Details

simplify5.8m (40.0%)

sample3.4m (23.1%)

Algorithm
61×intervals
Results
43.3s252518×body80valid
40.6s29536×body1280valid
28.6s160829×body80nan
19.3s20035×body640valid
18.9s8657×body2560valid
10.5s3467×body5120valid
6.3s9925×body320valid
2.8s8868×body160valid
977.0ms814×body10240exit
847.0ms598×body640nan
444.0ms8256×pre80true
384.0ms620×body1280nan
169.0ms401×body320nan
40.0ms190×body160nan

series2.4m (16.9%)

Calls

435 calls:

7.8s
(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*)))))
7.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
6.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.1s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

prune1.4m (9.5%)

rewrite1.1m (7.9%)

Algorithm
115×rewrite-expression-head
Calls

435 calls:

10.0s
(/ (+ (pow 1.0 3) (pow (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)) 3)) (+ (* (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)) (- (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)) 1.0)) (* 1.0 1.0)))
8.5s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
3.7s
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
3.4s
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (* (/ (pow (cbrt t) 3.0) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
2.7s
(- (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)) 1.0)
Rules
49000×add-exp-log
35818×prod-exp
24365×pow-exp
17768×div-exp
12131×pow-to-exp
8527×times-frac
6346×add-sqr-sqrt
6333×*-un-lft-identity
5313×add-cube-cbrt
5084×sqrt-prod
3630×rec-exp 1-exp
2934×add-cbrt-cube
1327×cbrt-unprod
1289×unpow-prod-down
1144×pow1
1021×associate-*r*
823×associate-*l*
626×associate-/l*
567×cbrt-undiv
534×add-log-exp
528×cbrt-prod
517×associate-*r/
422×associate-*l/
419×associate-/r*
400×distribute-lft-out
390×div-inv
372×pow-prod-down
363×pow-unpow
350×frac-times
330×sqr-pow
303×sqrt-div
274×unswap-sqr
271×difference-of-squares
234×associate-/r/
198×flip-+ flip3-+
191×distribute-lft-out--
169×flip3-- flip--
144×*-commutative cube-prod
141×tan-quot
131×pow-pow
130×distribute-rgt-neg-in
126×exp-prod
97×clear-num frac-2neg
91×div-sub
88×distribute-lft-neg-in
83×sqrt-pow1
76×rem-sqrt-square
73×distribute-rgt-in distribute-lft-in
67×sub-neg
62×pow1/2
61×unpow2
54×pow-sub
46×associate-/l/
45×pow1/3
39×frac-sub
37×sum-log
29×+-commutative
27×cbrt-div
22×frac-add
20×associate--l+
16×associate-+r+
14×diff-log log-pow
12×neg-sub0
10×neg-mul-1 log-prod
un-div-inv
pow-neg pow-flip
exp-sum
cos-sum inv-pow associate-+l+ swap-sqr associate--r+
cube-div exp-diff difference-cubes unpow3 cube-mult sum-cubes
acos-asin
rem-cube-cbrt associate-+r- cos-diff unsub-neg
rem-exp-log pow-sqr distribute-frac-neg pow-prod-up distribute-neg-frac rem-log-exp
exp-neg pow2 associate--l- pow-plus sub-div asin-acos associate--r- mul0 rem-cbrt-cube exp-to-pow

regimes15.1s (1.7%)

Accuracy

Total 45.6b remaining (21.1%)

Threshold costs 5.7b (2.6%)

9.1b-16%Toniolo and Linder, Equation (10+)
8.3b20.5%Toniolo and Linder, Equation (13)
5.7b0%Toniolo and Linder, Equation (10-)
5.6b76.6%Toniolo and Linder, Equation (7)
5.2b-7.4%Henrywood and Agarwal, Equation (12)

localize4.7s (0.5%)

bsearch3.5s (0.4%)

end1.0ms (0.0%)