Details

rewrite10.9m (69.7%)

Algorithm
158×rewrite-expression-head
Calls

485 calls:

8.7s
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
2.9s
(* (/ 1 (sqrt (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))))) (/ x (exp (log (/ (sqrt (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442))))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))))))
2.9s
(* (/ 1 (sqrt (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))))) (/ x (/ (sqrt (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442))))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))))
1.8s
(/ (/ 1 (sqrt (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))))) (* (cbrt (/ (sqrt (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442))))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))) (cbrt (/ (sqrt (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442))))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))))
1.4s
(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))
Rules
8416×times-frac
7628×*-un-lft-identity
6170×add-sqr-sqrt
4849×add-cube-cbrt
3716×add-exp-log
2169×sqrt-prod
2034×add-cbrt-cube
1749×prod-exp
1580×pow1
1568×associate-*r*
1278×distribute-lft-out
1203×flip-+ flip3-+
1007×associate-*r/
951×div-exp
860×associate-*l*
844×associate-/r/
782×add-log-exp
772×frac-add
708×cbrt-unprod
634×associate-/l*
503×sqrt-div
492×frac-times
480×pow-exp
463×cbrt-prod
432×pow-prod-down
427×associate-/r*
419×log-prod
363×div-inv
356×cbrt-undiv
330×pow-to-exp
319×unpow-prod-down
315×associate-*l/
305×difference-of-squares
266×unswap-sqr
244×distribute-lft-out--
214×log-pow
212×cbrt-div
200×flip3-- flip--
171×associate-/l/
155×exp-sum
133×*-commutative
130×cube-prod
128×sqr-pow
127×swap-sqr
120×distribute-rgt-in sqrt-pow1 distribute-lft-in
112×1-exp
97×diff-log
92×pow1/3 sub-neg
86×frac-2neg clear-num
84×pow1/2
74×pow-unpow
71×sum-log
70×rem-sqrt-square
62×associate-+r+
55×associate-+l+
50×pow-prod-up
49×associate--l+
48×exp-prod
47×+-commutative
39×cube-div
38×pow-sqr
36×log-div
33×pow-plus
30×pow-pow
28×rec-exp
24×rem-cube-cbrt
23×unpow3 cube-mult
22×pow2 rem-log-exp
17×un-div-inv associate--l-
16×unpow2
15×inv-pow pow-flip
14×exp-diff div-sub
11×rem-exp-log
10×distribute-rgt-out frac-sub associate--r+
distribute-rgt-neg-in distribute-lft-neg-in log-rec
sin-sum
distribute-lft-neg-out distribute-neg-in distribute-neg-frac
cos-sum associate-+r- unpow-prod-up rem-cbrt-cube associate-+l- neg-mul-1
distribute-neg-out pow3 pow-sub unsub-neg distribute-rgt-neg-out exp-to-pow
difference-cubes distribute-frac-neg associate--r- sum-cubes

sample1.8m (11.5%)

Algorithm
99×intervals
Results
43.8s11927×body10240exit
22.5s517040×body80valid
10.7s27104×body1280valid
4.9s21470×body640valid
2.4s69203×body80nan
1.7s1583×body1280nan
1.5s10603×body320valid
974.0ms1343×body640nan
959.0ms9530×body160valid
731.0ms49536×pre80true
342.0ms654×body320nan
334.0ms1468×body2560valid
138.0ms593×body5120valid
124.0ms358×body160nan

series1.4m (9.1%)

Calls

482 calls:

20.2s
(- (pow 1.0 3) (/ (pow (* (- (* 0.254829592 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 (* 0.3275911 (fabs x)))) 1.061405429))))))) (* (/ 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 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))) 3) (pow (* (- 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 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (exp (pow (fabs x) 2))) 3)))
3.1s
(pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)
3.0s
(- (pow 1.0 3) (pow (* (/ 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 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (/ 1 (exp (pow (fabs x) 2))))) 3))
1.4s
(* (* (/ 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 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (/ 1 (exp (pow (fabs x) 2))))) (+ (* (/ 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 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (/ 1 (exp (pow (fabs x) 2))))) 1.0))
1.4s
(* (* (/ 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 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (/ 1 (exp (pow (fabs x) 2))))) (+ (* (/ 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 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (/ 1 (exp (pow (fabs x) 2))))) 1.0))

prune1.1m (7.0%)

simplify13.9s (1.5%)

Algorithm
256×egg-herbie

regimes6.9s (0.7%)

Accuracy

Total 97.4b remaining (35.6%)

Threshold costs 4.0b (1.5%)

18.4b45.6%math.sqrt on complex, imaginary part, im greater than 0 branch
10.8b56.1%math.log/2 on complex, real part
10.2b57.8%math.log10 on complex, real part
9.9b58.8%math.log/1 on complex, real part
9.8b58%math.abs on complex

localize2.6s (0.3%)

bsearch2.1s (0.2%)

end1.0ms (0.0%)