Details

simplify3.5m (29.9%)

sample3.4m (29.2%)

Algorithm
61×intervals
Results
47.0s253385×body80valid
39.2s29360×body1280valid
29.2s160172×body80nan
20.2s20162×body640valid
17.4s8856×body2560valid
11.7s3430×body5120valid
6.6s9835×body320valid
2.9s8924×body160valid
1.4s835×body10240exit
542.0ms654×body1280nan
287.0ms626×body640nan
239.0ms360×body320nan
209.0ms8256×pre80true
36.0ms193×body160nan

series2.4m (20.2%)

Calls

444 calls:

7.6s
(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*))))))
7.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.4s
(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*)))))
6.4s
(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 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))

prune1.3m (11.3%)

rewrite39.9s (5.7%)

Algorithm
116×rewrite-expression-head
Calls

444 calls:

1.4s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.2s
(* (/ 4.0 (* (* (* 3.0 PI) (- (pow 1.0 3) (pow (* v v) 3))) (sqrt (- (* 2.0 2.0) (* (* 6.0 (* v v)) (* 6.0 (* v v))))))) (* (+ (* 1.0 1.0) (+ (* (* v v) (* v v)) (* 1.0 (* v v)))) (sqrt (+ 2.0 (* 6.0 (* v v))))))
1.1s
(* (* (* (/ (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))
985.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
974.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
25310×add-exp-log
16891×prod-exp
7970×pow-exp
6805×div-exp
4868×times-frac
4517×add-sqr-sqrt
4309×*-un-lft-identity
3381×add-cube-cbrt
2979×pow-to-exp
2448×add-cbrt-cube
1206×sqrt-prod
1193×pow1
1132×unpow-prod-down
1067×associate-*r*
960×cbrt-unprod
866×associate-*l*
848×1-exp
839×rec-exp
536×add-log-exp
529×pow-unpow
421×cbrt-undiv
390×associate-*r/
380×associate-/l*
379×unswap-sqr
377×associate-/r*
358×pow-prod-down
319×distribute-lft-out
307×sqr-pow
302×sqrt-div
300×div-inv
251×cbrt-prod
207×associate-*l/
180×flip-+ flip3-+
166×frac-times
165×distribute-lft-out--
156×*-commutative
143×flip3-- flip--
129×difference-of-squares
119×distribute-rgt-neg-in
117×sqrt-pow1
104×associate-/r/
95×distribute-lft-neg-in
86×clear-num frac-2neg
82×pow1/2
81×distribute-rgt-in distribute-lft-in
69×pow-pow
66×rem-sqrt-square sub-neg
57×tan-quot
50×frac-sub
45×cbrt-div
44×associate-/l/
43×pow1/3
42×unpow2
39×sum-log
35×cube-prod
33×log-prod
29×+-commutative exp-prod
26×associate--l+
25×div-sub
24×frac-add
22×log-pow
18×pow-sub
16×pow-prod-up
14×pow-flip swap-sqr
13×neg-sub0
12×pow-neg
11×neg-mul-1
10×cos-sum
9×associate-+r+ inv-pow diff-log
8×pow-plus pow-sqr exp-sum
7×unpow3 cube-mult rem-log-exp
6×un-div-inv
5×cube-div cos-diff
4×rem-cube-cbrt associate-+l+ pow2 distribute-neg-frac
3×distribute-rgt-out-- acos-asin asin-acos
2×exp-diff associate-+r- unpow-prod-up unsub-neg distribute-frac-neg sub-div log-div
1×sqrt-undiv difference-cubes sqrt-pow2 rem-exp-log sqrt-unprod pow3 rem-square-sqrt distribute-rgt-out mul0 rem-cbrt-cube exp-to-pow

regimes16.8s (2.4%)

Accuracy

Total 49.3b remaining (22.7%)

Threshold costs 4.0b (1.8%)

8.5b10%Toniolo and Linder, Equation (13)
7.0b45.5%Henrywood and Agarwal, Equation (3)
5.0b-142.2%Henrywood and Agarwal, Equation (9a)
4.9b0%Henrywood and Agarwal, Equation (12)
4.9b79%Toniolo and Linder, Equation (7)

bsearch4.9s (0.7%)

localize4.5s (0.6%)

end1.0ms (0.0%)