Details

analyze4.3s (29.7%)

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
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
19.5%	80.3%	0.2%	12
21.2%	78.6%	0.2%	13
33%	66.8%	0.2%	14

Compiler

Compiled 34 to 30 computations (11.8% saved)

sample4.2s (29%)

Symmetry

(sort kx ky)

Results

2.1s	6617×	body	128	valid
1.2s	798×	body	1024	valid
684.0ms	547×	body	512	valid
183.0ms	294×	body	256	valid

Compiler

Compiled 67 to 59 computations (11.9% saved)

simplify54.0ms (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

1.8b

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)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (sin.f64 ky) 2)
✓	0.7b	(/.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)))
✓	2.6b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	10.0b	(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))

series1.4s (9.6%)

Counts

4 → 148

Calls

4 calls:

1.1s	(/.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)))
228.0ms	(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)
3.0ms	(pow.f64 (sin.f64 ky) 2)

rewrite13.0ms (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 ky) 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)

simplify258.0ms (1.8%)

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

prune382.0ms (2.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	220	5	225
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	221	5	226

Error

0.2b

Counts

226 → 5

Alt Table

Status	Error	Program
	25.9b	(sqrt.f64 (+.f64 1/2 1/2))
▶	1.8b	(sqrt.f64 (+.f64 1/2 (log1p.f64 (expm1.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)))))))
	26.9b	(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)))))
	33.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (.f64 (/.f64 4 Om) (/.f64 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) Om))))))
	33.9b	(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 13234 to 9475 computations (28.4% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (sin.f64 ky) 2)
	0.7b	(/.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)))
	2.6b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
	10.0b	(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))

prune408.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	225	0	225
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	225	5	230

Error

0.2b

Counts

230 → 5

Alt Table

Status	Error	Program
▶	25.9b	(sqrt.f64 (+.f64 1/2 1/2))
✓	1.8b	(sqrt.f64 (+.f64 1/2 (log1p.f64 (expm1.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)))))))
	26.9b	(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)))))
	33.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (.f64 (/.f64 4 Om) (/.f64 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) Om))))))
	33.9b	(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 13654 to 9899 computations (27.5% saved)

localize2.0ms (0%)

prune8.0ms (0.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	1	1
Total	5	5

Error

0.2b

Counts

5 → 5

Alt Table

Status	Error	Program
✓	25.9b	(sqrt.f64 (+.f64 1/2 1/2))
✓	1.8b	(sqrt.f64 (+.f64 1/2 (log1p.f64 (expm1.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)))))))
▶	26.9b	(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)))))
	33.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (.f64 (/.f64 4 Om) (/.f64 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) Om))))))
	33.9b	(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 300 to 220 computations (26.7% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.6b	(/.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)))
✓	3.9b	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
✓	23.6b	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
✓	24.0b	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series1.2s (8.1%)

Counts

4 → 156

Calls

4 calls:

787.0ms	(/.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)))
255.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
88.0ms	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
51.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite42.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`pow1_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`

Counts

4 → 95

Calls

4 calls:

11.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
11.0ms	(sqrt.f64 (.f64 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)))
2.0ms	(/.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)))

simplify278.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

895×	`times-frac_binary64`
515×	`fma-def_binary64`
223×	`*-commutative_binary64`
106×	`cancel-sign-sub-inv_binary64`
105×	`+-commutative_binary64`

Counts

251 → 248

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	684	14415
1	2199	13387
2	4902	13256
3	5011	13256

prune475.0ms (3.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	301	2	303
Fresh	2	0	2
Picked	1	0	1
Done	0	2	2
Total	304	4	308

Error

0.0b

Counts

308 → 4

Alt Table

Status	Error	Program
✓	25.9b	(sqrt.f64 (+.f64 1/2 1/2))
	26.9b	(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 (.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) l) -2) Om)))))
✓	1.8b	(sqrt.f64 (+.f64 1/2 (log1p.f64 (expm1.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)))))))
	25.9b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 2 (/.f64 (.f64 (sin.f64 kx) l) Om) (.f64 1/4 (/.f64 Om (*.f64 (sin.f64 kx) l)))))))

Compiler

Compiled 21898 to 13159 computations (39.9% saved)

regimes1.3s (9%)

Accuracy

Total 0.2b remaining (81.6%)

Threshold costs 0.2b (81.6%)

Counts

49 → 2

Compiler

Compiled 31263 to 24974 computations (20.1% saved)

bsearch3.0ms (0%)

Compiler: Compiled 21 to 17 computations (19% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	106
1	49	106
2	48	106

end145.0ms (1%)

Remove: (sort kx ky)
Compiler: Compiled 391 to 292 computations (25.3% saved)

Details

analyze4.3s (29.7%)

sample4.2s (29%)

simplify54.0ms (0.4%)

prune4.0ms (0%)

localize19.0ms (0.1%)

series1.4s (9.6%)

rewrite13.0ms (0.1%)

simplify258.0ms (1.8%)

prune382.0ms (2.6%)

localize24.0ms (0.2%)

prune408.0ms (2.8%)

localize2.0ms (0%)

prune8.0ms (0.1%)

localize24.0ms (0.2%)

series1.2s (8.1%)

rewrite42.0ms (0.3%)

simplify278.0ms (1.9%)

prune475.0ms (3.3%)

regimes1.3s (9%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end145.0ms (1%)

Profiling