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

sample211.0ms

Algorithm

intervals

Results

144.0ms	126×	body	1280	valid
38.0ms	57×	body	640	valid
6.0ms	14×	body	320	valid
6.0ms	48×	body	80	valid
3.0ms	11×	body	160	valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4766	16
1	4766	16

prune15.0ms

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: 3.7b

Counts

2 → 2

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)))) (sin th))
0.2b	(pow (sin kx) 2.0)
0.2b	(pow (sin ky) 2.0)
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

15.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
2.0ms	(pow (sin kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
155.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series108.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
18.0ms	(pow (sin kx) 2.0)
20.0ms	(pow (sin ky) 2.0)
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify79.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5228	1477

prune288.0ms

Filtered

77 candidates to 113 candidates (-46.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	100	13	113
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	102	13	115

Merged error: 2.2b

Counts

115 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
30×	`cbrt-prod` `sqrt-prod`
25×	`add-sqr-sqrt`
24×	`times-frac`
22×	`add-cube-cbrt`
12×	`unpow-prod-down` `distribute-lft-out`
8×	`sqrt-div`
7×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 90

Calls

4 calls:

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

series110.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5542	1796

prune420.0ms

Filtered

68 candidates to 102 candidates (-50.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	102	13	115

Merged error: 2.2b

Counts

115 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2.0)
0.3b	(* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.0b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.0b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt`
11×	`associate-r`
10×	`sqrt-prod`
9×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
6×	`cbrt-div` `add-cbrt-cube` `distribute-lft-out`
4×	`add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-l` `flip-+` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`pow-to-exp` `pow-pow` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

3.0ms	(pow (sin ky) 2.0)
13.0ms	(* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
10.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series118.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin ky) 2.0)
41.0ms	(* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
27.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
31.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify79.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4891	1498
1	4891	1498

prune314.0ms

Filtered

62 candidates to 89 candidates (-43.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	89	13	102

Merged error: 2.2b

Counts

102 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin ky))
0.6b	(cbrt (sin ky))
0.6b	(cbrt (sin ky))
3.5b	(sqrt (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))

rewrite13.0ms

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

series73.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt (sin ky))
18.0ms	(cbrt (sin ky))
18.0ms	(cbrt (sin ky))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))

simplify70.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4876	603
1	4876	603

prune113.0ms

Filtered

44 candidates to 60 candidates (-36.4%)

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: 2.2b

Counts

73 → 13

regimes1.2s

Accuracy

53.6% (0.9b remaining)

Error of 3.3b against oracle of 2.4b and baseline of 4.3b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	84
1	41	84

end0.0ms

sample6.3s

Algorithm

intervals

Results

4.0s	3692×	body	1280	valid
1.4s	2071×	body	640	valid
319.0ms	693×	body	320	valid
168.0ms	1256×	body	80	valid
82.0ms	288×	body	160	valid

Details

analyze1.3s

sample211.0ms

simplify61.0ms

prune15.0ms

localize16.0ms

rewrite179.0ms

series108.0ms

simplify79.0ms

prune288.0ms

localize23.0ms

rewrite38.0ms

series110.0ms

simplify68.0ms

prune420.0ms

localize21.0ms

rewrite36.0ms

series118.0ms

simplify79.0ms

prune314.0ms

localize21.0ms

rewrite13.0ms

series73.0ms

simplify70.0ms

prune113.0ms

regimes1.2s

bsearch2.0ms

simplify1.0ms

end0.0ms

sample6.3s

Profiling