Details

simplify22.3m

Calls

8627 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)))
1.7s
(/ (* (* (/ 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))))
1.6s
(* (cbrt (* (* (+ (* (/ (exp (* (log k) m)) (* (/ k a) k)) (/ (exp (* (log k) m)) (* (/ k a) k))) (+ (* (* (/ (exp (* (log k) m)) (* (/ k a) k)) (/ 10 k)) (* (/ (exp (* (log k) m)) (* (/ k a) k)) (/ 10 k))) (* (/ (exp (* (log k) m)) (* (/ k a) k)) (* (/ (exp (* (log k) m)) (* (/ k a) k)) (/ 10 k))))) (+ (/ (exp (* (log k) m)) (* (/ k a) k)) (* (/ (exp (* (log k) m)) (* (/ k a) k)) (/ 10 k)))) (+ (* (/ (exp (* (log k) m)) (* (/ k a) k)) (/ (exp (* (log k) m)) (* (/ k a) k))) (+ (* (* (/ (exp (* (log k) m)) (* (/ k a) k)) (/ 10 k)) (* (/ (exp (* (log k) m)) (* (/ k a) k)) (/ 10 k))) (* (/ (exp (* (log k) m)) (* (/ k a) k)) (* (/ (exp (* (log k) m)) (* (/ k a) k)) (/ 10 k))))))) (/ (pow k 4) (exp (* (log k) m))))
1.4s
(/ (* (* (/ 2 (* (/ k t) (/ k t))) (/ 2 (* (/ k t) (/ k t)))) (/ 2 (* (/ k t) (/ k t)))) (* (* (* (* (tan k) (/ t (* (/ l t) (/ l t)))) (* (tan k) (/ t (* (/ l t) (/ l t))))) (* (tan k) (/ t (* (/ l t) (/ l t))))) (* (* (sin k) (sin k)) (sin k))))
1.4s
(* (* (* (/ 2 (tan k)) (/ 2 (tan k))) (/ 2 (tan k))) (/ (* (* (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t))))) (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t))))) (/ (* (* (sin k) (sin k)) (sin k)) (* (* (/ l t) (/ l t)) (/ l t)))))

sample4.4m

Algorithm
56×intervals
Results
1.0m247501×body80valid
48.2s24106×body1280valid
40.2s160073×body80nan
25.2s18167×body640valid
21.4s8669×body10240exit
18.6s7306×body2560valid
14.0s3282×body5120valid
10.3s8998×body320valid
5.2s8854×body160valid
1.1s612×body1280nan
767.0ms657×body640nan
210.0ms348×body320nan
72.0ms196×body160nan

prune2.7m

series1.1m

Calls

414 calls:

Slowest
1.8s
(sqrt (+ (* (* 2 U) (* n t)) (* (* (* 2 U) (* (/ l Om) n)) (- (* -2 l) (* (- U U*) (* (/ l Om) n))))))
1.8s
(sqrt (* (* (* (* 2 n) U) 1) (- t (* (/ l Om) (- (* l 2) (* (* (- U U*) (- (/ l Om))) n))))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.3s
(sqrt (+ (* t (* (* (* 2 n) U) 1)) (* (* (* 2 U) (* (/ l Om) n)) (- (* -2 l) (* (- U U*) (* (/ l Om) n))))))
1.3s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

regimes17.5s

Accuracy

Total 46.1b remaining (27.2%)

8.4b0.2%Maksimov and Kolovsky, Equation (3)
7.7b14.2%Toniolo and Linder, Equation (13)
7.4b69.7%Toniolo and Linder, Equation (7)
6.4b0%Henrywood and Agarwal, Equation (13)
4.7b60.5%Henrywood and Agarwal, Equation (12)

bsearch5.2s

rewrite4.9s

Algorithm
107×rewrite-expression-head
Calls

414 calls:

Slowest
350.0ms
(* (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))))
134.0ms
(cbrt (* (* (- (/ (exp (* (log k) m)) (* (/ k a) k)) (* (/ (exp (* (log k) m)) (* (/ k a) k)) (/ 10 k))) (- (/ (exp (* (log k) m)) (* (/ k a) k)) (* (/ (exp (* (log k) m)) (* (/ k a) k)) (/ 10 k)))) (- (/ (exp (* (log k) m)) (* (/ k a) k)) (* (/ (exp (* (log k) m)) (* (/ k a) k)) (/ 10 k)))))
131.0ms
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J))))
118.0ms
(+ (- (/ (exp (* (log k) m)) (* (/ k a) k)) (* (/ (exp (* (log k) m)) (* (/ k a) k)) (/ 10 k))) (/ (* 99 a) (/ (pow k 4) (exp (* (log k) m)))))
74.0ms
(+ (cbrt (* (* (- (/ (exp (* (log k) m)) (* (/ k a) k)) (* (/ (exp (* (log k) m)) (* (/ k a) k)) (/ 10 k))) (- (/ (exp (* (log k) m)) (* (/ k a) k)) (* (/ (exp (* (log k) m)) (* (/ k a) k)) (/ 10 k)))) (- (/ (exp (* (log k) m)) (* (/ k a) k)) (* (/ (exp (* (log k) m)) (* (/ k a) k)) (/ 10 k))))) (/ (* 99 a) (/ (pow k 4) (exp (* (log k) m)))))
Rules
3419×times-frac
2404×*-un-lft-identity
2402×add-sqr-sqrt
2324×add-cube-cbrt
1499×frac-times
1009×add-exp-log
985×associate-*l/
906×frac-sub
877×add-cbrt-cube
796×div-inv
735×cbrt-div
688×pow1
686×associate-*r/
643×sqrt-prod
627×associate-*r*
552×associate-*l*
484×add-log-exp
418×flip3-- flip--
413×insert-posit16
411×frac-add
409×associate-/r*
344×associate-/r/
320×associate-/l*
299×sub-div
199×sqrt-div
194×prod-exp
192×flip-+ flip3-+
168×unpow-prod-down
155×div-exp
149×cbrt-prod
145×*-commutative
138×cbrt-unprod
135×cbrt-undiv
114×frac-2neg clear-num
105×exp-prod
95×pow-prod-down
87×log-pow
81×associate-/l/
80×sub-neg
66×distribute-rgt-in distribute-lft-in
50×rem-sqrt-square
47×pow-to-exp
46×pow-exp pow1/2
40×pow-unpow pow1/3
38×unpow-prod-up
32×div-sub
26×sum-log rec-exp tan-quot
25×log-prod
23×pow-prod-up
22×pow-plus
20×pow-pow
19×pow2
18×associate-+r+ distribute-lft-out-- distribute-lft-out
16×exp-sum
14×difference-of-squares distribute-rgt-out--
13×distribute-lft-neg-in +-commutative sqr-sin distribute-rgt-neg-in
12×associate-+r- distribute-neg-frac unpow2 diff-log
10×pow-flip
sin-mult inv-pow pow-sub
associate--l+
associate-+l+ exp-diff cube-prod difference-cubes associate-+l-
asin-acos cos-sum rem-exp-log log-div
associate--r+ neg-mul-1
neg-sub0 distribute-frac-neg pow3 rem-log-exp cos-diff un-div-inv
pow-div remove-posit16 distribute-rgt-neg-out exp-to-pow rem-cbrt-cube acos-asin
sqrt-undiv unpow3 associate--l- cube-mult distribute-lft-neg-out associate--r-

localize3.0s

end1.0ms