Details

analyze907.0ms (10%)

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 (45.6%)

Symmetry

(sort kx ky)

Results

2.1s	6586×	body	128	valid
1.1s	770×	body	1024	valid
614.0ms	556×	body	512	valid
226.0ms	343×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 101 to 89 computations (11.9% saved)

simplify42.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

699×	`fma-neg_binary64`
303×	`rules-4_binary64`
291×	`rules-1_binary64`
280×	`rules-6_binary64`
254×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	42
1	49	37
2	125	37
3	543	37
4	4608	37
5	5164	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)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (sin.f64 kx) 2)
✓	0.3b	(pow.f64 (sin.f64 ky) 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)
✓	10.1b	(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))

series231.0ms (2.5%)

Counts

4 → 104

Calls

4 calls:

143.0ms	(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))
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)
4.0ms	(pow.f64 (sin.f64 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)

rewrite97.0ms (1.1%)

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:

93.0ms	(pow.f64 (sin.f64 kx) 2)
93.0ms	(pow.f64 (sin.f64 ky) 2)
93.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
93.0ms	(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

simplify129.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

598×	`rules-21_binary64`
335×	`fma-def_binary64`
268×	`rules-20_binary64`
246×	`rules-13_binary64`
176×	`rules-4_binary64`

Counts

268 → 251

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	274	6569
1	932	5966
2	4417	5966
3	5122	5966

prune309.0ms (3.4%)

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

0.4b

Counts

252 → 3

Alt Table

Status	Error	Program
▶	24.6b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))
✓	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)))))
	32.9b	(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))))))

Compiler

Compiled 11475 to 7967 computations (30.6% saved)

localize3.0ms (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

0.4b

Counts

3 → 3

Alt Table

Status	Error	Program
✓	24.6b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))
✓	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)))))
▶	32.9b	(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))))))

Compiler

Compiled 148 to 106 computations (28.4% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.4b	(/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))
✓	7.2b	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
✓	26.9b	(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)))))
✓	27.2b	(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)))))

series482.0ms (5.3%)

Counts

4 → 120

Calls

4 calls:

290.0ms	(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)))))
135.0ms	(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)))))
29.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
27.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))

rewrite85.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

369×	`prod-diff_binary64`
181×	`add-sqr-sqrt_binary64`
179×	`log1p-expm1-u_binary64`
179×	`expm1-log1p-u_binary64`
174×	`add-cbrt-cube_binary64`

Counts

4 → 117

Calls

4 calls:

83.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))
83.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
83.0ms	(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)))))
83.0ms	(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	450	52
2	4671	52
3	5267	52
0	0	0
1	0	0

simplify80.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-neg_binary64`
805×	`rules-20_binary64`
402×	`rules-21_binary64`
151×	`fma-def_binary64`
140×	`rules-14-rev_binary64`

Counts

237 → 177

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	186	3208
1	647	3066
2	3116	3066
3	5049	3066

prune306.0ms (3.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	245	3	248

Error

0.4b

Counts

248 → 3

Alt Table

Status	Error	Program
✓	24.6b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))
✓	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)))))
✓	32.9b	(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))))))

Compiler

Compiled 13578 to 7774 computations (42.7% saved)

regimes2.1s (23.4%)

Accuracy

Total 0.8b remaining (65.7%)

Threshold costs 0.8b (65.7%)

Counts

80 → 1

Compiler

Compiled 71644 to 51277 computations (28.4% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	36
1	23	36
2	22	36

end102.0ms (1.1%)

Remove: (sort kx ky)
Compiler: Compiled 201 to 162 computations (19.4% saved)

Details

analyze907.0ms (10%)

sample4.1s (45.6%)

simplify42.0ms (0.5%)

prune5.0ms (0%)

localize22.0ms (0.2%)

series231.0ms (2.5%)

rewrite97.0ms (1.1%)

simplify129.0ms (1.4%)

prune309.0ms (3.4%)

localize3.0ms (0%)

prune3.0ms (0%)

localize23.0ms (0.3%)

series482.0ms (5.3%)

rewrite85.0ms (0.9%)

simplify80.0ms (0.9%)

prune306.0ms (3.4%)

regimes2.1s (23.4%)

simplify1.0ms (0%)

end102.0ms (1.1%)

Profiling