Details

analyze777.0ms (4%)

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)

sample4.7s (24.3%)

Symmetry

(sort kx ky)

Results

2.2s	6612×	body	128	valid
1.7s	788×	body	1024	valid
532.0ms	568×	body	512	valid
162.0ms	286×	body	256	valid
4.0ms	2×	body	2048	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

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

0.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.8b	(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
✓	0.3b	(pow.f64 (sin.f64 ky) 2)
✓	0.3b	(pow.f64 (sin.f64 kx) 2)
✓	1.7b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	8.2b	(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))

series354.0ms (1.8%)

Counts

4 → 104

Calls

4 calls:

238.0ms	(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))
108.0ms	(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)

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)

simplify151.0ms (0.8%)

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

prune310.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	3	162

Error

0.0b

Counts

162 → 3

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)))))
▶	0.8b	(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)))))))
	32.6b	(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 7993 to 5703 computations (28.7% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (sin.f64 kx) 2)
	1.7b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	7.4b	(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)))
	8.2b	(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))

series4.8s (24.9%)

Counts

1 → 48

Calls

1 calls:

4.8s	(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)))

simplify123.0ms (0.6%)

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

prune883.0ms (4.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	416	0	416
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	416	3	419

Error

0.0b

Counts

419 → 3

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)))))
✓	0.8b	(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)))))))
	32.6b	(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 35400 to 25173 computations (28.9% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(/.f64 (sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)
✓	1.5b	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
✓	27.5b	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
✓	28.1b	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series497.0ms (2.6%)

Counts

4 → 156

Calls

4 calls:

235.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
129.0ms	(/.f64 (sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)
84.0ms	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
48.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite50.0ms (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:

13.0ms	(/.f64 (sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)
10.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.0ms	(sqrt.f64 (.f64 4 (.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)))))

simplify184.0ms (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

prune425.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	292	0	292
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	292	3	295

Error

0.0b

Counts

295 → 3

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)))))
✓	0.8b	(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)))))))
▶	32.6b	(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 16151 to 10085 computations (37.6% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.1b	(/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))
✓	7.3b	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
✓	30.9b	(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)))))
✓	30.9b	(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)))))

series641.0ms (3.3%)

Counts

4 → 120

Calls

4 calls:

403.0ms	(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)))))
169.0ms	(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)))))
34.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
34.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))

rewrite50.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`times-frac_binary64`
41×	`*-un-lft-identity_binary64`
30×	`add-exp-log_binary64`
29×	`sqrt-prod_binary64`
26×	`add-sqr-sqrt_binary64`

Counts

4 → 132

Calls

4 calls:

17.0ms	(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)))))
13.0ms	(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)))))
6.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
5.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))

simplify176.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-def_binary64`
284×	`times-frac_binary64`
257×	`associate-/r*_binary64`
215×	`fma-neg_binary64`
214×	`associate-/l*_binary64`

Counts

252 → 228

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	413	6807
1	959	6321
2	3651	5907
3	4896	5907
4	4951	5907

prune462.0ms (2.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	340	0	340
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	340	3	343

Error

0.0b

Counts

343 → 3

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)))))
✓	0.8b	(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)))))))
✓	32.6b	(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 20566 to 11931 computations (42% saved)

regimes4.4s (22.9%)

Accuracy

Total 0.6b remaining (56.4%)

Threshold costs 0.6b (56.4%)

Counts

171 → 1

Compiler

Compiled 130160 to 101463 computations (22% saved)

simplify3.0ms (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

end152.0ms (0.8%)

Remove: (sort kx ky)
Compiler: Compiled 352 to 270 computations (23.3% saved)

Details

analyze777.0ms (4%)

sample4.7s (24.3%)

simplify54.0ms (0.3%)

prune4.0ms (0%)

localize20.0ms (0.1%)

series354.0ms (1.8%)

rewrite7.0ms (0%)

simplify151.0ms (0.8%)

prune310.0ms (1.6%)

localize22.0ms (0.1%)

series4.8s (24.9%)

rewrite3.0ms (0%)

simplify123.0ms (0.6%)

prune883.0ms (4.6%)

localize24.0ms (0.1%)

series497.0ms (2.6%)

rewrite50.0ms (0.3%)

simplify184.0ms (1%)

prune425.0ms (2.2%)

localize25.0ms (0.1%)

series641.0ms (3.3%)

rewrite50.0ms (0.3%)

simplify176.0ms (0.9%)

prune462.0ms (2.4%)

regimes4.4s (22.9%)

simplify3.0ms (0%)

end152.0ms (0.8%)

Profiling