Details

simplify25.6m

Calls

13571 calls:

Slowest
2.0s
(/ (* (/ (* (* (* 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)))
2.0s
(/ (* (* (* (/ (* 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
(/ (* (* (* (/ (* 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)))
1.6s
(/ (* (* (/ 2 (* (/ k t) (/ k t))) (/ 2 (* (/ k t) (/ k t)))) (/ 2 (* (/ k t) (/ k t)))) (* (* (* (* (tan k) (tan k)) (tan k)) (* (* (/ t (* (/ l t) (/ l t))) (/ t (* (/ l t) (/ l t)))) (/ t (* (/ l t) (/ l t))))) (* (* (sin k) (sin k)) (sin k))))
1.4s
(/ (* (* (cos k) (cos k)) (cos k)) (/ (* (* (* (* k k) t) (* (* k k) t)) (* (* k k) t)) (* (* (* (/ l (sin k)) (/ l (sin k))) (/ l (sin k))) (* (* (/ l (sin k)) (/ l (sin k))) (/ l (sin k))))))

sample4.3m

Algorithm
55×intervals
Results
57.0s227251×body80valid
46.8s23962×body1280valid
41.4s159551×body80nan
27.7s18248×body640valid
20.9s8710×body10240exit
19.2s7255×body2560valid
15.4s3419×body5120valid
8.2s8882×body320valid
5.3s8794×body160valid
659.0ms600×body1280nan
528.0ms615×body640nan
190.0ms340×body320nan
90.0ms180×body160nan

prune3.3m

series43.6s

Calls

412 calls:

Slowest
1.2s
(sqrt (* (* 2 n) (* U (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))))
1.2s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))
1.1s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
955.0ms
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
825.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

regimes15.2s

Accuracy

Total 50.7b remaining (31.5%)

11.0b0.5%Henrywood and Agarwal, Equation (13)
8.9b28.4%Toniolo and Linder, Equation (13)
8.2b3.3%Maksimov and Kolovsky, Equation (3)
7.4b70.3%Toniolo and Linder, Equation (7)
4.1b64.4%Henrywood and Agarwal, Equation (3)

rewrite8.2s

Algorithm
106×rewrite-expression-head
Calls

412 calls:

Slowest
610.0ms
(/ (- (pow (* (+ (* (+ (* a a) a) a) (* (* b b) (- 1 (* 3 a)))) 4) 3) (pow (- 1 (+ (+ (pow a 4) (* (* (* a b) (* a b)) 2)) (pow b 4))) 3)) (+ (* (* (+ (* (+ (* a a) a) a) (* (* b b) (- 1 (* 3 a)))) 4) (* (+ (* (+ (* a a) a) a) (* (* b b) (- 1 (* 3 a)))) 4)) (+ (* (- 1 (+ (+ (pow a 4) (* (* (* a b) (* a b)) 2)) (pow b 4))) (- 1 (+ (+ (pow a 4) (* (* (* a b) (* a b)) 2)) (pow b 4)))) (* (* (+ (* (+ (* a a) a) a) (* (* b b) (- 1 (* 3 a)))) 4) (- 1 (+ (+ (pow a 4) (* (* (* a b) (* a b)) 2)) (pow b 4)))))))
394.0ms
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) J))))
314.0ms
(cbrt (* (* (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l) (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l)) (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l)))
288.0ms
(log (exp (+ (+ (+ (pow b 4) (pow a 4)) (* 4 (* b b))) (* (* b a) (+ (* b a) (* b a))))))
124.0ms
(sqrt (+ (* (* (* (cbrt (* (cbrt (sin kx)) (cbrt (sin kx)))) (cbrt (cbrt (sin kx)))) (sin kx)) (pow (cbrt (sin kx)) 2)) (pow (sin ky) 2)))
Rules
40099×associate-*l/
29703×frac-add
18278×associate-*r/
15849×flip3-- flip--
14856×frac-times
10724×flip-+ flip3-+
10340×times-frac
8221×associate-/r/
5618×sqrt-prod
5497×add-sqr-sqrt
5472×*-un-lft-identity
5391×add-cube-cbrt
1092×add-exp-log
949×div-inv
942×add-cbrt-cube
705×pow1
672×associate-*r*
582×associate-/l*
471×sqrt-div
470×add-log-exp
441×associate-/r*
412×insert-posit16
338×associate-*l*
286×cbrt-div
270×div-exp
262×unpow-prod-up
205×sub-neg
190×unpow-prod-down
168×cbrt-undiv
167×frac-sub
161×cbrt-prod
158×prod-exp
146×cbrt-unprod
145×*-commutative
109×pow-prod-down
106×frac-2neg clear-num
99×distribute-rgt-in distribute-lft-in
83×associate-/l/
71×pow-to-exp
69×pow1/2
55×rem-sqrt-square
48×cube-div pow-sub
45×pow1/3
39×pow-exp
36×rec-exp
35×pow-prod-up
32×tan-quot
31×neg-sub0
30×pow-neg
29×associate-+r+ pow-plus
25×difference-of-squares
24×sum-log pow2
23×associate--l+
22×distribute-lft-out
21×distribute-lft-out--
20×+-commutative
18×log-pow
15×pow-unpow pow-pow exp-prod
14×sub-div
13×log-prod
12×pow-flip distribute-rgt-out-- div-sub
unpow2
associate--r+ diff-log
acos-asin
inv-pow cos-sum
associate-+l+ difference-of-sqr-1 sin-mult difference-cubes sqr-sin un-div-inv cube-prod
associate-+r- pow3 asin-acos
distribute-lft-neg-in distribute-rgt-neg-in cos-diff distribute-rgt-out
distribute-lft1-in sqrt-unprod distribute-neg-frac neg-mul-1 associate-+l- rem-square-sqrt rem-cbrt-cube associate--r- rem-log-exp distribute-rgt1-in
remove-posit16 distribute-frac-neg exp-sum unpow1/2

bsearch6.7s

localize3.1s

end1.0ms