Details

analyze856.0ms (5.9%)

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)

sample4.0s (27.5%)

Symmetry

(sort kx ky)

Results

2.1s	6529×	body	128	valid
1.1s	808×	body	1024	valid
512.0ms	572×	body	512	valid
222.0ms	347×	body	256	valid

Compiler

Compiled 101 to 89 computations (11.9% saved)

simplify53.0ms (0.4%)

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

1.0b

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)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (sin.f64 kx) 2)
✓	0.4b	(/.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)))
✓	1.5b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	9.1b	(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))

series660.0ms (4.6%)

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)))
142.0ms	(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))
78.0ms	(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)

rewrite80.0ms (0.6%)

Algorithm

1×	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:

78.0ms	(pow.f64 (sin.f64 kx) 2)
78.0ms	(/.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)))
78.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
78.0ms	(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: 1 (0.0ms)

Iter	Nodes	Cost
0	19	94
1	398	85
2	4552	85
3	5667	85

simplify323.0ms (2.2%)

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

prune416.0ms (2.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	221	4	225
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	222	4	226

Error

0.6b

Counts

226 → 4

Alt Table

Status	Error	Program
	27.3b	(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)))))
▶	1.0b	(sqrt.f64 (+.f64 1/2 (expm1.f64 (log1p.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)))))))
	25.6b	(sqrt.f64 (+.f64 1/2 1/2))
	1.0b	(sqrt.f64 (+.f64 1/2 (-.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1))))) 1)))

Compiler

Compiled 12426 to 8728 computations (29.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)))
✓	0.4b	(pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2)
✓	1.5b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)
✓	9.1b	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1))

series817.0ms (5.7%)

Counts

4 → 168

Calls

4 calls:

494.0ms	(/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)))
168.0ms	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1))
118.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)
36.0ms	(pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2)

rewrite79.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

305×	`expm1-udef_binary64`
305×	`log1p-udef_binary64`
175×	`add-sqr-sqrt_binary64`
166×	`log1p-expm1-u_binary64`
166×	`expm1-log1p-u_binary64`

Counts

4 → 99

Calls

4 calls:

77.0ms	(/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)))
77.0ms	(pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2)
77.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)
77.0ms	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	90
1	367	87
2	4068	87
3	5185	87

simplify254.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

417×	`fma-neg_binary64`
356×	`fma-def_binary64`
268×	`*-commutative_binary64`
262×	`associate-r_binary64`
197×	`+-commutative_binary64`

Counts

267 → 233

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	377	11424
1	1229	10553
2	4652	10547
3	4980	10547

prune332.0ms (2.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	231	2	233
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	235	2	237

Error

0.0b

Counts

237 → 2

Alt Table

Status	Error	Program
	0.0b	(sqrt.f64 (+.f64 1/2 (expm1.f64 (log1p.f64 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2))))))))))
▶	0.0b	(sqrt.f64 (+.f64 1/2 (expm1.f64 (log1p.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2))))))))

Status

Error

Program

0.0b

(sqrt.f64 (+.f64 1/2 (expm1.f64 (log1p.f64 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (pow.f64 (*.f64 (/.f64 (*.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2))))))))))

▶

0.0b

(sqrt.f64 (+.f64 1/2 (expm1.f64 (log1p.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (pow.f64 (*.f64 (/.f64 (*.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2))))))))

Compiler

Compiled 12878 to 9094 computations (29.4% 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)
✓	0.4b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2))))
✓	2.3b	(.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
✓	9.1b	(sqrt.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)))

series1.2s (8.1%)

Counts

4 → 192

Calls

4 calls:

585.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2))))
261.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)))
203.0ms	(pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)
116.0ms	(.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))

rewrite81.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

633×	`prod-diff_binary64`
181×	`add-sqr-sqrt_binary64`
175×	`log1p-expm1-u_binary64`
175×	`expm1-log1p-u_binary64`
171×	`add-cbrt-cube_binary64`

Counts

4 → 107

Calls

4 calls:

78.0ms	(pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)
78.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2))))
78.0ms	(.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
78.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	90
1	380	80
2	4459	80
3	5631	80

simplify166.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

377×	`fma-def_binary64`
304×	`associate-r_binary64`
242×	`associate-*r/_binary64`
241×	`associate-/l*_binary64`
240×	`times-frac_binary64`

Counts

299 → 241

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	426	12038
1	1428	11261
2	4982	11261

prune339.0ms (2.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	240	1	241
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	241	2	243

Error

0.0b

Counts

243 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1/2 (expm1.f64 (log1p.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2))))))))
▶	0.0b	(sqrt.f64 (+.f64 1/2 (expm1.f64 (log1p.f64 (log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))))))))

Status

Error

Program

✓

0.0b

(sqrt.f64 (+.f64 1/2 (expm1.f64 (log1p.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (pow.f64 (*.f64 (/.f64 (*.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2))))))))

▶

0.0b

(sqrt.f64 (+.f64 1/2 (expm1.f64 (log1p.f64 (log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 (*.f64 (/.f64 (*.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))))))))

Compiler

Compiled 13094 to 9074 computations (30.7% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(hypot.f64 (sin.f64 kx) (sin.f64 ky))
✓	0.4b	(/.f64 1/2 (hypot.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
	2.3b	(.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
✓	4.7b	(log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))))

series1.1s (7.4%)

Counts

3 → 120

Calls

3 calls:

554.0ms

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

490.0ms

(log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 (*.f64 (/.f64 (*.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))))

24.0ms

(hypot.f64 (sin.f64 kx) (sin.f64 ky))

rewrite69.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

301×	`expm1-udef_binary64`
301×	`log1p-udef_binary64`
169×	`add-sqr-sqrt_binary64`
159×	`log1p-expm1-u_binary64`
159×	`expm1-log1p-u_binary64`

Counts

3 → 77

Calls

3 calls:

67.0ms

(hypot.f64 (sin.f64 kx) (sin.f64 ky))

67.0ms

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

67.0ms

(log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 (*.f64 (/.f64 (*.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	54
1	344	54
2	4040	54
3	5224	54

simplify799.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

454×	`cancel-sign-sub-inv_binary64`
256×	`unswap-sqr_binary64`
222×	`fma-neg_binary64`
207×	`fma-def_binary64`
182×	`sub-neg_binary64`

Counts

197 → 117

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	299	9818
1	888	9238
2	3354	9238
3	5004	9238

prune211.0ms (1.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	165	2	167

Error

0.0b

Counts

167 → 2

Alt Table

Status

Error

Program

✓

0.0b

(sqrt.f64 (+.f64 1/2 (expm1.f64 (log1p.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (pow.f64 (*.f64 (/.f64 (*.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) 2))))))))

✓

0.0b

(sqrt.f64 (+.f64 1/2 (expm1.f64 (log1p.f64 (log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 (*.f64 (/.f64 (*.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))))))))

Compiler

Compiled 7987 to 5557 computations (30.4% saved)

regimes2.5s (17.5%)

Accuracy

Total 0.0b remaining (42.4%)

Threshold costs 0.0b (42.4%)

Counts

105 → 1

Compiler

Compiled 60813 to 51274 computations (15.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	34
1	30	34
2	32	34
3	33	34
4	32	34

end85.0ms (0.6%)

Remove: (sort kx ky)
Compiler: Compiled 153 to 129 computations (15.7% saved)

Details

analyze856.0ms (5.9%)

sample4.0s (27.5%)

simplify53.0ms (0.4%)

prune4.0ms (0%)

localize17.0ms (0.1%)

series660.0ms (4.6%)

rewrite80.0ms (0.6%)

simplify323.0ms (2.2%)

prune416.0ms (2.9%)

localize19.0ms (0.1%)

series817.0ms (5.7%)

rewrite79.0ms (0.6%)

simplify254.0ms (1.8%)

prune332.0ms (2.3%)

localize18.0ms (0.1%)

series1.2s (8.1%)

rewrite81.0ms (0.6%)

simplify166.0ms (1.1%)

prune339.0ms (2.4%)

localize20.0ms (0.1%)

series1.1s (7.4%)

rewrite69.0ms (0.5%)

simplify799.0ms (5.5%)

prune211.0ms (1.5%)

regimes2.5s (17.5%)

simplify2.0ms (0%)

end85.0ms (0.6%)

Profiling