Details

series1.9m (36.8%)

Calls

451 calls:

4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.2s
(pow (exp (sqrt (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))) (sqrt (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))

sample1.4m (26.0%)

Algorithm
61×intervals
Results
16.0s29755×body1280valid
15.7s252561×body80valid
9.7s159714×body80nan
8.8s8758×body2560valid
7.1s19986×body640valid
5.7s3401×body5120valid
2.4s9980×body320valid
1.3s8875×body160valid
395.0ms658×body10240exit
143.0ms621×body1280nan
118.0ms641×body640nan
115.0ms8256×pre80true
50.0ms374×body320nan
19.0ms194×body160nan

prune1.1m (20.4%)

rewrite25.4s (8.1%)

Algorithm
118×rewrite-expression-head
Calls

451 calls:

4.2s
(* (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
4.1s
(* (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.0s
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
1.0s
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k))
622.0ms
(* (* (* (* (/ (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
58610×add-exp-log
42625×prod-exp
27999×pow-exp
21012×div-exp
12976×pow-to-exp
5504×times-frac
5209×add-sqr-sqrt
5190×*-un-lft-identity
4683×1-exp
4053×rec-exp
3892×add-cube-cbrt
2916×add-cbrt-cube
2361×cbrt-prod
2079×sqrt-prod
1339×cbrt-unprod
1271×pow1
1253×associate-*r*
937×unpow-prod-down
691×associate-*l*
612×cbrt-undiv
608×distribute-lft-out
530×add-log-exp
455×associate-*r/
451×log1p-expm1-u expm1-log1p-u
444×associate-*l/
429×pow-prod-down
402×associate-/l*
400×exp-prod
375×pow-unpow
358×associate-/r*
352×frac-times
343×unswap-sqr
316×sqr-pow
313×div-inv
298×sqrt-div
290×prod-diff
241×distribute-rgt-neg-in
211×distribute-lft-out--
171×flip3-- flip--
170×difference-of-squares
160×distribute-rgt-in distribute-lft-in
143×*-commutative
137×pow-pow
130×flip-+ flip3-+
120×associate-/r/
117×log-prod
107×distribute-lft-neg-in
105×tan-quot
100×fma-def
92×clear-num frac-2neg
79×pow1/3
74×rem-sqrt-square
69×sqrt-pow1
51×pow1/2 sub-neg
45×swap-sqr cbrt-div
42×unpow2 associate--l+
34×div-sub
33×frac-sub
30×associate-/l/
29×sum-log
27×associate-+r+
26×fma-udef
24×cos-sum
21×+-commutative cube-prod
19×pow-prod-up pow-sqr
18×fma-neg
17×neg-mul-1
16×pow-sub
14×neg-sub0 hypot-def exp-sum
12×rem-exp-log log-pow
11×exp-diff
10×rem-log-exp
pow-plus diff-log
associate-+r- frac-add
inv-pow pow2 pow-flip
un-div-inv distribute-neg-frac log-div
pow-neg unsub-neg unpow3 cube-mult distribute-frac-neg distribute-rgt-out acos-asin
rem-cube-cbrt exp-neg neg-log hypot-udef asin-acos sin-mult associate-+l-
cube-div sqrt-pow2 unpow-prod-up cos-mult exp-to-pow
sqrt-undiv expm1-def associate-+l+ sin-neg log1p-udef cos-diff sub-div distribute-lft1-in difference-of-sqr-1 expm1-log1p mul0 rem-cbrt-cube distribute-rgt-neg-out expm1-udef

simplify13.7s (4.4%)

Algorithm
178×egg-herbie

regimes9.9s (3.2%)

Accuracy

Total 43.0b remaining (21.9%)

Threshold costs 4.7b (2.4%)

8.2b14.4%Toniolo and Linder, Equation (10+)
8.0b16.2%Toniolo and Linder, Equation (13)
6.0b0%Henrywood and Agarwal, Equation (12)
5.4b77.2%Toniolo and Linder, Equation (7)
3.9b35.1%Toniolo and Linder, Equation (10-)

localize2.4s (0.8%)

bsearch1.2s (0.4%)

end1.0ms (0.0%)