Details

Time bar (total: 6.4s)

sample114.0ms

Algorithm
intervals
Results
39.0ms191×body80valid
24.0ms21×body1280valid
16.0ms20×body640valid
9.0ms15×body320valid
4.0msbody160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02229
15229
211729
327129
482129
5360929
done500029

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
0.3b
(pow (sin ky) 2.0)
2.1b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite32.0ms

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*
sqrt-div pow-exp 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 → 110
Calls
4 calls:
6.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
3.0ms
(pow (sin ky) 2.0)
16.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series481.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
21.0ms
(pow (sin ky) 2.0)
122.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
148.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify553.0ms

Counts
122 → 122
Iterations

Useful iterations: 2 (172.0ms)

IterNodesCost
02533103
16202821
220412689
done50002689

prune363.0ms

Filtered
84 candidates to 122 candidates (-45.2%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New1220122
Fresh000
Picked011
Done000
Total1221123

Merged error: 0.0b

Counts
123 → 1

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02229
12829
done2829

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.2s6256×body80valid
829.0ms522×body1280valid
571.0ms658×body640valid
229.0ms357×body320valid
84.0ms207×body160valid

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