Details

Time bar (total: 9.3s)

sample61.0ms

Algorithm
intervals
Results
43.0ms256×body80valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
113116
234216
3120216
4500216

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize24.0ms

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))))))
1.5b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite54.0ms

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:
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)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
101.0ms
(pow (sin ky) 2.0)
375.0ms
(/ 1.0 (sqrt (+ 1.0 (* (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)))
309.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify67.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05211686
121361580
250011576

prune625.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

localize33.0ms

Local error

Found 4 expressions with local error:

8.0b
(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))))))
12.6b
(cbrt (/ (* 2.0 l) Om))
12.6b
(cbrt (/ (* 2.0 l) Om))
12.6b
(cbrt (/ (* 2.0 l) Om))

rewrite10.0ms

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))))))
2.0ms
(cbrt (/ (* 2.0 l) Om))
2.0ms
(cbrt (/ (* 2.0 l) Om))
2.0ms
(cbrt (/ (* 2.0 l) Om))

series728.0ms

Counts
4 → 12
Calls
4 calls:
454.0ms
(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))
91.0ms
(cbrt (/ (* 2.0 l) Om))
93.0ms
(cbrt (/ (* 2.0 l) Om))

simplify151.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0200866
1610818
23836811
35001811

prune596.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize37.0ms

Local error

Found 4 expressions with local error:

8.0b
(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))))))
12.6b
(cbrt (/ (* 2.0 l) Om))
12.6b
(cbrt (/ (* 2.0 l) Om))
12.6b
(cbrt (/ (* 2.0 l) Om))

rewrite10.0ms

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))))))
2.0ms
(cbrt (/ (* 2.0 l) Om))
2.0ms
(cbrt (/ (* 2.0 l) Om))
2.0ms
(cbrt (/ (* 2.0 l) Om))

series731.0ms

Counts
4 → 12
Calls
4 calls:
453.0ms
(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))))))
92.0ms
(cbrt (/ (* 2.0 l) Om))
93.0ms
(cbrt (/ (* 2.0 l) Om))
92.0ms
(cbrt (/ (* 2.0 l) Om))

simplify152.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0200866
1610818
23836811
35001811

prune660.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.8b

localize50.0ms

Local error

Found 4 expressions with local error:

4.2b
(cbrt (/ l (cbrt Om)))
8.0b
(sqrt (+ 1.0 (* (pow (* (* (cbrt (/ 2.0 (* (cbrt Om) (cbrt Om)))) (cbrt (/ l (cbrt 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))))))
12.6b
(cbrt (/ (* 2.0 l) Om))
12.6b
(cbrt (/ (* 2.0 l) Om))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
45×cbrt-prod
24×times-frac
23×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
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 → 86
Calls
4 calls:
2.0ms
(cbrt (/ l (cbrt Om)))
3.0ms
(sqrt (+ 1.0 (* (pow (* (* (cbrt (/ 2.0 (* (cbrt Om) (cbrt Om)))) (cbrt (/ l (cbrt 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))))))
2.0ms
(cbrt (/ (* 2.0 l) Om))
2.0ms
(cbrt (/ (* 2.0 l) Om))

series897.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(cbrt (/ l (cbrt Om)))
426.0ms
(sqrt (+ 1.0 (* (pow (* (* (cbrt (/ 2.0 (* (cbrt Om) (cbrt Om)))) (cbrt (/ l (cbrt 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))))))
218.0ms
(cbrt (/ (* 2.0 l) Om))
96.0ms
(cbrt (/ (* 2.0 l) Om))

simplify47.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04161205
114631152
250021141

prune928.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.8b

regimes572.0ms

Accuracy

0% (0.1b remaining)

Error of 1.6b against oracle of 1.5b and baseline of 1.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04434
14434

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.4s8000×body80valid