Details

analyze821.0ms (9.9%)

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 (46.7%)

Symmetry

(sort kx ky)

Results

2.0s	6602×	body	128	valid
1.1s	771×	body	1024	valid
529.0ms	580×	body	512	valid
193.0ms	302×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 101 to 89 computations (11.9% saved)

simplify22.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
578×	`associate-l_binary64`
512×	`unswap-sqr_binary64`
433×	`associate-r_binary64`
328×	`associate-*l/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	42
1	56	37
2	126	37
3	580	37
4	3386	37

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.1%)

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

0.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.5b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 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)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (*.f64 2 (/.f64 l Om)) 2)
✓	0.3b	(pow.f64 (sin.f64 ky) 2)
✓	1.0b	(fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	8.5b	(sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))

series218.0ms (2.6%)

Counts

4 → 124

Calls

4 calls:

130.0ms	(sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))
74.0ms	(fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
10.0ms	(pow.f64 (*.f64 2 (/.f64 l Om)) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)

rewrite67.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

641×	`prod-diff_binary64`
167×	`add-sqr-sqrt_binary64`
163×	`log1p-expm1-u_binary64`
163×	`expm1-log1p-u_binary64`
159×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	72
1	355	66
2	4367	66

Stop Event

1×	node limit

Counts

4 → 98

Calls

4 calls:

65.0ms	(pow.f64 (*.f64 2 (/.f64 l Om)) 2)
65.0ms	(pow.f64 (sin.f64 ky) 2)
65.0ms	(fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
65.0ms	(sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1))

simplify95.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

489×	`cancel-sign-sub-inv_binary64`
262×	`unswap-sqr_binary64`
223×	`fma-neg_binary64`
197×	`fma-def_binary64`
188×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	6812
1	827	6253
2	3354	6245

Stop Event

1×	node limit

Counts

222 → 179

prune217.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	177	3	180

Error

Counts

180 → 3

Alt Table

Status	Error	Program
✓	0.5b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
	28.5b	(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 (.f64 (.f64 l l) 4) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) Om)))))
▶	23.5b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))

Compiler

Compiled 8308 to 5644 computations (32.1% saved)

localize3.0ms (0%)

prune3.0ms (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

Counts

3 → 3

Alt Table

Status	Error	Program
✓	0.5b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
▶	28.5b	(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 (.f64 (.f64 l l) 4) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) Om)))))
✓	23.5b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))

Compiler

Compiled 132 to 102 computations (22.7% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.3b	(.f64 (.f64 (*.f64 l l) 4) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
✓	2.3b	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
✓	27.5b	(sqrt.f64 (.f64 (.f64 (*.f64 l l) 4) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
✓	28.0b	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series344.0ms (4.2%)

Counts

4 → 144

Calls

4 calls:

190.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
61.0ms	(sqrt.f64 (.f64 (.f64 (*.f64 l l) 4) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
55.0ms	(.f64 (.f64 (*.f64 l l) 4) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
38.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite50.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

192×	`add-sqr-sqrt_binary64`
190×	`log1p-expm1-u_binary64`
190×	`expm1-log1p-u_binary64`
187×	`add-cbrt-cube_binary64`
186×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	93
1	417	59

Stop Event

1×	node limit

Counts

4 → 120

Calls

4 calls:

48.0ms	(.f64 (.f64 (*.f64 l l) 4) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
48.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
48.0ms	(sqrt.f64 (.f64 (.f64 (*.f64 l l) 4) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
48.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

742×	`associate-/l*_binary64`
378×	`cancel-sign-sub-inv_binary64`
192×	`fma-neg_binary64`
181×	`fma-def_binary64`
159×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	3900
1	621	3576
2	2427	3487

Stop Event

1×	node limit

Counts

264 → 196

prune235.0ms (2.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	196	3	199

Error

Counts

199 → 3

Alt Table

Status	Error	Program
✓	0.5b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)))))
✓	28.5b	(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 (.f64 (.f64 l l) 4) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) Om)))))
✓	23.5b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 1)))

Compiler

Compiled 9712 to 6035 computations (37.9% saved)

regimes2.1s (25.6%)

Accuracy

Total 0.6b remaining (56.9%)

Threshold costs 0.6b (56.9%)

Counts

79 → 1

Compiler

Compiled 64474 to 48891 computations (24.2% 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	21	36
1	26	36

Stop Event

1×

saturated

end97.0ms (1.2%)

Remove: (sort kx ky)
Compiler: Compiled 193 to 160 computations (17.1% saved)

Details

analyze821.0ms (9.9%)

sample3.9s (46.7%)

simplify22.0ms (0.3%)

prune4.0ms (0.1%)

localize18.0ms (0.2%)

series218.0ms (2.6%)

rewrite67.0ms (0.8%)

simplify95.0ms (1.1%)

prune217.0ms (2.6%)

localize3.0ms (0%)

prune3.0ms (0%)

localize23.0ms (0.3%)

series344.0ms (4.2%)

rewrite50.0ms (0.6%)

simplify69.0ms (0.8%)

prune235.0ms (2.8%)

regimes2.1s (25.6%)

simplify2.0ms (0%)

end97.0ms (1.2%)

Profiling