Details

simplify6.4m (41.7%)

sample3.3m (21.9%)

Algorithm
61×intervals
Results
44.8s253418×body80valid
38.3s29403×body1280valid
27.4s160338×body80nan
19.0s20091×body640valid
18.8s8792×body2560valid
10.7s3435×body5120valid
7.2s10024×body320valid
3.3s8958×body160valid
909.0ms669×body10240exit
798.0ms591×body1280nan
477.0ms188×body160nan
315.0ms610×body640nan
164.0ms8256×pre80true
122.0ms352×body320nan

series2.5m (16.5%)

Calls

449 calls:

7.7s
(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*)))))
7.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* 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 (/ 2.0 2)))) (- U U*))))))
6.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.0s
(* (* (* 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*))))

prune1.8m (11.7%)

rewrite50.2s (5.5%)

Algorithm
118×rewrite-expression-head
Calls

449 calls:

1.5s
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
1.4s
(* (* (* (/ (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))
1.3s
(* (* (* (/ (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))
1.2s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
1.2s
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
45683×add-exp-log
32686×prod-exp
20226×pow-exp
14817×div-exp
13143×times-frac
9074×pow-to-exp
8246×add-sqr-sqrt
7532×*-un-lft-identity
6682×add-cube-cbrt
2724×1-exp
2718×rec-exp
2628×add-cbrt-cube
2446×sqrt-prod
1673×unpow-prod-down
1329×pow1
1196×cbrt-prod
1091×cbrt-unprod
1077×associate-*r*
1057×associate-*l*
663×associate-/r*
610×div-inv
560×distribute-rgt-neg-in
551×add-log-exp
549×distribute-lft-neg-in
529×cbrt-undiv sqr-pow
512×pow-unpow
500×associate-*r/
488×associate-/l*
447×unswap-sqr
414×pow-prod-down
350×sqrt-div
334×associate-*l/
294×difference-of-squares exp-prod
287×frac-times
279×distribute-lft-out--
232×associate-/r/
220×flip-+ flip3-+
202×flip3-- flip--
195×distribute-lft-out
159×neg-mul-1
153×*-commutative
111×sqrt-pow1
108×unpow2
107×tan-quot
99×cbrt-div
92×frac-2neg clear-num
83×pow-pow
75×pow1/2
74×distribute-rgt-in distribute-lft-in
72×pow1/3
69×rem-sqrt-square
64×associate-/l/
61×sub-neg
53×pow-prod-up
38×div-sub sum-log swap-sqr
35×pow-sqr
32×frac-sub
26×+-commutative associate--l+
25×cube-prod
23×pow-plus
20×frac-add log-prod
19×log-pow
18×pow2
15×pow-sub neg-sub0
12×exp-diff diff-log
10×cube-div
9×unpow3 pow-flip cube-mult
8×pow-neg associate-+r+
7×rem-cube-cbrt rem-exp-log inv-pow
6×cos-sum acos-asin distribute-neg-frac
5×exp-sum rem-log-exp
4×distribute-frac-neg neg-log asin-acos associate-+l-
3×exp-neg cos-diff
2×un-div-inv associate--l- associate-+l+ exp-to-pow associate--r+
1×sqrt-unprod associate-+r- unsub-neg rem-square-sqrt mul0 rem-cbrt-cube

regimes16.8s (1.8%)

Accuracy

Total 42.1b remaining (20.1%)

Threshold costs 4.8b (2.3%)

9.3b25.8%Toniolo and Linder, Equation (13)
5.9b75.5%Toniolo and Linder, Equation (7)
5.6b4%Henrywood and Agarwal, Equation (12)
4.8b32.8%Toniolo and Linder, Equation (10+)
4.6b-47.3%Henrywood and Agarwal, Equation (13)

localize4.4s (0.5%)

bsearch3.4s (0.4%)

end0.0ms (0.0%)