Details

analyze1.3s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
25%	74.9%	0.1%	8
54.6%	45.2%	0.1%	9
56.2%	43.7%	0.1%	10
62.4%	37.4%	0.1%	11
65.9%	33.9%	0.1%	12
66.3%	33.5%	0.1%	13
69%	30.8%	0.1%	14

sample201.0ms

Algorithm

intervals

Results

131.0ms	123×	body	1280	valid
39.0ms	62×	body	640	valid
10.0ms	23×	body	320	valid
5.0ms	41×	body	80	valid
2.0ms	7×	body	160	valid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4766	16
1	4766	16

prune18.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 3.2b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite26.0ms

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:

11.0ms	(/ (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)))

series96.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
22.0ms	(pow (sin ky) 2.0)
20.0ms	(pow (sin kx) 2.0)
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5107	1507

prune238.0ms

Filtered

70 candidates to 112 candidates (-60.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	102	10	112
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	103	11	114

Merged error: 2.8b

Counts

114 → 11

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))))
0.3b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b	(pow (sin kx) 2.0)
3.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite43.0ms

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-r`
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-l` `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` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `sqr-pow`

Counts

4 → 133

Calls

4 calls:

11.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
18.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (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)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
44.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
21.0ms	(pow (sin kx) 2.0)
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify78.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4936	2217
1	4936	2217

prune277.0ms

Filtered

87 candidates to 145 candidates (-66.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	140	5	145
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	143	13	156

Merged error: 2.8b

Counts

156 → 13

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)))
0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.1b	(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 ky) 2.0)
3.0ms	(pow (sin kx) 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	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
18.0ms	(pow (sin ky) 2.0)
21.0ms	(pow (sin kx) 2.0)
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify75.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4949	3593
1	4949	3593

prune302.0ms

Filtered

94 candidates to 199 candidates (-111.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	198	1	199
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	199	13	212

Merged error: 2.8b

Counts

212 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2)
0.2b	(* (sin ky) (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))))
0.3b	(pow (sin kx) 2)
3.2b	(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
45×	`sqrt-prod`
41×	`add-sqr-sqrt`
34×	`times-frac`
28×	`add-cube-cbrt`
24×	`associate-r`
18×	`unpow-prod-down`
12×	`distribute-lft-out`
10×	`pow1`
8×	`add-exp-log`
6×	`pow-unpow` `add-cbrt-cube`
4×	`associate-/r/` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `associate-l`
2×	`pow-to-exp` `pow-pow` `flip3-+` `sqrt-div` `pow-exp` `flip-+` `div-inv` `unpow2` `sqr-pow`
1×	`pow-flip` `pow1/2` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `inv-pow`

Counts

4 → 115

Calls

4 calls:

3.0ms	(pow (sin ky) 2)
18.0ms	(* (sin ky) (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))))
3.0ms	(pow (sin kx) 2)
10.0ms	(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))

series72.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (sin ky) 2)
34.0ms	(* (sin ky) (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))))
3.0ms	(pow (sin kx) 2)
31.0ms	(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))

simplify58.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4943	1483
1	4943	1483

prune177.0ms

Filtered

73 candidates to 127 candidates (-74.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	9	10
Picked	1	0	1
Done	0	2	2
Total	128	12	140

Merged error: 2.8b

Counts

140 → 12

regimes859.0ms

Accuracy

0% (1.3b remaining)

Error of 3.7b against oracle of 2.4b and baseline of 3.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	16
1	15	16

end0.0ms

analyze1.2s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
25%	74.9%	0.1%	8
54.6%	45.2%	0.1%	9
56.2%	43.7%	0.1%	10
62.4%	37.4%	0.1%	11
65.9%	33.9%	0.1%	12
66.3%	33.5%	0.1%	13
69%	30.8%	0.1%	14

sample6.2s

Algorithm

intervals

Results

4.0s	3738×	body	1280	valid
1.3s	1960×	body	640	valid
336.0ms	718×	body	320	valid
166.0ms	1269×	body	80	valid
93.0ms	315×	body	160	valid

Details

analyze1.3s

sample201.0ms

simplify60.0ms

prune18.0ms

localize16.0ms

rewrite26.0ms

series96.0ms

simplify47.0ms

prune238.0ms

localize15.0ms

rewrite43.0ms

series127.0ms

simplify78.0ms

prune277.0ms

localize17.0ms

rewrite36.0ms

series92.0ms

simplify75.0ms

prune302.0ms

localize16.0ms

rewrite37.0ms

series72.0ms

simplify58.0ms

prune177.0ms

regimes859.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.2s

sample6.2s

Profiling