Details

simplify5.8m (39.8%)

sample3.4m (23.3%)

Algorithm
61×intervals
Results
45.8s252518×body80valid
39.7s29536×body1280valid
29.2s160829×body80nan
20.3s20035×body640valid
17.9s8657×body2560valid
10.2s3467×body5120valid
6.8s9925×body320valid
3.6s8868×body160valid
1.7s814×body10240exit
341.0ms598×body640nan
338.0ms620×body1280nan
297.0ms8256×pre80true
171.0ms401×body320nan
34.0ms190×body160nan

series2.5m (17.0%)

Calls

434 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*)))))
7.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.5s
(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*)))))
6.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.2s
(* (* (* 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*))))

prune1.4m (9.8%)

rewrite1.1m (7.4%)

Algorithm
115×rewrite-expression-head
Calls

434 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)))
4.1s
(* (* (* (* (/ (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))
3.9s
(* (exp (- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))) (cos (- (/ (* K (+ m n)) 2.0) M)))
3.5s
(* (* (* (/ (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))
2.6s
(- (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)) 1.0)
Rules
39078×add-exp-log
27670×prod-exp
16203×pow-exp
12739×div-exp
8851×times-frac
8597×pow-to-exp
6484×*-un-lft-identity
6473×add-sqr-sqrt
5437×sqrt-prod
5296×add-cube-cbrt
2923×add-cbrt-cube
1605×rec-exp 1-exp
1549×associate-*l*
1409×unpow-prod-down
1326×cbrt-unprod
1124×pow1
1017×associate-*r*
564×cbrt-undiv
539×add-log-exp
524×cbrt-prod
518×associate-/l*
516×associate-*r/
480×distribute-lft-out
431×associate-*l/
414×div-inv
398×associate-/r*
359×pow-prod-down
356×frac-times
342×pow-unpow
333×sqr-pow
326×sqrt-div
313×unswap-sqr
268×difference-of-squares
253×associate-/r/
221×flip-+ flip3-+
188×distribute-lft-out--
163×flip3-- flip--
144×*-commutative cube-prod
138×tan-quot
130×distribute-rgt-neg-in pow-pow
126×exp-prod
116×div-sub
93×sqrt-pow1
91×clear-num frac-2neg
88×distribute-lft-neg-in
78×distribute-rgt-in distribute-lft-in
75×rem-sqrt-square
70×sub-neg
65×pow-sub
64×pow1/2
61×unpow2
49×pow1/3
45×associate-/l/
40×sum-log
39×frac-sub
32×+-commutative
27×cbrt-div
22×frac-add associate--l+
16×associate-+r+
14×diff-log log-pow
13×pow-flip
12×neg-sub0
10×neg-mul-1 log-prod
8×pow-neg un-div-inv exp-sum
7×inv-pow
6×cos-sum associate-+l+ swap-sqr associate--r+
5×cube-div exp-diff difference-cubes cos-diff unpow3 cube-mult sum-cubes
4×unpow-prod-up acos-asin
3×rem-cube-cbrt associate-+r- unsub-neg
2×pow-div rem-exp-log pow-sqr distribute-frac-neg pow-prod-up distribute-neg-frac rem-log-exp
1×exp-neg pow2 associate--l- pow-plus sub-div asin-acos mul0 rem-cbrt-cube exp-to-pow

regimes16.5s (1.9%)

Accuracy

Total 46.2b remaining (21.7%)

Threshold costs 6.0b (2.8%)

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)

localize4.5s (0.5%)

bsearch3.2s (0.4%)

end1.0ms (0.0%)