Details

sample2.2m (40.3%)

Algorithm
61×intervals
Results
36.9s252816×body80valid
24.3s162291×body80nan
21.6s29330×body1280valid
11.4s8826×body2560valid
10.5s20086×body640valid
6.7s3343×body5120valid
3.7s9824×body320valid
2.3s9023×body160valid
896.0ms861×body10240exit
329.0ms606×body1280nan
258.0ms589×body640nan
183.0ms8256×pre80true
121.0ms354×body320nan
45.0ms191×body160nan

series1.6m (28.8%)

Calls

437 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*)))))
4.8s
(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)) (- 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*))))))
1.4s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

prune52.1s (15.7%)

rewrite19.8s (6.0%)

Algorithm
116×rewrite-expression-head
Calls

437 calls:

1.4s
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.3s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
560.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
559.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
540.0ms
(/ 1 (exp (/ (- (- (- Ec Vef) EDonor) mu) KbT)))
Rules
37887×add-exp-log
26491×prod-exp
12335×pow-exp
10779×div-exp
5654×pow-to-exp
4687×add-sqr-sqrt
4619×times-frac
4449×*-un-lft-identity
3333×add-cube-cbrt
2784×add-cbrt-cube
2660×sqrt-prod
1372×pow1
1333×rec-exp 1-exp
1273×cbrt-unprod
1220×associate-*l*
814×associate-*r*
781×unpow-prod-down
568×associate-*r/
541×add-log-exp
511×cbrt-undiv
437×pow-prod-down
402×pow-unpow
399×associate-*l/
398×frac-times
354×distribute-lft-out
345×associate-/l*
340×sqrt-div
335×cbrt-prod unswap-sqr
324×distribute-lft-out--
320×difference-of-squares
297×associate-/r* exp-prod
261×sqr-pow
244×flip-+ flip3-+ div-inv
180×flip3-- flip--
171×associate-/r/ distribute-rgt-neg-in
153×*-commutative
132×sqrt-pow1
114×tan-quot
101×distribute-lft-neg-in
93×pow1/2
90×pow1/3
87×frac-2neg clear-num
85×cbrt-div
71×pow-prod-up
66×rem-sqrt-square
63×distribute-rgt-in sub-neg distribute-lft-in
61×associate-/l/
59×unpow2 pow-flip
56×swap-sqr pow-pow
47×frac-sub
46×div-sub
45×pow-sqr
32×pow-plus
31×cube-prod sum-log
25×+-commutative
23×exp-diff neg-sub0 pow2
22×associate--l+
21×diff-log
20×frac-add
19×pow-neg pow-sub
11×neg-mul-1
un-div-inv
cos-sum associate-+r+ associate--r+
rem-exp-log inv-pow associate-+r- unsub-neg
cube-div difference-cubes cos-diff log-pow unpow3 cube-mult neg-log asin-acos log-prod
associate-+l+ acos-asin
associate--l- sqrt-unprod rem-square-sqrt distribute-frac-neg associate--r- rem-cbrt-cube distribute-neg-frac log-div
pow3 exp-neg sub-div exp-sum mul0 rem-log-exp

simplify12.3s (3.7%)

Algorithm
176×egg-herbie

regimes10.9s (3.3%)

Accuracy

Total 49.9b remaining (22.1%)

Threshold costs 5.0b (2.2%)

9.5b-1.9%Toniolo and Linder, Equation (13)
9.0b40.3%Henrywood and Agarwal, Equation (3)
7.2b10.6%Toniolo and Linder, Equation (10+)
5.9b7%Henrywood and Agarwal, Equation (12)
5.2b78.1%Toniolo and Linder, Equation (7)

bsearch4.8s (1.4%)

localize2.3s (0.7%)

end1.0ms (0.0%)