Details

simplify3.5m (30.2%)

sample3.3m (28.6%)

Algorithm
59×intervals
Results
44.2s244216×body80valid
39.3s30211×body1280valid
26.6s156651×body80nan
19.6s19925×body640valid
18.0s8748×body2560valid
10.2s3413×body5120valid
7.5s9807×body320valid
3.2s8937×body160valid
2.0s684×body10240exit
346.0ms617×body1280nan
274.0ms599×body640nan
194.0ms8256×pre80true
146.0ms332×body320nan
35.0ms186×body160nan

series2.3m (19.6%)

Calls

417 calls:

7.5s
(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*)))))
7.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.2s
(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*))))))
6.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.4s
(* (* (* 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*))))

prune1.4m (12.4%)

rewrite42.0s (6.0%)

Algorithm
110×rewrite-expression-head
Calls

417 calls:

1.9s
(/ (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
1.8s
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.2s
(* (* (* (/ (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))
1.1s
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
987.0ms
(exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))
Rules
34618×add-exp-log
23492×prod-exp
13463×pow-exp
10984×div-exp
7573×times-frac
6537×pow-to-exp
5630×add-sqr-sqrt
5521×*-un-lft-identity
4840×add-cube-cbrt
3877×sqrt-prod
2495×add-cbrt-cube
1489×unpow-prod-down
1439×pow1
1350×associate-*l*
1025×cbrt-unprod
804×distribute-rgt-neg-in
794×associate-*r/
780×distribute-lft-neg-in
687×associate-*r*
676×cbrt-prod
576×rec-exp 1-exp
569×associate-/r*
540×pow-unpow
514×add-log-exp
456×cbrt-undiv
431×associate-/l*
406×sqr-pow
401×pow-prod-down
308×sqrt-div
277×div-inv
269×unswap-sqr
264×frac-times
240×associate-*l/
232×flip-- flip3--
231×distribute-lft-out--
185×flip-+ flip3-+
179×distribute-lft-out
168×associate-/r/
160×neg-mul-1
140×difference-of-squares
139×*-commutative
128×frac-add
117×pow-prod-up
94×sqrt-pow1
93×exp-prod
88×pow-pow
87×frac-2neg clear-num
79×distribute-rgt-in distribute-lft-in
75×pow-sqr
72×tan-quot
69×sub-neg
62×associate-/l/ cube-prod
61×frac-sub
60×pow-plus
59×pow1/2
58×unpow2 pow1/3
46×rem-sqrt-square
45×pow2
42×div-sub
38×sum-log
33×cbrt-div
32×pow-sub
30×log-prod
26×associate--l+
25×swap-sqr
24×+-commutative
21×neg-sub0
20×cube-div log-pow pow-neg
19×rem-cube-cbrt
18×associate-+r+
13×unpow3 cube-mult diff-log
12×exp-sum
pow-flip
cos-sum rem-log-exp
un-div-inv associate-+r-
distribute-neg-frac
difference-cubes rem-exp-log sub-div distribute-frac-neg
exp-diff distribute-neg-in unsub-neg log-div
associate-+l+ inv-pow cos-diff acos-asin rem-cbrt-cube
pow-div sqrt-pow2 unpow-prod-up asin-acos
sqrt-undiv e-exp-1 quot-tan exp-neg distribute-rgt-out-- neg-log mul0

regimes14.9s (2.1%)

Accuracy

Total 43.6b remaining (19.7%)

Threshold costs 5.8b (2.6%)

8.0b42.2%Henrywood and Agarwal, Equation (3)
7.7b21.8%Toniolo and Linder, Equation (13)
5.3b77.7%Toniolo and Linder, Equation (7)
4.9b0%Henrywood and Agarwal, Equation (12)
3.9b21.3%Toniolo and Linder, Equation (10-)

localize4.5s (0.6%)

bsearch3.0s (0.4%)

end1.0ms (0.0%)