Details

simplify42.0m

Calls

15656 calls:

Slowest
3.2s
(/ (* (* (* U U) U) (/ (* (* U U) U) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J))))) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J))))
3.1s
(/ (* (* (* U U) U) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J))))) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J))))
3.1s
(/ (* (* (* U U) U) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ U (* 2 (* (cos (/ K 2)) J))))) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J))))
2.8s
(/ (* (* (* U (/ U (* 2 (* (cos (/ K 2)) J)))) (* U (/ U (* 2 (* (cos (/ K 2)) J))))) (* U (/ U (* 2 (* (cos (/ K 2)) J))))) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J))))
2.8s
(/ (* (* (* U U) U) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J))))) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J))))

prune4.4m

sample3.7m

Algorithm
54×intervals
Results
59.4s238791×body80valid
44.8s159416×body80nan
31.7s17810×body1280valid
20.6s8686×body10240exit
18.0s14155×body640valid
8.0s7372×body320valid
7.5s5010×body2560valid
5.5s2331×body5120valid
4.7s8088×body160valid
732.0ms647×body1280nan
588.0ms657×body640nan
317.0ms352×body320nan
62.0ms174×body160nan

series1.3m

Calls

405 calls:

Slowest
2.6s
(sqrt (* 2 (+ (* (* (- t (* (* l (/ l Om)) 2)) n) U) (* (* (- (* (* (/ l Om) n) (* (/ l Om) n))) (- U U*)) U))))
2.1s
(sqrt (* 2 (* U (* n (- (- t (* (* l (/ l Om)) 2)) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))))
2.0s
(sqrt (* 2 (* (* U n) (- (- t (* (/ (* l l) Om) 2)) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))
2.0s
(sqrt (* 2 (* (* U n) (- (- t (* (* l (/ l Om)) 2)) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))
1.6s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite32.4s

Algorithm
104×rewrite-expression-head
Calls

405 calls:

Slowest
4.9s
(* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) (* (cbrt J) (cbrt J))) (cbrt J))
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
1.2s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) (* (cbrt J) (cbrt J)))
802.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
743.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
Rules
36756×times-frac
17532×*-un-lft-identity
16860×add-sqr-sqrt
15733×add-cube-cbrt
7929×add-exp-log
4688×add-cbrt-cube
4475×sqrt-prod
3999×prod-exp
2665×cbrt-prod
2313×div-exp
1763×cbrt-unprod
1616×cbrt-undiv
1467×pow1
1411×div-inv
1164×associate-/r/
1099×associate-/l*
1008×associate-*r/
853×associate-*r*
831×sqrt-div
827×associate-*l*
823×pow-exp
595×associate-*l/
589×frac-times
562×associate-/r*
506×add-log-exp
502×distribute-lft-out
485×distribute-lft-out--
473×pow-prod-down
462×pow-to-exp
461×difference-of-squares
435×flip-+ flip3-+
405×insert-posit16
390×distribute-rgt-neg-in
360×distribute-lft-neg-in
293×swap-sqr
277×unswap-sqr
263×flip3-- flip--
215×unpow-prod-down
214×1-exp
202×rec-exp
176×pow-unpow
160×exp-prod
156×*-commutative
136×frac-sub
135×frac-add
118×div-sub
113×tan-quot
108×sin-mult
96×frac-2neg clear-num
95×sqrt-pow1
81×sqr-pow
78×pow1/2 pow-prod-up
67×cbrt-div
63×distribute-rgt-in distribute-lft-in
61×pow-sub
59×sub-neg
58×associate-/l/
53×rem-sqrt-square
49×pow-sqr
43×log-prod pow-plus
42×neg-mul-1
37×distribute-neg-frac
36×pow2
33×pow1/3
31×associate-+l+
28×diff-log
25×sum-log
22×pow-pow
19×+-commutative
18×pow-flip log-pow associate--l+
12×associate-+r+ difference-of-sqr-1 unpow2
11×distribute-rgt-out--
10×sqr-sin inv-pow
neg-sub0
associate-+r-
distribute-frac-neg neg-log associate--r+ rem-exp-log
exp-diff log-div
remove-posit16 pow3 asin-acos acos-asin
exp-sum associate--l- associate--r- rem-log-exp
sub-div cos-sum
un-div-inv sqrt-undiv cube-unmult exp-neg sqrt-unprod sqrt-pow2 distribute-lft-neg-out exp-to-pow associate-+l- rem-square-sqrt rem-cbrt-cube cos-diff

regimes16.2s

Accuracy

Total 44.2b remaining (27.2%)

9.0b5.1%Maksimov and Kolovsky, Equation (3)
8.7b30.9%Henrywood and Agarwal, Equation (3)
7.2b-8.7%Toniolo and Linder, Equation (13)
6.3b73.9%Toniolo and Linder, Equation (7)
4.0b25%Henrywood and Agarwal, Equation (12)

localize5.9s

bsearch3.0s

end1.0ms