Details

series1.7m (35.5%)

Calls

447 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*)))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- 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*))))))
4.7s
(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 (27.5%)

Algorithm
61×intervals
Results
16.0s29755×body1280valid
15.8s252561×body80valid
9.7s159714×body80nan
8.9s8758×body2560valid
7.1s19986×body640valid
5.8s3401×body5120valid
2.4s9980×body320valid
1.3s8875×body160valid
411.0ms658×body10240exit
145.0ms621×body1280nan
116.0ms641×body640nan
115.0ms8256×pre80true
50.0ms374×body320nan
20.0ms194×body160nan

prune1.0m (20.5%)

rewrite19.7s (6.7%)

Algorithm
118×rewrite-expression-head
Calls

447 calls:

1.3s
(* (* (* (* (/ (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))
1.3s
(* (* (* (/ (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))
451.0ms
(* (* (* (/ (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))
318.0ms
(exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))
318.0ms
(exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))
Rules
59961×add-exp-log
43743×prod-exp
28231×pow-exp
21112×div-exp
13011×pow-to-exp
7549×times-frac
6620×sqrt-prod
6395×*-un-lft-identity
6153×add-sqr-sqrt
4969×add-cube-cbrt
4743×1-exp
4119×rec-exp
3075×add-cbrt-cube
2294×associate-*l*
1455×cbrt-unprod
1323×pow1
1207×associate-*r*
1021×unpow-prod-down
665×distribute-lft-out
632×associate-*r/
578×cbrt-undiv
539×add-log-exp
518×distribute-rgt-neg-in
513×cbrt-prod
450×pow-prod-down
422×sqrt-div
419×frac-times
413×associate-*l/
395×distribute-lft-neg-in
358×unswap-sqr
351×pow-unpow
338×associate-/l*
327×associate-/r*
304×exp-prod
301×div-inv
271×sqr-pow
240×flip3-- flip--
212×distribute-lft-out--
211×flip-+ flip3-+
208×associate-/r/
180×difference-of-squares
156×*-commutative
105×tan-quot
99×sqrt-pow1
93×cbrt-div
89×pow-pow
79×rem-sqrt-square clear-num frac-2neg
78×pow1/2 pow1/3
76×neg-mul-1
73×distribute-rgt-in swap-sqr distribute-lft-in
64×unpow2
60×sub-neg
50×frac-sub
44×cube-prod
35×div-sub
30×sum-log
28×associate-/l/
25×pow-prod-up
24×+-commutative
23×pow-sqr
22×associate--l+
18×frac-add
16×pow-sub
15×diff-log
12×associate-+r+ neg-sub0
10×pow-plus
exp-diff
pow2
asin-acos
cube-div rem-cube-cbrt unpow3 rem-exp-log associate-+r- cube-mult distribute-frac-neg distribute-neg-frac
un-div-inv inv-pow pow-flip
pow-neg unsub-neg associate--r+
sub-div exp-neg sin-mult
cos-sum associate-+l+ cos-mult associate--r- rem-cbrt-cube distribute-rgt-neg-out
sqrt-undiv sqrt-pow2 sin-neg sqrt-unprod cube-unmult cos-diff rem-square-sqrt acos-asin mul0

simplify15.0s (5.1%)

Algorithm
178×egg-herbie

regimes10.6s (3.6%)

Accuracy

Total 40.7b remaining (18.8%)

Threshold costs 4.8b (2.2%)

8.3b9.8%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)
2.4b46.5%Toniolo and Linder, Equation (10-)

localize2.4s (0.8%)

bsearch1.2s (0.4%)

end1.0ms (0.0%)