Details

rewrite10.6m (65.5%)

Algorithm
163×rewrite-expression-head
Calls

493 calls:

2.1s
(* (sqrt (+ (+ (* (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))))) (/ x (/ (+ (+ (* (* 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)))) (sqrt (+ (+ (* (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))))))))
1.5s
(/ (+ (+ (* (* 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)))))
1.5s
(/ (+ (+ (* (* 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)))) (sqrt (cbrt (+ (+ (* (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)))))))
1.5s
(/ (+ (+ (* (* 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)))) (sqrt (+ (+ (* (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
(* (* (fabs (cbrt (+ (+ (* (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)))))) (sqrt (+ (+ (* (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)))))) (/ x (/ (+ (+ (* (* 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)))) (sqrt (cbrt (+ (+ (* (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
8570×times-frac
7055×*-un-lft-identity
6875×add-sqr-sqrt
4961×add-cube-cbrt
2537×add-exp-log
2515×associate-*r*
2103×add-cbrt-cube
2034×sqrt-prod
1641×pow1
1058×associate-*l*
967×flip-+ flip3-+
829×prod-exp
781×add-log-exp
773×distribute-lft-out
756×associate-*r/
727×associate-/r/
653×cbrt-prod
644×cbrt-unprod
608×div-exp
560×difference-of-squares
543×sqrt-div
532×frac-add
483×associate-/l*
472×cbrt-undiv
386×pow-prod-down
381×associate-/r*
368×div-inv
334×distribute-lft-out--
300×unswap-sqr
299×cbrt-div
298×unpow-prod-down
252×swap-sqr
227×log-pow
226×frac-times
216×log-prod
212×associate-*l/
160×flip3-- flip--
148×*-commutative
138×sqrt-pow1
122×pow1/2
121×associate-/l/
119×exp-prod
115×distribute-rgt-in distribute-lft-in
114×pow-prod-up pow1/3
91×sqr-pow
86×pow-unpow
85×distribute-rgt-neg-in
82×sum-log
80×diff-log
79×clear-num frac-2neg
77×distribute-lft-neg-in
75×cube-prod
73×pow-exp
70×pow-sqr sub-neg
69×rem-sqrt-square
61×pow-plus
59×pow-to-exp 1-exp
58×distribute-neg-frac
50×+-commutative
41×rec-exp
39×pow2
36×pow-pow associate--l+
28×associate-+r+
26×associate-+l+ neg-mul-1
19×unpow3 cube-mult
17×div-sub
16×associate--l-
15×rem-log-exp
14×cube-div inv-pow pow-flip
13×pow3
10×distribute-rgt-out
exp-diff exp-neg
neg-sub0 log-div
unpow2
un-div-inv rem-exp-log sin-sum associate-+l- associate--r+
rem-cube-cbrt distribute-neg-in rem-cbrt-cube
log-rec neg-log
cos-sum unpow1/2 exp-sum
sqrt-pow2 sqrt-unprod sum-cubes frac-sub distribute-rgt-neg-out exp-to-pow
distribute-neg-out associate-+r- distribute-lft-neg-out distribute-rgt-out-- unpow-prod-up pow-sub unsub-neg rem-square-sqrt

sample2.7m (16.4%)

Algorithm
99×intervals
Results
51.0s11926×body10240exit
43.0s468990×body80valid
17.5s27017×body1280valid
10.3s21094×body640valid
5.2s68547×body80nan
3.6s1641×body1280nan
3.3s10734×body320valid
2.4s9441×body160valid
1.7s1348×body640nan
1.2s49536×pre80true
737.0ms669×body320nan
621.0ms1522×body2560valid
563.0ms600×body5120valid
152.0ms335×body160nan

series1.3m (7.9%)

Calls

491 calls:

4.0s
(* (+ (sqrt (+ (- (* d1 d2) (* d1 d3)) (* d4 d1))) d1) (- (sqrt (+ (- (* d1 d2) (* d1 d3)) (* d4 d1))) d1))
2.4s
(/ (* (/ (/ (* 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)))
2.4s
(* (/ (/ (* 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))))
2.4s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
1.3s
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* -0.284496736 (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) (* (* (/ 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 (fabs x)) (* 0.3275911 (fabs x))))) (* (- 1.0 (* 0.3275911 (fabs x))) 1.061405429)))))) (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))))) (exp (- (* (fabs x) (fabs x))))))

prune1.2m (7.3%)

simplify14.5s (1.5%)

regimes7.3s (0.8%)

Accuracy

Total 99.7b remaining (37.8%)

Threshold costs 5.1b (1.9%)

17.8b52.3%math.sqrt on complex, imaginary part, im greater than 0 branch
11.4b54.1%math.log/2 on complex, real part
10.6b57.2%math.log10 on complex, real part
10.5b56.3%math.abs on complex
10.5b57.6%math.log/1 on complex, real part

localize3.8s (0.4%)

bsearch2.6s (0.3%)

end1.0ms (0.0%)