Details

simplify5.6m (31.3%)

prune4.1m (23.2%)

sample3.2m (17.8%)

Algorithm
61×intervals
Results
41.9s252181×body80valid
40.7s29453×body1280valid
27.1s160173×body80nan
19.0s20296×body640valid
17.7s8772×body2560valid
10.7s3360×body5120valid
6.7s9995×body320valid
3.4s9078×body160valid
994.0ms644×body10240exit
420.0ms623×body1280nan
344.0ms670×body640nan
232.0ms8256×pre80true
168.0ms340×body320nan
32.0ms176×body160nan

series3.1m (17.3%)

Calls

444 calls:

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))
15.1s
(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))
15.0s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))
14.3s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (* (cbrt (pow (/ l Om) (/ 2.0 2))) (cbrt (pow (/ l Om) (/ 2.0 2)))) (* (cbrt (pow (/ l Om) (/ 2.0 2))) (- U* U)))) (* (* 2.0 l) (/ l Om))))) U))
2.2s
(* (* (* 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)

rewrite1.2m (6.6%)

Algorithm
114×rewrite-expression-head
Calls

444 calls:

4.9s
(* (* (* (* (/ (/ (pow (cbrt t) 3.0) (cbrt l)) (cbrt l)) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
4.0s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (* (cbrt (pow (/ l Om) (/ 2.0 2))) (cbrt (pow (/ l Om) (/ 2.0 2)))) (* (cbrt (pow (/ l Om) (/ 2.0 2))) (- U* U)))) (* (* 2.0 l) (/ l Om))))) U))
3.3s
(exp (- (- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0)) l))
3.2s
(exp (- (- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0)) l))
3.0s
(* (* (* (/ (/ (pow (cbrt t) 3.0) (cbrt l)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
42331×times-frac
24076×add-exp-log
19794×add-sqr-sqrt
19049×*-un-lft-identity
18523×add-cube-cbrt
12902×prod-exp
9908×div-exp
9724×sqrt-prod
7292×unpow-prod-down
7197×pow-exp
2861×add-cbrt-cube
2823×pow-to-exp
2388×associate-*r*
1568×cbrt-prod
1496×sqr-pow
1440×associate-/l*
1372×pow1
1266×1-exp rec-exp
1131×div-inv
1129×cbrt-unprod
921×associate-/r*
827×associate-*l*
792×associate-/r/
735×cbrt-undiv
634×frac-times
622×associate-*r/
581×associate-*l/
550×add-log-exp
532×sqrt-div
430×pow-prod-down
380×flip-+ flip3-+
327×unswap-sqr
290×pow-unpow
261×pow-sub
251×frac-add
247×neg-sub0 pow-neg
229×flip3-- flip--
151×cbrt-div
143×difference-of-squares
141×*-commutative
138×sqrt-pow1
137×distribute-lft-out
136×distribute-lft-out--
111×pow1/3
108×pow1/2
104×tan-quot
94×distribute-rgt-in distribute-lft-in rem-sqrt-square
89×frac-2neg clear-num
74×pow-prod-up
68×swap-sqr
58×log-prod
57×exp-sum
55×sub-neg
49×associate-/l/
48×distribute-neg-in pow-sqr
42×pow-pow
40×distribute-lft-neg-in distribute-rgt-neg-in
31×frac-sub
30×associate--l+
28×pow-plus diff-log
27×sum-log
26×div-sub
25×+-commutative
20×pow2
16×exp-prod
12×associate--r+
8×unpow-prod-up cube-unmult pow3 sum-cubes
6×pow-flip associate-+l+ inv-pow un-div-inv exp-neg rem-exp-log log-pow
4×distribute-rgt-neg-out neg-mul-1 cos-sum
3×distribute-lft-neg-out unpow2 acos-asin
2×exp-diff associate-+r- sqrt-undiv sqrt-unprod associate--l- asin-acos rem-square-sqrt e-exp-1
1×sub-div rem-log-exp cos-diff

regimes28.7s (2.7%)

Accuracy

Total 49.0b remaining (22.2%)

Threshold costs 4.8b (2.2%)

8.4b-11.5%Henrywood and Agarwal, Equation (13)
8.4b-0.4%Henrywood and Agarwal, Equation (12)
7.9b45.1%Henrywood and Agarwal, Equation (3)
6.5b31.1%Toniolo and Linder, Equation (13)
5.8b60.6%Toniolo and Linder, Equation (10+)

localize8.7s (0.8%)

bsearch2.5s (0.2%)

end1.0ms (0.0%)