Time: 39.8m
Passed: 31/38
Tests: 50
Bits: 504/629

Date:Tuesday, January 22nd, 2019
Commit:45d4082dea7f80b56c44622251112721670e87cb on develop
Hostname:warfa
Points:256
Fuel:4
Seed:2019022
Flags:
setup:simplifyrules:numericsrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
+o rules:numerics
TestStartResult ?Target ?∞ ↔ ℝTime
powComplex, real part31.00.02.2m»
powComplex, imaginary part31.70.23.7m»
normal distribution0.40.519.9s»
math.square on complex, real part0.00.01.9s»
math.square on complex, imaginary part0.00.01.1s»
math.sqrt on complex, imaginary part, im greater than 0 branch37.213.010.2s»
math.sin on complex, real part0.00.018.0s»
math.log10 on complex, real part31.20.618.2s»
math.log10 on complex, imaginary part85.0ms»
math.log/2 on complex, real part30.90.41.4m»
math.log/2 on complex, imaginary part167.0ms»
math.log/1 on complex, real part30.901.5s»
math.log/1 on complex, imaginary part37.0ms»
math.exp on complex, real part0.00.012.4s»
math.exp on complex, imaginary part0.00.07.6s»
math.cos on complex, real part0.00.09.2s»
math.arg on complex20.0ms»
math.abs on complex29.70.01.1s»
_multiplyComplex, real part0.00.02.2s»
_multiplyComplex, imaginary part0.00.01.8s»
_divideComplex, real part26.112.519.9s»
_divideComplex, imaginary part26.17.126.2s»
Octave 3.8, oct_fill_randg0.10.142.5s»
Octave 3.8, jcobi/4, as called45.30.07.3s»
Octave 3.8, jcobi/452.538.92.0m»
Octave 3.8, jcobi/33.51.13.7m»
Octave 3.8, jcobi/223.812.640.0s»
Octave 3.8, jcobi/116.05.851.8s»
Jmat.Real.lambertw, estimator0.30.05.3s»
Jmat.Real.gamma, branch z less than 0.51.80.63.1m»
Jmat.Real.gamma, branch z greater than 0.510.0m»
Jmat.Real.erfi, branch x less than or equal to 0.50.20.132.5s»
Jmat.Real.erfi, branch x greater than or equal to 519.0s»
Jmat.Real.erf13.913.91.3m»
Jmat.Real.dawson28.40.02.5m»
math.sqrt on complex, real part37.913.632.711.9s»
math.sin on complex, imaginary part58.00.80.243.1s»
math.cube on real0.1001.1s»
math.cube on complex, real part7.20.20.243.1s»
math.cube on complex, imaginary part7.10.20.233.5s»
math.cos on complex, imaginary part43.40.80.342.8s»
Jmat.Real.lambertw, newton loop step13.22.112.718.5s»
FastMath test50.1004.2s»
FastMath test30.10.00.113.3s»
FastMath test20.20.00.07.1s»
FastMath test10.300691.0ms»
FastMath repmul0.1001.1s»
FastMath dist40.00.00.014.9s»
FastMath dist30.00.00.012.3s»
FastMath dist0.00.00.08.8s»

Details

simplify22.5m

Calls

10096 calls:

Slowest
1.5s
(* (- x.re x.im) (+ (* (* x.re x.im) (* x.re x.im)) (- (* (* x.im x.re) (* x.im x.re)) (* (* x.re x.im) (* x.im x.re)))))
1.5s
(* (+ x.re x.im) (+ (* (* x.re x.im) (* x.re x.im)) (- (* (* x.im x.re) (* x.im x.re)) (* (* x.re x.im) (* x.im x.re)))))
1.3s
(* (+ (* (* x.re x.re) (* x.re x.re)) (+ (* (* x.im x.im) (* x.im x.im)) (* (* x.re x.re) (* x.im x.im)))) (- (* x.re x.im) (* x.im x.re)))
1.2s
(* (* (- x.re x.im) (+ x.re x.im)) (- (* x.re x.im) (* x.im x.re)))
1.2s
(* (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))))

sample9.0m

Algorithm
90×intervals
Results
6.3m98569×body10240exit
1.2m405449×body80valid
25.4s22897×body1280valid
14.1s17862×body640valid
11.4s70612×body80nan
6.9s1595×body1280nan
5.0s9271×body320valid
3.5s1275×body640nan
3.3s8889×body160valid
2.6s49536×pre80true
1.3s679×body320nan
993.0ms1385×body2560valid
587.0ms630×body5120valid
401.0ms339×body160nan

prune4.5m

series1.0m

Calls

444 calls:

Slowest
3.5s
(log (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (/ (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (- (* -0.284496736 -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))))) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) (/ -1 (fma 0.3275911 (fabs x) 1)) -0.284496736)))) (exp (- (* (fabs x) (fabs x)))))))
2.9s
(exp (log (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (/ (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (- (* -0.284496736 -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))))) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) (/ -1 (fma 0.3275911 (fabs x) 1)) -0.284496736)))) (exp (- (* (fabs x) (fabs x))))))))
2.9s
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (/ (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (- (* -0.284496736 -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))))) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) (/ -1 (fma 0.3275911 (fabs x) 1)) -0.284496736)))) (exp (- (* (fabs x) (fabs x))))))
2.9s
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (/ (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (- (* -0.284496736 -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))))) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) (/ -1 (fma 0.3275911 (fabs x) 1)) -0.284496736)))) (exp (- (* (fabs x) (fabs x))))))
1.8s
(+ 0.254829592 (/ (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (- (* -0.284496736 -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))))) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) (/ -1 (fma 0.3275911 (fabs x) 1)) -0.284496736)))

regimes7.9s

Accuracy

Total 28.7b remaining (22.9%)

10.0b28.9%_divideComplex, real part
5.4b32.1%_divideComplex, imaginary part
3.0b76.6%Octave 3.8, jcobi/1
2.8b0%Octave 3.8, jcobi/4
1.6b0%Jmat.Real.lambertw, newton loop step

rewrite7.9s

Algorithm
142×rewrite-expression-head
Calls

444 calls:

Slowest
515.0ms
(* (* (/ (pow (+ (+ 6 0.5) z) (+ (- z 1) 0.5)) (exp (+ 6 0.5))) (/ (sqrt (* PI 2)) (exp z))) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z))))))
503.0ms
(* (/ (* (pow (+ (+ 6 0.5) z) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (+ 6 0.5) z))) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z))))))
477.0ms
(/ (+ (+ (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (* (* x x) 0.0008327945)) (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (* (* (* x x) (* x x)) (* 2 0.0001789971)))) (fma (* (* (* x x) (* x x)) (* (* x x) (* x x))) 0.0140005442 (+ (fma 0.2909738639 (* (* x x) (* x x)) (fma (* x x) 0.7715471019 1)) (* (* (* x x) (* x x)) (* (* x x) 0.0694555761))))) (+ (fma 0.0005064034 (* (* (* x x) (* x x)) (* (* x x) (* x x))) (+ (* (* 0.0072644182 (* x x)) (* (* x x) (* x x))) (fma (* (* x x) (* x x)) 0.0424060604 (fma 0.1049934947 (* x x) 1)))) (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (* (* x x) 0.0001789971))))
393.0ms
(+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z)))))
359.0ms
(* (/ (pow (+ (+ 6 0.5) z) (+ (- z 1) 0.5)) (exp (+ 6 0.5))) (* (/ (sqrt (* PI 2)) (exp z)) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z)))))))
Rules
8008×frac-add
3303×flip-+
3303×flip3-+
3014×*-un-lft-identity
2445×times-frac
2226×add-sqr-sqrt
2195×add-cube-cbrt
1745×frac-times
1421×associate-*r/
1173×add-exp-log
1157×pow1
1017×add-cbrt-cube
700×add-log-exp
600×associate-*l*
574×distribute-lft-out
469×cbrt-prod
463×associate-*r*
445×expm1-log1p-u
444×log1p-expm1-u
426×associate-*l/
348×associate-/l*
343×associate-/r*
311×sqrt-prod
302×associate-/r/
300×prod-exp
296×unpow-prod-down
262×pow-prod-down
251×prod-diff
234×cbrt-unprod
232×div-inv
189×div-exp
175×sqrt-div
158×sum-log
142×*-commutative
141×pow-prod-up
136×cube-prod
128×cbrt-undiv
120×fma-def
110×log-pow
109×flip3--
109×flip--
102×distribute-rgt-in
102×distribute-lft-in
93×cbrt-div
93×pow1/3
88×associate-/l/
85×unpow-prod-up
78×exp-sum
78×pow2
77×pow-plus
77×pow1/2
75×frac-2neg
75×clear-num
66×sub-neg
60×fma-udef
57×rec-exp
53×unpow3
53×fma-neg
53×cube-mult
47×log-prod
34×pow-flip
33×+-commutative
32×pow-exp
32×inv-pow
31×pow-to-exp
24×frac-sub
20×diff-log
16×difference-of-squares
16×un-div-inv
16×hypot-udef
15×associate-+l+
13×associate--l+
12×rem-sqrt-square
11×associate-+r+
11×associate--r+
11×exp-prod
11×div-sub
10×distribute-lft-out--
sin-sum
sqrt-unprod
pow-pow
associate-+l-
rem-square-sqrt
exp-diff
associate--r-
pow-sub
log-div
rem-cube-cbrt
pow3
rem-log-exp
distribute-lft-neg-in
cube-unmult
distribute-rgt-neg-in
cube-div
expm1-log1p
expm1-udef
sqrt-undiv
log1p-def
rem-exp-log
cos-sum
rem-cbrt-cube
distribute-lft-neg-out
associate--l-
exp-neg
difference-cubes
sub0-neg
log1p-expm1
neg-mul-1
distribute-rgt-out
log1p-udef

localize4.2s

bsearch1.2s

end1.0ms