Details

rewrite3.7m (46.1%)

Algorithm
73×rewrite-expression-head
Calls

167 calls:

1.3m
(* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099))))))
1.0m
(/ (+ (/ -1259.1392167224028 (+ (- z) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))))))) (exp (+ 0.5 (+ (- z) 7.0))))
25.3s
(+ (/ -1259.1392167224028 (+ (- z) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z))))))))
25.1s
(* (/ (+ (+ (+ (+ (+ 1.0 (* 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 (* 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 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x)
14.1s
(/ (+ (+ (+ (+ (+ 1.0 (* 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 (* 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 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x)))))
Rules
3088×*-un-lft-identity
2224×times-frac
2192×add-sqr-sqrt
1720×add-cube-cbrt
1030×frac-add
863×distribute-lft-out
758×add-exp-log
623×add-cbrt-cube
546×prod-diff
484×pow1
455×sqrt-prod
414×flip-+ flip3-+
377×add-log-exp
373×associate-*l*
285×associate-*r*
265×prod-exp
215×associate-/l*
200×cbrt-unprod
169×unpow-prod-down associate-*r/
167×log1p-expm1-u expm1-log1p-u
155×cbrt-prod
145×frac-times
137×div-exp
135×pow-prod-down exp-sum
132×associate-/r* associate-/r/
122×sum-log
116×unswap-sqr
115×div-inv
111×distribute-rgt-in distribute-lft-in
99×cbrt-undiv
98×difference-of-squares
94×fma-def
75×associate-/l/
74×distribute-lft-out-- log-pow
60×associate-*l/
57×cube-prod
54×fma-neg
48×associate--l+
46×*-commutative
43×log-prod
38×sqr-pow
35×sub-neg
32×pow-exp
31×sqrt-div clear-num frac-2neg
30×pow-unpow
27×fma-udef flip3-- flip--
26×diff-log
22×swap-sqr
20×pow-to-exp pow1/3 cbrt-div
17×+-commutative
15×rec-exp 1-exp sqrt-pow1
11×pow1/2 pow-pow
10×associate-+l-
9×associate-+l+
8×rem-cube-cbrt
7×rem-sqrt-square div-sub
6×rem-log-exp
5×pow-prod-up pow-sqr unpow3 cube-mult associate--l-
4×cube-div associate-+r+ associate--r+
3×distribute-rgt-neg-in exp-diff un-div-inv pow2 pow-flip pow-plus exp-prod
2×pow-sub unpow-prod-up
1×cos-sum inv-pow associate-+r- sin-sum distribute-rgt-out neg-sub0 associate--r- log-div

simplify3.1m (38.5%)

sample34.9s (7.3%)

Algorithm
68×intervals
Results
18.3s193952×body80valid
2.6s500×body10240exit
1.9s4551×body160valid
1.9s2428×body1280valid
1.5s1960×body640valid
1.2s26306×body80nan
283.0ms980×body320valid
158.0ms95×body1280nan
126.0ms70×body640nan
76.0ms1536×pre80true
44.0ms18×body5120valid
39.0ms43×body320nan
35.0ms53×body2560valid
12.0ms20×body160nan

prune19.4s (4.0%)

series17.1s (3.6%)

Calls

92 calls:

1.0s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
745.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) (* (* (cbrt (/ 1.0 (fma (fabs x) 0.3275911 1.0))) (cbrt (/ 1.0 (fma (fabs x) 0.3275911 1.0)))) (cbrt (/ 1.0 (fma (fabs x) 0.3275911 1.0)))) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x))))) 1.0)
638.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ (/ 1.0 (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (fma (fabs x) 0.3275911 1.0))) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x))))) 1.0)
628.0ms
(/ (* (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (/ (* 1.0 (fma (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 6)) (fma (pow (/ 1.0 (fabs x)) 4) (/ 3.0 4.0) 1))) (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
622.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x))))) 1.0)

localize2.1s (0.4%)

regimes398.0ms (0.1%)

Accuracy

Total 0.3b remaining (2.2%)

Threshold costs 0.3b (2.2%)

0.2b0%Jmat.Real.erfi, branch x less than or equal to 0.5
0.1b0%math.log10 on complex, imaginary part
0.0b0%Jmat.Real.erf
0.0b0%FastMath dist
0.0b0%Jmat.Real.lambertw, estimator

bsearch0.0ms (0.0%)

end0.0ms (0.0%)