Details

simplify18.1m

Calls

8078 calls:

Slowest
2.1s
(/ (* (/ (* (* (* 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 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)))
1.7s
(/ (* (* (* (/ (* 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)))
1.7s
(/ (* (* (/ 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
(* (+ (* 1 1) (+ (* (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d)))) (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d))))) (* 1 (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d))))))) (sqrt h))

sample4.3m

Algorithm
56×intervals
Results
59.0s247582×body80valid
48.0s24286×body1280valid
42.8s159854×body80nan
25.8s18196×body640valid
19.6s8509×body10240exit
16.9s7213×body2560valid
15.6s3309×body5120valid
9.6s9015×body320valid
5.0s8938×body160valid
1.1s641×body1280nan
486.0ms570×body640nan
254.0ms350×body320nan
88.0ms191×body160nan

prune2.6m

series49.8s

Calls

419 calls:

Slowest
2.8s
(pow (exp (sqrt (/ (+ EAccept (- (+ Ev Vef) mu)) KbT))) (sqrt (/ (+ EAccept (- (+ Ev Vef) mu)) KbT)))
1.6s
(sqrt (* (* (* (* 2 n) U) 1) (- t (* (/ l Om) (- (* l 2) (* (* (- U U*) (- (/ l Om))) n))))))
1.3s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.2s
(sqrt (+ (* t (* (* (* 2 n) U) 1)) (* (* (* (cbrt (* (* 2 U) (* (/ l Om) n))) (cbrt (* (* 2 U) (* (/ l Om) n)))) (cbrt (* (* 2 U) (* (/ l Om) n)))) (- (* -2 l) (* (- U U*) (* (/ l Om) n))))))
849.0ms
(sqrt (+ (* t (* (* (* 2 n) U) 1)) (* (* (* 2 U) (* (/ l Om) n)) (- (* -2 l) (* (- U U*) (* (/ l Om) n))))))

regimes16.2s

Accuracy

Total 51.4b remaining (28.2%)

8.0b9%Maksimov and Kolovsky, Equation (3)
7.4b11.5%Toniolo and Linder, Equation (13)
7.1b72%Toniolo and Linder, Equation (7)
6.6b49.8%Henrywood and Agarwal, Equation (3)
6.3b0%Henrywood and Agarwal, Equation (13)

bsearch8.0s

rewrite5.6s

Algorithm
107×rewrite-expression-head
Calls

419 calls:

Slowest
432.0ms
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (* (cbrt (cos (/ K 2))) (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2)))))) (* (cbrt (cos (/ K 2))) J))))
175.0ms
(* (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))))
130.0ms
(+ (+ (+ (pow a 4) (* (* (* a b) (* a b)) 2)) (pow b 4)) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
129.0ms
(/ (* (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2) (/ t (sin k))) k)
113.0ms
(* (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2) (/ t (sin k)))
Rules
3489×times-frac
2386×add-sqr-sqrt
2377×*-un-lft-identity
2313×add-cube-cbrt
1041×add-exp-log
918×add-cbrt-cube
758×sqrt-prod
748×associate-*r*
736×pow1
695×div-inv
494×add-log-exp
485×associate-*r/
418×insert-posit16
386×associate-*l*
370×associate-/r*
354×sqrt-div
329×associate-/r/
291×associate-/l*
263×frac-times
259×associate-*l/
252×flip-+ flip3-+
192×unpow-prod-up
190×prod-exp
187×div-exp
186×flip3-- flip--
163×cbrt-unprod
162×cbrt-prod
156×frac-add
148×*-commutative
142×sub-neg
138×cbrt-undiv
132×pow-prod-down
130×unpow-prod-down
103×associate-/l/
102×frac-2neg clear-num
99×cbrt-div
74×pow1/2
61×distribute-rgt-in distribute-lft-in
57×rem-sqrt-square
52×pow-to-exp
46×difference-of-sqr-1
37×tan-quot
35×pow1/3
33×sum-log
28×exp-prod
25×associate-+r+
24×pow-sub
23×distribute-lft-out
22×pow-exp pow-unpow pow-prod-up
21×pow-pow log-div
19×pow2 pow-plus
18×frac-sub +-commutative div-sub rec-exp
17×sin-mult
12×distribute-lft-out--
11×difference-of-squares
10×distribute-lft-neg-in distribute-rgt-neg-in un-div-inv distribute-neg-frac
pow-flip sqr-sin inv-pow unpow2
associate--l+ diff-log
associate-+r- log-pow
remove-posit16 exp-diff cos-sum
rem-exp-log rem-log-exp
associate-+l+ neg-sub0 difference-of-sqr--1 distribute-frac-neg acos-asin distribute-rgt1-in
log-prod sqrt-unprod sub-div neg-mul-1 associate-+l- rem-square-sqrt cos-diff
distribute-rgt-neg-out exp-neg distribute-rgt-out--
associate--l- exp-sum unpow3 distribute-lft-neg-out asin-acos cube-mult

localize3.5s

end1.0ms