Details

rewrite12.2m (36.5%)

Algorithm
160×rewrite-expression-head
Calls

490 calls:

23.5s
(* (/ (+ (+ (+ (+ (+ 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)
13.5s
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
13.3s
(/ (+ (+ (+ (+ (+ 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)))))
8.5s
(* (* (+ (+ (pow (/ alpha (+ (+ alpha beta) 2.0)) 6) (pow 1.0 6)) (* (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))) (+ (* (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (- (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))))) (* (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (/ alpha (+ (+ alpha beta) 2.0))))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
3.0s
(* (/ 1 (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 (* (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)))))))
Rules
90721×times-frac
53966×*-un-lft-identity
41009×frac-times
37354×associate-*r/
35562×add-sqr-sqrt
33451×sqrt-prod
33205×add-cube-cbrt
23459×flip-+ flip3-+
22610×frac-add
17641×associate-*l/
11595×cube-div
10105×distribute-lft-out
7356×frac-sub
5010×associate-/r/
3827×add-exp-log
3007×add-cbrt-cube
2597×div-inv
2581×pow1
2183×associate-*r*
1674×prod-exp
1381×flip3-- flip--
1376×associate-*l*
1271×cbrt-unprod
1247×unpow-prod-down
1110×cbrt-prod
853×cube-prod
833×associate-/r*
815×div-exp
786×associate-/l*
785×sqrt-div
767×pow-prod-down
760×add-log-exp
745×difference-of-squares
555×cbrt-undiv
537×log-pow
376×cbrt-div
364×unswap-sqr
354×sqr-pow
349×distribute-lft-out--
308×swap-sqr
279×sqrt-pow1
210×pow-prod-up
201×associate-/l/
164×*-commutative
157×pow-plus
153×pow1/2
134×pow-exp
118×log-prod
98×pow1/3
90×clear-num frac-2neg
88×sub-neg
86×distribute-rgt-in distribute-lft-in
83×pow-to-exp
82×pow-sqr
78×diff-log
70×sum-log
68×rem-sqrt-square 1-exp
59×rec-exp
58×pow-unpow
56×exp-prod
47×pow2
45×+-commutative
41×unpow3 cube-mult
37×pow-pow
34×inv-pow pow-flip
33×associate--l+
26×rem-cube-cbrt
25×exp-sum
22×difference-cubes
18×associate-+l+
17×div-sub
16×log-div
15×distribute-rgt-neg-in distribute-lft-neg-in
14×associate-+r+
12×associate--l-
10×un-div-inv rem-exp-log
9×pow3
8×exp-diff rem-log-exp
7×distribute-neg-in
6×distribute-neg-frac associate--r+
4×sum-cubes sqrt-unprod distribute-rgt1-in rem-square-sqrt distribute-rgt-out neg-log neg-mul-1 rem-cbrt-cube
3×sin-sum distribute-rgt-neg-out associate-+l- unpow2
2×associate--r-
1×cos-sum sqrt-pow2 exp-neg unpow-prod-up pow-sub distribute-frac-neg neg-sub0 log-rec

prune8.8m (26.4%)

simplify6.5m (19.6%)

sample4.0m (12.0%)

Algorithm
99×intervals
Results
1.3m546929×body80valid
1.2m12132×body10240exit
25.4s27362×body1280valid
12.2s20565×body640valid
6.2s68997×body80nan
4.6s1649×body1280nan
4.2s10634×body320valid
3.0s9422×body160valid
2.2s1310×body640nan
2.1s49536×pre80true
1.2s1503×body2560valid
659.0ms632×body320nan
337.0ms597×body5120valid
205.0ms306×body160nan

series1.5m (4.5%)

Calls

490 calls:

3.2s
(* (/ (/ 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))))
3.0s
(* (/ (/ (* 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))))
2.0s
(/ (+ (pow (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 3) (pow 0.5 3)) (+ (* 0.5 (- 0.5 (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))) (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))))
1.8s
(* (* beta (+ (pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3) (pow (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 3))) (+ (* (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow (/ alpha (+ (+ alpha beta) 2.0)) 3)) (+ (* (pow 1.0 3) (pow 1.0 3)) (* (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))))
1.3s
(- 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 (* (/ 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))))

regimes10.7s (0.5%)

Accuracy

Total 103.8b remaining (38.8%)

Threshold costs 4.9b (1.8%)

11.1b56.2%math.log10 on complex, real part
10.9b56.7%math.log/1 on complex, real part
10.7b56.5%math.log/2 on complex, real part
10.7b56.6%math.abs on complex
10.0b53.9%math.sqrt on complex, real part

localize5.5s (0.3%)

bsearch3.2s (0.2%)

end1.0ms (0.0%)