Details

analyze978.0ms (9.4%)

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)

sample4.4s (42%)

Symmetry

(sort kx ky)

Results

2.3s	6543×	body	128	valid
1.2s	814×	body	1024	valid
585.0ms	597×	body	512	valid
226.0ms	301×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 101 to 89 computations (11.9% saved)

simplify61.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1214×	`rules-42_binary64`
847×	`rules-41_binary64`
847×	`rules-43_binary64`
573×	`rules-40_binary64`
417×	`rules-20_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	42
1	140	37
2	438	37
3	2035	37
4	3994	37
5	39	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

0.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.8b	(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)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (sin.f64 ky) 2)
✓	0.3b	(pow.f64 (sin.f64 kx) 2)
✓	1.2b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	11.4b	(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))

series323.0ms (3.1%)

Counts

4 → 104

Calls

4 calls:

219.0ms	(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))
97.0ms	(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)
3.0ms	(pow.f64 (sin.f64 ky) 2)

rewrite98.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

603×	`prod-diff_binary64`
164×	`egg-rr`
161×	`add-sqr-sqrt_binary64`
156×	`log1p-expm1-u_binary64`
156×	`expm1-log1p-u_binary64`

Counts

4 → 164

Calls

4 calls:

95.0ms	(pow.f64 (sin.f64 ky) 2)
95.0ms	(pow.f64 (sin.f64 kx) 2)
95.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
95.0ms	(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	17	68
1	391	62
2	4460	62
3	5574	62
0	0	0
1	0	0

simplify104.0ms (1%)

Algorithm

1×	egg-herbie

Rules

694×	`fma-neg_binary64`
521×	`rules-20_binary64`
483×	`rules-40_binary64`
483×	`rules-41_binary64`
483×	`rules-42_binary64`

Counts

268 → 251

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	274	6563
1	2024	6563
2	4917	6563

prune941.0ms (9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	249	2	251
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	249	3	252

Error

0.2b

Counts

252 → 3

Alt Table

Status	Error	Program
	34.3b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (/.f64 (sqrt.f64 (.f64 4 (+.f64 (.f64 (.f64 l l) (pow.f64 (sin.f64 kx) 2)) (.f64 (.f64 l l) (pow.f64 (sin.f64 ky) 2))))) Om) (.f64 1/2 (.f64 Om (sqrt.f64 (/.f64 1 (.f64 4 (+.f64 (.f64 (.f64 l l) (pow.f64 (sin.f64 kx) 2)) (.f64 (.f64 l l) (pow.f64 (sin.f64 ky) 2))))))))))))
✓	0.8b	(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)))))
▶	25.3b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))

Compiler

Compiled 11635 to 8081 computations (30.5% saved)

localize3.0ms (0%)

prune4.0ms (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

0.2b

Counts

3 → 3

Alt Table

Status	Error	Program
▶	34.3b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (/.f64 (sqrt.f64 (.f64 4 (+.f64 (.f64 (.f64 l l) (pow.f64 (sin.f64 kx) 2)) (.f64 (.f64 l l) (pow.f64 (sin.f64 ky) 2))))) Om) (.f64 1/2 (.f64 Om (sqrt.f64 (/.f64 1 (.f64 4 (+.f64 (.f64 (.f64 l l) (pow.f64 (sin.f64 kx) 2)) (.f64 (.f64 l l) (pow.f64 (sin.f64 ky) 2))))))))))))
✓	0.8b	(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)))))
✓	25.3b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))

Compiler

Compiled 154 to 112 computations (27.3% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.9b	(.f64 (.f64 l l) (pow.f64 (sin.f64 ky) 2))
✓	9.2b	(.f64 (.f64 l l) (pow.f64 (sin.f64 kx) 2))
✓	27.7b	(sqrt.f64 (.f64 4 (+.f64 (.f64 (.f64 l l) (pow.f64 (sin.f64 kx) 2)) (.f64 (*.f64 l l) (pow.f64 (sin.f64 ky) 2)))))
✓	27.8b	(sqrt.f64 (/.f64 1 (.f64 4 (+.f64 (.f64 (.f64 l l) (pow.f64 (sin.f64 kx) 2)) (.f64 (*.f64 l l) (pow.f64 (sin.f64 ky) 2))))))

series473.0ms (4.5%)

Counts

4 → 120

Calls

4 calls:

325.0ms	(sqrt.f64 (/.f64 1 (.f64 4 (+.f64 (.f64 (.f64 l l) (pow.f64 (sin.f64 kx) 2)) (.f64 (*.f64 l l) (pow.f64 (sin.f64 ky) 2))))))
110.0ms	(sqrt.f64 (.f64 4 (+.f64 (.f64 (.f64 l l) (pow.f64 (sin.f64 kx) 2)) (.f64 (*.f64 l l) (pow.f64 (sin.f64 ky) 2)))))
19.0ms	(.f64 (.f64 l l) (pow.f64 (sin.f64 ky) 2))
18.0ms	(.f64 (.f64 l l) (pow.f64 (sin.f64 kx) 2))

rewrite89.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

282×	`prod-diff_binary64`
177×	`add-sqr-sqrt_binary64`
174×	`log1p-expm1-u_binary64`
174×	`expm1-log1p-u_binary64`
170×	`add-log-exp_binary64`

Counts

4 → 166

Calls

4 calls:

86.0ms	(.f64 (.f64 l l) (pow.f64 (sin.f64 ky) 2))
86.0ms	(.f64 (.f64 l l) (pow.f64 (sin.f64 kx) 2))
86.0ms	(sqrt.f64 (.f64 4 (+.f64 (.f64 (.f64 l l) (pow.f64 (sin.f64 kx) 2)) (.f64 (*.f64 l l) (pow.f64 (sin.f64 ky) 2)))))
86.0ms	(sqrt.f64 (/.f64 1 (.f64 4 (+.f64 (.f64 (.f64 l l) (pow.f64 (sin.f64 kx) 2)) (.f64 (*.f64 l l) (pow.f64 (sin.f64 ky) 2))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	74
1	447	52
2	4732	52
3	5190	52
0	0	0
1	0	0

simplify109.0ms (1%)

Algorithm

1×	egg-herbie

Rules

451×	`fma-neg_binary64`
340×	`rules-40_binary64`
340×	`rules-41_binary64`
340×	`rules-42_binary64`
340×	`rules-43_binary64`

Counts

286 → 230

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	186	2976
1	1395	2874
2	5017	2874

prune446.0ms (4.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	340	0	340
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	340	3	343

Error

0.2b

Counts

343 → 3

Alt Table

Status	Error	Program
✓	34.3b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (/.f64 (sqrt.f64 (.f64 4 (+.f64 (.f64 (.f64 l l) (pow.f64 (sin.f64 kx) 2)) (.f64 (.f64 l l) (pow.f64 (sin.f64 ky) 2))))) Om) (.f64 1/2 (.f64 Om (sqrt.f64 (/.f64 1 (.f64 4 (+.f64 (.f64 (.f64 l l) (pow.f64 (sin.f64 kx) 2)) (.f64 (.f64 l l) (pow.f64 (sin.f64 ky) 2))))))))))))
✓	0.8b	(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)))))
✓	25.3b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))

Compiler

Compiled 20635 to 12274 computations (40.5% saved)

regimes2.3s (21.6%)

Accuracy

Total 0.7b remaining (67.3%)

Threshold costs 0.7b (67.3%)

Counts

82 → 1

Compiler

Compiled 73586 to 53398 computations (27.4% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	42
1	26	42
2	24	42

end104.0ms (1%)

Remove: (sort kx ky)
Compiler: Compiled 220 to 181 computations (17.7% saved)

Details

analyze978.0ms (9.4%)

sample4.4s (42%)

simplify61.0ms (0.6%)

prune4.0ms (0%)

localize22.0ms (0.2%)

series323.0ms (3.1%)

rewrite98.0ms (0.9%)

simplify104.0ms (1%)

prune941.0ms (9%)

localize3.0ms (0%)

prune4.0ms (0%)

localize25.0ms (0.2%)

series473.0ms (4.5%)

rewrite89.0ms (0.9%)

simplify109.0ms (1%)

prune446.0ms (4.3%)

regimes2.3s (21.6%)

simplify1.0ms (0%)

end104.0ms (1%)

Profiling