Details

analyze914.0ms (6.3%)

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)

sample4.2s (29.2%)

Symmetry

(sort kx ky)

Results

2.1s	6612×	body	128	valid
1.1s	751×	body	1024	valid
675.0ms	575×	body	512	valid
204.0ms	318×	body	256	valid

Compiler

Compiled 101 to 89 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

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

1.5b

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)

localize20.0ms (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)))
✓	3.0b	(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))

series1.2s (8.4%)

Counts

4 → 148

Calls

4 calls:

880.0ms	(/.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)))
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))
100.0ms	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
4.0ms	(pow.f64 (sin.f64 ky) 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:

4.0ms	(/.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)

simplify262.0ms (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

prune1.1s (7.7%)

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

0.6b

Counts

226 → 3

Alt Table

Status	Error	Program
	33.5b	(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))))))
▶	1.5b	(sqrt.f64 (+.f64 1/2 (log.f64 (exp.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)))))))
	25.0b	(sqrt.f64 (+.f64 1/2 1/2))

Compiler

Compiled 13082 to 9361 computations (28.4% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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)))
	3.0b	(fma.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	3.2b	(log.f64 (exp.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)))))
	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))

series855.0ms (5.9%)

Counts

1 → 48

Calls

1 calls:

855.0ms

(log.f64 (exp.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)))))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`log-pow_binary64`
22×	`exp-prod_binary64`
18×	`times-frac_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`

Counts

1 → 36

Calls

1 calls:

4.0ms

(log.f64 (exp.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)))))

simplify147.0ms (1%)

Algorithm

1×	egg-herbie

Rules

838×	`fma-def_binary64`
318×	`cancel-sign-sub-inv_binary64`
252×	`unswap-sqr_binary64`
197×	`fma-neg_binary64`
161×	`associate-r_binary64`

Counts

84 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	328	5968
1	839	5642
2	2940	5606
3	4981	5606

prune554.0ms (3.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	300	0	300
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	300	3	303

Error

0.6b

Counts

303 → 3

Alt Table

Status	Error	Program
	33.5b	(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))))))
✓	1.5b	(sqrt.f64 (+.f64 1/2 (log.f64 (exp.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)))))))
▶	25.0b	(sqrt.f64 (+.f64 1/2 1/2))

Compiler

Compiled 19362 to 14024 computations (27.6% saved)

localize2.0ms (0%)

prune4.0ms (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

0.6b

Counts

3 → 3

Alt Table

Status	Error	Program
▶	33.5b	(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))))))
✓	1.5b	(sqrt.f64 (+.f64 1/2 (log.f64 (exp.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)))))))
✓	25.0b	(sqrt.f64 (+.f64 1/2 1/2))

Compiler

Compiled 148 to 106 computations (28.4% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.9b	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
✓	9.8b	(/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))
✓	26.8b	(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)))))
✓	27.1b	(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)))))

series651.0ms (4.5%)

Counts

4 → 120

Calls

4 calls:

400.0ms	(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)))))
176.0ms	(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)))))
38.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
36.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))

rewrite51.0ms (0.4%)

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)))))
15.0ms	(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)))))
6.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
5.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))

simplify183.0ms (1.3%)

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

prune439.0ms (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

0.6b

Counts

343 → 3

Alt Table

Status	Error	Program
✓	33.5b	(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))))))
✓	1.5b	(sqrt.f64 (+.f64 1/2 (log.f64 (exp.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)))))))
✓	25.0b	(sqrt.f64 (+.f64 1/2 1/2))

Compiler

Compiled 20507 to 11890 computations (42% saved)

regimes3.5s (24.6%)

Accuracy

Total 0.7b remaining (61.8%)

Threshold costs 0.7b (61.8%)

Counts

137 → 1

Compiler

Compiled 101810 to 80930 computations (20.5% 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	23	41
1	28	41
2	27	41

end116.0ms (0.8%)

Remove: (sort kx ky)
Compiler: Compiled 213 to 174 computations (18.3% saved)

Details

analyze914.0ms (6.3%)

sample4.2s (29.2%)

simplify54.0ms (0.4%)

prune5.0ms (0%)

localize20.0ms (0.1%)

series1.2s (8.4%)

rewrite12.0ms (0.1%)

simplify262.0ms (1.8%)

prune1.1s (7.7%)

localize29.0ms (0.2%)

series855.0ms (5.9%)

rewrite9.0ms (0.1%)

simplify147.0ms (1%)

prune554.0ms (3.9%)

localize2.0ms (0%)

prune4.0ms (0%)

localize28.0ms (0.2%)

series651.0ms (4.5%)

rewrite51.0ms (0.4%)

simplify183.0ms (1.3%)

prune439.0ms (3%)

regimes3.5s (24.6%)

simplify2.0ms (0%)

end116.0ms (0.8%)

Profiling