Details

simplify3.4m (23.7%)

prune3.2m (22.3%)

sample3.2m (22.2%)

Algorithm
61×intervals
Results
40.8s253239×body80valid
40.7s29317×body1280valid
28.5s160933×body80nan
20.9s20690×body640valid
19.3s8872×body2560valid
10.3s3487×body5120valid
5.1s9713×body320valid
3.6s9130×body160valid
1.3s829×body10240exit
301.0ms646×body640nan
288.0ms617×body1280nan
182.0ms8256×pre80true
100.0ms346×body320nan
38.0ms197×body160nan

series2.7m (19.0%)

Calls

441 calls:

14.2s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))
13.4s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))
3.9s
(cbrt (+ (sqrt 1.0) (* 2.0 (* (pow (/ 1 (pow -1 2.0)) 1.0) (* (* (/ l Om) (/ l Om)) (+ (/ (pow (sin kx) 2) (sqrt 1.0)) (/ (pow (sin ky) 2) (sqrt 1.0))))))))
3.8s
(cbrt (+ (sqrt 1.0) (* 2.0 (* (pow (/ 1 (pow -1 2.0)) 1.0) (* (* (/ l Om) (/ l Om)) (+ (/ (pow (sin kx) 2) (sqrt 1.0)) (/ (pow (sin ky) 2) (sqrt 1.0))))))))
3.0s
(sqrt (* (+ (- (* (- U* U) (* n (pow (/ l Om) (/ (* 2 2.0) 2)))) (* (* (/ l Om) l) 2.0)) t) (* (* n 2.0) U)))

rewrite1.2m (8.2%)

Algorithm
116×rewrite-expression-head
Calls

441 calls:

13.7s
(* (sqrt (exp (- (+ (pow (- (/ (+ n m) 2.0) M) 2.0) (- l (fabs (- m n))))))) (sqrt (exp (- (+ (pow (- (/ (+ n m) 2.0) M) 2.0) (- l (fabs (- m n))))))))
6.7s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
2.2s
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
2.2s
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
1.8s
(* (sqrt (+ (exp (/ (- (+ Vef Ev) (- mu EAccept)) KbT)) 1.0)) (sqrt (+ (exp (/ (- (+ Vef Ev) (- mu EAccept)) KbT)) 1.0)))
Rules
64312×add-exp-log
41410×prod-exp
24859×div-exp
24426×pow-exp
21398×times-frac
10842×add-sqr-sqrt
10667×*-un-lft-identity
10202×pow-to-exp
9559×add-cube-cbrt
4027×1-exp
4019×rec-exp
3483×add-cbrt-cube
3257×unpow-prod-down
1821×sqrt-prod
1625×pow1
1396×associate-/l*
1325×cbrt-undiv
1324×cbrt-unprod
1271×associate-*r*
1072×associate-/r*
954×sqr-pow
798×div-inv
699×associate-*l*
668×associate-/r/
602×pow-prod-down
599×add-log-exp
577×associate-*l/
569×sqrt-pow1
494×cbrt-prod
393×distribute-lft-out
385×frac-times
369×sqrt-div
367×associate-*r/
358×pow-unpow
303×exp-prod
295×unswap-sqr
283×flip-+ flip3-+
275×difference-of-squares
207×distribute-lft-out--
145×pow-prod-up
139×*-commutative
132×pow1/2
121×distribute-rgt-neg-in
102×flip3-- flip--
101×frac-2neg clear-num pow-sqr
98×distribute-lft-neg-in
93×cbrt-div
82×frac-add
79×rem-sqrt-square
66×cube-prod
60×swap-sqr
59×pow1/3
55×associate-/l/
51×sum-log
45×pow-pow
37×+-commutative
36×pow-plus sub-neg
34×distribute-rgt-in distribute-lft-in
33×diff-log
30×unpow2
27×div-sub
25×pow2 pow-sub
22×frac-sub
21×neg-sub0
20×unpow3 cube-mult
15×pow-flip
14×neg-mul-1 tan-quot
13×exp-sum rem-exp-log pow-neg
12×exp-diff inv-pow
11×neg-log log-pow
9×log-prod
8×associate-+l+ associate-+r+
7×associate--l+
6×sqrt-unprod exp-neg un-div-inv associate--r-
5×associate-+l- rem-square-sqrt
4×associate--r+ distribute-neg-in cos-sum
3×unpow-prod-up distribute-neg-frac acos-asin
2×associate-+r- associate--l- rem-log-exp cos-diff
1×sqrt-undiv mul0 rem-cube-cbrt pow3 sub-div asin-acos e-exp-1

regimes24.8s (2.9%)

Accuracy

Total 47.2b remaining (22.5%)

Threshold costs 4.4b (2.1%)

7.2b10.4%Henrywood and Agarwal, Equation (12)
6.3b52.1%Henrywood and Agarwal, Equation (3)
6.1b34.6%Toniolo and Linder, Equation (13)
5.7b22%Toniolo and Linder, Equation (10-)
5.5b77.4%Toniolo and Linder, Equation (7)

localize8.8s (1.0%)

bsearch6.3s (0.7%)

end1.0ms (0.0%)