Details

sample4.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 70.898438%

Results

126.0ms	122×	body	1280	valid
45.0ms	65×	body	640	valid
8.0ms	19×	body	320	valid
4.0ms	37×	body	80	valid
3.0ms	13×	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

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: 4.2b

Counts

2 → 1

localize20.0ms

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)
3.8b	(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:

33.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
21.0ms	(pow (sin kx) 2.0)
19.0ms	(pow (sin ky) 2.0)
18.0ms	(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

prune244.0ms

Filtered

70 candidates to 112 candidates (-60.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	102	10	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	10	113

Merged error: 3.0b

Counts

113 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky))) (sin th))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

166×	`times-frac`
127×	`*-un-lft-identity`
106×	`add-sqr-sqrt`
89×	`associate-l`
84×	`add-cube-cbrt`
52×	`sqrt-prod`
26×	`unpow-prod-down`
25×	`add-exp-log`
20×	`distribute-lft-out`
13×	`add-cbrt-cube`
9×	`pow1`
7×	`div-exp` `prod-exp` `unswap-sqr`
6×	`pow-unpow`
4×	`div-inv` `add-log-exp`
3×	`cbrt-undiv` `associate-r` `cbrt-unprod`
2×	`pow-to-exp` `rec-exp` `pow-pow` `sqrt-div` `1-exp` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `flip-+`

Counts

4 → 170

Calls

4 calls:

25.0ms	(* (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky))) (sin th))
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)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky))) (sin th))
18.0ms	(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)))

simplify76.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	685	1984
1	3093	1819
2	5001	1762

prune402.0ms

Filtered

127 candidates to 182 candidates (-43.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	178	4	182
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	180	12	192

Merged error: 2.9b

Counts

192 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin th) (/ (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)
3.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite34.0ms

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`
11×	`add-exp-log`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`pow-unpow`
5×	`div-inv`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`pow-to-exp` `pow-pow` `sqrt-div` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `clear-num` `associate-/r/` `flip-+`

Counts

4 → 181

Calls

4 calls:

14.0ms	(/ (sin th) (/ (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)))

series101.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (sin th) (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
18.0ms	(pow (sin kx) 2.0)
17.0ms	(pow (sin ky) 2.0)
21.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify83.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	721	2809
1	3041	2660
2	5002	2660

prune335.0ms

Filtered

111 candidates to 193 candidates (-73.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	193	12	205

Merged error: 2.9b

Counts

205 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(pow (sin ky) 2.0)
0.3b	(* (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin ky))
3.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
50×	`times-frac`
49×	`add-sqr-sqrt`
41×	`sqrt-prod`
40×	`add-cube-cbrt`
30×	`associate-l`
19×	`unpow-prod-down`
16×	`distribute-lft-out`
12×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1` `associate-/r*`
6×	`sqrt-div`
4×	`associate-/r/` `add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-r` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `pow-exp` `clear-num` `-commutative` `sqr-pow`

Counts

4 → 133

Calls

4 calls:

10.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.0ms	(pow (sin ky) 2.0)
15.0ms	(* (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin ky))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series124.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
17.0ms	(pow (sin ky) 2.0)
48.0ms	(* (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin ky))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	412	1628
1	1645	1500
2	5002	1489

prune232.0ms

Filtered

94 candidates to 145 candidates (-54.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	145	12	157

Merged error: 2.9b

Counts

157 → 12

regimes836.0ms

Accuracy

0% (1.4b 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	14	10
1	14	10

end0.0ms

sample10.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 70.898438%

Results

4.3s	3805×	body	1280	valid
1.3s	2009×	body	640	valid
296.0ms	685×	body	320	valid
155.0ms	1217×	body	80	valid
79.0ms	284×	body	160	valid

Details

sample4.2s

simplify50.0ms

prune4.0ms

localize20.0ms

rewrite25.0ms

series92.0ms

simplify41.0ms

prune244.0ms

localize17.0ms

rewrite48.0ms

series100.0ms

simplify76.0ms

prune402.0ms

localize15.0ms

rewrite34.0ms

series101.0ms

simplify83.0ms

prune335.0ms

localize15.0ms

rewrite38.0ms

series124.0ms

simplify53.0ms

prune232.0ms

regimes836.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample10.5s

Profiling