Details

simplify7.7m (44.5%)

sample3.2m (18.5%)

Algorithm
61×intervals
Results
46.5s252728×body80valid
37.2s29502×body1280valid
27.9s159842×body80nan
19.6s19777×body640valid
17.2s8847×body2560valid
10.7s3467×body5120valid
7.1s10183×body320valid
3.1s9070×body160valid
1.0s661×body10240exit
342.0ms604×body1280nan
333.0ms637×body640nan
197.0ms8256×pre80true
124.0ms329×body320nan
74.0ms212×body160nan

series2.6m (14.8%)

Calls

450 calls:

7.8s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))
7.5s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
6.9s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
6.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.1s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

prune2.4m (13.9%)

rewrite43.2s (4.1%)

Algorithm
116×rewrite-expression-head
Calls

450 calls:

1.5s
(* (exp (/ (+ EDonor (+ Vef (- mu Ec))) KbT)) (exp (/ (+ EDonor (+ Vef (- mu Ec))) KbT)))
1.4s
(cos (* (* (* (* (cbrt (cbrt (- (* (+ m n) (/ K 2.0)) M))) (cbrt (cbrt (- (* (+ m n) (/ K 2.0)) M)))) (cbrt (cbrt (- (* (+ m n) (/ K 2.0)) M)))) (cbrt (- (* (+ m n) (/ K 2.0)) M))) (cbrt (- (* (+ m n) (/ K 2.0)) M))))
1.4s
(/ (/ (- 1.0 (* (* 5.0 v) v)) PI) (* (sqrt (* 2.0 (- (* (* 1.0 1.0) 1.0) (* (* (* 3.0 (* v v)) (* 3.0 (* v v))) (* 3.0 (* v v)))))) t))
1.4s
(* (/ (/ 1 (sqrt PI)) (sqrt (* 2.0 (- (* (* 1.0 1.0) 1.0) (* (* (* 3.0 (* v v)) (* 3.0 (* v v))) (* 3.0 (* v v))))))) (/ (- 1.0 (* (* v v) 5.0)) (* t (sqrt PI))))
1.4s
(* (sqrt (* 2.0 (- (* (* 1.0 1.0) 1.0) (* (* (* 3.0 (* v v)) (* 3.0 (* v v))) (* 3.0 (* v v)))))) t)
Rules
46342×add-exp-log
31560×prod-exp
14580×div-exp
13921×pow-exp
8780×times-frac
7919×*-un-lft-identity
6227×add-sqr-sqrt
5464×sqrt-prod
5396×add-cube-cbrt
5256×pow-to-exp
3128×1-exp rec-exp
2912×add-cbrt-cube
1773×associate-*l*
1409×pow1
1162×cbrt-prod
1121×cbrt-unprod
915×exp-prod
786×distribute-lft-out--
743×distribute-lft-out
731×associate-*r*
726×unpow-prod-down
686×associate-*r/
677×cbrt-undiv
546×pow-prod-down
531×add-log-exp
475×associate-/l*
464×associate-/r*
378×flip-+ flip3-+
368×sqrt-div
361×div-inv
332×frac-times
327×pow-unpow
322×associate-*l/
270×unswap-sqr
248×pow-prod-up
221×flip3-- flip--
211×sqr-pow
210×pow-sqr
193×associate-/r/
132×*-commutative
121×frac-sub
118×sqrt-pow1
109×distribute-rgt-in distribute-lft-in
104×frac-2neg clear-num
100×frac-add
96×pow1/3
91×cbrt-div
90×difference-of-squares associate-/l/
84×pow1/2
77×swap-sqr
69×tan-quot
68×sub-neg
67×rem-sqrt-square
57×pow-pow
56×pow-plus
38×pow2
36×distribute-rgt-neg-in distribute-lft-neg-in
33×div-sub
30×associate--l+
26×sum-log cube-div
24×+-commutative
16×distribute-rgt-out--
15×diff-log
12×associate-+r- pow-sub neg-mul-1
10×associate-+r+
pow-flip exp-diff sub-div
cube-unmult pow3
pow-neg neg-sub0 distribute-frac-neg associate--r+
difference-cubes inv-pow
cube-prod log-prod un-div-inv distribute-rgt-out distribute-rgt1-in
asin-acos sum-cubes cos-sum acos-asin log-div
associate-+l+ rem-cube-cbrt distribute-lft1-in unpow3 sqrt-unprod rem-log-exp rem-square-sqrt log-pow rem-cbrt-cube cube-mult cos-diff count-2

regimes31.0s (3.0%)

Accuracy

Total 57.9b remaining (24.2%)

Threshold costs 4.8b (2%)

9.2b34.2%Toniolo and Linder, Equation (13)
8.8b6.7%Maksimov and Kolovsky, Equation (3)
6.7b24%Henrywood and Agarwal, Equation (12)
6.6b18.3%Toniolo and Linder, Equation (10+)
6.3b51.3%Henrywood and Agarwal, Equation (3)

localize9.5s (0.9%)

bsearch3.2s (0.3%)

end1.0ms (0.0%)