Details

Time bar (total: 5.6s)

sample144.0ms

Algorithm
intervals
Results
59.0ms256×body80valid

simplify5.3s

Counts
1 → 1
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
02229
15229
213128
333028
4115228
5477228
done500028

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.5b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
1.5b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.7b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
30×*-un-lft-identity
26×add-cube-cbrt
21×times-frac
19×add-exp-log
15×sqrt-prod
13×unpow-prod-down
11×associate-*l*
add-cbrt-cube
pow1 prod-exp associate-/r*
associate-*r*
expm1-log1p-u sqrt-div pow-exp log1p-expm1-u add-log-exp
pow-unpow flip3-+ div-exp flip-+ associate-/l* unswap-sqr sqr-pow
pow-to-exp associate-*r/ associate-/r/ div-inv distribute-lft-out
cbrt-undiv distribute-rgt-in rem-sqrt-square pow-pow frac-2neg distribute-lft-in sqrt-pow1 pow1/2 clear-num *-commutative cbrt-unprod
Counts
4 → 118
Calls
4 calls:
4.0ms
(pow (sin ky) 2.0)
12.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
98.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series6.0ms