Details

sample2.4m (31.2%)

Algorithm
61×intervals
Results
32.6s253625×body80valid
27.3s29567×body1280valid
21.2s161758×body80nan
13.3s20460×body640valid
13.0s8754×body2560valid
7.8s3394×body5120valid
5.1s9846×body320valid
2.6s9186×body160valid
624.0ms661×body10240exit
589.0ms642×body1280nan
210.0ms8256×pre80true
202.0ms635×body640nan
134.0ms327×body320nan
24.0ms191×body160nan

prune2.2m (28.0%)

series1.9m (24.9%)

Calls

441 calls:

5.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
5.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
5.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.0s
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (- (+ (* 0.04444444444444444 (pow ky 6)) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))))))

rewrite41.8s (9.0%)

Algorithm
118×rewrite-expression-head
Calls

441 calls:

4.3s
(/ (+ (pow 1.0 3) (pow (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)) 3)) (+ (* (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)) (- (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)) 1.0)) (* 1.0 1.0)))
1.5s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))
954.0ms
(- (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)) 1.0)
910.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
738.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
37346×add-exp-log
32285×times-frac
23563×prod-exp
15706×add-sqr-sqrt
15278×*-un-lft-identity
14066×div-exp
14047×add-cube-cbrt
13298×pow-exp
8799×unpow-prod-down
6766×pow-to-exp
4876×cbrt-prod
4626×associate-*r*
2681×add-cbrt-cube
1641×sqr-pow
1225×1-exp
1203×rec-exp
1200×pow1
1174×cbrt-unprod
1147×sqrt-prod
974×associate-*l*
875×associate-*r/
733×unpow2
668×sqrt-div
591×associate-/l*
588×add-log-exp
548×cbrt-undiv
543×div-inv
514×frac-times
490×unswap-sqr
468×distribute-lft-out
388×flip3-- flip--
376×pow-prod-down
369×associate-/r*
361×associate-*l/
329×cbrt-div
311×pow-unpow
306×exp-prod
244×distribute-lft-out--
233×associate-/r/
191×flip-+ flip3-+
190×difference-of-squares
144×*-commutative
143×distribute-rgt-neg-in
138×sqrt-pow1
85×pow1/2
84×frac-sub
80×clear-num frac-2neg
78×distribute-lft-neg-in
75×distribute-rgt-in distribute-lft-in
73×pow1/3 tan-quot
72×sub-neg
70×associate-/l/
67×swap-sqr
60×rem-sqrt-square sum-log
52×div-sub
42×pow-pow
41×+-commutative
29×associate--l+
28×pow-sub
26×frac-add cube-prod
25×pow-prod-up
17×exp-diff associate-+r+
16×neg-sub0
15×diff-log pow-sqr
13×pow-flip
12×neg-mul-1
11×pow-plus
10×cos-sum
9×log-prod
8×rem-exp-log associate-+r-
7×inv-pow pow2
6×unsub-neg exp-sum
5×associate-+l+ sum-cubes cos-diff
4×un-div-inv distribute-neg-frac neg-log associate-+l- pow-neg log-div
3×exp-neg log-pow distribute-frac-neg asin-acos
2×unpow3 distribute-lft-neg-out cube-mult acos-asin
1×rem-cube-cbrt associate--l- sqrt-unprod pow3 rem-square-sqrt associate--r- mul0 rem-log-exp rem-cbrt-cube

simplify13.3s (2.9%)

regimes12.2s (2.6%)

Accuracy

Total 35.8b remaining (17.5%)

Threshold costs 5.7b (2.8%)

7.1b24.1%Toniolo and Linder, Equation (13)
5.0b-3%Toniolo and Linder, Equation (10-)
4.9b79.1%Toniolo and Linder, Equation (7)
4.1b38.3%Toniolo and Linder, Equation (10+)
3.5b30%Henrywood and Agarwal, Equation (12)

localize3.5s (0.7%)

bsearch2.7s (0.6%)

end1.0ms (0.0%)