{"bit_width":64,"date":1470220615,"note":"libraries","iterations":2,"flags":["rules:numerics","rules:arithmetic","rules:polynomials","rules:fractions","rules:exponents","rules:trigonometry","setup:simplify","reduce:regimes","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":33.638504359798354,"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":20897.991943359375,"target":false,"output":"(if (<= y.re -2.909518210854262e-13) (* (/ (pow (hypot x.im x.re) y.re) (+ (* (atan2 x.im x.re) y.im) (+ 1 (* 1/2 (* (sqr (atan2 x.im x.re)) (sqr y.im)))))) (cos (fma y.im (log (hypot x.im x.re)) (* y.re (atan2 x.im x.re))))) (* (/ (pow (hypot x.im x.re) y.re) (exp (* y.im (atan2 x.im x.re)))) (cube (cbrt (cos (fma y.im (log (hypot x.im x.re)) (* y.re (atan2 x.im x.re))))))))","end":4.450993392857686,"name":"powComplex, real part","status":"imp-start","end-est":6.0429832115018485},{"samplers":["default","default","default","default"],"bits":128,"start":32.374212840381254,"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":47628.77099609375,"target":false,"output":"(if (<= y.re -2.9335963728403624e+168) (* (/ (pow (hypot x.im x.re) y.re) (exp (/ (atan2 (/ 1 x.im) (/ 1 x.re)) y.im))) (sin (fma y.im (log (hypot x.im x.re)) (* y.re (atan2 x.im x.re))))) (* (/ (pow (hypot x.im x.re) y.re) (pow (exp y.im) (atan2 x.im x.re))) (+ (* (sin (* y.im (log (hypot x.im x.re)))) (cos (* y.re (atan2 x.im x.re)))) (* (cos (* y.im (log (hypot x.im x.re)))) (sin (* y.re (atan2 x.im x.re)))))))","end":1.5839432266146742,"name":"powComplex, imaginary part","status":"imp-start","end-est":8.367466500445069},{"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":6614.62890625,"target":false,"output":"(+ (* (/ (pow (* -2 (log u1)) 0.5) 6) (cbrt (cube (cos (* PI (* u2 2)))))) 0.5)","end":0.43647288957612246,"name":"normal distribution","status":"ex-start","end-est":0.4546135705249879},{"samplers":["default","default"],"bits":128,"start":0.00775,"link":"3-mathsquareoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(- (* re re) (* im im))","time":3297.952880859375,"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":1415.10888671875,"target":false,"output":"(* im (+ re re))","end":0.007722519833140027,"name":"math.square on complex, imaginary part","status":"ex-start","end-est":0},{"samplers":["default","default"],"bits":128,"start":42.860630354148526,"link":"5-mathsqrtoncompleximaginarypartimgreaterthan0branch","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* 0.5 (sqrt (* 2.0 (+ (sqrt (- (* re re) (* im im))) re))))","time":9240.85498046875,"target":false,"output":"(if (<= re 2.1871018712012548e-249) (* (sqrt (* (fma -1 re re) 2.0)) 0.5) (* 0.5 (sqrt (* 2.0 (+ (* (sqrt (+ re im)) (sqrt (- re im))) re)))))","end":0.06287644644755248,"name":"math.sqrt on complex, imaginary part, im greater than 0 branch","status":"imp-start","end-est":0.48146434417223927},{"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":9108.406005859375,"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":4018.6640625,"target":false,"output":"(/ (log (cube (cbrt (hypot im re)))) (log 10))","end":0.5960775956130271,"name":"math.log10 on complex, real part","status":"imp-start","end-est":0.5449600586106521},{"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":2998.85986328125,"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":6600.802978515625,"target":false,"output":"(/ 3 (/ (log base) (log (cbrt (hypot im re)))))","end":0.4365867844231973,"name":"math.log/2 on complex, real part","status":"imp-start","end-est":0.40138627930532605},{"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":6097.239013671875,"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":2475.998046875,"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":1162.556884765625,"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":2198.3828125,"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":3595.927978515625,"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":27653.632080078125,"target":false,"output":"(fma x.im (* (- x.re) (fma 3 x.im x.re)) (* (+ x.re x.im) (sqr x.re)))","end":0.240035526564393,"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":6091.908935546875,"target":false,"output":"(fma (* (- x.re x.im) (+ x.re x.im)) x.im (* (* (+ x.im x.im) x.re) x.re))","end":7.012388524129386,"name":"math.cube on complex, imaginary part","status":"apx-start","end-est":5.258542397590655},{"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":9254.86279296875,"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":1393.612060546875,"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":1946.551025390625,"target":false,"output":"(hypot im re)","end":0.0045,"name":"math.abs on complex","status":"imp-start","end-est":0.0078125},{"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":5602.69091796875,"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":4075.18798828125,"target":false,"output":"(fma y.im x.re (* y.re x.im))","end":0.005448120312590145,"name":"_multiplyComplex, imaginary part","status":"ex-start","end-est":0.0078125},{"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":5828.924072265625,"target":false,"output":"(/ 1 (/ (fma y.im y.im (* y.re y.re)) (fma y.re x.re (* y.im x.im))))","end":25.4375217233804,"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":7908.745849609375,"target":false,"output":"(/ 1 (/ (fma y.im y.im (* y.re y.re)) (- (* y.re x.im) (* y.im x.re))))","end":25.637041854191423,"name":"_divideComplex, imaginary part","status":"apx-start","end-est":22.528667948281143},{"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":15237.5048828125,"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":7929.5439453125,"target":false,"output":"(if (<= i 112873629.87382902) (/ (sqr (/ i 2)) (- (* (* i 2) (* i 2)) 1.0)) (+ (/ 0.00390625 (pow i 4)) (fma (/ 0.015625 i) (/ 1 i) 1/16)))","end":0.0053231203125901445,"name":"Octave 3.8, jcobi/4, as called","status":"imp-start","end-est":0},{"samplers":["default","default","default"],"bits":128,"start":51.937314554480615,"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":85878.16821289062,"target":false,"output":"(if (<= alpha 1.1910052422077304e+176) (/ (* (/ i (+ (fma i 2 alpha) beta)) (/ (+ (+ alpha i) beta) (+ (fma i 2 alpha) beta))) (sqr (sqrt (/ (fma (fma i 2 alpha) (fma beta 2 (fma i 2 alpha)) (- (sqr beta) 1.0)) (fma i (+ (+ alpha i) beta) (* alpha beta)))))) (/ (* (/ i (+ (fma i 2 alpha) beta)) (/ (+ (+ alpha i) beta) (+ (fma i 2 alpha) beta))) (/ (fma (fma (/ 1 i) 2 (/ 1 alpha)) (fma (/ 1 beta) 2 (fma (/ 1 i) 2 (/ 1 alpha))) (- (/ 1 (sqr beta)) 1.0)) (fma (/ 1 i) (+ (/ 1 beta) (+ (/ 1 alpha) (/ 1 i))) (/ 1 (* beta alpha))))))","end":30.532746639071,"name":"Octave 3.8, jcobi/4","status":"imp-start","end-est":36.344378574403926},{"samplers":["default","default"],"bits":128,"start":3.419087277405878,"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":32626.458984375,"target":false,"output":"(if (<= alpha 1.2543987852557203e+178) (/ (/ (/ (+ (+ alpha 1.0) (fma beta alpha beta)) (+ alpha (+ 2 beta))) (+ (+ alpha 1.0) (+ 2 beta))) (+ alpha (+ 2 beta))) 0)","end":1.2981309046807514,"name":"Octave 3.8, jcobi/3","status":"imp-start","end-est":1.206987163855098},{"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":35141.968017578125,"target":false,"output":"(/ (exp (log (fma (- (/ beta (+ (fma i 2 beta) (+ 2.0 alpha))) (/ alpha (+ (fma i 2 beta) (+ 2.0 alpha)))) (/ (+ alpha beta) (fma 2 i (+ alpha beta))) 1.0))) 2.0)","end":12.264839586248888,"name":"Octave 3.8, jcobi/2","status":"imp-start","end-est":12.634278880057886},{"samplers":["default","default"],"bits":128,"start":16.346565875132423,"link":"29-Octave38jcobi1","pinf":0,"ninf":0,"vars":["alpha","beta"],"input":"(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)","time":18251.63916015625,"target":false,"output":"(if (<= (/ (- beta alpha) (+ (+ alpha beta) 2.0)) -1.1615325132018979e-05) (+ (/ (+ 2.0 (/ 8.0 (* alpha alpha))) (* 2.0 alpha)) (- (/ (/ beta 2.0) (+ (+ alpha 2.0) beta)) (/ (/ 4.0 (* alpha alpha)) 2.0))) (/ (- (cbrt (cube (/ beta (+ (+ alpha beta) 2.0)))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))","end":0.019969360937770436,"name":"Octave 3.8, jcobi/1","status":"imp-start","end-est":5.264735391370873},{"samplers":["default"],"bits":128,"start":0.25707312031259016,"link":"30-JmatReallambertwestimator","pinf":0,"ninf":0,"vars":["x"],"input":"(- (log x) (log (log x)))","time":4747.2138671875,"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":28332.19189453125,"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":0.5915699018613291,"name":"Jmat.Real.gamma, branch z less than 0.5","status":"imp-start","end-est":0.5462875976844203},{"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":94814.98095703125,"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))))) (/ (expm1 (log1p (* (pow (+ (- z 1) (+ 0.5 7)) (+ 0.5 (- z 1))) (sqrt (* 2 PI))))) (exp (+ (- z 1) (+ 0.5 7)))))","end":0.8280174708610762,"name":"Jmat.Real.gamma, branch z greater than 0.5","status":"imp-start","end-est":0.593157778641476},{"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":11309.97412109375,"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)))) (* 1/21 (* (* (cube (fabs x)) (cube (fabs x))) (fabs x))))))","end":0.20385832066696588,"name":"Jmat.Real.erfi, branch x less than or equal to 0.5","status":"ex-start","end-est":0.19789757069442182},{"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":92866.5830078125,"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":0.9820991910523375,"name":"Jmat.Real.erfi, branch x greater than or equal to 5","status":"apx-start","end-est":1.0569811272029055},{"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":5674.218994140625,"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)) (/ (/ 1 (fma 0.3275911 (fabs x) 1)) (fma 0.3275911 (fabs x) 1)) (cube (cbrt (/ 0.254829592 (fma 0.3275911 (fabs x) 1))))) (exp (* (fabs x) (fabs x)))))","end":13.80001520826847,"name":"Jmat.Real.erf","status":"apx-start","end-est":14.129018584841875},{"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":20217.85791015625,"target":false,"output":"(fma (/ (* (cube (cube x)) (sqr x)) (fma 0.0003579942 (* (cube x) (* (cube x) (pow x 6))) (+ (fma 0.0008327945 (* (cube (sqr x)) (pow x 4)) (fma 0.2909738639 (pow x 4) (fma (* x 0.7715471019) x 1))) (fma (pow x 8) 0.0140005442 (* (cube (sqr x)) 0.0694555761))))) 0.0001789971 (* (/ x (fma 0.0003579942 (* (pow x 6) (cube (* x x))) (+ (fma 0.0008327945 (* (* (* x x) (* x x)) (* (* x x) (pow x 4))) (fma 0.2909738639 (pow x 4) (fma (* 0.7715471019 x) x 1))) (fma (pow x 8) 0.0140005442 (* 0.0694555761 (cube (* x x))))))) (+ (fma 0.0005064034 (pow x 8) (* 0.0072644182 (cube (* x x)))) (fma 0.0424060604 (pow x 4) (fma (* 0.1049934947 x) x 1)))))","end":28.61955598377297,"name":"Jmat.Real.dawson","status":"apx-start","end-est":28.29801608581879},{"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":3915.055908203125,"target":32.60641754523864,"output":"(* 0.5 (sqrt (fma (hypot re im) 2.0 (* 2.0 re))))","end":13.49351089075337,"name":"math.sqrt on complex, real part","status":"gt-target","end-est":12.372743602610411},{"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":12285.10107421875,"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":1230.9541015625,"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":10349.35400390625,"target":12.107803271003817,"output":"(* (fma (cube im) 1/3 (fma (pow im 5) 1/60 (* im 2))) (* (sin re) (- 0.5)))","end":2.5441687058728806,"name":"math.cos on complex, imaginary part","status":"gt-target","end-est":1.3668947814221528},{"samplers":["default","default"],"bits":128,"start":28.488867641060725,"link":"41-JmatReallambertwnewtonloopstep","pinf":0,"ninf":0,"vars":["wj","x"],"input":"(- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj)))))","time":6524.858154296875,"target":28.43174672620656,"output":"(fma (- wj (* 2 x)) wj x)","end":0.02860589431040347,"name":"Jmat.Real.lambertw, newton loop step","status":"gt-target","end-est":1.7314035943799555},{"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":3840.35888671875,"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":4565.02783203125,"target":0.0625,"output":"(fma (+ d2 d3) d1 (* d1 3))","end":0.06369812031259015,"name":"FastMath test3","status":"eq-target","end-est":0.0390625},{"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":3651.625,"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":1031.614013671875,"target":0,"output":"(* (+ 10 20) d)","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":1783.511962890625,"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":7636.1689453125,"target":0.023,"output":"(* d1 (+ (- d2 d3) (- d4 d1)))","end":0.0236009193652572,"name":"FastMath dist4","status":"eq-target","end-est":0.03125},{"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":6162.524169921875,"target":0.02339624062518029,"output":"(fma (+ d3 37) d1 (* d1 d2))","end":0.019,"name":"FastMath dist3","status":"eq-target","end-est":0.0234375},{"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":3763.641845703125,"target":0.012,"output":"(* (+ d2 d3) d1)","end":0.012,"name":"FastMath dist","status":"eq-target","end-est":0.01171875}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}