Details

analyze636.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
49.9%	49.9%	0.2%	3
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
74.9%	25%	0.2%	7
74.9%	25%	0.2%	8
74.9%	25%	0.2%	9
74.9%	25%	0.2%	10
87.3%	12.5%	0.2%	11
87.3%	12.5%	0.2%	12
87.3%	12.5%	0.2%	13
87.3%	12.5%	0.2%	14

sample101.0ms

Algorithm

intervals

Results

36.0ms	195×	body	80	valid
24.0ms	27×	body	640	valid
19.0ms	15×	body	1280	valid
5.0ms	8×	body	320	valid
5.0ms	11×	body	160	valid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5326	39

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 1.3b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.2b	(pow.f64 (sin.f64 ky) 2)
2.9b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
11.3b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
17×	`*-un-lft-identity_binary64`
16×	`unpow-prod-down_binary64`
13×	`add-cube-cbrt_binary64`
12×	`associate-l_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64` `add-cbrt-cube_binary64` `prod-exp_binary64`
5×	`associate-r_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64` `unpow2_binary64` `sqr-pow_binary64` `unswap-sqr_binary64`
3×	`pow-to-exp_binary64` `times-frac_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `pow-pow_binary64` `div-exp_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `*-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)
15.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series609.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow.f64 (sin.f64 kx) 2)
17.0ms	(pow.f64 (sin.f64 ky) 2)
185.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
389.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5002	2191

prune118.0ms

Filtered

66 candidates to 102 candidates (-54.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	2	103

Merged error: 1.0b

Counts

103 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
3.8b	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
11.3b	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-exp-log_binary64`
67×	`add-cbrt-cube_binary64`
32×	`cbrt-unprod_binary64` `prod-exp_binary64`
16×	`*-un-lft-identity_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`associate-l_binary64`
13×	`pow1_binary64`
12×	`add-cube-cbrt_binary64`
11×	`associate-*r/_binary64` `frac-times_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`associate-r_binary64` `times-frac_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unpow-prod-down_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-*l/_binary64`
3×	`pow-unpow_binary64` `sqrt-prod_binary64`
2×	`distribute-lft-out_binary64` `div-inv_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `pow-exp_binary64`

Counts

4 → 125

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 ky) 2)
23.0ms	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
15.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))

series779.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow.f64 (sin.f64 ky) 2)
186.0ms	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
198.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
378.0ms	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))

simplify99.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4996	3724
1	4996	3724

prune138.0ms

Filtered

79 candidates to 137 candidates (-73.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	137	2	139

Merged error: 1.0b

Counts

139 → 2

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify11.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	1	1
Total	2	2

Merged error: 1.0b

Counts

2 → 2

regimes103.0ms

Accuracy

0% (0.1b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	45
1	30	45

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	6208×	body	80	valid
687.0ms	568×	body	1280	valid
544.0ms	634×	body	640	valid
235.0ms	379×	body	320	valid
82.0ms	211×	body	160	valid

Details

analyze636.0ms

sample101.0ms

simplify63.0ms

prune5.0ms

localize21.0ms

rewrite27.0ms

series609.0ms

simplify56.0ms

prune118.0ms

localize20.0ms

rewrite50.0ms

series779.0ms

simplify99.0ms

prune138.0ms

localize4.0ms

rewrite0.0ms

series0.0ms

simplify11.0ms

prune1.0ms

regimes103.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample2.9s

Profiling