Details

Time bar (total: 6.2s)

analyze602.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
49.9%49.9%0.2%3
49.9%49.9%0.2%4
49.9%49.9%0.2%5
49.9%49.9%0.2%6
74.9%25%0.2%7
74.9%25%0.2%8
74.9%25%0.2%9
74.9%25%0.2%10
87.3%12.5%0.2%11
87.3%12.5%0.2%12
87.3%12.5%0.2%13
87.3%12.5%0.2%14

sample88.0ms

Algorithm
intervals
Results
35.0ms202×body80valid
16.0ms19×body640valid
13.0ms12×body1280valid
8.0ms15×body320valid
3.0ms8×body160valid

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
0488229
1488229

prune10.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 0.3b

Counts
2 → 1

localize25.0ms

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))))))
2.0b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite28.0ms

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*
8×add-cbrt-cube
6×pow1 prod-exp associate-/r*
5×associate-*r*
4×sqrt-div pow-exp add-log-exp
3×pow-unpow flip3-+ div-exp flip-+ associate-/l* unswap-sqr sqr-pow
2×pow-to-exp associate-*r/ associate-/r/ div-inv distribute-lft-out
1×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:
3.0ms
(pow (sin ky) 2.0)
6.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
14.0ms
(* (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)))))

series416.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (sin ky) 2.0)
162.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
107.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
129.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify62.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049582674
149582674

prune361.0ms

Filtered
88 candidates to 122 candidates (-38.6%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1202122
Fresh000
Picked101
Done000
Total1212123

Merged error: 0.2b

Counts
123 → 2

localize28.0ms

Local error

Found 4 expressions with local error:

7.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (* (cbrt (pow (sin ky) 2.0)) (cbrt (pow (sin ky) 2.0))) (cbrt (pow (sin ky) 2.0)))))))
13.9b
(cbrt (pow (sin ky) 2.0))
13.9b
(cbrt (pow (sin ky) 2.0))
13.9b
(cbrt (pow (sin ky) 2.0))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×unpow-prod-down
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×pow1/3 sqrt-prod sqr-pow
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 60
Calls
4 calls:
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (* (cbrt (pow (sin ky) 2.0)) (cbrt (pow (sin ky) 2.0))) (cbrt (pow (sin ky) 2.0)))))))
2.0ms
(cbrt (pow (sin ky) 2.0))
2.0ms
(cbrt (pow (sin ky) 2.0))
3.0ms
(cbrt (pow (sin ky) 2.0))

series236.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (* (cbrt (pow (sin ky) 2.0)) (cbrt (pow (sin ky) 2.0))) (cbrt (pow (sin ky) 2.0)))))))
36.0ms
(cbrt (pow (sin ky) 2.0))
40.0ms
(cbrt (pow (sin ky) 2.0))
36.0ms
(cbrt (pow (sin ky) 2.0))

simplify30.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
05046894

prune254.0ms

Filtered
59 candidates to 72 candidates (-22.0%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New72072
Fresh011
Picked011
Done000
Total72274

Merged error: 0.2b

Counts
74 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (* (/ 2.0 Om) l) 2.0)
0.2b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
1.0b
(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×pow-unpow
13×unpow-prod-down
12×add-exp-log add-sqr-sqrt add-cube-cbrt
10×pow1 pow-pow
6×pow-exp
5×exp-prod sqr-pow
4×pow-to-exp add-cbrt-cube add-log-exp
2×prod-exp distribute-lft-out
1×unpow-prod-up div-exp pow-prod-down
Counts
4 → 77
Calls
4 calls:
6.0ms
(pow (* (/ 2.0 Om) l) 2.0)
3.0ms
(pow (sin kx) 2.0)
3.0ms
(pow (sin ky) 2.0)
12.0ms
(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series110.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(pow (* (/ 2.0 Om) l) 2.0)
18.0ms
(pow (sin kx) 2.0)
18.0ms
(pow (sin ky) 2.0)
58.0ms
(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify52.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
050761020

prune233.0ms

Filtered
61 candidates to 89 candidates (-45.9%)
Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New89089
Fresh000
Picked011
Done011
Total89291

Merged error: 0.2b

Counts
91 → 2

regimes666.0ms

Accuracy

0% (0.3b remaining)

Error of 0.9b against oracle of 0.5b and baseline of 0.9b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03242
13242

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.1s6217×body80valid
613.0ms519×body1280valid
544.0ms644×body640valid
248.0ms416×body320valid
77.0ms204×body160valid

Profiling

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