Details

sample1.9m (35.4%)

Algorithm
61×intervals
Results
27.9s253101×body80valid
20.0s29512×body1280valid
17.8s159180×body80nan
10.6s8739×body2560valid
9.7s20266×body640valid
6.4s3393×body5120valid
3.5s9929×body320valid
2.0s9102×body160valid
501.0ms583×body10240exit
271.0ms578×body1280nan
241.0ms643×body640nan
146.0ms8256×pre80true
96.0ms335×body320nan
38.0ms188×body160nan
6.0ms72×body80overflowed

series1.7m (31.3%)

Calls

435 calls:

5.1s
(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*)))))
4.8s
(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 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*)))))
1.3s
(* (* (* 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*)))))

prune1.0m (18.8%)

rewrite18.3s (5.7%)

Algorithm
116×rewrite-expression-head
Calls

435 calls:

1.8s
(* (/ 1 (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))) (/ NdChar (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))))
562.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
560.0ms
(* (* (* (/ (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))
558.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
447.0ms
(* (* (* (/ (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
40217×add-exp-log
28191×prod-exp
17193×pow-exp
13246×div-exp
8397×pow-to-exp
4258×add-sqr-sqrt
3801×*-un-lft-identity
3661×frac-times
3645×times-frac
2896×add-cube-cbrt
2604×add-cbrt-cube
2089×associate-*r/
1851×flip3-- flip--
1790×associate-*l/
1531×rec-exp 1-exp
1284×frac-sub
1186×pow1
1169×sqrt-prod
1095×cbrt-unprod
1073×associate-*r*
1057×unpow-prod-down
1018×cbrt-prod
1012×associate-*l*
544×add-log-exp
485×cbrt-undiv
399×unswap-sqr
380×pow-prod-down
372×sqrt-div
366×pow-unpow
303×associate-/r*
298×associate-/l*
289×distribute-lft-out--
280×sqr-pow
251×div-inv
238×distribute-lft-out
210×difference-of-squares
185×associate-/r/
183×flip-+ flip3-+
164×distribute-rgt-neg-in
159×exp-prod
146×cube-prod
142×*-commutative
132×distribute-lft-neg-in
86×clear-num frac-2neg
80×pow1/3
77×tan-quot
76×distribute-rgt-in distribute-lft-in
73×cbrt-div sqrt-pow1
70×swap-sqr
66×unpow2
65×sub-neg
63×associate-/l/
57×rem-sqrt-square
54×pow1/2
47×pow-pow
39×frac-add
35×sum-log
32×associate--l+
27×div-sub
26×+-commutative
21×diff-log
18×neg-mul-1
17×pow-sqr pow-prod-up
14×neg-sub0
11×pow-flip
10×cos-sum exp-diff associate-+r+ pow-sub
9×pow-plus
8×rem-cube-cbrt
7×inv-pow pow2 neg-log distribute-neg-frac
6×unpow3 cube-mult
5×rem-exp-log cos-diff log-pow asin-acos
4×cube-div difference-cubes pow-neg associate-+l- associate--r+
3×associate-+l+ associate-+r- unsub-neg associate--l- distribute-frac-neg associate--r- log-prod
2×un-div-inv acos-asin rem-cbrt-cube
1×exp-neg mul0 rem-log-exp

simplify12.9s (4.0%)

Algorithm
176×egg-herbie

regimes10.8s (3.4%)

Accuracy

Total 38.2b remaining (18.7%)

Threshold costs 5.6b (2.7%)

7.5b18.4%Toniolo and Linder, Equation (13)
5.3b77.8%Toniolo and Linder, Equation (7)
4.5b-0.5%Henrywood and Agarwal, Equation (12)
4.2b37.7%Toniolo and Linder, Equation (10+)
2.5b31.6%VandenBroeck and Keller, Equation (6)

localize2.4s (0.7%)

bsearch2.3s (0.7%)

end0.0ms (0.0%)