Details

simplify3.7m (30.2%)

sample3.4m (27.9%)

Algorithm
61×intervals
Results
45.2s253431×body80valid
40.5s29598×body1280valid
26.3s159961×body80nan
20.9s8763×body2560valid
19.4s20274×body640valid
10.5s3367×body5120valid
6.4s9945×body320valid
3.6s9170×body160valid
1.5s764×body10240exit
325.0ms712×body640nan
308.0ms606×body1280nan
157.0ms8256×pre80true
97.0ms330×body320nan
40.0ms205×body160nan

series2.3m (18.7%)

Calls

427 calls:

8.1s
(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*)))))
7.6s
(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 l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* 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*)))))

prune1.6m (13.0%)

rewrite50.4s (6.9%)

Algorithm
112×rewrite-expression-head
Calls

427 calls:

8.3s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
1.9s
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.6s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.4s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
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
32192×add-exp-log
22231×prod-exp
14558×pow-exp
11493×div-exp
9171×times-frac
7654×pow-to-exp
6295×add-sqr-sqrt
5748×*-un-lft-identity
5199×add-cube-cbrt
3526×sqrt-prod
2520×add-cbrt-cube
1565×1-exp rec-exp
1555×unpow-prod-down
1353×associate-*l*
1192×pow1
1159×associate-*r*
995×cbrt-unprod
909×cbrt-prod
608×associate-/l*
583×associate-*r/
552×add-log-exp
481×cbrt-undiv
452×pow-unpow
392×div-inv
377×pow-prod-down
372×sqr-pow
361×associate-/r*
337×sqrt-div
335×unswap-sqr
288×associate-*l/
239×associate-/r/
218×flip-+ flip3-+
200×frac-times
195×flip-- flip3--
154×difference-of-squares
150×distribute-lft-out
147×distribute-lft-out--
144×*-commutative
136×sqrt-pow1
109×unpow2
102×tan-quot
97×clear-num frac-2neg
73×distribute-rgt-in pow1/2 distribute-lft-in
64×frac-sub
62×sub-neg
58×pow1/3
56×pow-pow
53×distribute-rgt-neg-in
52×exp-prod
49×associate-/l/
47×rem-sqrt-square sum-log
39×distribute-lft-neg-in
38×cbrt-div
37×div-sub
30×frac-add +-commutative
26×pow-prod-up
25×swap-sqr
24×cube-prod
23×log-pow pow-sub
22×log-prod
20×diff-log
19×exp-sum
18×pow-sqr associate--l+
16×neg-sub0
14×pow-neg
13×pow-flip
11×associate-+l+
neg-log
sub-div associate--r+
inv-pow
exp-diff un-div-inv pow2 cos-sum
unpow3 pow-plus associate-+r-
cube-div rem-exp-log distribute-neg-frac cube-mult asin-acos associate-+l- log-div
cos-diff associate-+r+ acos-asin neg-mul-1 associate--r-
pow-div rem-cube-cbrt sqrt-pow2 associate--l- sqrt-unprod distribute-rgt-out-- rem-square-sqrt sum-cubes rem-log-exp
sqrt-undiv e-exp-1 unsub-neg distribute-rgt-out mul0

regimes15.4s (2.1%)

Accuracy

Total 46.5b remaining (22.3%)

Threshold costs 4.6b (2.2%)

8.1b16%Maksimov and Kolovsky, Equation (3)
7.5b16.2%Toniolo and Linder, Equation (13)
6.1b74.3%Toniolo and Linder, Equation (7)
5.9b0%Henrywood and Agarwal, Equation (12)
4.9b28.2%Toniolo and Linder, Equation (10-)

bsearch4.5s (0.6%)

localize4.2s (0.6%)

end1.0ms (0.0%)