Details

simplify4.1m (27.4%)

prune3.8m (25.4%)

sample3.4m (22.2%)

Algorithm
61×intervals
Results
44.2s252126×body80valid
36.4s29254×body1280valid
30.6s159379×body80nan
20.6s20038×body640valid
18.0s8921×body2560valid
11.0s3380×body5120valid
7.1s10006×body320valid
3.3s9161×body160valid
733.0ms608×body10240exit
533.0ms334×body320nan
400.0ms622×body1280nan
329.0ms600×body640nan
283.0ms8256×pre80true
34.0ms169×body160nan

series2.4m (15.9%)

Calls

430 calls:

7.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.3s
(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 (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
2.0s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

rewrite1.0m (6.7%)

Algorithm
113×rewrite-expression-head
Calls

430 calls:

5.0s
(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (* (* (cbrt (cbrt (cos (/ K 2.0)))) (cbrt (cbrt (cos (/ K 2.0))))) (cbrt (cbrt (cos (/ K 2.0))))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
3.4s
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
3.2s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
2.7s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))
1.5s
(/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (* (+ (* (* 5.0 (* v v)) (+ (* 5.0 (* v v)) 1.0)) (* 1.0 1.0)) (* (* (* (sqrt PI) (* (sqrt PI) t)) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v)))))
Rules
46854×times-frac
45491×add-exp-log
29770×prod-exp
24040×*-un-lft-identity
21461×add-sqr-sqrt
19154×add-cube-cbrt
16102×div-exp
15475×pow-exp
15201×associate-*r/
10933×sqrt-prod
8635×unpow-prod-down
7603×pow-to-exp
5851×frac-add
4602×cbrt-prod
4477×associate-*r*
4342×associate-/r/
4164×frac-times
4077×flip3-- flip--
2903×add-cbrt-cube
2311×sqr-pow
2200×distribute-lft-out
1820×associate-*l/
1745×rec-exp 1-exp
1499×associate-/l*
1381×cbrt-unprod
1207×pow1
1136×flip-+ flip3-+
1079×associate-*l*
856×difference-of-squares
696×unpow2
634×div-inv
563×cbrt-undiv
516×add-log-exp
460×exp-prod
456×unswap-sqr
416×pow-prod-down
412×pow-unpow
386×distribute-lft-out--
358×associate-/r*
297×sqrt-div
242×distribute-rgt-neg-in
173×difference-cubes
136×*-commutative
130×distribute-lft-neg-in
112×tan-quot
100×pow1/3
98×sqrt-pow1
88×frac-2neg clear-num
69×rem-sqrt-square
64×distribute-rgt-in distribute-lft-in
62×pow1/2
59×sub-neg
58×pow-pow
56×div-sub
49×cube-prod
48×swap-sqr
42×log-prod
40×frac-sub
38×associate-/l/
33×sum-log
29×exp-diff
26×associate--l+
25×neg-sub0
22×pow-sub +-commutative
16×pow-flip neg-mul-1
15×cube-div
14×pow-neg exp-sum
13×rem-exp-log
12×pow-prod-up pow-sqr unpow3 cube-mult cbrt-div
9×associate-+r- unsub-neg
8×un-div-inv inv-pow associate-+l+ associate-+r+
6×diff-log cos-sum rem-cube-cbrt pow-plus pow2 rem-log-exp log-div
5×distribute-neg-frac
4×distribute-frac-neg
3×exp-neg cos-diff log-pow acos-asin neg-log rem-cbrt-cube associate-+l-
2×pow-div sqrt-pow2 sqrt-undiv asin-acos
1×mul0

regimes16.1s (1.8%)

Accuracy

Total 58.7b remaining (26.1%)

Threshold costs 4.6b (2%)

9.7b0.9%Toniolo and Linder, Equation (13)
8.7b36.4%Henrywood and Agarwal, Equation (3)
8.2b-4.4%Toniolo and Linder, Equation (10+)
5.7b0%Maksimov and Kolovsky, Equation (3)
5.5b0%Henrywood and Agarwal, Equation (12)

localize4.5s (0.5%)

bsearch1.8s (0.2%)

end1.0ms (0.0%)