Details

prune3.3m (43.0%)

series1.6m (20.8%)

Calls

441 calls:

4.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.4s
(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*)))))
4.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.2s
(* (* (* 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*))))

sample1.5m (19.9%)

Algorithm
61×intervals
Results
18.5s253420×body80valid
18.0s29516×body1280valid
11.9s161922×body80nan
9.8s8746×body2560valid
8.5s20381×body640valid
6.6s3321×body5120valid
2.7s9886×body320valid
1.4s8928×body160valid
904.0ms944×body10240exit
201.0ms613×body1280nan
168.0ms657×body640nan
91.0ms8256×pre80true
66.0ms362×body320nan
26.0ms209×body160nan

rewrite32.3s (7.0%)

Algorithm
115×rewrite-expression-head
Calls

441 calls:

2.2s
(/ (/ NdChar (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))) (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))))
1.7s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt (cbrt h)) (cbrt (cbrt h)))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt (cbrt h))) (/ 1.0 2.0)))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
1.1s
(* (* (* (/ (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))
883.0ms
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
872.0ms
(/ NdChar (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))))
Rules
88743×add-exp-log
65978×prod-exp
32769×pow-exp
23072×div-exp
11006×pow-to-exp
6735×times-frac
5683×add-sqr-sqrt
5259×*-un-lft-identity
4525×add-cube-cbrt
4094×sqrt-prod
2856×1-exp rec-exp
2568×add-cbrt-cube
1798×associate-*l*
1291×pow1
1195×unpow-prod-down
1040×cbrt-unprod
963×associate-*r*
828×cbrt-prod
526×add-log-exp
515×associate-*r/
469×associate-/l*
464×cbrt-undiv
437×pow-prod-down
423×associate-/r*
362×sqrt-div
348×unswap-sqr
299×sqr-pow
296×div-inv
289×pow-unpow
269×frac-times
263×associate-*l/
259×distribute-lft-out
229×flip-+ flip3-+
175×flip3-- flip--
171×difference-of-squares
165×cbrt-div
152×distribute-lft-out--
148×*-commutative
144×associate-/r/
121×distribute-rgt-neg-in
105×pow1/3
98×clear-num frac-2neg
95×distribute-lft-neg-in
93×sqrt-pow1
75×tan-quot
73×distribute-rgt-in distribute-lft-in
61×pow1/2
56×associate-/l/ sub-neg
52×rem-sqrt-square
49×log-prod
47×unpow2
38×swap-sqr frac-sub
36×pow-pow
35×sum-log
28×cube-prod
27×pow-prod-up frac-add exp-prod
26×div-sub
25×pow-sqr log-pow +-commutative
23×associate--l+
19×pow-sub
16×exp-diff log-div
15×distribute-rgt-out--
14×pow-plus neg-sub0
12×associate--r+
11×exp-sum neg-mul-1
10×diff-log pow2
9×un-div-inv associate-+r+
8×pow-neg
7×distribute-neg-frac
6×cos-sum pow-flip
5×inv-pow
4×cube-div associate-+r- acos-asin rem-log-exp
3×rem-exp-log sqrt-unprod cos-diff neg-log associate-+l-
2×sub-div unsub-neg sqrt-undiv distribute-frac-neg asin-acos
1×difference-cubes unpow3 associate-+l+ quot-tan pow3 cube-mult mul0 rem-cbrt-cube

regimes21.8s (4.7%)

Accuracy

Total 45.8b remaining (21.4%)

Threshold costs 3.7b (1.7%)

9.1b9.6%Toniolo and Linder, Equation (13)
8.3b42.4%Henrywood and Agarwal, Equation (3)
5.4b77.4%Toniolo and Linder, Equation (7)
4.2b44.9%Henrywood and Agarwal, Equation (12)
3.9b44.8%Toniolo and Linder, Equation (10-)

simplify15.3s (3.3%)

Algorithm
175×egg-herbie

bsearch3.4s (0.7%)

localize2.3s (0.5%)

end0.0ms (0.0%)