Details

analyze872.0ms (9.5%)

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 (44.4%)

Symmetry

(sort kx ky)

Results

2.1s	6576×	body	128	valid
1.1s	777×	body	1024	valid
534.0ms	555×	body	512	valid
227.0ms	348×	body	256	valid

Compiler

Compiled 101 to 89 computations (11.9% saved)

simplify56.0ms (0.6%)

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)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (sin.f64 kx) 2)
✓	0.2b	(pow.f64 (sin.f64 ky) 2)
✓	0.9b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	9.2b	(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))

series332.0ms (3.6%)

Counts

4 → 104

Calls

4 calls:

221.0ms	(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)
5.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)

rewrite6.0ms (0.1%)

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 (1.6%)

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

prune337.0ms (3.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	159	3	162

Error

0.2b

Counts

162 → 3

Alt Table

Status	Error	Program
▶	24.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))
✓	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)))))
	28.3b	(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)))))

Compiler

Compiled 7831 to 5595 computations (28.6% saved)

localize3.0ms (0%)

prune3.0ms (0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	1	1
Total	3	3

Error

0.2b

Counts

3 → 3

Alt Table

Status	Error	Program
✓	24.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))
✓	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)))))
▶	28.3b	(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)))))

Compiler

Compiled 132 to 102 computations (22.7% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
✓	2.5b	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
✓	25.4b	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
✓	25.4b	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series1.3s (14.3%)

Counts

4 → 156

Calls

4 calls:

924.0ms	(.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
224.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
109.0ms	(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)))

rewrite54.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`pow1_binary64`
20×	`sqrt-prod_binary64`
17×	`associate-r_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`

Counts

4 → 97

Calls

4 calls:

13.0ms	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
13.0ms	(.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
10.0ms	(.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)))))

simplify222.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

312×	`associate-r_binary64`
304×	`fma-neg_binary64`
281×	`associate-l_binary64`
257×	`associate-/r*_binary64`
244×	`times-frac_binary64`

Counts

253 → 222

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	361	7391
1	1076	6804
2	4340	6748
3	4897	6748
4	4998	6748
5	4949	6748

prune387.0ms (4.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	277	3	280

Error

0.2b

Counts

280 → 3

Alt Table

Status	Error	Program
✓	24.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))
✓	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)))))
✓	28.3b	(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)))))

Compiler

Compiled 15190 to 9593 computations (36.8% saved)

regimes1.2s (13.2%)

Accuracy

Total 0.6b remaining (56.2%)

Threshold costs 0.6b (56.2%)

Counts

39 → 1

Compiler

Compiled 29364 to 22620 computations (23% 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	37
1	26	37
2	25	37

end102.0ms (1.1%)

Remove: (sort kx ky)
Compiler: Compiled 197 to 164 computations (16.8% saved)

Details

analyze872.0ms (9.5%)

sample4.1s (44.4%)

simplify56.0ms (0.6%)

prune4.0ms (0%)

localize17.0ms (0.2%)

series332.0ms (3.6%)

rewrite6.0ms (0.1%)

simplify147.0ms (1.6%)

prune337.0ms (3.7%)

localize3.0ms (0%)

prune3.0ms (0%)

localize23.0ms (0.2%)

series1.3s (14.3%)

rewrite54.0ms (0.6%)

simplify222.0ms (2.4%)

prune387.0ms (4.2%)

regimes1.2s (13.2%)

simplify2.0ms (0%)

end102.0ms (1.1%)

Profiling