Details

series1.6m (33.3%)

Calls

436 calls:

5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (* (cbrt (pow (/ l Om) (/ 2.0 2))) (cbrt (pow (/ l Om) (/ 2.0 2))))) (cbrt (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.4s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

sample1.4m (29.5%)

Algorithm
61×intervals
Results
16.5s252281×body80valid
16.3s29802×body1280valid
10.6s160918×body80nan
8.9s8820×body2560valid
7.5s19767×body640valid
5.1s3260×body5120valid
2.5s10066×body320valid
1.4s9200×body160valid
520.0ms850×body10240exit
159.0ms615×body1280nan
126.0ms610×body640nan
118.0ms8256×pre80true
55.0ms367×body320nan
22.0ms219×body160nan

prune57.8s (20.4%)

rewrite19.8s (7.0%)

Algorithm
115×rewrite-expression-head
Calls

436 calls:

1.3s
(* (* (* (/ (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 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))
1.1s
(/ 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)))
1.1s
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
1.0s
(/ 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)))
Rules
31247×add-exp-log
21082×prod-exp
8072×div-exp
8048×pow-exp
6310×times-frac
5635×add-sqr-sqrt
5137×*-un-lft-identity
4375×add-cube-cbrt
4140×sqrt-prod
3066×pow-to-exp
2959×add-cbrt-cube
1460×pow1
1361×cbrt-unprod
1288×unpow-prod-down
1284×associate-*l*
848×associate-*r*
622×cbrt-prod
588×cbrt-undiv
558×associate-*r/
537×add-log-exp
519×1-exp rec-exp
509×associate-/l*
470×associate-*l/
467×frac-times
436×unswap-sqr
410×pow-prod-down
385×sqr-pow
373×associate-/r*
338×pow-unpow
290×sqrt-div
284×div-inv
249×distribute-lft-out
235×associate-/r/
216×flip-+ flip3-+
207×distribute-lft-out--
156×flip3-- flip--
152×tan-quot
141×*-commutative exp-prod
130×pow-prod-up
124×distribute-rgt-neg-in
117×swap-sqr
115×difference-of-squares
99×sqrt-pow1
98×clear-num frac-2neg
88×distribute-lft-neg-in
83×unpow2
78×pow-sqr
69×pow1/3
67×pow1/2
65×distribute-rgt-in distribute-lft-in
64×pow-plus
61×sub-neg
51×pow-pow
48×log-pow
47×rem-sqrt-square
45×pow2
41×cbrt-div
40×frac-add
38×frac-sub
37×sum-log
36×log-prod
32×associate-/l/ cube-prod
31×div-sub associate--l+
29×+-commutative
25×exp-sum
18×pow-sub associate-+r+
15×neg-sub0 diff-log
12×pow-neg
11×exp-diff
10×neg-mul-1
9×pow-flip
8×log-div
7×associate-+r-
6×cube-div e-exp-1
5×unpow3 rem-exp-log cube-mult rem-log-exp
4×cos-sum un-div-inv inv-pow
3×sqrt-undiv unsub-neg acos-asin asin-acos
2×rem-cube-cbrt associate-+l+ quot-tan sqrt-unprod cos-diff rem-square-sqrt distribute-frac-neg distribute-neg-frac
1×pow3 exp-neg sub-div associate--r- mul0 rem-cbrt-cube

simplify12.0s (4.3%)

Algorithm
175×egg-herbie

regimes10.9s (3.8%)

Accuracy

Total 41.7b remaining (19.1%)

Threshold costs 4.8b (2.2%)

9.0b5.2%Toniolo and Linder, Equation (13)
5.7b54.8%Henrywood and Agarwal, Equation (3)
5.6b-3.9%Henrywood and Agarwal, Equation (12)
5.3b77.8%Toniolo and Linder, Equation (7)
5.1b15.8%Toniolo and Linder, Equation (10+)

localize2.4s (0.8%)

bsearch2.3s (0.8%)

end0.0ms (0.0%)