Details

prune13.7m (52.8%)

simplify5.5m (21.2%)

sample4.2m (16.0%)

Algorithm
61×intervals
Results
1.0m253094×body80valid
50.8s29579×body1280valid
41.9s161693×body80nan
27.9s20380×body640valid
20.5s8839×body2560valid
10.0s3318×body5120valid
9.4s9914×body320valid
5.1s8759×body160valid
1.6s659×body10240exit
785.0ms632×body1280nan
524.0ms605×body640nan
268.0ms8256×pre80true
207.0ms370×body320nan
64.0ms176×body160nan

series1.4m (5.2%)

Calls

437 calls:

2.2s
(sqrt (* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (* (cbrt (* (/ l Om) (- U U*))) (cbrt (* (/ l Om) (- U U*)))) (cbrt (* (/ l Om) (- U U*))))) (* (* (/ l Om) 2) l))))))
2.0s
(sqrt (* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (* (cbrt (* (/ l Om) (- U U*))) (cbrt (* (/ l Om) (- U U*)))) (cbrt (* (/ l Om) (- U U*))))) (* (* (/ l Om) 2) l))))))
1.9s
(sqrt (* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (* (cbrt (* (/ l Om) (- U U*))) (cbrt (* (/ l Om) (- U U*)))) (cbrt (* (/ l Om) (- U U*))))) (* (* (/ l Om) 2) l))))))
1.9s
(sqrt (* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U*)) (* (* (/ l Om) 2) l))))))
1.7s
(sqrt (* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (/ l Om) (- U U*))) (* (* (/ l Om) 2) l))))))

rewrite46.7s (3.0%)

Algorithm
111×rewrite-expression-head
Calls

437 calls:

5.6s
(* (* (* (* (/ (cbrt h) (cbrt l)) (/ (* (cbrt M) (cbrt M)) (/ 1 (/ 1 (* (cbrt d) (cbrt d)))))) (/ (cbrt M) (/ 2 (/ D (cbrt d))))) (* (/ (* (cbrt h) (* (/ (cbrt D) (cbrt d)) (/ (cbrt D) (cbrt d)))) (cbrt l)) (/ M (/ 2 (/ (cbrt D) (cbrt d)))))) (/ (cbrt h) (cbrt l)))
1.7s
(* (* (* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d)))) (* (/ (* (cbrt h) (* (/ (cbrt D) (cbrt d)) (/ (cbrt D) (cbrt d)))) (cbrt l)) (/ M (/ 2 (/ (cbrt D) (cbrt d)))))) (/ (cbrt h) (cbrt l)))
1.3s
(* (* (/ 1 2) (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h)) (/ 1 l))
1.2s
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
1.2s
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* (/ 1 2) (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h)) (/ 1 l))))
Rules
331554×add-exp-log
163850×div-exp
156079×prod-exp
139795×times-frac
57712×add-sqr-sqrt
56285×*-un-lft-identity
55813×add-cube-cbrt
43827×add-cbrt-cube
37276×cbrt-undiv
35005×cbrt-unprod
28269×sqrt-prod
15682×cbrt-prod
12334×1-exp
12307×rec-exp
4975×div-inv
2833×associate-/l*
2648×sqrt-div
2561×frac-times
2397×associate-*r*
2160×pow1
1696×associate-*l/
1482×associate-*l*
1358×associate-*r/
1058×associate-/r/
839×associate-/r*
750×flip3-- flip--
697×pow-prod-down
636×unpow-prod-down
519×add-log-exp
449×unswap-sqr
437×insert-posit16
314×unpow-prod-up
291×flip-+ flip3-+
290×sqrt-pow1
261×pow-exp
260×sqr-pow
236×pow-prod-up
221×sub-neg
215×frac-add
189×tan-quot
175×difference-of-squares
170×*-commutative
157×distribute-lft-out--
150×pow1/2
149×swap-sqr
141×pow-sqr
119×pow-to-exp
113×pow-plus
101×frac-2neg clear-num
97×pow-unpow
89×distribute-lft-out
85×distribute-rgt-in distribute-lft-in
81×pow2
65×sin-mult exp-prod
64×rem-sqrt-square
59×associate-/l/
57×cbrt-div
40×log-pow
36×pow1/3
24×sum-log cube-prod
23×pow-sub
22×+-commutative
21×pow-pow
20×log-prod
19×div-sub
17×distribute-rgt-out
16×diff-log
15×pow-flip
13×exp-sum
10×associate-+r+
inv-pow
difference-of-sqr-1 distribute-rgt-out--
rem-exp-log
associate-+l+ pow-div
sqr-sin rem-log-exp asin-acos
exp-diff distribute-lft1-in associate--l+ sqrt-unprod rem-square-sqrt cos-sum unpow1/3
associate-+r- frac-sub un-div-inv associate-+l- acos-asin log-div
cube-unmult sub-div unpow2 cos-diff distribute-rgt1-in
remove-posit16 cos-mult sqrt-undiv pow3 sqrt-pow2 count-2 difference-cubes exp-to-pow sqr-cos rem-cbrt-cube associate--r-

regimes18.8s (1.2%)

Accuracy

Total 47.2b remaining (21.6%)

Threshold costs 4.3b (2%)

7.8b39.7%Henrywood and Agarwal, Equation (3)
7.4b-4%Henrywood and Agarwal, Equation (13)
5.5b38.7%Toniolo and Linder, Equation (13)
5.3b77.4%Toniolo and Linder, Equation (7)
5.1b0%Maksimov and Kolovsky, Equation (3)

localize6.1s (0.4%)

bsearch2.7s (0.2%)

end1.0ms (0.0%)