Details

sample3.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 71.777344%

Results

140.0ms	125×	body	1280	valid
45.0ms	68×	body	640	valid
8.0ms	18×	body	320	valid
5.0ms	39×	body	80	valid
2.0ms	6×	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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 3.6b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite25.0ms

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:

10.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.0ms	(pow (sin kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series92.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
18.0ms	(pow (sin kx) 2.0)
21.0ms	(pow (sin ky) 2.0)
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	363	1053
1	1249	978
2	5002	961

prune248.0ms

Filtered

70 candidates to 112 candidates (-60.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	100	12	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	12	113

Merged error: 2.8b

Counts

113 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite36.0ms

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:

14.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
2.0ms	(pow (sin kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series89.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
17.0ms	(pow (sin kx) 2.0)
18.0ms	(pow (sin ky) 2.0)
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify75.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	675	2618
1	3016	2355
2	5002	2204

prune247.0ms

Filtered

80 candidates to 199 candidates (-148.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	198	1	199
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	199	12	211

Merged error: 2.8b

Counts

211 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.5b	(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

100×	`sqrt-prod`
52×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
34×	`sqrt-pow1`
30×	`pow1`
28×	`sqrt-div`
20×	`add-cube-cbrt`
19×	`swap-sqr`
18×	`pow1/2`
15×	`unpow-prod-down`
14×	`distribute-lft-out`
11×	`associate-r` `associate-l`
9×	`pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `add-log-exp`
3×	`pow-unpow`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`pow2` `pow-to-exp` `pow-pow` `pow-plus` `sqrt-unprod` `pow-exp` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 142

Calls

4 calls:

2.0ms	(pow (sin ky) 2.0)
22.0ms	(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (sin ky) 2.0)
21.0ms	(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	330	1472
1	1266	1371
2	5002	1333

prune287.0ms

Filtered

71 candidates to 154 candidates (-116.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	155	11	166

Merged error: 2.7b

Counts

166 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
1.2b	(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.4b	(exp (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
16×	`log-prod`
15×	`sqrt-prod`
13×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
10×	`pow1`
9×	`unpow-prod-down`
8×	`exp-sum`
6×	`add-exp-log` `exp-prod` `sqrt-div` `log-pow` `distribute-lft-out`
4×	`log-div` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`exp-diff`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `rem-log-exp` `pow-exp` `rem-exp-log` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

2.0ms	(pow (sin ky) 2.0)
7.0ms	(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
9.0ms	(exp (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
9.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (sin ky) 2.0)
23.0ms	(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
18.0ms	(exp (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify84.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	268	791
1	771	745
2	2592	714
3	5001	708

prune158.0ms

Filtered

57 candidates to 91 candidates (-59.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	89	13	102

Merged error: 2.7b

Counts

102 → 13

regimes873.0ms

Accuracy

0% (1.3b remaining)

Error of 4.0b against oracle of 2.6b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	11
1	19	11

end0.0ms

sample10.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 71.777344%

Results

4.3s	3696×	body	1280	valid
1.4s	2076×	body	640	valid
327.0ms	713×	body	320	valid
174.0ms	1241×	body	80	valid
84.0ms	274×	body	160	valid

Details

sample3.9s

simplify51.0ms

prune4.0ms

localize15.0ms

rewrite25.0ms

series92.0ms

simplify41.0ms

prune248.0ms

localize16.0ms

rewrite36.0ms

series89.0ms

simplify75.0ms

prune247.0ms

localize18.0ms

rewrite46.0ms

series75.0ms

simplify56.0ms

prune287.0ms

localize20.0ms

rewrite29.0ms

series80.0ms

simplify84.0ms

prune158.0ms

regimes873.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample10.3s

Profiling