Details

series1.6m (35.5%)

Calls

438 calls:

4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- 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*)))))
4.6s
(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*))))))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

sample1.4m (30.2%)

Algorithm
61×intervals
Results
16.2s29598×body1280valid
16.2s253256×body80valid
10.2s162450×body80nan
8.9s8843×body2560valid
7.6s20361×body640valid
5.4s3321×body5120valid
2.4s9998×body320valid
1.3s8975×body160valid
502.0ms816×body10240exit
153.0ms628×body1280nan
123.0ms652×body640nan
111.0ms8256×pre80true
52.0ms372×body320nan
18.0ms192×body160nan

prune52.6s (18.9%)

rewrite15.4s (5.5%)

Algorithm
115×rewrite-expression-head
Calls

438 calls:

585.0ms
(* (* (* (/ (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))
475.0ms
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
472.0ms
(/ 1 (* (cbrt (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))) (cbrt (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))
466.0ms
(* (* (* (/ (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))
426.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
33752×add-exp-log
23699×prod-exp
11952×pow-exp
9500×div-exp
5291×pow-to-exp
4221×add-sqr-sqrt
3821×times-frac
3589×*-un-lft-identity
2961×add-cube-cbrt
2518×add-cbrt-cube
1367×1-exp rec-exp
1189×pow1
1064×cbrt-unprod
1004×sqrt-prod
966×associate-*r*
946×unpow-prod-down
915×associate-*l*
871×pow-unpow
854×associate-*r/
798×cbrt-prod
548×sqrt-div
524×add-log-exp
451×cbrt-undiv
361×unswap-sqr
358×pow-prod-down frac-times
341×cbrt-div
328×flip3-- flip--
322×associate-*l/
285×sqr-pow
271×associate-/l*
269×difference-of-squares
255×associate-/r*
251×div-inv
238×associate-/r/
197×flip-+ flip3-+
192×distribute-lft-out--
153×*-commutative
151×sqrt-pow1
146×distribute-lft-out
93×unpow2 pow1/3
92×cube-prod
91×distribute-rgt-neg-in
88×pow1/2
81×distribute-lft-neg-in frac-2neg clear-num
74×distribute-rgt-in distribute-lft-in
66×pow-pow
59×sub-neg
58×tan-quot
53×frac-sub
49×rem-sqrt-square
46×swap-sqr
43×associate-/l/
35×div-sub exp-prod
34×sum-log pow-prod-up
27×pow-sub
26×+-commutative
22×frac-add pow-sqr associate--l+
21×pow-neg
17×neg-sub0
15×un-div-inv
13×associate-+r+ pow-plus
12×unpow3 pow-flip cube-mult
10×diff-log pow2
rem-cube-cbrt neg-mul-1
cube-div
exp-sum log-prod
exp-diff associate-+l+ inv-pow asin-acos rem-cbrt-cube distribute-neg-frac associate--r+
cos-sum sqrt-pow2 rem-exp-log sqrt-unprod rem-square-sqrt acos-asin neg-log associate-+l-
sqrt-undiv pow3 associate-+r- cos-diff log-pow unsub-neg distribute-frac-neg sub-div associate--r- mul0 distribute-rgt-neg-out log-div

simplify11.9s (4.3%)

Algorithm
175×egg-herbie

regimes11.5s (4.1%)

Accuracy

Total 46.3b remaining (21%)

Threshold costs 4.5b (2.1%)

9.6b34.6%Henrywood and Agarwal, Equation (3)
8.3b8.2%Toniolo and Linder, Equation (13)
5.6b0%Henrywood and Agarwal, Equation (12)
5.5b76.8%Toniolo and Linder, Equation (7)
4.7b36.8%Toniolo and Linder, Equation (10+)

localize2.3s (0.8%)

bsearch1.4s (0.5%)

end1.0ms (0.0%)