Details

sample117.0ms

Algorithm

intervals

Results

63.0ms	81×	body	1280	valid
22.0ms	55×	body	640	valid
8.0ms	30×	body	320	valid
7.0ms	77×	body	80	valid
2.0ms	13×	body	160	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	10
1	35	10
2	63	10
3	137	10
4	417	10
5	1798	10
6	5002	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b	(pow (sin kx) 2.0)
0.2b	(pow (sin ky) 2.0)
4.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
16×	`unpow-prod-down`
10×	`distribute-lft-out`
8×	`add-exp-log` `associate-/r*`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

25.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.0ms	(pow (sin kx) 2.0)
1.0ms	(pow (sin ky) 2.0)
16.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
105.0ms	(pow (sin kx) 2.0)
107.0ms	(pow (sin ky) 2.0)
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify38.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	329	1021
1	1106	946
2	5002	943

prune419.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin kx) 2.0)
0.2b	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
0.2b	(pow (sin ky) 2.0)
4.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
150×	`*-un-lft-identity`
99×	`add-sqr-sqrt`
98×	`add-cube-cbrt`
65×	`sqrt-prod`
32×	`unpow-prod-down`
28×	`associate-/r*`
26×	`distribute-lft-out`
17×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
7×	`div-exp`
6×	`pow-unpow`
5×	`div-inv`
4×	`add-log-exp`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow-to-exp` `rec-exp` `pow-pow` `sqrt-div` `1-exp` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `clear-num` `associate-/r/` `flip-+` `inv-pow`

Counts

4 → 187

Calls

4 calls:

1.0ms	(pow (sin kx) 2.0)
24.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
4.0ms	(pow (sin ky) 2.0)
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(pow (sin kx) 2.0)
121.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
107.0ms	(pow (sin ky) 2.0)
82.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify72.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	642	2588
1	2882	2325
2	5003	2177

prune491.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 10.8b

localize23.0ms

Local error

Found 4 expressions with local error:

4.8b	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
17.2b	(cbrt (pow (sin kx) 2.0))
17.2b	(cbrt (pow (sin kx) 2.0))
17.2b	(cbrt (pow (sin kx) 2.0))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqrt-prod` `sqr-pow`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 60

Calls

4 calls:

44.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
1.0ms	(cbrt (pow (sin kx) 2.0))
1.0ms	(cbrt (pow (sin kx) 2.0))
1.0ms	(cbrt (pow (sin kx) 2.0))

series695.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
203.0ms	(cbrt (pow (sin kx) 2.0))
202.0ms	(cbrt (pow (sin kx) 2.0))
208.0ms	(cbrt (pow (sin kx) 2.0))

simplify59.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	204	682
1	478	640
2	1705	640
3	5001	634

prune406.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 10.8b

localize26.0ms

Local error

Found 4 expressions with local error:

17.2b	(cbrt (pow (sin kx) 2.0))
17.2b	(cbrt (pow (sin kx) 2.0))
17.2b	(cbrt (pow (sin kx) 2.0))
17.2b	(cbrt (pow (sin kx) 2.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp` `sqr-pow`

Counts

4 → 60

Calls

4 calls:

1.0ms	(cbrt (pow (sin kx) 2.0))
1.0ms	(cbrt (pow (sin kx) 2.0))
1.0ms	(cbrt (pow (sin kx) 2.0))
1.0ms	(cbrt (pow (sin kx) 2.0))

series809.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(cbrt (pow (sin kx) 2.0))
200.0ms	(cbrt (pow (sin kx) 2.0))
210.0ms	(cbrt (pow (sin kx) 2.0))
197.0ms	(cbrt (pow (sin kx) 2.0))

simplify105.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (13.0ms)

Iter	Nodes	Cost
0	91	444
1	174	416
2	407	408
3	1110	400
4	3922	400
5	5002	400

prune396.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 10.8b

regimes1.0s

Accuracy

69.9% (0.4b remaining)

Error of 11.6b against oracle of 11.2b and baseline of 12.6b

bsearch4.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	32
1	37	32

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.1s	2769×	body	1280	valid
874.0ms	1737×	body	640	valid
247.0ms	799×	body	320	valid
209.0ms	2326×	body	80	valid
67.0ms	369×	body	160	valid