Details

Time bar (total: 8.3s)

sample47.0ms

Algorithm
intervals
Results
29.0ms256×body80valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
112316
229416
3108316
4500116

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ (* 2.0 l) Om) 2.0)
0.3b
(pow (sin kx) 2.0)
2.7b
(* (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)))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
20×add-sqr-sqrt unpow-prod-down
18×*-un-lft-identity
14×add-cube-cbrt
11×associate-*l*
7×pow1 pow-exp prod-exp
6×pow-unpow times-frac add-cbrt-cube
5×associate-*r*
4×div-exp add-log-exp sqr-pow
3×pow-to-exp sqrt-prod unswap-sqr
2×pow-pow flip3-+ sqrt-div associate-*r/ flip-+ div-inv distribute-lft-out
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 *-commutative cbrt-unprod
Counts
4 → 92
Calls
4 calls:
4.0ms
(pow (/ (* 2.0 l) Om) 2.0)
1.0ms
(pow (sin kx) 2.0)
45.0ms
(* (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)))))

series866.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(pow (/ (* 2.0 l) Om) 2.0)
101.0ms
(pow (sin kx) 2.0)
373.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
309.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify60.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0499897
11984856
25002856

prune426.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.5b

localize31.0ms

Local error

Found 4 expressions with local error:

6.9b
(cbrt (sqrt (+ 1.0 (* (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)))))
7.5b
(sqrt (+ 1.0 (* (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)))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×add-cube-cbrt *-un-lft-identity
8×sqrt-div
7×pow1
6×cbrt-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 61
Calls
4 calls:
2.0ms
(cbrt (sqrt (+ 1.0 (* (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)))))
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
6.0ms
(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:
280.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
304.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
304.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
311.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify81.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01281122
14031067
221671065
350021065

prune429.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.5b

localize40.0ms

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) (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)))))
7.5b
(sqrt (+ 1.0 (* (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)))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
3.0ms
(sqrt (+ 1.0 (* (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)))))
3.0ms
(sqrt (+ 1.0 (* (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:
324.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
310.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
308.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
307.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify81.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0106996
1375956
22118956
35001956

prune460.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ (* 2.0 l) Om) 2.0)
0.3b
(pow (sin kx) 2.0)
2.5b
(log (exp (* (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)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
20×unpow-prod-down
19×add-sqr-sqrt
18×*-un-lft-identity
14×add-cube-cbrt
11×associate-*l*
7×pow1 pow-exp prod-exp
6×pow-unpow times-frac add-cbrt-cube
5×log-prod associate-*r* add-log-exp
4×div-exp sqr-pow
3×pow-to-exp log-pow unswap-sqr
2×distribute-rgt-in pow-pow distribute-lft-in associate-*r/ exp-sum div-inv distribute-lft-out
1×exp-prod exp-to-pow flip3-+ rem-log-exp *-commutative cbrt-unprod flip-+
Counts
4 → 93
Calls
4 calls:
4.0ms
(pow (/ (* 2.0 l) Om) 2.0)
1.0ms
(pow (sin kx) 2.0)
4.0ms
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
45.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series938.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(pow (/ (* 2.0 l) Om) 2.0)
103.0ms
(pow (sin kx) 2.0)
376.0ms
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
376.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify56.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0473900
11851820
25001820

prune468.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 2.5b

regimes458.0ms

Accuracy

0% (0.3b remaining)

Error of 1.6b against oracle of 1.2b and baseline of 1.6b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03672
13672

end0.0ms

sample1.2s

Algorithm
intervals
Results
949.0ms8000×body80valid