Details

analyze824.0ms (3.3%)

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)

sample4.2s (16.7%)

Symmetry

(sort kx ky)

Results

2.2s	6587×	body	128	valid
1.2s	801×	body	1024	valid
560.0ms	541×	body	512	valid
196.0ms	327×	body	256	valid

Compiler

Compiled 101 to 89 computations (11.9% saved)

simplify70.0ms (0.3%)

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

1.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.8b	(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)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (sin.f64 ky) 2)
✓	0.2b	(pow.f64 (sin.f64 kx) 2)
✓	2.3b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	10.3b	(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))

series388.0ms (1.5%)

Counts

4 → 104

Calls

4 calls:

278.0ms	(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))
103.0ms	(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 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)

rewrite287.0ms (1.1%)

Algorithm

4×	egg-rewrite

Rules

39×	`egg`
39×	`egg`
25×	`egg`
25×	`egg`

Counts

4 → 128

Calls

4 calls:

73.0ms	(pow.f64 (sin.f64 kx) 2)
73.0ms	(pow.f64 (sin.f64 ky) 2)
72.0ms	(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))
67.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	351	26
2	4013	26
3	5134	26
0	16	27
1	332	24
2	3824	24
3	4962	24
0	5	6
1	101	6
2	989	6
3	4808	6
4	4894	6
0	5	6
1	101	6
2	989	6
3	4808	6
4	4894	6

simplify212.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

527×	`cancel-sign-sub-inv_binary64`
321×	`fma-neg_binary64`
256×	`unswap-sqr_binary64`
211×	`fma-def_binary64`
193×	`associate-r_binary64`

Counts

232 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	274	6568
1	850	6001
2	3268	5991
3	4911	5991
4	4982	5991
5	4970	5991

prune295.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	209	4	213
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	210	4	214

Error

0.6b

Counts

214 → 4

Alt Table

Status	Error	Program
▶	1.8b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (pow.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1) 1/4) 2))))
	32.0b	(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))))))
	24.6b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))
	29.3b	(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)))))

Compiler

Compiled 9314 to 6632 computations (28.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
✓	0.4b	(pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2)
✓	2.3b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)
✓	17.4b	(pow.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1) 1/4)

series5.7s (22.5%)

Counts

4 → 144

Calls

4 calls:

5.4s	(pow.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1) 1/4)
251.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)
46.0ms	(pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2)
13.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)

rewrite290.0ms (1.1%)

Algorithm

4×	egg-rewrite

Rules

48×	`egg`
44×	`egg`
34×	`egg`
24×	`egg`

Counts

4 → 150

Calls

4 calls:

95.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)
80.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
66.0ms	(pow.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1) 1/4)
46.0ms	(pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	27
1	348	26
2	3751	26
3	4892	26
0	15	24
1	301	23
2	3339	23
3	4975	23
4	5281	23
0	8	11
1	160	11
2	1637	11
3	5096	11
0	7	10
1	149	10
2	1799	10
3	4935	10
4	5073	10

simplify206.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

457×	`cancel-sign-sub-inv_binary64`
377×	`unswap-sqr_binary64`
191×	`fma-def_binary64`
188×	`associate-r_binary64`
177×	`fma-neg_binary64`

Counts

294 → 235

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	275	8017
1	884	7476
2	3429	7468
3	4999	7468
4	4981	7468

prune391.0ms (1.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	234	1	235
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	238	1	239

Error

0.0b

Counts

239 → 1

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (pow.f64 (pow.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)) 1/4) 2))))

Compiler

Compiled 11410 to 8024 computations (29.7% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (pow.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)) 1/4) 2)
✓	0.2b	(pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)
✓	1.0b	(.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
✓	17.4b	(pow.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)) 1/4)

series9.7s (38.2%)

Counts

4 → 192

Calls

4 calls:

4.9s	(pow.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)) 1/4)
4.4s	(pow.f64 (pow.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)) 1/4) 2)
189.0ms	(pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)
141.0ms	(.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))

rewrite296.0ms (1.2%)

Algorithm

4×	egg-rewrite

Rules

51×	`egg`
35×	`egg`
33×	`egg`
23×	`egg`

Counts

4 → 142

Calls

4 calls:

81.0ms	(pow.f64 (pow.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)) 1/4) 2)
73.0ms	(pow.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)) 1/4)
70.0ms	(pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)
68.0ms	(.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	26
1	361	22
2	4139	22
3	5269	22
0	12	17
1	246	17
2	3042	17
3	5548	17
0	13	20
1	271	20
2	3225	20
3	5856	20
0	18	26
1	384	20
2	4271	20
3	5395	20

simplify198.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

354×	`fma-def_binary64`
313×	`associate-r_binary64`
312×	`times-frac_binary64`
299×	`associate-/r*_binary64`
294×	`associate-/l*_binary64`

Counts

334 → 271

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	443	13672
1	1512	12934
2	5318	12934

prune381.0ms (1.5%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	271	0	271
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	271	1	272

Error

0.0b

Counts

272 → 1

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (pow.f64 (pow.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)) 1/4) 2))))

Compiler

Compiled 16503 to 10963 computations (33.6% saved)

regimes1.8s (6.9%)

Accuracy

Total 0.0b remaining (19.7%)

Threshold costs 0.0b (19.7%)

Counts

76 → 1

Compiler

Compiled 44247 to 37178 computations (16% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	33
1	26	33
2	25	33

end69.0ms (0.3%)

Remove: (sort kx ky)
Compiler: Compiled 128 to 108 computations (15.6% saved)

Details

analyze824.0ms (3.3%)

sample4.2s (16.7%)

simplify70.0ms (0.3%)

prune4.0ms (0%)

localize19.0ms (0.1%)

series388.0ms (1.5%)

rewrite287.0ms (1.1%)

simplify212.0ms (0.8%)

prune295.0ms (1.2%)

localize20.0ms (0.1%)

series5.7s (22.5%)

rewrite290.0ms (1.1%)

simplify206.0ms (0.8%)

prune391.0ms (1.5%)

localize19.0ms (0.1%)

series9.7s (38.2%)

rewrite296.0ms (1.2%)

simplify198.0ms (0.8%)

prune381.0ms (1.5%)

regimes1.8s (6.9%)

simplify2.0ms (0%)

end69.0ms (0.3%)

Profiling