Details

simplify5.3m (31.8%)

series3.3m (19.9%)

Calls

454 calls:

17.8s
(sqrt (* (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) (* (cbrt U) (cbrt U))) (cbrt U)))
15.2s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))
14.9s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))
14.6s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))
13.8s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

sample3.2m (19.2%)

Algorithm
61×intervals
Results
40.0s253027×body80valid
37.8s29233×body1280valid
26.7s158791×body80nan
21.7s20385×body640valid
16.7s8750×body2560valid
12.0s3484×body5120valid
7.5s10238×body320valid
3.6s8964×body160valid
1.4s695×body10240exit
857.0ms639×body640nan
594.0ms345×body320nan
320.0ms598×body1280nan
185.0ms8256×pre80true
65.0ms193×body160nan

prune3.1m (18.5%)

rewrite1.1m (6.5%)

Algorithm
116×rewrite-expression-head
Calls

454 calls:

6.4s
(sqrt (* (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) (* (cbrt U) (cbrt U))) (cbrt U)))
3.2s
(exp (- (- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0)) l))
3.1s
(exp (- (- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0)) l))
1.8s
(- (- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0)) l)
1.8s
(* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
Rules
29361×add-exp-log
23221×times-frac
15281×prod-exp
12528×div-exp
12336×add-sqr-sqrt
11326×*-un-lft-identity
10619×add-cube-cbrt
7875×pow-exp
4916×add-cbrt-cube
3883×sqrt-prod
3443×unpow-prod-down
2906×pow-to-exp
2069×cbrt-unprod
1822×1-exp
1810×pow1
1576×rec-exp
1565×cbrt-undiv
1475×associate-/l*
1150×associate-*r*
1035×associate-*l*
913×sqr-pow
834×associate-/r*
779×div-inv
551×add-log-exp
535×sqrt-div
495×pow-prod-down
419×cbrt-prod
410×unswap-sqr
396×associate-*r/
337×associate-/r/
269×frac-times
267×pow-unpow flip-+ flip3-+ associate-*l/
255×difference-of-squares
242×distribute-lft-out--
202×pow-prod-up
159×flip3-- flip--
147×sqrt-pow1
143×exp-prod
139×*-commutative
122×pow-sqr
110×frac-add
105×cbrt-div rem-sqrt-square
103×pow1/2
102×frac-2neg clear-num
98×pow-plus
94×distribute-lft-out
73×pow2
56×distribute-rgt-in sub-neg distribute-lft-in
50×swap-sqr
49×pow1/3
39×associate-/l/
36×pow-pow
28×log-pow
27×diff-log
25×tan-quot
24×div-sub
21×sum-log
20×+-commutative
18×log-prod
17×exp-sum
16×frac-sub associate--l+ pow-sub
13×distribute-rgt-neg-in distribute-lft-neg-in
12×rem-exp-log
10×exp-diff sin-mult
9×cube-unmult
8×pow-flip neg-sub0 associate-+r+ inv-pow
7×pow3 difference-cubes
6×pow-neg associate--r+
4×associate-+l+ unpow-prod-up cos-sum unpow2 acos-asin
3×un-div-inv rem-log-exp
2×associate--l- associate-+r- exp-neg pow-div sub-div asin-acos log-div
1×sqrt-unprod neg-mul-1 sqr-sin rem-square-sqrt cos-diff e-exp-1

regimes28.6s (2.9%)

Accuracy

Total 62.4b remaining (28.5%)

Threshold costs 4.6b (2.1%)

20.2b-15.6%Henrywood and Agarwal, Equation (13)
8.5b0.9%Henrywood and Agarwal, Equation (12)
8.1b40.8%Henrywood and Agarwal, Equation (3)
6.1b36.2%Toniolo and Linder, Equation (13)
5.6b76.1%Toniolo and Linder, Equation (7)

localize8.0s (0.8%)

bsearch3.8s (0.4%)

end1.0ms (0.0%)