Details

analyze832.0ms (4.3%)

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)

sample4.1s (21%)

Symmetry

(sort kx ky)

Results

2.2s	6587×	body	128	valid
1.1s	801×	body	1024	valid
517.0ms	541×	body	512	valid
205.0ms	327×	body	256	valid

Compiler

Compiled 101 to 89 computations (11.9% saved)

simplify54.0ms (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

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

1.8b

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)

localize18.0ms (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))

series359.0ms (1.8%)

Counts

4 → 104

Calls

4 calls:

250.0ms	(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))
102.0ms	(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)

rewrite72.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

91× egg-rr

Counts

4 → 91

Calls

2 calls:

69.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	68
1	351	62
2	4013	62
3	5134	62
0	0	0
1	0	0

simplify197.0ms (1%)

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

195 → 178

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

prune280.0ms (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	174	4	178
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	4	179

Error

0.6b

Counts

179 → 4

Alt Table

Status	Error	Program
	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)))))
	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)))
▶	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))))

Compiler

Compiled 8426 to 5922 computations (29.7% saved)

localize19.0ms (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)

series5.4s (27.6%)

Counts

4 → 144

Calls

4 calls:

5.2s	(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)
160.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)
44.0ms	(pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2)
11.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)

rewrite74.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

121× egg-rr

Counts

4 → 121

Calls

2 calls:

71.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	72
1	348	70
2	3751	70
3	4892	70
0	0	0
1	0	0

simplify215.0ms (1.1%)

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

265 → 208

Iterations

Useful iterations: 2 (0.0ms)

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

prune296.0ms (1.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	207	1	208
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	211	1	212

Error

0.0b

Counts

212 → 1

Alt Table

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

Compiler

Compiled 10590 to 7450 computations (29.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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)))
✓	6.9b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2))))
✓	10.3b	(sqrt.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)))

series5.3s (27.2%)

Counts

4 → 192

Calls

4 calls:

4.6s	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2))))
370.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)))
202.0ms	(pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)
138.0ms	(.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))

rewrite76.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

110× egg-rr

Counts

4 → 110

Calls

2 calls:

74.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	89
1	351	79
2	4081	79
3	5258	79
0	0	0
1	0	0

simplify160.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

349×	`fma-def_binary64`
325×	`associate-r_binary64`
266×	`times-frac_binary64`
264×	`associate-/r*_binary64`
263×	`associate-/l*_binary64`

Counts

302 → 243

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	456	12687
1	1519	11943
2	5191	11943

prune340.0ms (1.7%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	243	1	244

Error

0.0b

Counts

244 → 1

Alt Table

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

Compiler

Compiled 14521 to 10066 computations (30.7% saved)

regimes1.7s (8.5%)

Accuracy

Total -0.0b remaining (-1.4%)

Threshold costs -0.0b (-1.4%)

Counts

69 → 1

Compiler

Compiled 41591 to 35058 computations (15.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	35
1	26	35
2	25	35

end67.0ms (0.3%)

Remove: (sort kx ky)
Compiler: Compiled 132 to 112 computations (15.2% saved)

Details

analyze832.0ms (4.3%)

sample4.1s (21%)

simplify54.0ms (0.3%)

prune5.0ms (0%)

localize18.0ms (0.1%)

series359.0ms (1.8%)

rewrite72.0ms (0.4%)

simplify197.0ms (1%)

prune280.0ms (1.4%)

localize19.0ms (0.1%)

series5.4s (27.6%)

rewrite74.0ms (0.4%)

simplify215.0ms (1.1%)

prune296.0ms (1.5%)

localize18.0ms (0.1%)

series5.3s (27.2%)

rewrite76.0ms (0.4%)

simplify160.0ms (0.8%)

prune340.0ms (1.7%)

regimes1.7s (8.5%)

simplify2.0ms (0%)

end67.0ms (0.3%)

Profiling