Details

analyze855.0ms (7.1%)

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 (31.6%)

Symmetry

(sort kx ky)

Results

2.0s	6588×	body	128	valid
1.0s	758×	body	1024	valid
542.0ms	578×	body	512	valid
205.0ms	332×	body	256	valid

Compiler

Compiled 101 to 89 computations (11.9% saved)

simplify20.0ms (0.2%)

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%)

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

1.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.8b	(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)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (sin.f64 ky) 2)
✓	0.3b	(/.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)))
✓	2.4b	(fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	10.1b	(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))

series734.0ms (6.1%)

Counts

4 → 148

Calls

4 calls:

521.0ms	(/.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)))
134.0ms	(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))
75.0ms	(fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
3.0ms	(pow.f64 (sin.f64 ky) 2)

rewrite75.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

653×	`prod-diff_binary64`
189×	`add-sqr-sqrt_binary64`
184×	`log1p-expm1-u_binary64`
184×	`expm1-log1p-u_binary64`
180×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	94
1	402	85
2	4920	85

Stop Event

1×	node limit

Counts

4 → 93

Calls

4 calls:

71.0ms	(pow.f64 (sin.f64 ky) 2)
71.0ms	(/.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)))
71.0ms	(fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
71.0ms	(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))

simplify155.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

424×	`fma-neg_binary64`
336×	`fma-def_binary64`
266×	`*-commutative_binary64`
261×	`associate-r_binary64`
192×	`associate-*r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	373	11132
1	1219	10267
2	4887	10261

Stop Event

1×	node limit

Counts

241 → 221

prune343.0ms (2.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	218	3	221
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	218	4	222

Error

0.2b

Counts

222 → 4

Alt Table

Status	Error	Program
✓	1.8b	(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)))))
▶	25.8b	(sqrt.f64 (+.f64 1/2 1/2))
	27.1b	(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)))))
	32.6b	(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 (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))))) (/.f64 1/2 l))))))

Compiler

Compiled 12358 to 8547 computations (30.8% saved)

localize2.0ms (0%)

prune5.0ms (0%)

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

0.2b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	1.8b	(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)))))
✓	25.8b	(sqrt.f64 (+.f64 1/2 1/2))
▶	27.1b	(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)))))
	32.6b	(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 (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))))) (/.f64 1/2 l))))))

Compiler

Compiled 240 to 172 computations (28.3% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.6b	(.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
✓	4.3b	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
✓	28.6b	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
✓	29.1b	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series578.0ms (4.8%)

Counts

4 → 156

Calls

4 calls:

253.0ms	(.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
214.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
72.0ms	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
40.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite42.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

197×	`add-sqr-sqrt_binary64`
194×	`log1p-expm1-u_binary64`
194×	`expm1-log1p-u_binary64`
191×	`add-cbrt-cube_binary64`
190×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	98
1	428	59

Stop Event

1×	node limit

Counts

4 → 107

Calls

4 calls:

40.0ms	(.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
40.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
40.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
40.0ms	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

simplify85.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

480×	`cancel-sign-sub-inv_binary64`
236×	`associate-/r*_binary64`
230×	`fma-neg_binary64`
228×	`times-frac_binary64`
193×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	226	4662
1	785	4342
2	3332	4342

Stop Event

1×	node limit

Counts

263 → 185

prune300.0ms (2.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	234	0	234
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	234	4	238

Error

0.2b

Counts

238 → 4

Alt Table

Status	Error	Program
✓	1.8b	(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)))))
✓	25.8b	(sqrt.f64 (+.f64 1/2 1/2))
✓	27.1b	(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)))))
▶	32.6b	(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 (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))))) (/.f64 1/2 l))))))

Compiler

Compiled 11743 to 7185 computations (38.8% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	8.8b	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))
✓	9.9b	(/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))
✓	26.3b	(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)))))
✓	26.6b	(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)))))

series468.0ms (3.9%)

Counts

4 → 120

Calls

4 calls:

284.0ms	(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)))))
131.0ms	(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)))))
26.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 Om Om))
26.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 Om Om))

rewrite38.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

195×	`add-sqr-sqrt_binary64`
193×	`log1p-expm1-u_binary64`
193×	`expm1-log1p-u_binary64`
190×	`add-cbrt-cube_binary64`
189×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	86
1	421	52

Stop Event

1×	node limit

Counts

4 → 108

Calls

4 calls:

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

simplify60.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

942×	`associate-/l*_binary64`
547×	`fma-def_binary64`
300×	`cancel-sign-sub-inv_binary64`
227×	`associate-/r/_binary64`
156×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	3208
1	562	3064
2	2180	2780

Stop Event

1×	node limit

Counts

228 → 169

prune325.0ms (2.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	243	4	247

Error

0.2b

Counts

247 → 4

Alt Table

Status	Error	Program
✓	1.8b	(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)))))
✓	25.8b	(sqrt.f64 (+.f64 1/2 1/2))
✓	27.1b	(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)))))
✓	32.6b	(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 (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))))) (/.f64 1/2 l))))))

Compiler

Compiled 13497 to 7878 computations (41.6% saved)

regimes4.0s (32.7%)

Accuracy

Total 0.5b remaining (70.9%)

Threshold costs 0.5b (70.9%)

Counts

141 → 2

Compiler

Compiled 121125 to 88856 computations (26.6% saved)

bsearch9.0ms (0.1%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	137
1	64	137

Stop Event

1×

saturated

end148.0ms (1.2%)

Remove: (sort kx ky)
Compiler: Compiled 506 to 362 computations (28.5% saved)

Details

analyze855.0ms (7.1%)

sample3.8s (31.6%)

simplify20.0ms (0.2%)

prune4.0ms (0%)

localize20.0ms (0.2%)

series734.0ms (6.1%)

rewrite75.0ms (0.6%)

simplify155.0ms (1.3%)

prune343.0ms (2.8%)

localize2.0ms (0%)

prune5.0ms (0%)

localize24.0ms (0.2%)

series578.0ms (4.8%)

rewrite42.0ms (0.3%)

simplify85.0ms (0.7%)

prune300.0ms (2.5%)

localize23.0ms (0.2%)

series468.0ms (3.9%)

rewrite38.0ms (0.3%)

simplify60.0ms (0.5%)

prune325.0ms (2.7%)

regimes4.0s (32.7%)

bsearch9.0ms (0.1%)

simplify3.0ms (0%)

end148.0ms (1.2%)

Profiling