Details

rewrite7.7m (32.9%)

Algorithm
154×rewrite-expression-head
Calls

473 calls:

1.2m
(* (/ (* (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))) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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)))))))
50.1s
(* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (- z 1.0) 7.0))) (* (/ (sqrt (* PI 2.0)) (exp 0.5)) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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))))))))
48.7s
(* (/ (sqrt (* PI 2.0)) (exp 0.5)) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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)))))))
44.1s
(* (/ (sqrt (* PI 2.0)) (exp 0.5)) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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)))))))
43.1s
(* (/ (sqrt (* PI 2.0)) (exp 0.5)) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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)))))))
Rules
18085×times-frac
13657×*-un-lft-identity
10559×add-sqr-sqrt
8866×frac-add
8496×add-cube-cbrt
4715×sqrt-prod
3155×flip-+ flip3-+
2941×frac-times
2534×distribute-lft-out
2472×add-exp-log
2340×associate-*r/
1847×add-cbrt-cube
1813×associate-*l*
1404×associate-*r*
1323×pow1
922×associate-/r/
899×prod-exp
836×unpow-prod-down
757×cbrt-prod
733×associate-*l/
725×add-log-exp
705×div-exp
622×associate-/l*
602×associate-/r*
586×div-inv
540×cbrt-unprod
472×cbrt-div
412×cbrt-undiv
410×unswap-sqr
375×difference-of-squares
364×distribute-lft-out--
320×swap-sqr
298×pow-prod-down
286×sqrt-div
190×flip3-- flip--
179×log-pow
168×sqr-pow
160×exp-sum
145×unpow-prod-up
140×sub-neg
138×pow-exp
137×*-commutative sqrt-pow1
124×associate-/l/
122×pow1/3
111×pow-to-exp
97×sum-log
95×pow1/2
93×distribute-rgt-in distribute-lft-in
90×frac-2neg clear-num
79×pow-unpow
75×cube-prod
72×log-prod
60×+-commutative
58×rem-sqrt-square
42×diff-log
39×1-exp
35×pow-prod-up
31×pow-sqr rec-exp
30×pow-pow
28×associate-+r+
19×div-sub
18×associate-+l-
17×unpow3 cube-mult
16×exp-diff pow2 pow-plus
14×associate--r+
13×cube-div
11×exp-prod
10×log-div
rem-cube-cbrt associate-+l+ inv-pow pow-sub pow-flip
associate--r- sum-cubes rem-log-exp
distribute-rgt-neg-in associate-+r- associate--l+ unpow2
un-div-inv sin-sum rem-cbrt-cube
cos-sum
neg-sub0
sqrt-pow2 rem-exp-log unpow1/3 associate--l- sqrt-unprod pow3 unsub-neg rem-square-sqrt distribute-rgt-out

simplify7.2m (30.7%)

sample4.0m (16.9%)

Algorithm
99×intervals
Results
1.4m15908×body10240exit
52.9s435680×body80valid
32.6s30526×body1280valid
16.7s23536×body640valid
6.5s69906×body80nan
6.3s3002×body1280nan
5.5s12105×body320valid
3.6s2648×body640nan
3.5s9946×body160valid
2.0s1329×body320nan
1.9s49536×pre80true
1.4s1451×body2560valid
555.0ms589×body5120valid
334.0ms595×body160nan

prune2.6m (11.2%)

series1.6m (7.0%)

Calls

473 calls:

3.3s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
3.1s
(* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
1.6s
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ (sqrt 1.0) (* (cbrt (+ 1.0 (* 0.3275911 (fabs x)))) (cbrt (+ 1.0 (* 0.3275911 (fabs x)))))) (* (/ (sqrt 1.0) (cbrt (+ 1.0 (* 0.3275911 (fabs x))))) (+ (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429) -1.453152027))))))))) (exp (- (* (fabs x) (fabs x))))))
1.5s
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (* (sqrt (+ (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (/ (* (sqrt 1.0) (* (/ (sqrt 1.0) (cbrt (+ 1.0 (* 0.3275911 (fabs x))))) (+ (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429) -1.453152027))) (pow (+ 1.0 (* 0.3275911 (fabs x))) 2/3)))) -0.284496736)) 0.254829592)) (sqrt (+ (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (/ (* (sqrt 1.0) (* (/ (sqrt 1.0) (cbrt (+ 1.0 (* 0.3275911 (fabs x))))) (+ (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429) -1.453152027))) (pow (+ 1.0 (* 0.3275911 (fabs x))) 2/3)))) -0.284496736)) 0.254829592)))) (exp (- (* (fabs x) (fabs x))))))
1.4s
(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (- 0.5 (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))))

regimes10.1s (0.7%)

Accuracy

Total 122.7b remaining (43.2%)

Threshold costs 5.3b (1.9%)

17.6b27.8%math.log10 on complex, real part
17.3b28.5%math.log/1 on complex, real part
13.8b37.9%math.sqrt on complex, imaginary part, im greater than 0 branch
12.7b39%math.sqrt on complex, real part
10.8b55.9%math.log/2 on complex, real part

localize4.2s (0.3%)

bsearch3.1s (0.2%)

end1.0ms (0.0%)