Details

analyze852.0ms (7.6%)

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)

sample4.0s (35.4%)

Symmetry

(sort kx ky)

Results

2.1s	6582×	body	128	valid
1.1s	785×	body	1024	valid
506.0ms	559×	body	512	valid
225.0ms	329×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 101 to 89 computations (11.9% saved)

simplify54.0ms (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

prune5.0ms (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

1.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.3b	(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)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (sin.f64 ky) 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)))
✓	1.7b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	8.9b	(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))

series1.8s (16.2%)

Counts

4 → 148

Calls

4 calls:

865.0ms	(/.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)))
731.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
225.0ms	(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))
3.0ms	(pow.f64 (sin.f64 ky) 2)

rewrite11.0ms (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)

simplify237.0ms (2.1%)

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

prune351.0ms (3.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	221	4	225
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	222	4	226

Error

0.5b

Counts

226 → 4

Alt Table

Status	Error	Program
	1.3b	(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)))))))
	22.2b	(sqrt.f64 (+.f64 1/2 1/2))
	30.3b	(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)))))
▶	1.3b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (cbrt.f64 (pow.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)) 3)))))

Compiler

Compiled 13128 to 9411 computations (28.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1/2 (cbrt.f64 (pow.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)) 3)))
	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)
	8.9b	(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))
✓	13.4b	(cbrt.f64 (pow.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)) 3))

series1.3s (11.1%)

Counts

2 → 96

Calls

2 calls:

1.0s

(/.f64 1/2 (cbrt.f64 (pow.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)) 3)))

221.0ms

(cbrt.f64 (pow.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)) 3))

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`cbrt-prod_binary64`
63×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
53×	`add-sqr-sqrt_binary64`
53×	`add-cube-cbrt_binary64`

Counts

2 → 130

Calls

2 calls:

7.0ms

(/.f64 1/2 (cbrt.f64 (pow.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)) 3)))

2.0ms

(cbrt.f64 (pow.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)) 3))

simplify375.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

365×	`fma-neg_binary64`
296×	`fma-def_binary64`
254×	`*-commutative_binary64`
253×	`associate-r_binary64`
191×	`associate-l_binary64`

Counts

226 → 238

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	471	15429
1	1256	14856
2	4577	14818
3	4967	14818
4	4974	14818
5	4949	14818

prune597.0ms (5.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	336	4	340

Error

0.5b

Counts

340 → 4

Alt Table

Status	Error	Program
▶	1.3b	(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)))))))
	22.2b	(sqrt.f64 (+.f64 1/2 1/2))
	30.3b	(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)))))
✓	1.3b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (cbrt.f64 (pow.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)) 3)))))

Compiler

Compiled 21277 to 15500 computations (27.2% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (sin.f64 ky) 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)))
	1.7b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
	8.9b	(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))

prune367.0ms (3.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	225	0	225
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	225	4	229

Error

0.5b

Counts

229 → 4

Alt Table

Status	Error	Program
✓	1.3b	(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)))))))
▶	22.2b	(sqrt.f64 (+.f64 1/2 1/2))
	30.3b	(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)))))
✓	1.3b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (cbrt.f64 (pow.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)) 3)))))

Compiler

Compiled 13517 to 9808 computations (27.4% saved)

localize2.0ms (0%)

prune5.0ms (0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

0.5b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	1.3b	(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)))))))
✓	22.2b	(sqrt.f64 (+.f64 1/2 1/2))
	30.3b	(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)))))
✓	1.3b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (cbrt.f64 (pow.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)) 3)))))

Compiler

Compiled 116 to 95 computations (18.1% saved)

regimes1.1s (9.8%)

Accuracy

Total 0.6b remaining (54%)

Threshold costs 0.6b (54%)

Counts

47 → 1

Compiler

Compiled 27777 to 23442 computations (15.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	101
1	30	101
2	29	101

end144.0ms (1.3%)

Remove: (sort kx ky)
Compiler: Compiled 392 to 307 computations (21.7% saved)

Details

analyze852.0ms (7.6%)

sample4.0s (35.4%)

simplify54.0ms (0.5%)

prune5.0ms (0%)

localize16.0ms (0.1%)

series1.8s (16.2%)

rewrite11.0ms (0.1%)

simplify237.0ms (2.1%)

prune351.0ms (3.1%)

localize18.0ms (0.2%)

series1.3s (11.1%)

rewrite28.0ms (0.2%)

simplify375.0ms (3.3%)

prune597.0ms (5.3%)

localize21.0ms (0.2%)

prune367.0ms (3.3%)

localize2.0ms (0%)

prune5.0ms (0%)

regimes1.1s (9.8%)

simplify5.0ms (0%)

end144.0ms (1.3%)

Profiling