Details

analyze863.0ms (5.2%)

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 (24.7%)

Symmetry

(sort kx ky)

Results

2.1s	6587×	body	128	valid
1.2s	801×	body	1024	valid
519.0ms	541×	body	512	valid
206.0ms	327×	body	256	valid

Compiler

Compiled 101 to 89 computations (11.9% saved)

simplify53.0ms (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)

localize20.0ms (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))

series321.0ms (1.9%)

Counts

4 → 104

Calls

4 calls:

214.0ms	(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))
100.0ms	(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)

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64`

Counts

4 → 65

Calls

4 calls:

2.0ms	(pow.f64 (sin.f64 ky) 2)
2.0ms	(pow.f64 (sin.f64 kx) 2)
1.0ms	(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))
0.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)

simplify147.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

527×	`cancel-sign-sub-inv_binary64`
299×	`unswap-sqr_binary64`
244×	`fma-neg_binary64`
216×	`fma-def_binary64`
206×	`associate-r_binary64`

Counts

169 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	348	7820
1	970	7080
2	3540	7073
3	5110	7073

prune250.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	157	4	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	158	4	162

Error

0.6b

Counts

162 → 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 4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)))))
▶	1.8b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (.f64 (sqrt.f64 (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))) (sqrt.f64 (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)))))))
	32.0b	(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)))

Compiler

Compiled 8013 to 5723 computations (28.6% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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)
✓	6.9b	(sqrt.f64 (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)))
	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))

series4.1s (24.8%)

Counts

1 → 48

Calls

1 calls:

4.1s	(sqrt.f64 (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)))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`sqrt-prod_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`sqrt-pow1_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 21

Calls

1 calls:

2.0ms

(sqrt.f64 (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)))

simplify120.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-def_binary64`
377×	`cancel-sign-sub-inv_binary64`
373×	`unswap-sqr_binary64`
170×	`associate-r_binary64`
141×	`associate-/l*_binary64`

Counts

69 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	266	5973
1	786	5672
2	3050	5526
3	5104	5526

prune915.0ms (5.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	416	0	416
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	416	4	420

Error

0.6b

Counts

420 → 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 4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)))))
✓	1.8b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (.f64 (sqrt.f64 (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))) (sqrt.f64 (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)))))))
	32.0b	(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)))

Compiler

Compiled 35420 to 25193 computations (28.9% saved)

localize3.0ms (0%)

prune6.0ms (0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	1	1
Total	4	4

Error

0.6b

Counts

4 → 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 4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)))))
✓	1.8b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (.f64 (sqrt.f64 (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))) (sqrt.f64 (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)))))))
	32.0b	(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)))

Compiler

Compiled 264 to 190 computations (28% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.1b	(/.f64 (sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)
✓	2.1b	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
✓	28.6b	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
✓	29.0b	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series480.0ms (2.9%)

Counts

4 → 156

Calls

4 calls:

220.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
121.0ms	(/.f64 (sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)
82.0ms	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
57.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`pow1_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`

Counts

4 → 101

Calls

4 calls:

12.0ms	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
12.0ms	(/.f64 (sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)
9.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

simplify183.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

276×	`fma-neg_binary64`
234×	`associate-r_binary64`
234×	`associate-/r*_binary64`
225×	`times-frac_binary64`
222×	`associate-l_binary64`

Counts

257 → 237

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	380	7760
1	1078	6797
2	4061	6715
3	4915	6715
4	4953	6715

prune452.0ms (2.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	292	0	292
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	292	4	296

Error

0.6b

Counts

296 → 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 4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)))))
✓	1.8b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (.f64 (sqrt.f64 (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))) (sqrt.f64 (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)))))))
	32.0b	(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)))

Compiler

Compiled 16106 to 10059 computations (37.5% saved)

regimes4.3s (26%)

Accuracy

Total 0.8b remaining (81.7%)

Threshold costs 0.8b (81.7%)

Counts

143 → 1

Compiler

Compiled 104111 to 83299 computations (20% 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	23	72
1	28	72
2	27	72

end160.0ms (1%)

Remove: (sort kx ky)
Compiler: Compiled 362 to 280 computations (22.7% saved)

Details

analyze863.0ms (5.2%)

sample4.1s (24.7%)

simplify53.0ms (0.3%)

prune4.0ms (0%)

localize20.0ms (0.1%)

series321.0ms (1.9%)

rewrite7.0ms (0%)

simplify147.0ms (0.9%)

prune250.0ms (1.5%)

localize22.0ms (0.1%)

series4.1s (24.8%)

rewrite3.0ms (0%)

simplify120.0ms (0.7%)

prune915.0ms (5.5%)

localize3.0ms (0%)

prune6.0ms (0%)

localize28.0ms (0.2%)

series480.0ms (2.9%)

rewrite51.0ms (0.3%)

simplify183.0ms (1.1%)

prune452.0ms (2.7%)

regimes4.3s (26%)

simplify2.0ms (0%)

end160.0ms (1%)

Profiling