Details

analyze818.0ms (8.3%)

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)

sample3.8s (38.6%)

Symmetry

(sort kx ky)

Results

2.0s	6594×	body	128	valid
1.0s	774×	body	1024	valid
506.0ms	547×	body	512	valid
200.0ms	340×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 101 to 89 computations (11.9% saved)

simplify55.0ms (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

1.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.5b	(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)
✓	0.4b	(/.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)))
✓	1.6b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	10.4b	(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))

series668.0ms (6.8%)

Counts

4 → 148

Calls

4 calls:

446.0ms	(/.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)))
146.0ms	(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))
72.0ms	(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)

rewrite14.0ms (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)

simplify241.0ms (2.4%)

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

prune349.0ms (3.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	222	3	225
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	222	4	226

Error

0.4b

Counts

226 → 4

Alt Table

Status	Error	Program
▶	22.6b	(sqrt.f64 (+.f64 1/2 1/2))
✓	1.5b	(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)))))
	30.2b	(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)))))
	35.3b	(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 13144 to 9401 computations (28.5% saved)

localize2.0ms (0%)

prune6.0ms (0.1%)

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

0.4b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	22.6b	(sqrt.f64 (+.f64 1/2 1/2))
✓	1.5b	(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)))))
▶	30.2b	(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)))))
	35.3b	(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 240 to 172 computations (28.3% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(/.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)))
✓	3.0b	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
✓	25.7b	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
✓	25.8b	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series947.0ms (9.6%)

Counts

4 → 156

Calls

4 calls:

663.0ms	(/.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)))
173.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
71.0ms	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
39.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite39.0ms (0.4%)

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)))))
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	(.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)))

simplify253.0ms (2.6%)

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

prune497.0ms (5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	302	1	303
Fresh	1	0	1
Picked	1	0	1
Done	1	1	2
Total	305	2	307

Error

Counts

307 → 2

Alt Table

Status	Error	Program
▶	29.6b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 2 (/.f64 (.f64 (sin.f64 ky) l) Om) (.f64 1/4 (/.f64 Om (*.f64 (sin.f64 ky) l)))))))
✓	1.5b	(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)))))

Status

Error

Program

▶

29.6b

(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 2 (/.f64 (*.f64 (sin.f64 ky) l) Om) (*.f64 1/4 (/.f64 Om (*.f64 (sin.f64 ky) l)))))))

✓

1.5b

(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 21873 to 13137 computations (39.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sin.f64 ky) l)
✓	0.9b	(/.f64 Om (*.f64 (sin.f64 ky) l))
✓	0.9b	(/.f64 1/2 (fma.f64 2 (/.f64 (.f64 (sin.f64 ky) l) Om) (.f64 1/4 (/.f64 Om (*.f64 (sin.f64 ky) l)))))
✓	1.0b	(/.f64 (*.f64 (sin.f64 ky) l) Om)

series153.0ms (1.6%)

Counts

4 → 132

Calls

4 calls:

94.0ms	(/.f64 1/2 (fma.f64 2 (/.f64 (.f64 (sin.f64 ky) l) Om) (.f64 1/4 (/.f64 Om (*.f64 (sin.f64 ky) l)))))
31.0ms	(/.f64 Om (*.f64 (sin.f64 ky) l))
20.0ms	(/.f64 (*.f64 (sin.f64 ky) l) Om)
8.0ms	(*.f64 (sin.f64 ky) l)

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`

Counts

4 → 95

Calls

4 calls:

4.0ms	(/.f64 (*.f64 (sin.f64 ky) l) Om)
3.0ms	(/.f64 Om (*.f64 (sin.f64 ky) l))
3.0ms	(*.f64 (sin.f64 ky) l)
2.0ms	(/.f64 1/2 (fma.f64 2 (/.f64 (.f64 (sin.f64 ky) l) Om) (.f64 1/4 (/.f64 Om (*.f64 (sin.f64 ky) l)))))

simplify138.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

501×	`fma-def_binary64`
458×	`associate-/l/_binary64`
308×	`cancel-sign-sub-inv_binary64`
246×	`fma-neg_binary64`
198×	`associate-/l*_binary64`

Counts

227 → 199

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	284	4707
1	715	4321
2	2727	4299
3	4951	4294
4	5046	4294

prune167.0ms (1.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	236	0	236
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	236	2	238

Error

Counts

238 → 2

Alt Table

Status	Error	Program
✓	29.6b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 2 (/.f64 (.f64 (sin.f64 ky) l) Om) (.f64 1/4 (/.f64 Om (*.f64 (sin.f64 ky) l)))))))
✓	1.5b	(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)))))

Status

Error

Program

✓

29.6b

(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fma.f64 2 (/.f64 (*.f64 (sin.f64 ky) l) Om) (*.f64 1/4 (/.f64 Om (*.f64 (sin.f64 ky) l)))))))

✓

1.5b

(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 7274 to 3569 computations (50.9% saved)

regimes1.5s (15.5%)

Accuracy

Total 0.0b remaining (1.2%)

Threshold costs 0.0b (1.2%)

Counts

56 → 2

Compiler

Compiled 37365 to 28700 computations (23.2% saved)

bsearch3.0ms (0%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	98
1	46	98
2	45	98

end102.0ms (1%)

Remove: (sort kx ky)
Compiler: Compiled 325 to 245 computations (24.6% saved)

Details

analyze818.0ms (8.3%)

sample3.8s (38.6%)

simplify55.0ms (0.6%)

prune4.0ms (0%)

localize17.0ms (0.2%)

series668.0ms (6.8%)

rewrite14.0ms (0.1%)

simplify241.0ms (2.4%)

prune349.0ms (3.5%)

localize2.0ms (0%)

prune6.0ms (0.1%)

localize22.0ms (0.2%)

series947.0ms (9.6%)

rewrite39.0ms (0.4%)

simplify253.0ms (2.6%)

prune497.0ms (5%)

localize13.0ms (0.1%)

series153.0ms (1.6%)

rewrite17.0ms (0.2%)

simplify138.0ms (1.4%)

prune167.0ms (1.7%)

regimes1.5s (15.5%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end102.0ms (1%)

Profiling