Details

sample209.0ms

Algorithm

intervals

Results

139.0ms	130×	body	1280	valid
38.0ms	57×	body	640	valid
8.0ms	19×	body	320	valid
4.0ms	38×	body	80	valid
3.0ms	12×	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

prune14.0ms

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: 3.9b

Counts

2 → 2

localize19.0ms

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))
0.3b	(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)))

rewrite31.0ms

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:

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

series103.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify77.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5228	1477

prune254.0ms

Filtered

77 candidates to 113 candidates (-46.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	103	10	113
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	105	10	115

Merged error: 2.4b

Counts

115 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2)
0.3b	(* (sin ky) (* (sin th) (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))))
0.3b	(/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))
3.6b	(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
32×	`times-frac`
30×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
21×	`sqrt-prod`
17×	`unpow-prod-down`
14×	`add-exp-log` `distribute-lft-out`
13×	`pow1`
11×	`add-cbrt-cube`
5×	`associate-/r*`
4×	`associate-/r/` `add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`pow-flip` `flip3-+` `sqrt-div` `associate-*r/` `div-exp` `flip-+` `div-inv` `inv-pow`
1×	`cbrt-undiv` `pow-to-exp` `rec-exp` `pow-pow` `frac-2neg` `pow1/2` `1-exp` `associate-r` `pow-exp` `clear-num` `*-commutative` `unpow2` `sqr-pow`

Counts

4 → 114

Calls

4 calls:

2.0ms	(pow (sin kx) 2)
18.0ms	(* (sin ky) (* (sin th) (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))))
10.0ms	(/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))
10.0ms	(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))

series96.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (sin kx) 2)
46.0ms	(* (sin ky) (* (sin th) (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))))
19.0ms	(/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))
27.0ms	(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))

simplify47.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5040	1691

prune207.0ms

Filtered

70 candidates to 126 candidates (-80.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	126	10	136

Merged error: 2.4b

Counts

136 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2.0)
0.5b	(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (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)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

100×	`sqrt-prod`
52×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
34×	`sqrt-pow1`
30×	`pow1`
28×	`sqrt-div`
20×	`add-cube-cbrt`
19×	`swap-sqr`
18×	`pow1/2`
15×	`unpow-prod-down`
14×	`distribute-lft-out`
11×	`associate-r` `associate-l`
9×	`pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `add-log-exp`
3×	`pow-unpow`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`pow2` `pow-to-exp` `pow-pow` `pow-plus` `sqrt-unprod` `pow-exp` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 142

Calls

4 calls:

3.0ms	(pow (sin kx) 2.0)
23.0ms	(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (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)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify88.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4935	2018
1	4935	2018

prune271.0ms

Filtered

74 candidates to 154 candidates (-108.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	154	10	164

Merged error: 2.4b

Counts

164 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

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

series109.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(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)))
21.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
18.0ms	(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

prune324.0ms

Filtered

68 candidates to 102 candidates (-50.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	101	11	112

Merged error: 2.4b

Counts

112 → 11

regimes893.0ms

Accuracy

56.7% (0.8b remaining)

Error of 3.5b against oracle of 2.7b and baseline of 4.5b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	55
1	48	55

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.9s	3709×	body	1280	valid
1.3s	1984×	body	640	valid
311.0ms	710×	body	320	valid
157.0ms	1316×	body	80	valid
76.0ms	281×	body	160	valid

Details

sample209.0ms

simplify60.0ms

prune14.0ms

localize19.0ms

rewrite31.0ms

series103.0ms

simplify77.0ms

prune254.0ms

localize16.0ms

rewrite43.0ms

series96.0ms

simplify47.0ms

prune207.0ms

localize18.0ms

rewrite45.0ms

series76.0ms

simplify88.0ms

prune271.0ms

localize24.0ms

rewrite35.0ms

series109.0ms

simplify68.0ms

prune324.0ms

regimes893.0ms

bsearch2.0ms

simplify1.0ms

end0.0ms

sample6.3s

Profiling