Details

analyze866.0ms (7.5%)

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)

sample4.1s (35%)

Symmetry

(sort kx ky)

Results

2.2s	6608×	body	128	valid
1.0s	753×	body	1024	valid
568.0ms	551×	body	512	valid
216.0ms	343×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 101 to 89 computations (11.9% saved)

simplify22.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
578×	`associate-l_binary64`
512×	`unswap-sqr_binary64`
433×	`associate-r_binary64`
328×	`associate-*l/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	42
1	56	37
2	126	37
3	580	37
4	3386	37

Stop Event

1×	node limit

Counts

1 → 2

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

1.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.6b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 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 (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (sin.f64 ky) 2)
✓	0.5b	(/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))
✓	2.5b	(fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	10.5b	(sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))

series673.0ms (5.8%)

Counts

4 → 148

Calls

4 calls:

456.0ms	(/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))
140.0ms	(sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))
73.0ms	(fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
3.0ms	(pow.f64 (sin.f64 ky) 2)

rewrite71.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

653×	`prod-diff_binary64`
189×	`add-sqr-sqrt_binary64`
184×	`log1p-expm1-u_binary64`
184×	`expm1-log1p-u_binary64`
180×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	94
1	402	85
2	4920	85

Stop Event

1×	node limit

Counts

4 → 93

Calls

4 calls:

69.0ms	(pow.f64 (sin.f64 ky) 2)
69.0ms	(/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))
69.0ms	(fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
69.0ms	(sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))

simplify150.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	373	11132
1	1219	10267
2	4887	10261

Stop Event

1×	node limit

Counts

241 → 221

prune323.0ms (2.8%)

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

0.4b

Counts

222 → 3

Alt Table

Status	Error	Program
▶	25.5b	(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 4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)))))
	26.8b	(sqrt.f64 (+.f64 1/2 1/2))
✓	1.6b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))

Compiler

Compiled 12248 to 8475 computations (30.8% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
✓	3.0b	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
✓	27.2b	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
✓	27.4b	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series527.0ms (4.5%)

Counts

4 → 156

Calls

4 calls:

239.0ms	(.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
177.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
64.0ms	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
46.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite40.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

197×	`add-sqr-sqrt_binary64`
194×	`log1p-expm1-u_binary64`
194×	`expm1-log1p-u_binary64`
191×	`add-cbrt-cube_binary64`
190×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	98
1	428	59

Stop Event

1×	node limit

Counts

4 → 107

Calls

4 calls:

38.0ms	(.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
38.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
38.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
38.0ms	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

simplify80.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

480×	`cancel-sign-sub-inv_binary64`
236×	`associate-/r*_binary64`
230×	`fma-neg_binary64`
228×	`times-frac_binary64`
193×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	226	4662
1	785	4342
2	3332	4342

Stop Event

1×	node limit

Counts

263 → 185

prune297.0ms (2.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	234	0	234
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	234	3	237

Error

0.4b

Counts

237 → 3

Alt Table

Status	Error	Program
✓	25.5b	(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 4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)))))
▶	26.8b	(sqrt.f64 (+.f64 1/2 1/2))
✓	1.6b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))

Compiler

Compiled 11641 to 7121 computations (38.8% saved)

localize2.0ms (0%)

prune6.0ms (0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

0.4b

Counts

3 → 3

Alt Table

Status	Error	Program
✓	25.5b	(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 4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)))))
✓	26.8b	(sqrt.f64 (+.f64 1/2 1/2))
✓	1.6b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))

Compiler

Compiled 83 to 66 computations (20.5% saved)

regimes4.3s (37.1%)

Accuracy

Total 0.4b remaining (50.6%)

Threshold costs 0.4b (50.6%)

Counts

154 → 2

Compiler

Compiled 122296 to 93254 computations (23.7% saved)

bsearch10.0ms (0.1%)

Compiler: Compiled 11 to 9 computations (18.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	114
1	59	114

Stop Event

1×

saturated

end125.0ms (1.1%)

Remove: (sort kx ky)
Compiler: Compiled 391 to 294 computations (24.8% saved)

Details

analyze866.0ms (7.5%)

sample4.1s (35%)

simplify22.0ms (0.2%)

prune4.0ms (0%)

localize17.0ms (0.1%)

series673.0ms (5.8%)

rewrite71.0ms (0.6%)

simplify150.0ms (1.3%)

prune323.0ms (2.8%)

localize23.0ms (0.2%)

series527.0ms (4.5%)

rewrite40.0ms (0.3%)

simplify80.0ms (0.7%)

prune297.0ms (2.6%)

localize2.0ms (0%)

prune6.0ms (0%)

regimes4.3s (37.1%)

bsearch10.0ms (0.1%)

simplify3.0ms (0%)

end125.0ms (1.1%)

Profiling