (exp (- 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)) (/ (/ 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":13.767600547601115,"name":"Jmat.Real.erf","status":"apx-start","end-est":13.474280373759866},{"samplers":["default"],"bits":128,"start":28.920578777895592,"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":20484.72509765625,"target":false,"output":"(* (/ x 1) (/ (+ (fma 0.0001789971 (* (* (* x x) (* x x)) (* (cube x) (cube x))) (fma 0.0424060604 (* (* x x) (* x x)) (fma (* 0.1049934947 x) x 1))) (fma 0.0005064034 (* (* (* x x) (* x x)) (* (* x x) (* x x))) (* 0.0072644182 (* (cube x) (cube x))))) (fma (* 0.0001789971 2) (cube (* (* x x) (* x x))) (+ (fma 0.0008327945 (sqr (* (* x x) (cube x))) (fma 0.2909738639 (* (* x x) (* x x)) (fma (* 0.7715471019 x) x 1))) (fma (* (* (* x x) (* x x)) (* (* x x) (* x x))) 0.0140005442 (* (* (cube x) (cube x)) 0.0694555761))))))","end":28.93639148060814,"name":"Jmat.Real.dawson","status":"apx-start","end-est":31.251803248765288},{"samplers":["default","default"],"bits":128,"start":37.20471251667821,"link":"37-mathsqrtoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))","time":3241.74609375,"target":32.328307006129634,"output":"(* 0.5 (sqrt (fma (hypot re im) 2.0 (* 2.0 re))))","end":12.864823170784664,"name":"math.sqrt on complex, real part","status":"gt-target","end-est":13.42935836532443},{"samplers":["default","default"],"bits":128,"start":58.99250209497064,"link":"38-mathsinoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (cos re)) (- (exp (- 0 im)) (exp im)))","time":15098.932861328125,"target":9.76756719909256,"output":"(* (/ (fma 1/60 (pow im 5) (fma (cube im) 1/3 (* 2 im))) 1) (* (cos re) (- 0.5)))","end":0.1937195287057626,"name":"math.sin on complex, imaginary part","status":"gt-target","end-est":1.0311407315128904},{"samplers":["default"],"bits":128,"start":0.124125,"link":"39-mathcubeonreal","pinf":0,"ninf":0,"vars":["x"],"input":"(* (* x x) x)","time":945.087890625,"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":47.562363402195615,"link":"40-mathcosoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))","time":12260.8720703125,"target":11.733997486912378,"output":"(* (fma (cube im) 1/3 (fma (pow im 5) 1/60 (* im 2))) (* (sin re) (- 0.5)))","end":2.577807017761972,"name":"math.cos on complex, imaginary part","status":"gt-target","end-est":1.0077004274647317},{"samplers":["default","default"],"bits":128,"start":18.24946733816534,"link":"41-JmatReallambertwnewtonloopstep","pinf":0,"ninf":0,"vars":["wj","x"],"input":"(- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj)))))","time":9724.3759765625,"target":18.22436642016873,"output":"(+ (- (fma wj wj (pow wj 4)) (cube wj)) (/ x (fma wj (exp wj) (exp wj))))","end":0.03842053346954507,"name":"Jmat.Real.lambertw, newton loop step","status":"gt-target","end-est":1.275257772703098},{"samplers":["default"],"bits":128,"start":0.13104381446477587,"link":"42-FastMathtest5","pinf":0,"ninf":0,"vars":["d1"],"input":"(* (* d1 (* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)) d1)","time":3073.3310546875,"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":0.0778327222622215,"link":"43-FastMathtest3","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))","time":3898.15087890625,"target":0.0675,"output":"(fma d1 (+ d3 3) (* d1 d2))","end":0.044061481637041204,"name":"FastMath test3","status":"eq-target","end-est":0.02734375},{"samplers":["default","default"],"bits":128,"start":0.1843053679369811,"link":"44-FastMathtest2","pinf":0,"ninf":0,"vars":["d1","d2"],"input":"(+ (+ (* d1 10) (* d1 d2)) (* d1 20))","time":2276.4111328125,"target":0.026,"output":"(fma d1 (+ 20 10) (* d1 d2))","end":0.013896240625180288,"name":"FastMath test2","status":"eq-target","end-est":0.01171875},{"samplers":["default"],"bits":128,"start":0.265125,"link":"45-FastMathtest1","pinf":0,"ninf":0,"vars":["d"],"input":"(+ (* d 10) (* d 20))","time":634.9541015625,"target":0,"output":"(* (+ 10 20) d)","end":0,"name":"FastMath test1","status":"eq-target","end-est":0},{"samplers":["default"],"bits":128,"start":0.13363684218813102,"link":"46-FastMathrepmul","pinf":0,"ninf":0,"vars":["d1"],"input":"(* (* (* d1 d1) d1) d1)","time":1700.317138671875,"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":0.02125,"link":"47-FastMathdist4","pinf":0,"ninf":0,"vars":["d1","d2","d3","d4"],"input":"(- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1))","time":7350.156982421875,"target":0.02275,"output":"(+ (* d1 (- d2 d3)) (* d1 (- d4 d1)))","end":0.021625,"name":"FastMath dist4","status":"eq-target","end-est":0.04296875},{"samplers":["default","default","default"],"bits":128,"start":0.04760172264890213,"link":"48-FastMathdist3","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))","time":4632.0,"target":0.02575,"output":"(fma (+ d3 37) d1 (* d1 d2))","end":0.019988361324451066,"name":"FastMath dist3","status":"eq-target","end-est":0.01171875},{"samplers":["default","default","default"],"bits":128,"start":0.016238361324451066,"link":"49-FastMathdist","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (* d1 d2) (* d1 d3))","time":4166.3798828125,"target":0.013875,"output":"(* (+ d2 d3) d1)","end":0.013875,"name":"FastMath dist","status":"eq-target","end-est":0.01171875}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}