Details

analyze864.0ms (8.8%)

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)

sample158.0ms (1.6%)

Algorithm

1×

intervals

Symmetry

(sort kx ky)

Results

54.0ms	219×	body	128	valid
26.0ms	21×	body	1024	valid
6.0ms	8×	body	512	valid
4.0ms	8×	body	256	valid

Compiler

Compiled 71 to 63 computations (11.3% saved)

simplify53.0ms (0.5%)

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)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (sin.f64 kx) 2)
✓	0.3b	(/.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)))
✓	1.7b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	8.0b	(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))

series1.2s (12.6%)

Counts

4 → 148

Calls

4 calls:

894.0ms	(/.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)))
236.0ms	(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))
110.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
6.0ms	(pow.f64 (sin.f64 kx) 2)

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
15×	`sqrt-prod_binary64`

Counts

4 → 86

Calls

4 calls:

3.0ms	(/.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)))
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)

simplify245.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

417×	`fma-neg_binary64`
342×	`fma-def_binary64`
271×	`associate-r_binary64`
200×	`associate-l_binary64`
200×	`associate-*r/_binary64`

Counts

234 → 225

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	476	14253
1	1374	13174
2	4955	13168
3	5267	13168

prune369.0ms (3.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	222	3	225
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	223	3	226

Error

0.2b

Counts

226 → 3

Alt Table

Status	Error	Program
	34.8b	(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))))))
	21.1b	(sqrt.f64 (+.f64 1/2 1/2))
▶	0.8b	(sqrt.f64 (+.f64 1/2 (expm1.f64 (log1p.f64 (/.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 13082 to 9361 computations (28.4% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (sin.f64 kx) 2)
	0.3b	(/.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)))
	1.7b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
	8.0b	(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))

prune351.0ms (3.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	225	0	225
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	225	3	228

Error

0.2b

Counts

228 → 3

Alt Table

Status	Error	Program
	34.8b	(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))))))
▶	21.1b	(sqrt.f64 (+.f64 1/2 1/2))
✓	0.8b	(sqrt.f64 (+.f64 1/2 (expm1.f64 (log1p.f64 (/.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 13502 to 9785 computations (27.5% saved)

localize2.0ms (0%)

prune5.0ms (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
▶	34.8b	(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))))))
✓	21.1b	(sqrt.f64 (+.f64 1/2 1/2))
✓	0.8b	(sqrt.f64 (+.f64 1/2 (expm1.f64 (log1p.f64 (/.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 148 to 106 computations (28.4% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.7b	(/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))
✓	7.5b	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
✓	28.2b	(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)))))
✓	28.8b	(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)))))

series622.0ms (6.3%)

Counts

4 → 120

Calls

4 calls:

388.0ms	(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)))))
164.0ms	(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)))))
36.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
33.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))

rewrite48.0ms (0.5%)

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:

16.0ms	(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)))))
12.0ms	(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)))))
5.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
5.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))

simplify170.0ms (1.7%)

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

prune424.0ms (4.3%)

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

0.2b

Counts

343 → 3

Alt Table

Status	Error	Program
✓	34.8b	(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))))))
✓	21.1b	(sqrt.f64 (+.f64 1/2 1/2))
✓	0.8b	(sqrt.f64 (+.f64 1/2 (expm1.f64 (log1p.f64 (/.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 20507 to 11891 computations (42% saved)

regimes1.7s (17.4%)

Accuracy

Total 0.6b remaining (64.8%)

Threshold costs 0.6b (64.8%)

Counts

68 → 1

Compiler

Compiled 50254 to 39022 computations (22.4% 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	24	42
1	29	42
2	28	42

end7.0ms (0.1%)

Remove: (sort kx ky)
Compiler: Compiled 93 to 81 computations (12.9% saved)

sample3.5s (35.4%)

Algorithm

1×

intervals

Results

1.5s	6375×	body	128	valid
891.0ms	749×	body	1024	valid
453.0ms	539×	body	512	valid
173.0ms	337×	body	256	valid

Compiler

Compiled 162 to 131 computations (19.1% saved)

Details

analyze864.0ms (8.8%)

sample158.0ms (1.6%)

simplify53.0ms (0.5%)

prune4.0ms (0%)

localize18.0ms (0.2%)

series1.2s (12.6%)

rewrite12.0ms (0.1%)

simplify245.0ms (2.5%)

prune369.0ms (3.7%)

localize27.0ms (0.3%)

prune351.0ms (3.6%)

localize2.0ms (0%)

prune5.0ms (0%)

localize22.0ms (0.2%)

series622.0ms (6.3%)

rewrite48.0ms (0.5%)

simplify170.0ms (1.7%)

prune424.0ms (4.3%)

regimes1.7s (17.4%)

simplify2.0ms (0%)

end7.0ms (0.1%)

sample3.5s (35.4%)

Profiling