Details

analyze919.0ms (9.2%)

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 (40.9%)

Symmetry

(sort kx ky)

Results

2.0s	6498×	body	128	valid
1.2s	790×	body	1024	valid
561.0ms	594×	body	512	valid
226.0ms	374×	body	256	valid

Compiler

Compiled 101 to 89 computations (11.9% saved)

simplify54.0ms (0.5%)

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

prune5.0ms (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)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (sin.f64 ky) 2)
✓	0.3b	(/.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)))
✓	0.9b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	7.3b	(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))

series650.0ms (6.5%)

Counts

4 → 148

Calls

4 calls:

435.0ms	(/.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)))
137.0ms	(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))
74.0ms	(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 ky) 2)

rewrite82.0ms (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 → 97

Calls

4 calls:

80.0ms	(pow.f64 (sin.f64 ky) 2)
80.0ms	(/.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)))
80.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
80.0ms	(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

simplify189.0ms (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

245 → 225

Iterations

Useful iterations: 2 (0.0ms)

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

prune307.0ms (3.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	223	2	225
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	223	3	226

Error

0.5b

Counts

226 → 3

Alt Table

Status	Error	Program
▶	23.9b	(sqrt.f64 (+.f64 1/2 1/2))
	33.1b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 l (sqrt.f64 (.f64 4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om))))) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1/4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om))))) l))))))
✓	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 12354 to 8656 computations (29.9% 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

0.5b

Counts

3 → 3

Alt Table

Status	Error	Program
✓	23.9b	(sqrt.f64 (+.f64 1/2 1/2))
▶	33.1b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 l (sqrt.f64 (.f64 4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om))))) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1/4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om))))) l))))))
✓	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 146 to 104 computations (28.8% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.1b	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
✓	7.7b	(/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))
✓	27.4b	(sqrt.f64 (/.f64 1/4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om)))))
✓	27.6b	(sqrt.f64 (.f64 4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om)))))

series463.0ms (4.7%)

Counts

4 → 120

Calls

4 calls:

276.0ms	(sqrt.f64 (/.f64 1/4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om)))))
128.0ms	(sqrt.f64 (.f64 4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om)))))
32.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
28.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))

rewrite94.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

838×	`prod-diff_binary64`
195×	`add-sqr-sqrt_binary64`
193×	`log1p-expm1-u_binary64`
193×	`expm1-log1p-u_binary64`
189×	`add-log-exp_binary64`

Counts

4 → 108

Calls

4 calls:

92.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
92.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))
92.0ms	(sqrt.f64 (/.f64 1/4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om)))))
92.0ms	(sqrt.f64 (.f64 4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	86
1	419	52
2	4693	52
3	6392	52
0	0	0
1	0	0

simplify75.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

947×	`associate-/l*_binary64`
551×	`fma-def_binary64`
300×	`cancel-sign-sub-inv_binary64`
227×	`associate-/r/_binary64`
156×	`times-frac_binary64`

Counts

228 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	3208
1	556	3064
2	2077	2780
3	5055	2780

prune280.0ms (2.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	241	1	242
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	242	3	245

Error

0.5b

Counts

245 → 3

Alt Table

Status	Error	Program
▶	32.9b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 l (.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) Om) -2) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1/4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om))))) l))))))
✓	23.9b	(sqrt.f64 (+.f64 1/2 1/2))
✓	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 13446 to 7842 computations (41.7% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.6b	(/.f64 (sqrt.f64 (/.f64 1/4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om))))) l)
	6.1b	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
	7.7b	(/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))
	27.4b	(sqrt.f64 (/.f64 1/4 (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 Om Om)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 Om Om)))))

series573.0ms (5.8%)

Counts

1 → 48

Calls

1 calls:

573.0ms

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

rewrite73.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

903×	`prod-diff_binary64`
193×	`add-sqr-sqrt_binary64`
188×	`log1p-expm1-u_binary64`
188×	`expm1-log1p-u_binary64`
184×	`add-log-exp_binary64`

Counts

1 → 28

Calls

1 calls:

72.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	34
1	400	20
2	4731	20
3	6576	20
0	0	0
1	0	0

simplify54.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

837×	`associate-/l*_binary64`
803×	`associate-/r*_binary64`
405×	`fma-def_binary64`
230×	`associate-/r/_binary64`
168×	`cancel-sign-sub-inv_binary64`

Counts

76 → 48

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	1984
1	362	1896
2	1484	1828
3	5298	1828

prune267.0ms (2.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	0	0
Picked	1	0	1
Done	1	1	2
Total	172	2	174

Error

0.1b

Counts

174 → 2

Alt Table

Status	Error	Program
	28.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 l (.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) Om) -2) (.f64 1/2 (/.f64 (pow.f64 (/.f64 1/4 (pow.f64 (hypot.f64 (/.f64 (sin.f64 ky) Om) (/.f64 (sin.f64 kx) Om)) 2)) 1/2) l))))))
✓	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)))))

Status

Error

Program

28.0b

(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 l (*.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) Om) -2) (*.f64 1/2 (/.f64 (pow.f64 (/.f64 1/4 (pow.f64 (hypot.f64 (/.f64 (sin.f64 ky) Om) (/.f64 (sin.f64 kx) Om)) 2)) 1/2) l))))))

✓

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 7729 to 4200 computations (45.7% saved)

regimes1.6s (16.3%)

Accuracy

Total 1.0b remaining (85.2%)

Threshold costs 1.0b (85.2%)

Counts

61 → 1

Compiler

Compiled 43063 to 32413 computations (24.7% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	36
1	27	36
2	26	36

end89.0ms (0.9%)

Remove: (sort kx ky)
Compiler: Compiled 175 to 144 computations (17.7% saved)

Details

analyze919.0ms (9.2%)

sample4.1s (40.9%)

simplify54.0ms (0.5%)

prune5.0ms (0%)

localize19.0ms (0.2%)

series650.0ms (6.5%)

rewrite82.0ms (0.8%)

simplify189.0ms (1.9%)

prune307.0ms (3.1%)

localize3.0ms (0%)

prune4.0ms (0%)

localize24.0ms (0.2%)

series463.0ms (4.7%)

rewrite94.0ms (0.9%)

simplify75.0ms (0.8%)

prune280.0ms (2.8%)

localize27.0ms (0.3%)

series573.0ms (5.8%)

rewrite73.0ms (0.7%)

simplify54.0ms (0.5%)

prune267.0ms (2.7%)

regimes1.6s (16.3%)

simplify5.0ms (0%)

end89.0ms (0.9%)

Profiling