Details

sample4.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 70.898438%

Results

135.0ms	124×	body	1280	valid
41.0ms	55×	body	640	valid
13.0ms	28×	body	320	valid
5.0ms	41×	body	80	valid
2.0ms	8×	body	160	valid

simplify50.0ms

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

prune5.0ms

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: 3.9b

Counts

2 → 1

localize21.0ms

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 ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.6b	(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 ky) 2.0)
2.0ms	(pow (sin kx) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series95.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
22.0ms	(pow (sin ky) 2.0)
19.0ms	(pow (sin kx) 2.0)
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	363	1053
1	1249	978
2	5001	961

prune249.0ms

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: 2.4b

Counts

113 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
0.3b	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
30×	`associate-r`
28×	`times-frac`
25×	`add-cube-cbrt`
22×	`sqrt-prod`
15×	`add-exp-log`
14×	`unpow-prod-down`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
5×	`unswap-sqr`
4×	`sqrt-div` `prod-exp` `add-log-exp`
3×	`associate-l`
2×	`pow-to-exp` `pow-pow` `flip3-+` `div-exp` `pow-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 106

Calls

4 calls:

2.0ms	(pow (sin ky) 2.0)
2.0ms	(pow (sin kx) 2.0)
16.0ms	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (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:

17.0ms	(pow (sin ky) 2.0)
18.0ms	(pow (sin kx) 2.0)
36.0ms	(* (sin ky) (/ 1 (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

118 → 118

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	482	963
1	2275	882
2	5002	841

prune234.0ms

Filtered

70 candidates to 118 candidates (-68.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	117	13	130

Merged error: 2.4b

Counts

130 → 13

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
3.6b	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

2.0ms	(cbrt (sin kx))
2.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))
8.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(cbrt (sin kx))
17.0ms	(cbrt (sin kx))
17.0ms	(cbrt (sin kx))
19.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify88.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	189	553
1	571	525
2	2518	507
3	5002	503

prune167.0ms

Filtered

46 candidates to 60 candidates (-30.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	60	13	73

Merged error: 2.4b

Counts

73 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2.0)
0.4b	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

62×	`sqrt-prod`
56×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
33×	`times-frac`
32×	`add-cube-cbrt`
15×	`unpow-prod-down`
12×	`distribute-lft-out`
11×	`associate-/r*`
8×	`sqrt-div`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow` `flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `div-exp` `pow-exp` `clear-num` `div-inv` `sqr-pow`

Counts

4 → 112

Calls

4 calls:

2.0ms	(pow (sin kx) 2.0)
11.0ms	(/ (sin ky) (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)))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (sin kx) 2.0)
42.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
22.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	374	1454
1	1252	1344
2	5001	1333

prune284.0ms

Filtered

75 candidates to 124 candidates (-65.3%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	2	8	10
Picked	0	1	1
Done	0	2	2
Total	125	12	137

Merged error: 2.4b

Counts

137 → 12

regimes889.0ms

Accuracy

70.3% (0.4b remaining)

Error of 2.9b against oracle of 2.5b and baseline of 4.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	30
1	42	30

end0.0ms

sample10.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 70.898438%

Results

4.2s	3757×	body	1280	valid
1.4s	1998×	body	640	valid
365.0ms	736×	body	320	valid
172.0ms	1222×	body	80	valid
88.0ms	287×	body	160	valid

Details

sample4.3s

simplify50.0ms

prune5.0ms

localize21.0ms

rewrite25.0ms

series95.0ms

simplify43.0ms

prune249.0ms

localize17.0ms

rewrite31.0ms

series89.0ms

simplify56.0ms

prune234.0ms

localize24.0ms

rewrite14.0ms

series73.0ms

simplify88.0ms

prune167.0ms

localize21.0ms

rewrite31.0ms

series100.0ms

simplify47.0ms

prune284.0ms

regimes889.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample10.7s

Profiling