Details

series1.8m (34.9%)

Calls

427 calls:

4.9s
(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*)))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt 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)) (- 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 (/ l Om)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))

sample1.4m (27.2%)

Algorithm
61×intervals
Results
15.7s29350×body1280valid
15.1s253224×body80valid
9.3s158091×body80nan
8.6s8786×body2560valid
7.1s20641×body640valid
5.1s3346×body5120valid
2.3s9945×body320valid
1.2s9119×body160valid
386.0ms677×body10240exit
133.0ms617×body1280nan
110.0ms615×body640nan
108.0ms8256×pre80true
45.0ms340×body320nan
17.0ms195×body160nan

prune56.8s (18.6%)

rewrite33.1s (10.8%)

Algorithm
116×rewrite-expression-head
Calls

427 calls:

2.9s
(* (* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
2.6s
(* (* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.3s
(/ (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) (sqrt NdChar))
866.0ms
(* (* (* (* (/ (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))
858.0ms
(/ (sqrt NdChar) (/ (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) (sqrt NdChar)))
Rules
53456×add-exp-log
39573×prod-exp
27270×pow-exp
18734×div-exp
12528×pow-to-exp
4102×add-sqr-sqrt
4097×1-exp
4051×rec-exp
3704×*-un-lft-identity
3583×times-frac
3047×add-cube-cbrt
2421×add-cbrt-cube
1633×sqrt-prod
1227×pow1
1062×cbrt-unprod
978×cbrt-prod
866×associate-*r* associate-*r/
829×unpow-prod-down
691×associate-*l*
517×sqrt-div
514×pow-unpow
501×add-log-exp
491×frac-times
427×log1p-expm1-u expm1-log1p-u
426×pow-prod-down
390×cbrt-undiv
385×associate-*l/
376×flip-- flip3--
353×cbrt-div
336×associate-/l*
308×prod-diff
293×associate-/r*
273×unswap-sqr
264×associate-/r/
249×sqr-pow
244×div-inv
229×difference-of-squares
204×distribute-lft-out
200×distribute-rgt-neg-in
176×distribute-lft-out--
173×distribute-lft-neg-in
163×distribute-rgt-in distribute-lft-in
149×*-commutative
146×flip-+ flip3-+
105×swap-sqr
104×pow1/3
87×clear-num frac-2neg
72×tan-quot
65×fma-def
64×sqrt-pow1
54×sub-neg pow-pow
49×pow1/2
46×rem-sqrt-square
42×associate--l+
36×sum-log
35×associate-/l/
34×cube-div
33×frac-sub
31×fma-udef unpow2
30×div-sub
23×cos-sum
21×pow-prod-up +-commutative
19×pow-sqr pow-sub
17×neg-mul-1
16×exp-diff neg-sub0 log-div
13×hypot-def
12×pow-neg frac-add
11×fma-neg distribute-frac-neg
10×exp-prod
9×pow2 log-prod
8×exp-neg log-pow pow-plus cube-prod distribute-rgt-neg-out
6×un-div-inv exp-sum
5×diff-log
4×rem-cube-cbrt mul-1-neg associate-+l+ unpow3 cube-mult distribute-neg-frac log-rec
3×unsub-neg associate-+r- neg-log
2×inv-pow unpow1/3 associate-+r+ hypot-udef pow-flip acos-asin
1×rem-exp-log sqrt-unprod sqrt-undiv cos-diff expm1-log1p expm1-udef rem-square-sqrt mul0 rem-log-exp rem-cbrt-cube

simplify12.6s (4.1%)

Algorithm
176×egg-herbie

regimes9.3s (3.0%)

Accuracy

Total 41.0b remaining (21.3%)

Threshold costs 4.4b (2.3%)

7.9b22.9%Toniolo and Linder, Equation (13)
6.0b8.5%Toniolo and Linder, Equation (10+)
5.7b0%Henrywood and Agarwal, Equation (12)
5.0b78.6%Toniolo and Linder, Equation (7)
4.7b27.4%Toniolo and Linder, Equation (10-)

localize2.2s (0.7%)

bsearch2.2s (0.7%)

end1.0ms (0.0%)