Details

simplify46.9m

Calls

24255 calls:

Slowest
1.5s
(* (+ (* (* 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)))
1.3s
(* (* (- x.re x.im) (+ x.re x.im)) (- (* x.re x.im) (* x.im x.re)))
1.3s
(* (* (/ 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))))))
1.2s
(* (sqrt 0.5) (* (+ (* (* (* im -1/3) im) im) (* -2 im)) (* (sqrt 0.5) (sin re))))
1.1s
(fma (- (/ (* (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (exp (* (fabs x) (fabs x))))) (/ 1 1) (* (/ (* (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (exp (* (fabs x) (fabs x)))) (/ 1 1)))

sample9.0m

Algorithm
84×intervals
Results
6.3m99721×body10240exit
49.4s339790×body80valid
38.3s25703×body1280valid
18.6s19682×body640valid
11.5s69397×body80nan
8.0s10535×body320valid
4.8s1610×body1280nan
4.8s9318×body160valid
3.9s1309×body640nan
1.2s1446×body2560valid
1.1s25536×pre80true
1.0s663×body320nan
605.0ms582×body5120valid
400.0ms318×body160nan

prune4.2m

rewrite1.8m

Algorithm
121×rewrite-expression-head
Calls

341 calls:

Slowest
48.7s
(* (/ 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)))))
17.0s
(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
2.7s
(+ (+ (+ (/ -1259.1392167224028 (+ (- 1 z) 1)) 0.9999999999998099) (/ 676.5203681218851 (- 1 z))) (/ -176.6150291621406 (- 5 (+ z 1))))
1.3s
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
1.3s
(* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1))
Rules
164511×*-un-lft-identity
87338×add-sqr-sqrt
68454×frac-add
67967×associate-/l*
66514×times-frac
62289×associate-/r*
57342×add-cube-cbrt
52428×distribute-lft-out
51061×frac-times
24271×associate-/l/
19971×associate-*l*
18036×distribute-lft-out--
13314×clear-num
13243×frac-2neg
11559×associate-*r*
10543×difference-of-squares
8318×*-commutative
7215×prod-diff
5764×associate-*l/
5466×unswap-sqr
3347×sqrt-prod
3235×div-inv
2840×swap-sqr
2463×add-exp-log
2301×associate-*r/
2112×pow1
1917×flip-+ flip3-+
1382×add-cbrt-cube
1216×fma-def
1009×distribute-rgt-out
890×prod-exp
795×div-exp
616×distribute-rgt-in distribute-lft-in
505×pow-prod-up
504×add-log-exp
454×cbrt-unprod
432×exp-sum
407×associate-/r/
403×associate-+l+
382×fma-neg
379×pow-prod-down
370×log-pow
348×distribute-rgt1-in
343×expm1-log1p-u log1p-expm1-u
341×insert-posit16
311×unpow-prod-down
302×distribute-lft1-in
253×cbrt-undiv
233×pow-plus
207×un-div-inv
200×sqrt-pow1
189×associate--l+
148×associate--r+
136×1-exp rec-exp
133×cbrt-prod hypot-def
120×log-prod
118×flip3-- flip--
115×pow1/2
95×pow-sqr
92×sqrt-div
90×rem-sqrt-square
86×sub-neg
81×fma-udef
78×div-sub
74×pow-div
69×+-commutative
68×pow2
56×sum-log sqr-pow
52×unpow-prod-up
50×cube-unmult
48×frac-sub
47×pow-exp
41×pow-flip inv-pow
39×exp-prod diff-log
27×pow-to-exp
21×distribute-rgt-out--
19×pow-unpow
15×pow1/3
14×pow-pow
12×sin-sum
10×cbrt-div pow3 sqrt-unprod
7×rem-log-exp associate-+l-
5×exp-diff hypot-udef rem-square-sqrt
4×associate-+r+ pow-sub
3×expm1-log1p remove-double-div log1p-expm1 cos-sum
2×expm1-udef associate--r- log1p-udef
1×associate--l- log-div

series55.4s

Calls

341 calls:

Slowest
1.6s
(* (pow (* -2 (log u1)) (/ 0.5 2)) (exp (- (* (log (* -2 (log u1))) (/ 0.5 2)) (log 6))))
1.2s
(fma (- (cbrt z)) (* (cbrt z) (cbrt z)) (* (cbrt z) (* (cbrt z) (cbrt z))))
1.1s
(fma (- (/ (* (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (sqrt (exp (* (fabs x) (fabs x)))))) (/ 1 (sqrt (exp (* (fabs x) (fabs x))))) (* (/ (* (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (sqrt (exp (* (fabs x) (fabs x))))) (/ 1 (sqrt (exp (* (fabs x) (fabs x)))))))
1.0s
(fma (- (/ (* (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (sqrt (exp (* (fabs x) (fabs x)))))) (/ 1 (sqrt (exp (* (fabs x) (fabs x))))) (* (/ (* (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (sqrt (exp (* (fabs x) (fabs x))))) (/ 1 (sqrt (exp (* (fabs x) (fabs x)))))))
1.0s
(* (pow (* -2 (log u1)) 0.5) (/ 1 6))

regimes7.0s

Accuracy

Total 22.7b remaining (29.3%)

7.3b31.5%_divideComplex, real part
7.3b33.2%_divideComplex, imaginary part
3.1b75.5%Octave 3.8, jcobi/1
1.0b0%Jmat.Real.lambertw, newton loop step
0.8b0%math.sin on complex, imaginary part

localize3.5s

bsearch463.0ms

end1.0ms