Details

simplify31.5m

Calls

8946 calls:

Slowest
3.1s
(/ (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (* l 2) (* l 2)) (* l 2)))
2.4s
(/ (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ l h) (/ l h)) (/ l h)))
2.1s
(/ (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))) (* (* (* (/ l h) 2) (* (/ l h) 2)) (* (/ l h) 2)))
1.8s
(* (* (* (* (/ 2 (tan k)) (/ 2 (tan k))) (/ 2 (tan k))) (* (* (/ (/ (/ l t) 1) 1) (/ (/ (/ l t) 1) 1)) (/ (/ (/ l t) 1) 1))) (/ (* (* (/ (/ l t) (+ 2 (* (/ k t) (/ k t)))) (/ (/ l t) (+ 2 (* (/ k t) (/ k t))))) (/ (/ l t) (+ 2 (* (/ k t) (/ k t))))) (* (* (* t (sin k)) (* t (sin k))) (* t (sin k)))))
1.8s
(/ (* (* (* (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (* (* -2 J) (cos (/ K 2)))) (* (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (* (* -2 J) (cos (/ K 2))))) (* (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (* (* -2 J) (cos (/ K 2))))) (* (* (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))) (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))) (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))))

sample4.3m

Algorithm
56×intervals
Results
58.7s247085×body80valid
47.8s23889×body1280valid
41.2s159773×body80nan
25.2s18424×body640valid
20.4s8728×body10240exit
18.1s7217×body2560valid
15.6s3457×body5120valid
8.9s8922×body320valid
5.0s8882×body160valid
576.0ms609×body1280nan
545.0ms679×body640nan
241.0ms345×body320nan
103.0ms192×body160nan

prune3.3m

series50.9s

Calls

425 calls:

Slowest
1.4s
(cos (* (* (cbrt (- (/ K (/ 2 (+ m n))) M)) (cbrt (* m (/ K 2)))) (cbrt (- (/ K (/ 2 (+ m n))) M))))
1.2s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.1s
(sqrt (* (* (* (* 2 n) U) (* (cbrt (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))) (cbrt (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))) (cbrt (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*))))))
1.1s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.1s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

regimes17.2s

Accuracy

Total 44.5b remaining (25.3%)

7.5b12.2%Maksimov and Kolovsky, Equation (3)
6.3b33.2%Toniolo and Linder, Equation (13)
6.2b-3.3%Henrywood and Agarwal, Equation (13)
5.6b77.9%Toniolo and Linder, Equation (7)
4.0b53.1%Henrywood and Agarwal, Equation (3)

bsearch7.1s

rewrite6.0s

Algorithm
108×rewrite-expression-head
Calls

425 calls:

Slowest
369.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
306.0ms
(* (/ (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (sqrt (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))))) (/ (* (* -2 J) (cos (/ K 2))) (sqrt (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))))))
182.0ms
(sqrt (* (* (* (* 2 n) U) (* (cbrt (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))) (cbrt (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))) (cbrt (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*))))))
135.0ms
(cbrt (* (* (* (+ (* a a) (* b b)) (+ (* a a) (* b b))) (* (+ (* a a) (* b b)) (+ (* a a) (* b b)))) (* (+ (* a a) (* b b)) (+ (* a a) (* b b)))))
128.0ms
(/ (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (sqrt (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))))
Rules
3246×frac-times
3087×times-frac
2293×add-sqr-sqrt
2253×*-un-lft-identity
2148×add-cube-cbrt
2103×associate-*r/
1708×flip-+ flip3-+
1690×cbrt-div
1185×add-exp-log
1177×associate-*l/
1058×flip3-- flip--
1019×add-cbrt-cube
925×sqrt-div
737×pow1
693×associate-*l*
669×div-inv
665×associate-*r*
639×sqrt-prod
634×frac-sub
507×cbrt-prod
490×associate-/r/
489×add-log-exp
425×insert-posit16
333×associate-/r*
287×associate-/l* frac-add
255×prod-exp
212×div-exp
203×cbrt-unprod
188×cbrt-undiv
145×*-commutative
136×unpow-prod-down
117×pow-prod-down
109×frac-2neg clear-num
88×associate-/l/
71×pow1/2
69×distribute-rgt-in distribute-lft-in
63×rem-sqrt-square
56×sub-neg
50×pow1/3
47×cube-prod
45×difference-of-squares pow-to-exp
43×div-sub
40×pow2
38×rec-exp
33×pow-prod-up
28×pow-unpow
27×distribute-lft-out associate-+r+ pow-sub
26×distribute-lft-out--
25×sum-log tan-quot
24×pow-exp pow-plus
21×exp-prod
20×associate--l+ +-commutative
19×pow-pow
17×pow-flip
15×log-prod
13×inv-pow
12×unpow2
difference-of-sqr-1 diff-log
distribute-lft-neg-in distribute-rgt-neg-in asin-acos
exp-diff associate-+r- rem-exp-log
distribute-frac-neg neg-sub0 difference-cubes distribute-neg-frac log-pow
sin-mult sqr-sin associate-+l- distribute-rgt-out
associate-+l+ rem-cube-cbrt sqrt-undiv distribute-rgt-out-- pow-div pow3 unpow3 neg-mul-1 rem-log-exp exp-neg cos-sum rem-cbrt-cube cube-mult
sub-div associate--l- cube-div acos-asin cos-diff associate--r-

localize3.5s

end1.0ms