Details

simplify3.8m (26.4%)

sample3.2m (22.5%)

Algorithm
60×intervals
Results
43.6s243384×body80valid
39.7s29536×body1280valid
23.6s145810×body80nan
18.8s20035×body640valid
17.1s8657×body2560valid
11.1s3467×body5120valid
7.2s9925×body320valid
3.2s8868×body160valid
1.2s814×body10240exit
618.0ms8256×pre80true
561.0ms401×body320nan
344.0ms620×body1280nan
299.0ms598×body640nan
36.0ms190×body160nan

prune3.0m (20.7%)

series2.6m (17.8%)

Calls

437 calls:

15.6s
(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))
7.5s
(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*)))))
7.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.0s
(* (* (* 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*))))

rewrite1.4m (9.5%)

Algorithm
115×rewrite-expression-head
Calls

437 calls:

12.1s
(/ (+ (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)))
8.4s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
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))
3.5s
(* (* (* (/ (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))
2.9s
(- (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)) 1.0)
Rules
56113×times-frac
27083×*-un-lft-identity
25240×add-exp-log
24014×add-sqr-sqrt
20117×add-cube-cbrt
20025×sqrt-prod
16620×prod-exp
7124×div-exp
7020×pow-exp
5677×unpow-prod-down
5451×cbrt-prod
3357×distribute-lft-out
3071×pow-to-exp
2883×add-cbrt-cube
2082×div-inv
1746×associate-*r/
1475×associate-*l*
1287×pow1
1282×cbrt-unprod
1257×associate-*r*
1105×associate-/r*
1080×sqr-pow
980×frac-times
934×unswap-sqr
929×associate-/r/
926×sqrt-div
819×1-exp
695×associate-*l/
632×flip3-- flip--
624×associate-/l*
592×cbrt-undiv
549×add-log-exp
416×distribute-neg-frac
414×pow-prod-down
407×flip-+ flip3-+
355×rec-exp
333×pow-unpow
322×frac-add
293×distribute-rgt-neg-in
275×cbrt-div
233×frac-sub
167×swap-sqr
142×*-commutative
134×distribute-lft-out--
112×difference-of-squares
106×tan-quot
102×pow-pow
100×exp-prod
99×clear-num frac-2neg
91×div-sub
89×distribute-lft-neg-in
72×sqrt-pow1
67×distribute-rgt-in distribute-lft-in
62×sub-neg
56×pow1/2 pow1/3
54×pow-sub
53×associate-/l/ unpow2
52×rem-sqrt-square
48×cube-prod sum-log
40×pow-prod-up
31×+-commutative
29×cube-div
26×pow-sqr
21×log-pow
20×pow-plus
19×log-prod
15×associate-+r+ pow2
14×neg-sub0 associate--l+
11×associate-+l+ neg-mul-1
10×diff-log unpow3 cube-mult
8×pow-neg
7×exp-sum
6×rem-cube-cbrt cos-sum
5×exp-diff difference-cubes inv-pow associate-+r- unsub-neg pow-flip sum-cubes
4×associate--r+ acos-asin rem-log-exp
3×un-div-inv cos-diff unpow-prod-up exp-to-pow
2×rem-exp-log distribute-neg-in distribute-frac-neg neg-log asin-acos
1×e-exp-1 distribute-lft-neg-out exp-neg sub-div associate--r- mul0

regimes16.5s (1.9%)

Accuracy

Total 35.7b remaining (19.6%)

Threshold costs 5.9b (3.3%)

9.1b-16%Toniolo and Linder, Equation (10+)
5.6b76.6%Toniolo and Linder, Equation (7)
5.2b-7.4%Henrywood and Agarwal, Equation (12)
3.7b19.2%Toniolo and Linder, Equation (10-)
2.3b0%Henrywood and Agarwal, Equation (13)

bsearch5.5s (0.6%)

localize5.1s (0.6%)

end1.0ms (0.0%)