Details

prune9.6m (42.0%)

simplify5.7m (25.1%)

sample4.0m (17.8%)

Algorithm
60×intervals
Results
1.1m251371×body80valid
48.5s160289×body80nan
47.3s25525×body1280valid
24.1s17334×body640valid
14.6s6632×body2560valid
9.9s9011×body320valid
6.1s2380×body5120valid
4.4s8422×body160valid
1.7s648×body10240exit
745.0ms581×body1280nan
584.0ms582×body640nan
335.0ms366×body320nan
283.0ms8256×pre80true
140.0ms182×body160nan

series1.8m (7.7%)

Calls

436 calls:

5.0s
(/ (pow (pow PI (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k))
4.2s
(* (pow (* n 2) (- 1/2 (/ k 2))) (/ (pow (pow PI (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k)))
2.3s
(sqrt (* (* U 2) (* n (- t (+ (* (* (* (* n (/ l Om)) (/ l Om)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*))) (* (* (/ l Om) 2) l))))))
2.2s
(sqrt (* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U*)) (* (* (/ l Om) 2) l))))))
2.2s
(sqrt (* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U*)) (* (* (/ l Om) 2) l))))))

rewrite1.2m (5.2%)

Algorithm
113×rewrite-expression-head
Calls

436 calls:

6.6s
(* (/ 4/3 (- (* (* PI PI) PI) (* (* (* (* (* v v) PI) (* (* v v) PI)) (* v v)) PI))) (+ (* PI PI) (+ (* (* (* v v) PI) (* (* v v) PI)) (* PI (* (* v v) PI)))))
6.0s
(* n (- t (+ (* (* (* (* n (/ l Om)) (/ l Om)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*))) (* (* (/ l Om) 2) l))))
4.5s
(* (* U 2) (* n (- t (+ (* (* (* (* n (/ l Om)) (/ l Om)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*))) (* (* (/ l Om) 2) l)))))
4.3s
(sqrt (* (* U 2) (* n (- t (+ (* (* (* (* n (/ l Om)) (/ l Om)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*))) (* (* (/ l Om) 2) l))))))
1.3s
(* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U*)) (* (* (/ l Om) 2) l))))
Rules
686020×add-exp-log
571619×div-exp
169022×prod-exp
112306×1-exp
53710×rec-exp
38767×times-frac
21658×add-cbrt-cube
18764×add-sqr-sqrt
17541×*-un-lft-identity
17138×add-cube-cbrt
12944×cbrt-undiv
5849×cbrt-unprod
2240×unpow-prod-down
2196×sqrt-prod
1854×associate-*r*
1795×div-inv
1788×associate-*l*
1379×pow1
1302×associate-/l*
778×sqrt-div
772×frac-times
736×associate-*l/
684×associate-*r/
643×associate-/r/
530×add-log-exp
520×associate-/r*
465×sqr-pow
446×pow-prod-down
436×insert-posit16
381×cbrt-prod
346×flip-+ flip3-+
345×frac-add
342×unswap-sqr
270×difference-of-squares
248×flip3-- flip--
247×pow-exp
154×*-commutative
140×sqrt-pow1
114×pow-unpow
113×sub-neg
112×tan-quot
111×distribute-lft-out--
110×pow-to-exp
99×unpow-prod-up
96×cbrt-div
93×frac-2neg clear-num
90×exp-prod
88×distribute-lft-out cube-prod
87×pow1/2
85×distribute-rgt-in distribute-lft-in
72×swap-sqr
66×rem-sqrt-square
57×sin-mult
56×associate-/l/
49×pow1/3
48×log-pow
45×pow-prod-up
37×distribute-rgt-out
33×sum-log +-commutative
28×pow-pow
26×pow-sqr
25×log-prod
23×pow-plus
17×pow2
15×pow-sub
13×div-sub diff-log
12×difference-of-sqr-1
10×distribute-lft1-in
8×distribute-rgt-out--
7×exp-sum
6×associate-+l+ associate-+r+ asin-acos
5×pow-flip sqr-sin inv-pow unpow2
4×sqrt-undiv frac-sub pow3 difference-cubes rem-log-exp cos-sum distribute-rgt1-in
3×rem-cube-cbrt exp-diff remove-posit16 un-div-inv
2×distribute-lft-neg-out associate-+r- exp-neg unpow3 count-2 rem-exp-log associate-+l- cube-mult cos-diff associate--l+ associate--r-
1×cos-mult sqrt-unprod sub-div sqrt-pow2 rem-square-sqrt sqr-cos cube-div acos-asin log-div

regimes21.0s (1.5%)

Accuracy

Total 40.0b remaining (19%)

Threshold costs 5.5b (2.6%)

5.7b53.2%Henrywood and Agarwal, Equation (3)
5.7b35.5%Toniolo and Linder, Equation (13)
5.3b77.2%Toniolo and Linder, Equation (7)
5.2b0%Maksimov and Kolovsky, Equation (3)
4.9b26.6%Henrywood and Agarwal, Equation (12)

localize7.0s (0.5%)

bsearch1.0s (0.1%)

end1.0ms (0.0%)