Details

simplify1.1hr

Calls

20922 calls:

Slowest
2.5s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* (* h h) h) (* (* l l) l)))
2.4s
(* (* (* (* (sqrt (/ d l)) (sqrt (/ d l))) (sqrt (/ d l))) (* (* (sqrt (/ d h)) (sqrt (/ d h))) (sqrt (/ d h)))) (* (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))))) (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))))))
2.2s
(* (* (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* (sqrt (/ d l)) (sqrt (/ d h)))) (* (sqrt (/ d l)) (sqrt (/ d h)))) (* (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))))))
2.2s
(* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* (* h h) h) (* (* l l) l)))
2.2s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))))

prune4.6m

sample3.1m

Algorithm
55×intervals
Results
51.4s224711×body80valid
31.1s20188×body1280valid
26.4s113535×body80nan
20.3s8613×body10240exit
16.8s13696×body640valid
8.0s5738×body2560valid
6.4s2486×body5120valid
6.0s6818×body320valid
4.0s7788×body160valid
1.5s632×body1280nan
550.0ms614×body640nan
274.0ms8256×pre80true
216.0ms332×body320nan
52.0ms154×body160nan

series1.4m

Calls

442 calls:

Slowest
1.8s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (pow (* (/ l Om) (* (- U U*) (* (/ l Om) n))) 1))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (pow (* (/ l Om) (* (- U U*) (* (/ l Om) n))) 1))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (pow (* (/ l Om) (* (- U U*) (* (/ l Om) n))) 1))))
1.5s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite44.8s

Algorithm
114×rewrite-expression-head
Calls

442 calls:

Slowest
3.1s
(/ (* (* (sqrt (+ 1 (* (* (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))))) (* (cos (/ K 2)) J)) -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)))))
2.9s
(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))))
2.9s
(/ (* (* (sqrt (+ 1 (* (* (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))))) (* (cos (/ K 2)) J)) -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))))) (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)))))))
2.8s
(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)))))
1.6s
(* (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))))) (/ h l))
Rules
19516×times-frac
12077×add-exp-log
10009×add-cbrt-cube
9913×*-un-lft-identity
9835×add-sqr-sqrt
8757×add-cube-cbrt
6114×prod-exp
5960×cbrt-unprod
4828×sqrt-div
4359×sqrt-prod
4074×frac-times
3796×div-exp
3659×cbrt-undiv
2277×frac-add
2268×associate-*r/
2128×associate-*l/
1894×associate-/r/
1759×pow1
1409×associate-*l*
1279×associate-/l*
1233×flip3-- flip--
1003×cbrt-prod
932×div-inv
884×associate-*r*
729×difference-of-squares
582×sqrt-pow1
574×add-log-exp
559×pow-prod-down
443×associate-/r*
442×insert-posit16
327×unpow-prod-down
314×flip-+ flip3-+
307×pow1/2
299×exp-prod
272×pow-prod-up
245×distribute-lft-out
239×unswap-sqr
189×distribute-lft-out--
156×sqr-pow
135×distribute-rgt-out--
134×*-commutative
128×pow-sqr
126×pow-unpow
125×cbrt-div
112×swap-sqr
111×tan-quot
93×pow-exp
88×pow1/3
85×frac-2neg clear-num rem-sqrt-square
61×associate-/l/
60×distribute-rgt-neg-in
59×sin-mult
57×pow-to-exp
56×sub-neg
50×distribute-lft-neg-in div-sub
46×log-pow
43×distribute-rgt-in distribute-lft-in
37×pow-plus
36×1-exp
35×diff-log
32×sum-log pow2
28×+-commutative
27×rec-exp
25×unpow2
23×frac-sub pow-pow
22×associate--l+ rem-exp-log
19×exp-diff
15×associate-+r-
14×pow-sub
11×pow-flip neg-sub0
distribute-frac-neg exp-sum inv-pow
exp-neg neg-log neg-mul-1 cos-sum remove-posit16
log-prod associate-+r+
sqrt-unprod rem-log-exp
difference-of-sqr-1 sqr-sin associate--r-
associate--r+ cos-diff
associate-+l+ unpow-prod-up sub-div acos-asin
associate--l- distribute-neg-frac asin-acos rem-square-sqrt
distribute-lft-neg-out cos-mult pow3 un-div-inv rem-cbrt-cube e-exp-1 distribute-rgt-out distribute-rgt1-in

regimes15.6s

Accuracy

Total 29.8b remaining (19.4%)

Threshold costs 3.1b (2%)

7.6b22.3%Toniolo and Linder, Equation (13)
5.9b75.8%Toniolo and Linder, Equation (7)
4.8b-8.6%Henrywood and Agarwal, Equation (13)
4.5b15%Toniolo and Linder, Equation (3a)
1.6b0%Toniolo and Linder, Equation (3b), real

localize7.1s

bsearch3.3s

end1.0ms