{"bit_width":64,"date":1469871598,"note":"libraries","iterations":2,"flags":["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":"#(1065990927 2514927446 2806713580 2976231080 3799737104 4212629478)","points":256,"tests":[{"samplers":["default","default","default","default"],"bits":128,"start":32.083530452552445,"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":26441.284912109375,"target":false,"output":"(if (<= x.re -2.2367884420529847e-306) (/ (cos (+ (* y.re (atan2 x.im x.re)) (* (log (* -1 x.re)) y.im))) (/ (pow (exp y.im) (atan2 x.im x.re)) (pow (sqrt (+ (sqr x.re) (* x.im x.im))) y.re))) (/ (cos (+ (* y.re (atan2 x.im x.re)) (* (log x.re) y.im))) (/ (pow (exp y.im) (atan2 x.im x.re)) (pow (sqrt (+ (sqr x.re) (* x.im x.im))) y.re))))","end":17.210170414990902,"name":"powComplex, real part","status":"imp-start","end-est":23.956767096782894},{"samplers":["default","default","default","default"],"bits":128,"start":43.47338582121033,"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":37568.623779296875,"target":false,"output":"(if (<= x.re -2.2367884420529847e-306) (/ (sin (+ (* y.re (atan2 x.im x.re)) (* (log (* -1 x.re)) y.im))) (/ (+ (* (atan2 x.im x.re) y.im) (+ 1 (* 1/2 (* (sqr (atan2 x.im x.re)) (sqr y.im))))) (pow (sqrt (+ (sqr x.re) (* x.im x.im))) y.re))) (if (<= x.re 3.118801492845175e-232) (/ (sin (+ (* y.re (atan2 x.im x.re)) (* (log (sqrt (+ (sqr x.re) (* x.im x.im)))) y.im))) (/ (+ (* (atan2 x.im x.re) y.im) (+ 1 (* 1/2 (* (sqr (atan2 x.im x.re)) (sqr y.im))))) (pow (exp (log (sqrt (+ (sqr x.re) (* x.im x.im))))) y.re))) (/ (+ (* y.im (log x.re)) (* (atan2 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))))) (pow (sqrt (+ (sqr x.re) (* x.im x.im))) y.re)))))","end":25.535789827575154,"name":"powComplex, imaginary part","status":"imp-start","end-est":25.28250194734269},{"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":8894.762939453125,"target":false,"output":"(+ 0.5 (* (/ 1 6) (/ (pow (* -2 (log u1)) 0.5) (/ 1 (cos (* PI (* u2 2)))))))","end":0.41955637600483764,"name":"normal distribution","status":"ex-start","end-est":0.4185752316201496},{"samplers":["default","default"],"bits":128,"start":0.00725,"link":"3-mathsquareoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(- (* re re) (* im im))","time":4475.6669921875,"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":1968.218994140625,"target":false,"output":"(* re (+ im im))","end":0,"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":16746.68212890625,"target":false,"output":"(* 0.5 (sqrt (* 2.0 (+ (* (sqrt (+ re im)) (sqrt (- re im))) re))))","end":0.09050263159559746,"name":"math.sqrt on complex, imaginary part, im greater than 0 branch","status":"imp-start","end-est":0.00390625},{"samplers":["default","default"],"bits":128,"start":0.032050295710572156,"link":"6-mathsinoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))","time":9197.691162109375,"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":31.040517123703836,"link":"7-mathlog10oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))","time":8016.045166015625,"target":false,"output":"(if (<= re -5.954199484621813e+115) (/ (log (- re)) (log 10)) (if (<= re -8.68041930647669e-252) (/ 1 (/ (log 10) (log (sqrt (+ (sqr re) (* im im)))))) (if (<= re 1.9727183986347288e-223) (/ (log im) (log 10)) (if (<= re 1.6728927718931055e+97) (cbrt (cube (/ (log (sqrt (+ (sqr re) (* im im)))) (log 10)))) (/ (log re) (log 10))))))","end":11.211996052671784,"name":"math.log10 on complex, real part","status":"imp-start","end-est":15.577111777822457},{"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":2782.204833984375,"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":31.432003466240264,"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":14359.27587890625,"target":false,"output":"(if (<= im -5.051947517249776e+32) (/ (log (- im)) (log base)) (if (<= im -1.0784901626853544e-218) (/ (* (log (sqrt (+ (* im im) (* re re)))) (log base)) (* (log base) (log base))) (if (<= im 8.51308327519678e-216) (/ (log (- re)) (log base)) (if (<= im 1.5868349258537704e+124) (/ (* (log (sqrt (+ (* im im) (* re re)))) (log base)) (* (log base) (log base))) (/ (log im) (log base))))))","end":9.536116518070976,"name":"math.log/2 on complex, real part","status":"imp-start","end-est":14.796557426557236},{"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":5454.19091796875,"target":false,"output":"(/ (- (atan2 im re) 0) (log base))","end":0.31368872187554087,"name":"math.log/2 on complex, imaginary part","status":"imp-start","end-est":0.34212875976844204},{"samplers":["default","default"],"bits":128,"start":30.733177257250105,"link":"11-mathlog1oncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(log (sqrt (+ (* re re) (* im im))))","time":4203.134033203125,"target":false,"output":"(if (<= re -1.4760992303283469e+119) (log (- re)) (if (<= re -8.68041930647669e-252) (log (sqrt (+ (sqr re) (* im im)))) (if (<= re 1.9727183986347288e-223) (log im) (if (<= re 1.6728927718931055e+97) (log (sqrt (+ (sqr re) (* im im)))) (log re)))))","end":10.739485307523895,"name":"math.log/1 on complex, real part","status":"imp-start","end-est":15.18084337596408},{"samplers":["default","default"],"bits":128,"start":0,"link":"12-mathlog1oncompleximaginarypart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(atan2 im re)","time":1434.43603515625,"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":2848.032958984375,"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":3596.72802734375,"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":9490.2861328125,"target":false,"output":"(+ (* (sqr x.re) x.re) (* x.im (* x.re (- (- x.im) (+ x.im x.im)))))","end":0.25029492500144224,"name":"math.cube on complex, real part","status":"imp-start","end-est":0.2421875},{"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":11791.1650390625,"target":false,"output":"(- (* 3 (* (* x.im x.re) x.re)) (pow x.im 3))","end":0.17751672969029436,"name":"math.cube on complex, imaginary part","status":"imp-start","end-est":0.18359375},{"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":4869.591064453125,"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":1140.05517578125,"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":31.239394402388765,"link":"19-mathabsoncomplex","pinf":0,"ninf":0,"vars":["re","im"],"input":"(sqrt (+ (* re re) (* im im)))","time":3822.10205078125,"target":false,"output":"(if (<= re -1.560410170116619e+149) (- re) (if (<= re -8.68041930647669e-252) (sqrt (+ (sqr re) (* im im))) (if (<= re 1.9727183986347288e-223) im (if (<= re 7.79868197508907e+130) (sqrt (+ (sqr re) (* im im))) re))))","end":10.442348440546423,"name":"math.abs on complex","status":"imp-start","end-est":15.551927823798934},{"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":5924.880126953125,"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":4889.586181640625,"target":false,"output":"(+ (* x.re y.im) (* x.im y.re))","end":0.01164624062518029,"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":7199.0029296875,"target":false,"output":"(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))","end":25.58735883659281,"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":8483.06103515625,"target":false,"output":"(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))","end":25.718406102602565,"name":"_divideComplex, imaginary part","status":"apx-start","end-est":23.823219551014606},{"samplers":["default","default"],"bits":128,"start":0.1313445613087663,"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":15186.238037109375,"target":false,"output":"(* (- a (/ 1.0 3.0)) (+ 1 (* 1 (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9))))))","end":0.11651410974293096,"name":"Octave 3.8, oct_fill_randg","status":"ex-start","end-est":0.14291000976844204},{"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":8384.94091796875,"target":false,"output":"(if (<= i 6809.194157769488) (/ (sqr (/ i 2)) (- (* (* i 2) (* i 2)) 1.0)) (+ (+ 1/16 (/ 0.00390625 (pow i 4))) (/ 0.015625 (* i i))))","end":0.003875,"name":"Octave 3.8, jcobi/4, as called","status":"imp-start","end-est":0},{"samplers":["default","default","default"],"bits":128,"start":52.51883792551171,"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":60303.922119140625,"target":false,"output":"(if (<= alpha 9.899003901161565e+151) (sqr (/ (sqrt (/ (* i (+ beta (+ i alpha))) (/ (sqr (+ (+ beta alpha) (* 2 i))) (+ (* alpha beta) (* i (+ beta (+ i alpha))))))) (sqrt (- (sqr (+ (+ beta alpha) (* 2 i))) 1.0)))) 0)","end":29.543681603976268,"name":"Octave 3.8, jcobi/4","status":"imp-start","end-est":40.68394665935383},{"samplers":["default","default"],"bits":128,"start":8.522565684755232,"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":32108.18896484375,"target":false,"output":"(if (<= beta 2.0130633571779316e+196) (/ (/ (/ (+ (+ alpha 1.0) (+ beta (* beta alpha))) (+ alpha (+ 2 beta))) (+ (+ alpha 1.0) (+ 2 beta))) (+ alpha (+ 2 beta))) (/ (+ (* 0.25 (+ alpha beta)) 0.5) (* (+ (+ alpha beta) 2) (+ (+ alpha beta) (+ 2 1.0)))))","end":8.382055096336623,"name":"Octave 3.8, jcobi/3","status":"apx-start","end-est":1.6735031441335655},{"samplers":["default","default","default"],"bits":128,"start":24.214683457463213,"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":42862.22998046875,"target":false,"output":"(if (<= (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) -1.7219732253338127e+31) (/ (+ (- (/ 8.0 (cube alpha)) (/ (/ 4.0 alpha) alpha)) (/ 2.0 alpha)) 2.0) (/ (+ (* (/ (+ alpha beta) 1) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0) 2.0))","end":0.5915141600609288,"name":"Octave 3.8, jcobi/2","status":"imp-start","end-est":8.294123290447917},{"samplers":["default","default"],"bits":128,"start":16.582279531723735,"link":"29-Octave38jcobi1","pinf":0,"ninf":0,"vars":["alpha","beta"],"input":"(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)","time":17342.964111328125,"target":false,"output":"(if (<= (/ (- beta alpha) (+ (+ alpha beta) 2.0)) -0.9997063657335743) (+ (/ (+ 2.0 (/ (/ 8.0 alpha) alpha)) (* 2.0 alpha)) (- (/ (/ beta 2.0) (+ alpha (+ 2.0 beta))) (/ (/ 4.0 (* alpha alpha)) 2.0))) (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (* alpha (/ 1 (+ (+ alpha beta) 2.0))) 1.0)) 2.0))","end":0.029240951994590193,"name":"Octave 3.8, jcobi/1","status":"imp-start","end-est":3.7407653482526797},{"samplers":["default"],"bits":128,"start":0.261,"link":"30-JmatReallambertwestimator","pinf":0,"ninf":0,"vars":["x"],"input":"(- (log x) (log (log x)))","time":4874.727783203125,"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":26608.20703125,"target":false,"output":"(* (+ (+ (+ (+ (/ -0.13857109526572012 (- (- 1 z) (- 1 6))) (/ 9.984369578019572e-06 (- (- 1 z) (- 1 7)))) (+ (/ -176.6150291621406 (- (+ 4 1) (+ 1 z))) (/ 12.507343278686905 (- (+ 1 5) (+ 1 z))))) (+ (+ (/ 771.3234287776531 (- (- 1 z) (- 1 3))) (/ -1259.1392167224028 (- (- 1 z) (- 1 2)))) (+ 0.9999999999998099 (/ 676.5203681218851 (- (- 1 z) 0))))) (/ 1.5056327351493116e-07 (- (+ 1 8) (+ 1 z)))) (/ (* (/ (* PI (* (sqrt PI) (sqrt 2))) (sin (* z PI))) (pow (+ (+ 0.5 7) (- 1 (+ 1 z))) (- (+ 1 0.5) (+ 1 z)))) (exp (+ (+ 0.5 7) (- 1 (+ 1 z))))))","end":0.6079303683720584,"name":"Jmat.Real.gamma, branch z less than 0.5","status":"imp-start","end-est":0.5306625976844203},{"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":249427.81494140625,"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))))) (/ (pow (- (+ 7 z) (- 1 0.5)) (+ 0.5 (- z 1))) (exp (- (+ 7 z) 1)))) (/ (sqrt (* 2 PI)) (exp 0.5)))","end":0.8211929528267459,"name":"Jmat.Real.gamma, branch z greater than 0.5","status":"imp-start","end-est":0.5909242252345673},{"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":18356.59619140625,"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))) (/ 1 (sqrt PI))))","end":0.17116372345002992,"name":"Jmat.Real.erfi, branch x less than or equal to 0.5","status":"ex-start","end-est":0.17091752930532605},{"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":88862.22900390625,"target":false,"output":"(/ (+ (+ (+ (/ (cube (/ 1 (fabs x))) 2) (/ 1 (fabs x))) (* (* (cube (/ 1 (fabs x))) (* (/ 1 (fabs x)) (/ 3 4))) (/ 1 (fabs x)))) (* (/ 15 8) (/ (sqr (/ (cube 1) (cube (fabs x)))) (fabs x)))) (/ (sqr (sqrt (sqrt PI))) (exp (* (fabs x) (fabs x)))))","end":0.9884358904872822,"name":"Jmat.Real.erfi, branch x greater than or equal to 5","status":"apx-start","end-est":0.8766606809974781},{"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":16293.830078125,"target":false,"output":"(- 1 (/ (+ (+ (+ (/ -0.284496736 (+ 1 (* 0.3275911 (fabs x)))) 0.254829592) (/ (/ 1.421413741 (+ 1 (* 0.3275911 (fabs x)))) (+ 1 (* 0.3275911 (fabs x))))) (/ (+ -1.453152027 (/ 1.061405429 (+ 1 (* 0.3275911 (fabs x))))) (cube (+ 1 (* 0.3275911 (fabs x)))))) (* (exp (sqr (fabs x))) (+ 1 (* 0.3275911 (fabs x))))))","end":13.776064434846287,"name":"Jmat.Real.erf","status":"apx-start","end-est":13.490079042695623},{"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":22665.72900390625,"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":28.916560178500553,"name":"Jmat.Real.dawson","status":"apx-start","end-est":31.248364975473837},{"samplers":["default","default"],"bits":128,"start":37.72750797548922,"link":"37-mathsqrtoncomplexrealpart","pinf":0,"ninf":0,"vars":["re","im"],"input":"(* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))","time":9994.05810546875,"target":32.495018090775574,"output":"(if (<= re -8.68041930647669e-252) (* 0.5 (/ (sqrt (* (* 2.0 im) im)) (sqrt (- (sqrt (+ (sqr re) (* im im))) re)))) (if (<= re 1.9727183986347288e-223) (* 0.5 (sqrt (* 2.0 (+ im re)))) (if (<= re 3.873554890065949e+113) (* 0.5 (sqrt (* 2.0 (+ (sqr (sqrt (sqrt (+ (sqr re) (* im im))))) re)))) (* 0.5 (sqrt (* 2.0 (+ re re)))))))","end":21.188560225570257,"name":"math.sqrt on complex, real part","status":"gt-target","end-est":23.80281372962147},{"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":12353.156005859375,"target":9.76756719909256,"output":"(* (- (+ (* 1/60 (pow im 5)) (+ (* 2 im) (* 1/3 (pow im 3))))) (* (cos re) 0.5))","end":0.1964482880805823,"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":1550.6259765625,"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":11732.77783203125,"target":11.733997486912378,"output":"(* (* 0.5 (sin re)) (- (+ (* 1/60 (pow im 5)) (+ (* 2 im) (* 1/3 (pow im 3))))))","end":2.578380138074562,"name":"math.cos on complex, imaginary part","status":"gt-target","end-est":1.0077004274647317},{"samplers":["default","default"],"bits":128,"start":31.38206186269257,"link":"41-JmatReallambertwnewtonloopstep","pinf":0,"ninf":0,"vars":["wj","x"],"input":"(- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj)))))","time":10842.863037109375,"target":12.240053460326083,"output":"(if (<= (- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj))))) 3.691192269698134e-16) (- (+ (sqr wj) x) (* 2 (* wj x))) (+ (- wj (/ wj (+ 1 wj))) (/ x (+ (exp wj) (* wj (exp wj))))))","end":0.2416767796204309,"name":"Jmat.Real.lambertw, newton loop step","status":"gt-target","end-est":0.7537538407539558},{"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":3268.60205078125,"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":5404.371826171875,"target":0.0675,"output":"(* d1 (+ (+ 3 d2) d3))","end":0.0675,"name":"FastMath test3","status":"eq-target","end-est":0.06640625},{"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":3526.566162109375,"target":0.026,"output":"(* d1 (+ d2 30))","end":0.026,"name":"FastMath test2","status":"eq-target","end-est":0.03125},{"samplers":["default"],"bits":128,"start":0.265125,"link":"45-FastMathtest1","pinf":0,"ninf":0,"vars":["d"],"input":"(+ (* d 10) (* d 20))","time":1166.164794921875,"target":0,"output":"(* d (+ 10 20))","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":1328.593994140625,"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":6289.8740234375,"target":0.02275,"output":"(+ (* d1 d4) (* d1 (- d2 (+ d3 d1))))","end":0.020125,"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":7303.551025390625,"target":0.02575,"output":"(+ (* d1 (+ d2 d3)) (* d1 (+ 5 32)))","end":0.030738361324451065,"name":"FastMath dist3","status":"eq-target","end-est":0.01953125},{"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":2036.448974609375,"target":0.013875,"output":"(* d1 (+ d2 d3))","end":0.013875,"name":"FastMath dist","status":"eq-target","end-est":0.01171875}],"commit":"1d8a5a266b020440095bcd8cb501c635b072ad95","branch":"1.0-beta"}