Details

sample3.3m (37.9%)

Algorithm
61×intervals
Results
42.5s253490×body80valid
38.8s29594×body1280valid
26.3s161561×body80nan
21.1s20367×body640valid
17.3s8816×body2560valid
10.7s3295×body5120valid
7.5s9964×body320valid
3.9s8948×body160valid
922.0ms744×body10240exit
724.0ms664×body1280nan
277.0ms621×body640nan
199.0ms8256×pre80true
102.0ms382×body320nan
45.0ms182×body160nan

series2.3m (26.7%)

Calls

429 calls:

8.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.8s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
7.1s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*)))))))
6.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.1s
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*))))))

prune1.5m (17.6%)

rewrite50.1s (9.5%)

Algorithm
113×rewrite-expression-head
Calls

429 calls:

3.5s
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
3.0s
(/ 2.0 (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
2.5s
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
1.2s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
1.2s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
63516×add-exp-log
44962×prod-exp
27240×pow-exp
22343×div-exp
12930×pow-to-exp
6405×times-frac
5363×add-sqr-sqrt
4756×*-un-lft-identity
4086×add-cube-cbrt
3838×sqrt-prod
3596×1-exp
3590×rec-exp
3436×add-cbrt-cube
1735×cbrt-unprod
1647×associate-*l*
1553×associate-*r/
1297×pow1
1016×associate-*r*
885×pow-unpow
832×frac-times
814×unpow-prod-down
729×cbrt-undiv
654×cbrt-prod associate-*l/
576×cbrt-div
533×flip3-- flip--
511×add-log-exp
488×associate-/r/
471×pow-prod-down
349×unswap-sqr
344×associate-/l*
328×flip-+ flip3-+
324×sqr-pow
312×sqrt-div
306×div-inv
294×associate-/r*
287×difference-of-squares
239×distribute-lft-out--
232×frac-add
192×frac-sub
158×*-commutative
144×tan-quot
129×distribute-lft-out
122×sqrt-pow1
114×exp-prod
107×distribute-rgt-in distribute-lft-in
91×sub-neg
90×clear-num frac-2neg
89×unpow2
75×distribute-rgt-neg-in
66×pow1/3
64×pow1/2
63×distribute-lft-neg-in
59×rem-sqrt-square
54×pow-pow
40×div-sub associate--l+
37×log-pow
36×cos-sum
34×swap-sqr
30×exp-diff
29×sum-log
25×pow-flip
23×cube-div pow-prod-up
20×associate-/l/
19×pow-sqr +-commutative
17×pow-sub cube-prod
15×diff-log
10×associate-+r+ cos-diff exp-sum distribute-neg-frac log-div
9×inv-pow neg-mul-1
8×log-prod
7×unpow3 cube-mult
6×pow2 neg-sub0
5×difference-cubes pow-plus
4×rem-cube-cbrt associate-+l+ pow-neg distribute-neg-in acos-asin rem-log-exp
2×un-div-inv rem-exp-log distribute-frac-neg associate-+r-
1×sqrt-unprod exp-neg unsub-neg rem-square-sqrt asin-acos mul0 rem-cbrt-cube distribute-rgt-neg-out

simplify17.8s (3.4%)

regimes15.0s (2.8%)

Accuracy

Total 41.5b remaining (19.9%)

Threshold costs 5.0b (2.4%)

9.8b29.2%Toniolo and Linder, Equation (13)
7.1b10.9%Toniolo and Linder, Equation (10+)
5.3b78.2%Toniolo and Linder, Equation (7)
4.3b13.7%Henrywood and Agarwal, Equation (12)
3.4b0%Henrywood and Agarwal, Equation (13)

bsearch6.9s (1.3%)

localize4.4s (0.8%)

end1.0ms (0.0%)