Details

simplify6.5m (34.8%)

prune5.8m (31.0%)

sample4.1m (22.0%)

Algorithm
61×intervals
Results
1.0m252525×body80valid
50.5s28971×body1280valid
42.9s160588×body80nan
25.9s19841×body640valid
19.0s8851×body2560valid
10.9s3470×body5120valid
9.5s10000×body320valid
4.8s9047×body160valid
2.3s869×body10240exit
619.0ms592×body1280nan
474.0ms582×body640nan
333.0ms380×body320nan
287.0ms8256×pre80true
107.0ms202×body160nan

series1.3m (6.9%)

Calls

454 calls:

2.2s
(sqrt (* 2 (* (* U n) (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))
2.1s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (/ (* (/ M (/ 2 (/ D d))) (* (/ M (/ 2 (/ D d))) h)) (* 2 l))))
1.9s
(sqrt (* 2 (* U (* n (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U))))))))))
1.7s
(sqrt (* 2 (* (* U n) (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U)))))))))
1.6s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite31.0s (2.8%)

Algorithm
116×rewrite-expression-head
Calls

454 calls:

2.6s
(* (/ (/ (/ 2 t) (/ k (/ l 1))) (/ k (/ l 1))) (/ (/ 1 (tan k)) (sin k)))
854.0ms
(/ (+ (exp (/ (- EDonor (- Ec (+ Vef mu))) KbT)) 1) NdChar)
815.0ms
(/ 1 (/ (+ (exp (/ (- EDonor (- Ec (+ Vef mu))) KbT)) 1) NdChar))
724.0ms
(sqrt (- 1 (/ (/ (/ h l) (/ d (/ (* M D) 2))) (/ d (/ (* M D) 2)))))
684.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
Rules
163657×times-frac
65650×add-sqr-sqrt
63969×*-un-lft-identity
63324×add-cube-cbrt
27414×associate-*l*
8176×add-exp-log
7472×div-inv
5870×add-cbrt-cube
4266×sqrt-prod
3735×div-exp
2621×prod-exp
2411×cbrt-undiv
1842×cbrt-unprod
1562×associate-/r/
1525×pow1
956×associate-/r*
921×unpow-prod-down
900×associate-*r*
695×associate-/l*
585×add-log-exp
502×sqrt-div
488×frac-times
480×unswap-sqr
471×associate-*r/
456×pow-prod-down
454×insert-posit16 associate-*l/
421×cbrt-prod
347×flip-+ flip3-+
339×sqr-pow
274×pow-exp
211×1-exp
173×swap-sqr
170×frac-add
167×difference-of-squares pow-to-exp
166×distribute-lft-out
160×flip3-- flip--
158×*-commutative
135×pow-unpow
132×sqrt-pow1
111×sub-neg
109×distribute-lft-out--
108×frac-2neg clear-num
100×pow-prod-up
98×rec-exp
93×pow1/2
85×cbrt-div distribute-rgt-in distribute-lft-in
79×associate-/l/
72×unpow-prod-up
60×rem-sqrt-square tan-quot
54×pow-sqr
53×pow1/3
47×pow-plus
39×diff-log
37×pow2
32×sum-log
29×pow-pow
23×+-commutative
19×distribute-rgt-out
18×log-pow
16×log-div
15×pow-flip pow-sub
14×unpow2
11×exp-prod
10×cube-prod
sin-mult
associate-+l+ exp-diff log-prod distribute-neg-in div-sub
distribute-lft1-in pow3 inv-pow
remove-posit16 neg-log associate--r+ distribute-rgt-neg-in cube-div count-2 distribute-rgt1-in
associate--l+
associate-+r+ difference-of-sqr-1 rem-log-exp distribute-neg-frac cos-sum acos-asin
neg-sub0 associate-+r- cube-unmult associate--l- asin-acos associate-+l- rem-cbrt-cube associate--r-
frac-sub distribute-rgt-neg-out pow-div sqrt-unprod un-div-inv exp-to-pow rem-square-sqrt cos-diff
exp-sum unpow3 sub-div sqrt-pow2 sqr-sin rem-exp-log cube-mult

regimes19.0s (1.7%)

Accuracy

Total 33.6b remaining (17.4%)

Threshold costs 5.0b (2.6%)

5.2b77.7%Toniolo and Linder, Equation (7)
5.2b5.3%Henrywood and Agarwal, Equation (12)
4.3b33%Toniolo and Linder, Equation (13)
3.3b44.1%Toniolo and Linder, Equation (10+)
2.5b59.2%VandenBroeck and Keller, Equation (6)

localize6.1s (0.5%)

bsearch3.5s (0.3%)

end1.0ms (0.0%)