Details

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

sample198.0ms

Algorithm

intervals

Results

120.0ms	111×	body	1280	valid
44.0ms	70×	body	640	valid
12.0ms	29×	body	320	valid
5.0ms	37×	body	80	valid
3.0ms	9×	body	160	valid

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4866	16
1	4866	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: 3.2b

Counts

2 → 2

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))))
0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.0b	(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:

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)))

series93.0ms

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

simplify81.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4909	1511
1	4909	1511

prune415.0ms

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: 2.2b

Counts

114 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(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)
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`associate-r`
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-l` `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` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

2.0ms	(pow (sin ky) 2.0)
16.0ms	(* (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)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin ky) 2.0)
46.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
17.0ms	(pow (sin kx) 2.0)
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify60.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4964	1383
1	4964	1383

prune248.0ms

Filtered

71 candidates to 113 candidates (-59.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	112	12	124

Merged error: 2.2b

Counts

124 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(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)))))
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite32.0ms

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)
17.0ms	(* (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)))

series90.0ms

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)))))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4955	1340
1	4955	1340

prune240.0ms

Filtered

71 candidates to 118 candidates (-66.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	118	12	130

Merged error: 2.2b

Counts

130 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.6b	(cbrt (* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
4.6b	(cbrt (* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
4.6b	(cbrt (* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `associate-*r/`
2×	`unpow-prod-down` `sqrt-div` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 47

Calls

4 calls:

7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
12.0ms	(cbrt (* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
12.0ms	(cbrt (* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
12.0ms	(cbrt (* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

series249.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
76.0ms	(cbrt (* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
76.0ms	(cbrt (* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
78.0ms	(cbrt (* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

simplify48.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5039	1016

prune230.0ms

Filtered

47 candidates to 59 candidates (-25.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	0	9	9
Picked	1	0	1
Done	0	2	2
Total	58	13	71

Merged error: 2.2b

Counts

71 → 13

regimes783.0ms

Accuracy

0% (1.3b remaining)

Error of 3.8b against oracle of 2.5b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	16
1	47	16

end0.0ms

sample6.3s

Algorithm

intervals

Results

4.0s	3662×	body	1280	valid
1.5s	2151×	body	640	valid
313.0ms	685×	body	320	valid
172.0ms	1219×	body	80	valid
81.0ms	283×	body	160	valid

Details

analyze1.2s

sample198.0ms

simplify56.0ms

prune15.0ms

localize15.0ms

rewrite25.0ms

series93.0ms

simplify81.0ms

prune415.0ms

localize17.0ms

rewrite32.0ms

series100.0ms

simplify60.0ms

prune248.0ms

localize16.0ms

rewrite32.0ms

series90.0ms

simplify67.0ms

prune240.0ms

localize25.0ms

rewrite44.0ms

series249.0ms

simplify48.0ms

prune230.0ms

regimes783.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.3s

Profiling