Details

rewrite13.5m (42.1%)

Algorithm
159×rewrite-expression-head
Calls

471 calls:

5.1m
(* (+ (+ (/ 1.5056327351493116e-07 (+ (- z) 8.0)) (/ 9.984369578019572e-06 (+ (- z) 7.0))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (/ -176.6150291621406 (+ (- z) 4.0)))) (sqrt (* PI 2.0)))
4.2m
(* (+ (+ (/ 1.5056327351493116e-07 (+ (- z) 8.0)) (/ 9.984369578019572e-06 (+ (- z) 7.0))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (/ -176.6150291621406 (+ (- z) 4.0)))) (* (sqrt PI) (sqrt 2.0)))
1.2m
(* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- z 1.0)) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) 0.5) (sqrt (* PI 2.0)))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (+ (+ (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))))
1.2m
(* (* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp z)) (exp (- (- 1.0 7.0) 0.5))) (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (+ (+ (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))))
3.6s
(log (exp (+ (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)))
Rules
217126×times-frac
81207×*-un-lft-identity
78131×add-sqr-sqrt
75090×add-cube-cbrt
66193×cbrt-prod
64339×unpow-prod-down
64015×cube-prod
21443×sqr-pow
21322×unpow3 cube-mult
4072×sqrt-prod
3053×frac-add
2920×add-exp-log
2856×pow1
2532×distribute-lft-out
2145×flip-+ flip3-+
1999×associate-*r*
1878×add-cbrt-cube
1804×log-pow
1699×div-inv
1424×associate-*r/
1233×associate-*l*
1207×frac-times
1180×prod-exp
1042×associate-/r*
903×difference-of-squares
895×associate-/r/
722×associate-/l*
716×div-exp
684×add-log-exp
656×distribute-lft-out--
598×sqrt-pow1
522×cbrt-unprod
504×pow1/2
498×associate-*l/
441×pow-exp
426×unswap-sqr
417×pow-prod-down
388×cbrt-undiv
367×frac-sub
259×sqrt-div
250×associate-/l/
233×pow-to-exp
232×exp-diff
230×swap-sqr
206×distribute-rgt-neg-in
184×distribute-lft-neg-in
156×*-commutative
139×flip3-- flip--
118×cbrt-div
114×log-prod
103×1-exp
102×frac-2neg clear-num
100×rec-exp
86×pow-prod-up
81×distribute-rgt-in sum-log distribute-lft-in
74×exp-sum
70×sub-neg
57×pow1/3
56×rem-sqrt-square
52×pow-sqr
46×+-commutative
43×neg-mul-1
38×diff-log
37×pow-plus
33×pow-unpow
28×pow2
22×unpow-prod-up
17×exp-prod associate-+l-
15×div-sub
14×pow-pow associate--l+
12×associate--r+
11×unpow2
10×sin-sum
8×associate-+l+ associate-+r+ sqrt-unprod
7×un-div-inv pow-sub pow-flip rem-log-exp
6×neg-sub0
5×inv-pow distribute-rgt-out sqrt-undiv cos-sum log-div
4×rem-exp-log rem-square-sqrt
3×sin-mult
2×cube-div rem-cube-cbrt pow3 associate-+r- exp-neg sum-cubes exp-to-pow
1×difference-cubes sqr-sin distribute-frac-neg associate--r- associate--l-

prune8.1m (25.3%)

simplify5.4m (16.9%)

sample2.9m (8.9%)

Algorithm
99×intervals
Results
52.8s476676×body80valid
32.2s30783×body1280valid
17.2s12301×body10240exit
16.9s23594×body640valid
8.8s69113×body80nan
5.8s11786×body320valid
3.5s10211×body160valid
2.6s1533×body1280nan
1.9s1324×body640nan
1.5s49536×pre80true
1.4s1453×body2560valid
457.0ms342×body160nan
408.0ms670×body320nan
380.0ms577×body5120valid

series1.9m (5.8%)

Calls

468 calls:

20.7s
(- (pow 1.0 3) (pow (/ (* 1.0 (/ (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 0.3275911) (pow (fabs x) 2)))) (- 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (exp (pow (fabs x) 2)))) (+ (* 0.3275911 (fabs x)) 1.0)) 3))
7.3s
(+ (pow (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 3) (pow 1.0 3))
2.3s
(pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5)
1.9s
(- (sqrt (pow 1.0 3)) (sqrt (pow (/ (* 1.0 (/ (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 0.3275911) (pow (fabs x) 2)))) (- 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (exp (pow (fabs x) 2)))) (+ (* 0.3275911 (fabs x)) 1.0)) 3)))
1.8s
(* 0.16666666666666666 (* (pow (* (pow -1 1.0) (pow -2.0 1.0)) 0.5) (pow (pow (- (log u1)) 1.0) 0.5)))

regimes11.1s (0.6%)

Accuracy

Total 101.1b remaining (37.1%)

Threshold costs 4.8b (1.8%)

13.3b54.6%math.sqrt on complex, real part
13.1b55.2%math.sqrt on complex, imaginary part, im greater than 0 branch
10.5b56.3%math.log/1 on complex, real part
10.5b56.5%math.log10 on complex, real part
10.1b57.6%math.log/2 on complex, real part

localize5.5s (0.3%)

bsearch2.9s (0.2%)

end1.0ms (0.0%)