Details

simplify7.2m (42.5%)

sample3.2m (19.0%)

Algorithm
61×intervals
Results
43.3s253519×body80valid
40.2s29653×body1280valid
27.6s160386×body80nan
18.3s20115×body640valid
17.5s8614×body2560valid
10.1s3411×body5120valid
7.2s10106×body320valid
3.7s9107×body160valid
1.0s631×body10240exit
836.0ms595×body1280nan
307.0ms625×body640nan
192.0ms8256×pre80true
109.0ms343×body320nan
33.0ms181×body160nan

series2.7m (16.2%)

Calls

465 calls:

7.7s
(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*)))))
7.2s
(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*))))))
7.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.2s
(* (* (* 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*)))))

prune2.3m (13.9%)

rewrite43.5s (4.3%)

Algorithm
118×rewrite-expression-head
Calls

465 calls:

1.4s
(* (sqrt (* 2.0 (- (* (* 1.0 1.0) 1.0) (* (* (* 3.0 (* v v)) (* 3.0 (* v v))) (* 3.0 (* v v)))))) t)
1.3s
(* (sqrt (* 2.0 (- (* (* 1.0 1.0) 1.0) (* (* (* 3.0 (* v v)) (* 3.0 (* v v))) (* 3.0 (* v v)))))) t)
1.3s
(/ (/ (- 1.0 (* (* 5.0 v) v)) PI) (* (sqrt (* 2.0 (- (* (* 1.0 1.0) 1.0) (* (* (* 3.0 (* v v)) (* 3.0 (* v v))) (* 3.0 (* v v)))))) t))
1.2s
(/ (/ (- 1.0 (* (* 5.0 v) v)) PI) (* (sqrt (* 2.0 (- (* (* 1.0 1.0) 1.0) (* (* (* 3.0 (* v v)) (* 3.0 (* v v))) (* 3.0 (* v v)))))) t))
1.2s
(* (* (* (/ (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))
Rules
60214×add-exp-log
36017×prod-exp
24938×div-exp
21831×pow-exp
7719×pow-to-exp
7468×times-frac
6205×add-sqr-sqrt
5509×*-un-lft-identity
4779×add-cube-cbrt
4607×sqrt-prod
4022×1-exp
4017×rec-exp
2806×add-cbrt-cube
2226×associate-*l*
1461×pow1
1333×unpow-prod-down
1105×cbrt-unprod
1068×associate-*r*
846×associate-*r/
589×cbrt-prod
574×sqrt-div
573×cbrt-undiv
560×add-log-exp
487×pow-prod-down
463×frac-times
436×pow-unpow
408×flip-+ flip3-+
393×sqr-pow
381×cbrt-div
355×associate-*l/
351×associate-/l* unswap-sqr
332×div-inv
301×associate-/r*
283×difference-of-squares
259×distribute-lft-out
254×associate-/r/
223×frac-add
219×exp-prod
212×flip3-- flip--
166×*-commutative
164×distribute-lft-out--
146×sqrt-pow1
109×pow1/3
97×swap-sqr
95×pow-pow
79×frac-2neg clear-num pow1/2
65×tan-quot rem-sqrt-square
59×sub-neg
57×distribute-rgt-in distribute-lft-in
55×associate-/l/
49×pow-prod-up
40×div-sub
39×frac-sub
36×distribute-rgt-neg-in distribute-lft-neg-in
35×pow-sqr
29×sum-log
26×associate-+r- pow-plus
23×+-commutative
22×associate--l+
16×pow2 diff-log
15×pow-sub
14×exp-diff
13×rem-exp-log
12×neg-mul-1
10×cos-sum
pow-flip
exp-sum neg-sub0 distribute-frac-neg log-pow pow-neg
log-prod associate-+r+ sin-mult inv-pow
cos-diff
un-div-inv acos-asin
associate-+l+ pow3
rem-cube-cbrt rem-log-exp
cube-prod unpow3 sqrt-unprod sub-div cube-mult exp-to-pow asin-acos rem-square-sqrt rem-cbrt-cube

regimes27.6s (2.7%)

Accuracy

Total 58.8b remaining (24.9%)

Threshold costs 4.0b (1.7%)

8.5b43.6%Henrywood and Agarwal, Equation (3)
8.2b0%Henrywood and Agarwal, Equation (12)
7.9b16.2%Maksimov and Kolovsky, Equation (3)
7.8b23.9%Toniolo and Linder, Equation (13)
5.9b20.7%Toniolo and Linder, Equation (10+)

localize9.8s (1.0%)

bsearch4.1s (0.4%)

end1.0ms (0.0%)