Details

Time bar (total: 6.4s)

sample111.0ms

Algorithm
intervals
Results
36.0ms191×body80valid
25.0ms21×body1280valid
17.0ms20×body640valid
9.0ms15×body320valid
4.0msbody160valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02229
15229
211729
327129
482129
5362029
done500029

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 1

localize24.0ms

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)))))

rewrite33.0ms

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))))))
4.0ms
(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)))))

series482.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
24.0ms
(pow (sin ky) 2.0)
123.0ms
(* (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)))))

simplify572.0ms

Counts
122 → 122
Iterations

Useful iterations: done (566.0ms)

IterNodesCost
02533103
16202833
220032694
done50002690

prune368.0ms

Filtered
85 candidates to 122 candidates (-43.5%)
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

sample3.1s

Algorithm
intervals
Results
1.2s6256×body80valid
621.0ms522×body1280valid
574.0ms658×body640valid
240.0ms357×body320valid
84.0ms207×body160valid

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