Details

analyze888.0ms (9.3%)

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)

sample3.9s (41.1%)

Alt Table

Status	Error	Program
▶	1.0b	(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))))

Symmetry

(sort kx ky)

Results

2.0s	6534×	body	128	valid
1.1s	804×	body	1024	valid
550.0ms	588×	body	512	valid
197.0ms	330×	body	256	valid

Compiler

Compiled 167 to 147 computations (12% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (sin.f64 ky) 2)
✓	0.6b	(/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
✓	1.8b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
✓	7.1b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series1.5s (15.7%)

Counts

4 → 148

Calls

4 calls:

913.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
354.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
234.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 ky) 2)

rewrite80.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

318×	`prod-diff_binary64`
197×	`add-sqr-sqrt_binary64`
192×	`log1p-expm1-u_binary64`
192×	`expm1-log1p-u_binary64`
185×	`add-log-exp_binary64`

Counts

4 → 96

Calls

4 calls:

77.0ms	(pow.f64 (sin.f64 ky) 2)
77.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
77.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
77.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	97
1	411	69
2	4614	69
3	5243	69
0	0	0
1	0	0

prune309.0ms (3.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	243	1	244
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	244	1	245

Error

Counts

245 → 1

Alt Table

Status	Error	Program
▶	0b	(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (hypot.f64 1 (.f64 (/.f64 (*.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))))

Compiler

Compiled 11900 to 9241 computations (22.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 1 (hypot.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))
✓	0.1b	(hypot.f64 (sin.f64 kx) (sin.f64 ky))
✓	0.2b	(.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
✓	0.6b	(/.f64 1 (hypot.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))

series1.8s (19.2%)

Counts

4 → 168

Calls

4 calls:

870.0ms	(/.f64 1 (hypot.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
802.0ms	(+.f64 1 (/.f64 1 (hypot.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))
138.0ms	(.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
27.0ms	(hypot.f64 (sin.f64 kx) (sin.f64 ky))

rewrite77.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

295×	`log1p-udef_binary64`
252×	`prod-diff_binary64`
166×	`add-sqr-sqrt_binary64`
157×	`log1p-expm1-u_binary64`
157×	`expm1-log1p-u_binary64`

Counts

4 → 102

Calls

4 calls:

73.0ms	(+.f64 1 (/.f64 1 (hypot.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))
73.0ms	(hypot.f64 (sin.f64 kx) (sin.f64 ky))
73.0ms	(.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
73.0ms	(/.f64 1 (hypot.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	74
1	336	74
2	4065	74
3	5102	74
0	0	0
1	0	0

prune291.0ms (3%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	270	1	271

Error

Counts

271 → 1

Alt Table

Status	Error	Program
✓	0b	(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (hypot.f64 1 (.f64 (/.f64 (*.f64 2 l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))))

Compiler

Compiled 11824 to 8900 computations (24.7% saved)

regimes542.0ms (5.7%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

17 → 1

Compiler

Compiled 10958 to 9717 computations (11.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	31
1	26	31
2	24	31

end66.0ms (0.7%)

Remove: (sort kx ky)
Compiler: Compiled 122 to 102 computations (16.4% saved)

Details

analyze888.0ms (9.3%)

sample3.9s (41.1%)

localize19.0ms (0.2%)

series1.5s (15.7%)

rewrite80.0ms (0.8%)

prune309.0ms (3.2%)

localize15.0ms (0.2%)

series1.8s (19.2%)

rewrite77.0ms (0.8%)

prune291.0ms (3%)

regimes542.0ms (5.7%)

simplify2.0ms (0%)

end66.0ms (0.7%)

Profiling