Details

series1.8m (35.1%)

Calls

425 calls:

5.0s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
4.8s
(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*))))))
4.8s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.3s
(* (* 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*)))))

sample1.3m (25.8%)

Algorithm
61×intervals
Results
15.5s252823×body80valid
15.5s29286×body1280valid
9.9s161730×body80nan
8.5s8627×body2560valid
7.5s20781×body640valid
5.1s3283×body5120valid
2.4s10084×body320valid
1.3s8933×body160valid
476.0ms623×body10240exit
144.0ms596×body1280nan
126.0ms647×body640nan
118.0ms8256×pre80true
54.0ms378×body320nan
17.0ms174×body160nan

prune1.3m (24.8%)

rewrite15.1s (4.8%)

Algorithm
114×rewrite-expression-head
Calls

425 calls:

762.0ms
(* (* (* (/ (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))
520.0ms
(* (/ F (cbrt (sin B))) (* (* (cbrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (cbrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))) (cbrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))))
448.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (pow (sin k) (/ 2 2))))
446.0ms
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
427.0ms
(* (* (* (/ (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))
Rules
37365×add-exp-log
24848×prod-exp
14953×times-frac
12660×pow-exp
12086×div-exp
9920×add-sqr-sqrt
8104×*-un-lft-identity
7623×add-cube-cbrt
5897×pow-to-exp
4100×cbrt-prod
2663×add-cbrt-cube
2652×unpow-prod-down
2410×associate-*r*
2287×sqrt-prod
1333×1-exp rec-exp
1173×pow1
1129×cbrt-unprod
1115×associate-*l*
852×sqr-pow
598×associate-/l*
577×difference-of-squares
576×div-inv
574×cbrt-undiv
535×pow-unpow
486×add-log-exp
482×cube-prod
425×log1p-expm1-u expm1-log1p-u
408×unswap-sqr
406×associate-*r/
346×pow-prod-down prod-diff
341×associate-/r*
266×frac-times
232×associate-*l/
204×sqrt-div
193×distribute-rgt-in distribute-lft-in
166×distribute-lft-out--
152×associate-/r/
142×flip-+ flip3-+
137×cbrt-div
130×flip-- flip3--
129×distribute-rgt-neg-in
126×*-commutative
116×distribute-lft-neg-in
111×fma-def
100×distribute-lft-out
92×pow-sub
90×frac-2neg clear-num
78×sqrt-pow1
74×pow1/3
71×neg-sub0
69×pow-neg
57×tan-quot
55×swap-sqr
54×pow1/2
53×sub-neg
52×associate--l+
48×rem-sqrt-square
44×pow-prod-up
41×pow-pow
38×div-sub
35×frac-sub
32×associate-/l/ unpow2
30×pow-sqr
27×fma-udef cos-sum
24×associate-+r+ sum-log
23×pow-plus
22×fma-neg
18×pow2
17×+-commutative
13×neg-mul-1
12×difference-cubes hypot-def
11×frac-add
9×log-prod
8×exp-prod diff-log
7×un-div-inv log-pow
5×sub-div distribute-rgt-out-- distribute-neg-frac
4×rem-cube-cbrt acos-asin
3×cube-div inv-pow associate-+r- pow-flip unpow3 cube-mult neg-log asin-acos exp-sum associate-+l-
2×sin-sum hypot-udef sqrt-undiv rem-log-exp
1×rem-exp-log associate-+l+ cos-diff unsub-neg distribute-frac-neg mul0 rem-cbrt-cube

simplify13.8s (4.4%)

Algorithm
174×egg-herbie

regimes11.2s (3.6%)

Accuracy

Total 35.3b remaining (20.6%)

Threshold costs 5.2b (3%)

8.6b33.4%Toniolo and Linder, Equation (13)
5.3b77.8%Toniolo and Linder, Equation (7)
4.2b0%Henrywood and Agarwal, Equation (12)
3.4b57.8%Toniolo and Linder, Equation (10+)
3.1b0%Henrywood and Agarwal, Equation (13)

localize2.4s (0.8%)

bsearch2.2s (0.7%)

end0.0ms (0.0%)