Details

analyze809.0ms (8.5%)

Algorithm

1×

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

Compiler

Compiled 34 to 30 computations (11.8% saved)

sample3.9s (40.6%)

Symmetry

(sort kx ky)

Results

2.0s	6563×	body	128	valid
1.0s	776×	body	1024	valid
548.0ms	613×	body	512	valid
194.0ms	304×	body	256	valid

Compiler

Compiled 101 to 89 computations (11.9% saved)

simplify56.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
575×	`associate-l_binary64`
512×	`unswap-sqr_binary64`
437×	`associate-r_binary64`
369×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	42
1	56	37
2	113	37
3	465	37
4	2149	37
5	4982	37
6	4847	37
7	4964	37

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

1.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))

Compiler

Compiled 113 to 95 computations (15.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (sin.f64 kx) 2)
✓	0.5b	(/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))
✓	2.4b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	9.4b	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))

series1.1s (11.5%)

Counts

4 → 148

Calls

4 calls:

779.0ms	(/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))
202.0ms	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))
112.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
3.0ms	(pow.f64 (sin.f64 kx) 2)

rewrite80.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

662×	`prod-diff_binary64`
189×	`add-sqr-sqrt_binary64`
183×	`log1p-expm1-u_binary64`
183×	`expm1-log1p-u_binary64`
178×	`add-log-exp_binary64`

Counts

4 → 93

Calls

4 calls:

78.0ms	(pow.f64 (sin.f64 kx) 2)
78.0ms	(/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))
78.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
78.0ms	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	94
1	398	85
2	4552	85
3	5667	85
0	0	0
1	0	0

simplify181.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

424×	`fma-neg_binary64`
336×	`fma-def_binary64`
267×	`*-commutative_binary64`
261×	`associate-r_binary64`
192×	`associate-*r/_binary64`

Counts

241 → 221

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	373	11132
1	1211	10267
2	4613	10261
3	4978	10261

prune352.0ms (3.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	219	2	221
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	219	3	222

Error

0.0b

Counts

222 → 3

Alt Table

Status	Error	Program
	27.6b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 1/2 (.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 l l) 4) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) Om)))))
✓	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
▶	24.2b	(sqrt.f64 (+.f64 1/2 1/2))

Compiler

Compiled 12248 to 8589 computations (29.9% saved)

localize2.0ms (0%)

prune3.0ms (0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	1	1
Total	3	3

Error

0.0b

Counts

3 → 3

Alt Table

Status	Error	Program
▶	27.6b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 1/2 (.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 l l) 4) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) Om)))))
✓	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
✓	24.2b	(sqrt.f64 (+.f64 1/2 1/2))

Compiler

Compiled 130 to 100 computations (23.1% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.8b	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
✓	3.8b	(.f64 (.f64 (*.f64 l l) 4) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
✓	26.6b	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
✓	26.6b	(sqrt.f64 (.f64 (.f64 (*.f64 l l) 4) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

series404.0ms (4.2%)

Counts

4 → 144

Calls

4 calls:

213.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
80.0ms	(sqrt.f64 (.f64 (.f64 (*.f64 l l) 4) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
65.0ms	(.f64 (.f64 (*.f64 l l) 4) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
45.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite93.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

563×	`prod-diff_binary64`
192×	`add-sqr-sqrt_binary64`
190×	`log1p-expm1-u_binary64`
190×	`expm1-log1p-u_binary64`
186×	`add-log-exp_binary64`

Counts

4 → 120

Calls

4 calls:

91.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
91.0ms	(.f64 (.f64 (*.f64 l l) 4) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
91.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
91.0ms	(sqrt.f64 (.f64 (.f64 (*.f64 l l) 4) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	93
1	415	59
2	4700	59
3	5766	59
0	0	0
1	0	0

simplify107.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

751×	`associate-/l*_binary64`
378×	`cancel-sign-sub-inv_binary64`
355×	`fma-neg_binary64`
181×	`fma-def_binary64`
159×	`associate-/r/_binary64`

Counts

264 → 196

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	190	3900
1	619	3576
2	2288	3487
3	4939	3485
4	5066	3485

prune247.0ms (2.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	196	3	199

Error

0.0b

Counts

199 → 3

Alt Table

Status	Error	Program
✓	27.6b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 1/2 (.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 l l) 4) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) Om)))))
✓	1.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
✓	24.2b	(sqrt.f64 (+.f64 1/2 1/2))

Compiler

Compiled 9709 to 6034 computations (37.9% saved)

regimes2.1s (22%)

Accuracy

Total 0.7b remaining (63.2%)

Threshold costs 0.7b (63.2%)

Counts

82 → 1

Compiler

Compiled 64314 to 49301 computations (23.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	34
1	25	34
2	24	34

end97.0ms (1%)

Remove: (sort kx ky)
Compiler: Compiled 187 to 154 computations (17.6% saved)

Details

analyze809.0ms (8.5%)

sample3.9s (40.6%)

simplify56.0ms (0.6%)

prune4.0ms (0%)

localize17.0ms (0.2%)

series1.1s (11.5%)

rewrite80.0ms (0.8%)

simplify181.0ms (1.9%)

prune352.0ms (3.7%)

localize2.0ms (0%)

prune3.0ms (0%)

localize24.0ms (0.3%)

series404.0ms (4.2%)

rewrite93.0ms (1%)

simplify107.0ms (1.1%)

prune247.0ms (2.6%)

regimes2.1s (22%)

simplify2.0ms (0%)

end97.0ms (1%)

Profiling