Details

prune22.4m (65.8%)

simplify5.4m (15.7%)

sample3.7m (10.7%)

Algorithm
59×intervals
Results
1.0m241756×body80valid
44.5s25489×body1280valid
39.2s158750×body80nan
22.4s17791×body640valid
12.6s6646×body2560valid
9.0s8891×body320valid
5.1s2398×body5120valid
4.0s8372×body160valid
1.6s659×body10240exit
1.1s632×body1280nan
550.0ms8256×pre80true
490.0ms605×body640nan
261.0ms370×body320nan
64.0ms176×body160nan

series1.4m (4.2%)

Calls

437 calls:

2.1s
(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))))))
2.0s
(sqrt (* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (/ 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))))))

rewrite47.7s (2.3%)

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)))
1.5s
(* (* (* (/ (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
(* (* (* (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))))
1.1s
(* (* (/ 1 2) (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h)) (/ 1 l))
Rules
332591×add-exp-log
164572×div-exp
156337×prod-exp
133936×times-frac
55627×add-sqr-sqrt
53604×*-un-lft-identity
53042×add-cube-cbrt
44059×add-cbrt-cube
37471×cbrt-undiv
35080×cbrt-unprod
26249×sqrt-prod
13540×cbrt-prod
12435×1-exp
12343×rec-exp
4951×div-inv
4682×associate-*r*
2651×associate-/l*
2584×sqrt-div
2554×frac-times
2114×pow1
1699×associate-*l/
1506×associate-*l*
1349×associate-*r/
1048×associate-/r/
817×associate-/r*
750×flip3-- flip--
688×pow-prod-down
556×unswap-sqr
542×unpow-prod-down
517×add-log-exp
437×insert-posit16
314×unpow-prod-up
271×pow-exp flip-+ flip3-+
264×sqr-pow
221×pow-unpow sub-neg
215×frac-add
214×pow-prod-up
213×sqrt-pow1
179×tan-quot
175×difference-of-squares
169×*-commutative
157×distribute-lft-out--
131×pow-sqr
129×pow-to-exp
119×swap-sqr
106×pow-plus
105×pow1/2
100×frac-2neg clear-num
89×distribute-lft-out
79×pow2
77×distribute-rgt-in distribute-lft-in
68×exp-prod
65×sin-mult
58×associate-/l/
57×cbrt-div
56×rem-sqrt-square
41×log-pow
36×pow1/3
31×pow-pow
24×sum-log cube-prod
23×pow-sub
22×+-commutative
19×div-sub
17×log-prod distribute-rgt-out
16×diff-log
15×pow-flip
10×associate-+r+ exp-sum
inv-pow
distribute-rgt-out-- difference-of-sqr-1
rem-exp-log
associate-+l+ pow-div
rem-log-exp asin-acos sqr-sin
exp-diff distribute-lft1-in associate--l+ pow3 cos-sum unpow1/3
associate-+r- frac-sub un-div-inv associate-+l- acos-asin log-div
sqrt-unprod sub-div unpow2 rem-square-sqrt cos-diff distribute-rgt1-in
remove-posit16 cos-mult sqrt-undiv sqrt-pow2 count-2 difference-cubes sqr-cos rem-cbrt-cube associate--r-

regimes16.0s (0.8%)

Accuracy

Total 43.1b remaining (21.3%)

Threshold costs 3.4b (1.7%)

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)

localize6.5s (0.3%)

bsearch2.8s (0.1%)

end1.0ms (0.0%)