Details

Time bar (total: 8.8s)

sample108.0ms

Algorithm
intervals
Results
34.0ms194×body80valid
24.0ms20×body1280valid
18.0ms23×body640valid
7.0ms12×body320valid
3.0ms7×body160valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
113116
234216
3120216
4500216

prune5.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.5b

Counts
2 → 1

localize31.0ms

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))))))
2.3b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
6.6b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite29.0ms

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×expm1-log1p-u sqrt-div pow-exp log1p-expm1-u 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 → 118
Calls
4 calls:
3.0ms
(pow (sin ky) 2.0)
5.0ms
(/ 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)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
101.0ms
(pow (sin ky) 2.0)
379.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
369.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
324.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify74.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05211687
121351580
250021576

prune505.0ms

Filtered
130 candidates to 91 candidates (70.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1282130
Fresh000
Picked101
Done000
Total1292131

Merged error: 0.0b

Counts
131 → 2

localize33.0ms

Local error

Found 4 expressions with local error:

6.6b
(sqrt (+ 1.0 (* (pow (* (cbrt (/ (* 2.0 l) Om)) (cbrt (/ (* 2.0 l) Om))) 2.0) (* (pow (cbrt (/ (* 2.0 l) Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
16.4b
(cbrt (/ (* 2.0 l) Om))
16.4b
(cbrt (/ (* 2.0 l) Om))
16.4b
(cbrt (/ (* 2.0 l) Om))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×times-frac
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 71
Calls
4 calls:
3.0ms
(sqrt (+ 1.0 (* (pow (* (cbrt (/ (* 2.0 l) Om)) (cbrt (/ (* 2.0 l) Om))) 2.0) (* (pow (cbrt (/ (* 2.0 l) Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
3.0ms
(cbrt (/ (* 2.0 l) Om))
3.0ms
(cbrt (/ (* 2.0 l) Om))
3.0ms
(cbrt (/ (* 2.0 l) Om))

series723.0ms

Counts
4 → 12
Calls
4 calls:
456.0ms
(sqrt (+ 1.0 (* (pow (* (cbrt (/ (* 2.0 l) Om)) (cbrt (/ (* 2.0 l) Om))) 2.0) (* (pow (cbrt (/ (* 2.0 l) Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
89.0ms
(cbrt (/ (* 2.0 l) Om))
88.0ms
(cbrt (/ (* 2.0 l) Om))
90.0ms
(cbrt (/ (* 2.0 l) Om))

simplify154.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0200866
1610818
23836811
35001811

prune482.0ms

Filtered
83 candidates to 72 candidates (86.7%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New83083
Fresh011
Picked011
Done000
Total83285

Merged error: 0.0b

Counts
85 → 2

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
2.3b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.3b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.3b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
41×add-exp-log
33×add-sqr-sqrt unpow-prod-down associate-*l*
30×*-un-lft-identity
18×add-cube-cbrt prod-exp
15×associate-*r*
10×pow-exp add-cbrt-cube
9×times-frac unswap-sqr
7×sqr-pow
6×associate-*r/ div-exp distribute-lft-out
5×pow1
4×expm1-log1p-u pow-to-exp log1p-expm1-u add-log-exp
3×distribute-rgt-in pow-unpow distribute-lft-in flip3-+ *-commutative cbrt-unprod flip-+ div-inv
1×pow-pow
Counts
4 → 136
Calls
4 calls:
3.0ms
(pow (sin ky) 2.0)
15.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
18.0ms
(* (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)))

series1.2s

Counts
4 → 12
Calls
4 calls:
100.0ms
(pow (sin ky) 2.0)
377.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
373.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
369.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify56.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
03741499
115741393
250011393

prune710.0ms

Filtered
148 candidates to 105 candidates (70.9%)
Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1480148
Fresh000
Picked011
Done011
Total1482150

Merged error: 0.0b

Counts
150 → 2

regimes360.0ms

Accuracy

0% (0.0b remaining)

Error of 0.8b against oracle of 0.7b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03326
13326

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.3s6223×body80valid
614.0ms541×body1280valid
511.0ms626×body640valid
249.0ms404×body320valid
78.0ms206×body160valid