Details

Time bar (total: 6.1s)

sample104.0ms

Algorithm
intervals
Results
33.0ms191×body80valid
22.0ms19×body1280valid
17.0ms21×body640valid
9.0ms16×body320valid
3.0ms9×body160valid

simplify57.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
0488229
1488229

prune17.0ms

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: 1.0b

Counts
2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
0.4b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.7b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.6b
(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×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 kx) 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)))))

series427.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(pow (sin kx) 2.0)
165.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
109.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
134.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify63.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
049522674
149522674

prune351.0ms

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: 0.6b

Counts
123 → 2

localize29.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.7b
(* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
15.0b
(cbrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
15.0b
(cbrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
18×*-un-lft-identity
16×add-sqr-sqrt
14×prod-exp
10×add-cube-cbrt associate-*r* associate-*l*
8×add-cbrt-cube
6×cbrt-prod unpow-prod-down pow-exp
4×pow1 cbrt-div flip3-+ associate-*r/ flip-+ distribute-lft-out add-log-exp unswap-sqr sqr-pow
2×distribute-rgt-in pow-to-exp distribute-lft-in pow1/3 div-exp *-commutative cbrt-unprod
Counts
4 → 86
Calls
4 calls:
13.0ms
(* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
13.0ms
(* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms
(cbrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms
(cbrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series486.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
109.0ms
(* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
133.0ms
(cbrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
135.0ms
(cbrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify44.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
049782258
149782258

prune425.0ms

Filtered
74 candidates to 98 candidates (-32.4%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New98098
Fresh011
Picked011
Done000
Total982100

Merged error: 0.6b

Counts
100 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin ky) 2.0)
0.3b
(pow (sin kx) 2.0)
1.5b
(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
1.6b
(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
15×unpow-prod-down
13×add-sqr-sqrt add-cube-cbrt
11×pow-unpow
8×log-prod pow-pow
7×pow1 add-exp-log
5×exp-prod sqr-pow
4×pow-to-exp pow-exp add-cbrt-cube add-log-exp
3×rem-log-exp
2×unpow-prod-up distribute-lft-out
1×log-pow
Counts
4 → 78
Calls
4 calls:
3.0ms
(pow (sin ky) 2.0)
3.0ms
(pow (sin kx) 2.0)
13.0ms
(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0ms
(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))

series162.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (sin ky) 2.0)
18.0ms
(pow (sin kx) 2.0)
62.0ms
(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
63.0ms
(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))

simplify40.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
051531311

prune227.0ms

Filtered
62 candidates to 90 candidates (-45.2%)
Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New90090
Fresh000
Picked011
Done011
Total90292

Merged error: 0.6b

Counts
92 → 2

regimes542.0ms

Accuracy

0% (0.4b remaining)

Error of 1.1b against oracle of 0.6b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03252
13252

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.1s6251×body80valid
621.0ms528×body1280valid
487.0ms594×body640valid
242.0ms402×body320valid
87.0ms225×body160valid

Profiling

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