{"bit_width":64,"date":1470476376,"note":"libraries","iterations":3,"flags":["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":"#(1066021830 2830721961 259995540 547417586 81053319 3982124210)","points":256,"tests":[{"samplers":["default","default","default","default"],"bits":128,"start":31.72438351397661,"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":22802.38916015625,"target":false,"output":"(/ (cube (cbrt (cos (+ (* y.re (atan2 x.im x.re)) (* (log (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)))","end":31.21705533012538,"name":"powComplex, real part","status":"apx-start","end-est":33.27714085638727},{"samplers":["default","default","default","default"],"bits":128,"start":31.996172436809392,"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":26404.43798828125,"target":false,"output":"(/ (sin (+ (* y.re (atan2 x.im x.re)) (* (log (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)))","end":31.47994142026213,"name":"powComplex, imaginary part","status":"apx-start","end-est":33.477739820965695},{"samplers":["(uniform 0 1)","(uniform 0 1)"],"bits":128,"start":0.40329785167108795,"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":8685.379150390625,"target":false,"output":"(+ 0.5 (/ (pow (* -2 (log u1)) 0.5) (/ 6 (log (exp (cos (* PI (* u2 2))))))))","end":0.406036875047406,"name":"normal distribution","status":"ex-start","end-est":0.3924639106268993},{"samplers":["default","default"],"bits":128,"start":0.00775,"link":"3-mathsquareoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(- (* re re) (* im im))","time":2409.636962890625,"target":false,"output":"(* (+ re im) (- re im))","end":0.001125,"name":"math.square on complex, real part","status":"ex-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":0.007125,"link":"4-mathsquareoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(+ (* re im) (* im re))","time":1030.7958984375,"target":false,"output":"(* re (+ im im))","end":0.022566534347832387,"name":"math.square on complex, imaginary part","status":"ex-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":30.053000498612626,"link":"5-mathsqrtoncompleximaginarypartimgreaterthan0branch","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* 0.5 (sqrt (* 2.0 (+ (sqrt (- (* re re) (* im im))) re))))","time":16024.762939453125,"target":false,"output":"(* 0.5 (sqrt (* 2.0 (+ (* (sqrt (+ re im)) (sqrt (- re im))) re))))","end":0.15125312150124082,"name":"math.sqrt on complex, imaginary part, im greater than 0 branch","status":"imp-start","end-est":1.7187505615832945},{"samplers":["default","default"],"bits":128,"start":0.05402734388987778,"link":"6-mathsinoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))","time":12070.27197265625,"target":false,"output":"(+ (* (/ 0.5 (exp im)) (sin re)) (* (* 0.5 (sin re)) (exp im)))","end":0.049432982952107365,"name":"math.sin on complex, real part","status":"ex-start","end-est":0.01953125},{"samplers":["default","default"],"bits":128,"start":30.79420213303107,"link":"7-mathlog10oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))","time":5509.7119140625,"target":false,"output":"(/ (log (cube (cbrt (sqrt (+ (sqr re) (* im im)))))) (log 10))","end":30.790780289558793,"name":"math.log10 on complex, real part","status":"apx-start","end-est":29.224961946688275},{"samplers":["default","default"],"bits":128,"start":0.841790414066557,"link":"8-mathlog10oncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(/ (atan2 im re) (log 10))","time":3102.244873046875,"target":false,"output":"(/ 1 (cube (cbrt (/ (log 10) (atan2 im re)))))","end":0.8594219017306581,"name":"math.log10 on complex, imaginary part","status":"ex-start","end-est":0.7849084231620943},{"samplers":["default","default","default"],"bits":128,"start":30.336440127151036,"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":8079.615966796875,"target":false,"output":"(* (/ 1 (log base)) (log (sqrt (+ (sqr im) (* re re)))))","end":30.309953919947162,"name":"math.log/2 on complex, real part","status":"apx-start","end-est":30.476256227525123},{"samplers":["default","default","default"],"bits":128,"start":30.63356506791648,"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":5415.18798828125,"target":false,"output":"(/ (- (atan2 im re) 0) (log base))","end":0.3034387218755409,"name":"math.log/2 on complex, imaginary part","status":"imp-start","end-est":0.31478500976844204},{"samplers":["default","default"],"bits":128,"start":30.49135377586374,"link":"11-mathlog1oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(log (sqrt (+ (* re re) (* im im))))","time":1834.489990234375,"target":false,"output":"(log (sqrt (+ (sqr re) (* im im))))","end":30.49135377586374,"name":"math.log/1 on complex, real part","status":"apx-start","end-est":28.959548945054312},{"samplers":["default","default"],"bits":128,"start":0,"link":"12-mathlog1oncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(atan2 im re)","time":833.09814453125,"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":0.00675,"link":"13-mathexponcomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (exp re) (cos im))","time":1941.447021484375,"target":false,"output":"(* (exp re) (cos im))","end":0.00675,"name":"math.exp on complex, real part","status":"ex-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":0.027951048203707075,"link":"14-mathexponcompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (exp re) (sin im))","time":3447.243896484375,"target":false,"output":"(* (exp re) (sin im))","end":0.027951048203707075,"name":"math.exp on complex, imaginary part","status":"ex-start","end-est":0.0078125},{"samplers":["default","default"],"bits":128,"start":6.691239269523916,"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":8741.576904296875,"target":false,"output":"(+ (* (sqr x.re) x.re) (* x.im (* x.re (- (- x.im) (+ x.im x.im)))))","end":0.2397336468769831,"name":"math.cube on complex, real part","status":"imp-start","end-est":0.2578125},{"samplers":["default","default"],"bits":128,"start":7.028367487016786,"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":10021.55810546875,"target":false,"output":"(- (* (* 3 (* x.im x.re)) x.re) (pow x.im 3))","end":0.16738704570071306,"name":"math.cube on complex, imaginary part","status":"imp-start","end-est":0.15234375},{"samplers":["default","default"],"bits":128,"start":0.01151184218813101,"link":"17-mathcosoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))","time":7706.164794921875,"target":false,"output":"(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))","end":0.01151184218813101,"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":820.06298828125,"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":29.33811648873645,"link":"19-mathabsoncomplex","pinf":0,"ninf":0,"vars":["re","im"],"input":"(sqrt (+ (* re re) (* im im)))","time":2892.987060546875,"target":false,"output":"(sqrt (+ (sqr re) (* im im)))","end":29.33811648873645,"name":"math.abs on complex","status":"apx-start","end-est":28.00675049395359},{"samplers":["default","default","default","default"],"bits":128,"start":0.010600919365257202,"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":2537.43798828125,"target":false,"output":"(- (* x.re y.re) (* x.im y.im))","end":0.010600919365257202,"name":"_multiplyComplex, real part","status":"ex-start","end-est":0.01171875},{"samplers":["default","default","default","default"],"bits":128,"start":0.01064624062518029,"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":3813.47998046875,"target":false,"output":"(+ (* x.re y.im) (* x.im y.re))","end":0.01064624062518029,"name":"_multiplyComplex, imaginary part","status":"ex-start","end-est":0.01171875},{"samplers":["default","default","default","default"],"bits":128,"start":25.30007850262379,"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":6054.55908203125,"target":false,"output":"(/ 1 (/ (+ (sqr y.re) (* y.im y.im)) (+ (* y.re x.re) (* x.im y.im))))","end":25.438512349265984,"name":"_divideComplex, real part","status":"apx-start","end-est":24.872461666443588},{"samplers":["default","default","default","default"],"bits":128,"start":25.536003399743393,"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":7513.778076171875,"target":false,"output":"(- (/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im))) (/ x.re (+ y.im (/ (sqr y.re) y.im))))","end":17.117811248290195,"name":"_divideComplex, imaginary part","status":"imp-start","end-est":16.680606346228235},{"samplers":["default","default"],"bits":128,"start":0.12985169219101572,"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":15547.052001953125,"target":false,"output":"(+ (- a (/ 1.0 3.0)) (* rand (/ (- a (/ 1.0 3.0)) (sqrt (* (- a (/ 1.0 3.0)) 9)))))","end":0.10966992500144233,"name":"Octave 3.8, oct_fill_randg","status":"ex-start","end-est":0.11328125},{"samplers":["default"],"bits":128,"start":45.05129377705376,"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":5004.0390625,"target":false,"output":"(/ (sqr (/ i 2)) (- (* (* i 2) (* i 2)) 1.0))","end":15.460391528045871,"name":"Octave 3.8, jcobi/4, as called","status":"imp-start","end-est":16.4704303646082},{"samplers":["default","default","default"],"bits":128,"start":53.7655088871842,"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":62352.52685546875,"target":false,"output":"(* 1/16 (exp (/ (/ 0.25 i) i)))","end":0,"name":"Octave 3.8, jcobi/4","status":"imp-start","end-est":18.704579374536916},{"samplers":["default","default"],"bits":128,"start":3.3348211537028334,"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":40649.118896484375,"target":false,"output":"(/ (/ (/ (+ (+ alpha 1.0) (+ beta (* beta alpha))) (+ alpha (+ 2 beta))) (+ (+ alpha 1.0) (+ 2 beta))) (+ alpha (+ 2 beta)))","end":3.329594461511817,"name":"Octave 3.8, jcobi/3","status":"apx-start","end-est":4.343409508136733},{"samplers":["default","default","default"],"bits":128,"start":23.729257052775083,"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":33652.93701171875,"target":false,"output":"(/ (+ (* (* (/ (+ alpha beta) 1) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0) 2.0)","end":12.251715455071906,"name":"Octave 3.8, jcobi/2","status":"imp-start","end-est":12.638993082717567},{"samplers":["default","default"],"bits":128,"start":15.750979015995714,"link":"29-Octave38jcobi1","pinf":0,"ninf":0,"vars":["alpha","beta"],"input":"(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)","time":10932.779052734375,"target":false,"output":"(/ (- (/ (/ 1 (+ (+ alpha beta) 2.0)) (/ 1 beta)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)","end":15.286585091413476,"name":"Octave 3.8, jcobi/1","status":"apx-start","end-est":15.763825383957453},{"samplers":["default"],"bits":128,"start":0.25707312031259016,"link":"30-JmatReallambertwestimator","pinf":0,"ninf":0,"vars":["x"],"input":"(- (log x) (log (log x)))","time":4628.02197265625,"target":false,"output":"(log (/ x (log x)))","end":0.003625,"name":"Jmat.Real.lambertw, estimator","status":"ex-start","end-est":0.00390625},{"samplers":["default"],"bits":128,"start":1.8171757631993868,"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":103449.0361328125,"target":false,"output":"(* (/ (/ PI (/ (sin (* PI z)) (* (sqrt 2) (sqrt PI)))) (/ (exp (+ 7 (- 0.5 z))) (pow (+ 7 (- 0.5 z)) (- 0.5 z)))) (/ (+ (* (+ (* (+ (* 771.3234287776531 (- (- 1 z) (- 1 2))) (* (- (- 1 z) (- 1 3)) -1259.1392167224028)) (+ (sqr (+ (/ 676.5203681218851 (- 1 z)) 0.9999999999998099)) (- (sqr (/ 1.5056327351493116e-07 (- 8 z))) (* (+ (/ 676.5203681218851 (- 1 z)) 0.9999999999998099) (/ 1.5056327351493116e-07 (- 8 z)))))) (* (* (- (- 1 z) (- 1 3)) (- (- 1 z) (- 1 2))) (- (pow (+ (/ 676.5203681218851 (- 1 z)) 0.9999999999998099) 3) (pow (/ 1.5056327351493116e-07 (- 8 z)) 3)))) (* (- 7 z) (- (/ -0.13857109526572012 (- (- 1 z) (- 1 6))) (+ (/ -176.6150291621406 (- 4 z)) (/ 12.507343278686905 (- 5 z)))))) (* (* (* (- (- 1 z) (- 1 3)) (- (- 1 z) (- 1 2))) (+ (sqr (+ (/ 676.5203681218851 (- 1 z)) 0.9999999999998099)) (- (sqr (/ 1.5056327351493116e-07 (- 8 z))) (* (+ (/ 676.5203681218851 (- 1 z)) 0.9999999999998099) (/ 1.5056327351493116e-07 (- 8 z)))))) (+ (* 9.984369578019572e-06 (- (/ -0.13857109526572012 (- (- 1 z) (- 1 6))) (+ (/ -176.6150291621406 (- 4 z)) (/ 12.507343278686905 (- 5 z))))) (* (- 7 z) (- (sqr (/ -0.13857109526572012 (- (- 1 z) (- 1 6)))) (sqr (+ (/ -176.6150291621406 (- 4 z)) (/ 12.507343278686905 (- 5 z))))))))) (* (* (* (- (- 1 z) (- 1 3)) (- (- 1 z) (- 1 2))) (+ (sqr (+ (/ 676.5203681218851 (- 1 z)) 0.9999999999998099)) (- (sqr (/ 1.5056327351493116e-07 (- 8 z))) (* (+ (/ 676.5203681218851 (- 1 z)) 0.9999999999998099) (/ 1.5056327351493116e-07 (- 8 z)))))) (* (- 7 z) (- (/ -0.13857109526572012 (- (- 1 z) (- 1 6))) (+ (/ -176.6150291621406 (- 4 z)) (/ 12.507343278686905 (- 5 z))))))))","end":0.7416908792617738,"name":"Jmat.Real.gamma, branch z less than 0.5","status":"imp-start","end-est":0.6899377442110507},{"samplers":["default"],"bits":128,"start":59.82429927470537,"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":244050.56005859375,"target":false,"output":"(* (+ (+ (+ (/ 1.5056327351493116e-07 (+ (- z 1) 8)) (/ 9.984369578019572e-06 (+ 7 (- z 1)))) (+ (/ -0.13857109526572012 (+ (- z 1) 6)) (/ 12.507343278686905 (- (+ 5 z) 1)))) (+ (+ (+ (/ 676.5203681218851 (- z 0)) 0.9999999999998099) (/ -176.6150291621406 (+ (- z 1) 4))) (+ (/ -1259.1392167224028 (- z (- 1 2))) (/ 771.3234287776531 (+ (- z 1) 3))))) (/ (cbrt (* (cube (pow (- (+ 7 z) (- 1 0.5)) (+ 0.5 (- z 1)))) (cube (sqrt (* 2 PI))))) (exp (- (+ 7 z) (- 1 0.5)))))","end":0.875443371135853,"name":"Jmat.Real.gamma, branch z greater than 0.5","status":"imp-start","end-est":0.6104740263261483},{"samplers":["default"],"bits":128,"start":0.19188631246553187,"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":23345.177001953125,"target":false,"output":"(fabs (/ (+ (+ (* 2 (fabs x)) (* (* (fabs x) (/ 2 3)) (sqr (fabs x)))) (+ (/ (sqr (cube (fabs x))) (/ 21 (fabs x))) (/ (* (cube (fabs x)) (sqr (fabs x))) 5))) (sqr (sqrt (sqrt PI)))))","end":0.34331508554784257,"name":"Jmat.Real.erfi, branch x less than or equal to 0.5","status":"ex-start","end-est":0.33335878907376804},{"samplers":["default"],"bits":128,"start":1.536444957961919,"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":81537.44409179688,"target":false,"output":"(* (+ (+ (/ (/ 3/4 (cube (fabs x))) (* (fabs x) (fabs x))) (+ (/ 1/2 (cube (fabs x))) (/ 1 (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))))","end":0.5858628262481954,"name":"Jmat.Real.erfi, branch x greater than or equal to 5","status":"apx-start","end-est":0.879151495405026},{"samplers":["default"],"bits":128,"start":13.80355990527098,"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":45231.449951171875,"target":false,"output":"(/ (- (pow 1 3) (sqr (sqrt (cube (/ (+ 0.254829592 (/ (+ (/ (+ -1.453152027 (/ 1.061405429 (+ (* (fabs x) 0.3275911) 1))) (* (+ (* (fabs x) 0.3275911) 1) (+ (* (fabs x) 0.3275911) 1))) (+ (/ 1.421413741 (+ (* (fabs x) 0.3275911) 1)) -0.284496736)) (+ (* (fabs x) 0.3275911) 1))) (* (exp (* (fabs x) (fabs x))) (+ (* (fabs x) 0.3275911) 1))))))) (+ (+ (/ (+ 0.254829592 (/ (+ (/ (+ -1.453152027 (/ 1.061405429 (+ (* (fabs x) 0.3275911) 1))) (sqr (+ (* (fabs x) 0.3275911) 1))) (+ (/ 1.421413741 (+ (* (fabs x) 0.3275911) 1)) -0.284496736)) (+ (* (fabs x) 0.3275911) 1))) (* (exp (* (fabs x) (fabs x))) (+ (* (fabs x) 0.3275911) 1))) 1) (sqr (/ (+ 0.254829592 (/ (+ (/ (+ -1.453152027 (/ 1.061405429 (+ (* (fabs x) 0.3275911) 1))) (sqr (+ (* (fabs x) 0.3275911) 1))) (+ (/ 1.421413741 (+ (* (fabs x) 0.3275911) 1)) -0.284496736)) (+ (* (fabs x) 0.3275911) 1))) (* (exp (* (fabs x) (fabs x))) (+ (* (fabs x) 0.3275911) 1))))))","end":13.018430534456254,"name":"Jmat.Real.erf","status":"apx-start","end-est":13.311829884632077},{"samplers":["default"],"bits":128,"start":28.608090632936147,"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":30114.748046875,"target":false,"output":"(* (/ x (+ (+ (* (* (cube x) (cube x)) (+ 0.0694555761 (* x (* 0.0140005442 x)))) (* (* (* (cube x) (sqr x)) (* (cube x) (sqr x))) (+ (* (* 0.0001789971 x) (* x 2)) 0.0008327945))) (+ (+ (* (* x 0.7715471019) x) (* (cube x) (* x 0.2909738639))) 1))) (+ (+ (* x (* x 0.1049934947)) (+ (* (* 0.0424060604 x) (cube x)) 1)) (+ (* (sqr (* (sqr x) (sqr x))) (+ (* (sqr x) 0.0001789971) 0.0005064034)) (* 0.0072644182 (* (cube x) (cube x))))))","end":28.603858505206478,"name":"Jmat.Real.dawson","status":"apx-start","end-est":28.31159210577249},{"samplers":["default","default"],"bits":128,"start":37.639019726267655,"link":"37-mathsqrtoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))","time":29886.8349609375,"target":32.60641754523864,"output":"(* 0.5 (pow E (log (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))))","end":39.2269160610404,"name":"math.sqrt on complex, real part","status":"lt-start","end-est":37.038952174340515},{"samplers":["default","default"],"bits":128,"start":58.905332725630814,"link":"38-mathsinoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (cos re)) (- (exp (- 0 im)) (exp im)))","time":14646.656982421875,"target":10.166785054954918,"output":"(* (- (+ (* 1/60 (pow im 5)) (+ (* 2 im) (* 1/3 (pow im 3))))) (* (cos re) 0.5))","end":0.2513429554319718,"name":"math.sin on complex, imaginary part","status":"gt-target","end-est":1.30277827576616},{"samplers":["default"],"bits":128,"start":0.129,"link":"39-mathcubeonreal","pinf":0,"ninf":0,"vars":["x"],"input":"(* (* x x) x)","time":866.373046875,"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":47.13492235312706,"link":"40-mathcosoncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))","time":15429.39794921875,"target":12.107803271003817,"output":"(* (* 0.5 (sin re)) (- (+ (* 1/60 (pow im 5)) (+ (* 2 im) (* 1/3 (pow im 3))))))","end":2.5446899464980612,"name":"math.cos on complex, imaginary part","status":"gt-target","end-est":1.3668947814221528},{"samplers":["default","default"],"bits":128,"start":18.79808984929859,"link":"41-JmatReallambertwnewtonloopstep","pinf":0,"ninf":0,"vars":["wj","x"],"input":"(- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj)))))","time":8722.583984375,"target":18.75914244643103,"output":"(+ (+ (pow wj 4) (- (sqr wj) (cube wj))) (/ x (* (+ 1 wj) (exp wj))))","end":0.04760404380867064,"name":"Jmat.Real.lambertw, newton loop step","status":"gt-target","end-est":0.8865326792105557},{"samplers":["default"],"bits":128,"start":0.13491410001730797,"link":"42-FastMathtest5","pinf":0,"ninf":0,"vars":["d1"],"input":"(* (* d1 (* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)) d1)","time":3260.97509765625,"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":0.07302124062518028,"link":"43-FastMathtest3","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (+ (* d1 3) (* d1 d2)) (* d1 d3))","time":7721.137939453125,"target":0.0625,"output":"(* d1 (+ (+ 3 d2) d3))","end":0.0625,"name":"FastMath test3","status":"eq-target","end-est":0.046875},{"samplers":["default","default"],"bits":128,"start":0.1845,"link":"44-FastMathtest2","pinf":0,"ninf":0,"vars":["d1","d2"],"input":"(+ (+ (* d1 10) (* d1 d2)) (* d1 20))","time":3207.8310546875,"target":0.026625,"output":"(* d1 (+ d2 30))","end":0.026625,"name":"FastMath test2","status":"eq-target","end-est":0.01953125},{"samplers":["default"],"bits":128,"start":0.267125,"link":"45-FastMathtest1","pinf":0,"ninf":0,"vars":["d"],"input":"(+ (* d 10) (* d 20))","time":986.43310546875,"target":0,"output":"(* d (+ 10 20))","end":0,"name":"FastMath test1","status":"eq-target","end-est":0},{"samplers":["default"],"bits":128,"start":0.13501184218813103,"link":"46-FastMathrepmul","pinf":0,"ninf":0,"vars":["d1"],"input":"(* (* (* d1 d1) d1) d1)","time":1057.506103515625,"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":0.023738361324451066,"link":"47-FastMathdist4","pinf":0,"ninf":0,"vars":["d1","d2","d3","d4"],"input":"(- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1))","time":8239.18017578125,"target":0.023,"output":"(* d1 (- (+ d4 d2) (+ d3 d1)))","end":0.023198120312590144,"name":"FastMath dist4","status":"eq-target","end-est":0.02734375},{"samplers":["default","default","default"],"bits":128,"start":0.046698120312590144,"link":"48-FastMathdist3","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))","time":6665.44482421875,"target":0.02339624062518029,"output":"(* d1 (+ (+ d2 d3) (+ 5 32)))","end":0.022625,"name":"FastMath dist3","status":"eq-target","end-est":0.03125},{"samplers":["default","default","default"],"bits":128,"start":0.012375,"link":"49-FastMathdist","pinf":0,"ninf":0,"vars":["d1","d2","d3"],"input":"(+ (* d1 d2) (* d1 d3))","time":2946.56201171875,"target":0.012,"output":"(* d1 (+ d2 d3))","end":0.012,"name":"FastMath dist","status":"eq-target","end-est":0.01171875}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}