Details

Time bar (total: 10.6s)

sample60.0ms

Algorithm
intervals
Results
40.0ms256×body80valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
112316
229416
3108316
4500116

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.6b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.4b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.1b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite53.0ms

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:
1.0ms
(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))))))
40.0ms
(* (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)))))

series459.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(pow (sin ky) 2.0)
188.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
105.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
152.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05051608
120471504
250011501

prune1.6s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize32.0ms

Local error

Found 4 expressions with local error:

8.6b
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
9.1b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
9.1b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
9.1b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite11.0ms

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)))))
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series581.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
146.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
147.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
146.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify83.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01281119
14031064
221671062
350021062

prune1.7s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize35.0ms

Local error

Found 4 expressions with local error:

9.1b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
9.1b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
9.1b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
9.1b
(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)))))

series594.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(sqrt (+ 1.0 (* (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)))))
149.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
149.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify79.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0106996
1375956
22118956
35001956

prune2.2s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.2b

localize7.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune0.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 1.2b

regimes1.4s

Accuracy

0% (0.4b 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
04073
14073

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.3s8000×body80valid