Details

analyze833.0ms (5%)

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 (23.3%)

Results

2.0s	6580×	body	128	valid
1.1s	790×	body	1024	valid
522.0ms	548×	body	512	valid
208.0ms	338×	body	256	valid

Compiler

Compiled 68 to 60 computations (11.8% saved)

preprocess41.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

714×	`fma-def_binary64`
500×	`unswap-sqr_binary64`
324×	`associate-*l/_binary64`
288×	`associate-*r/_binary64`
262×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	294
1	237	259
2	654	259
3	3190	259
0	4	4
1	4	4

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort kx ky)

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify22.0ms (0.1%)

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

2.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.0b	(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 (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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)))
✓	0.3b	(pow.f64 (sin.f64 ky) 2)
✓	2.8b	(fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	7.3b	(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))

series752.0ms (4.5%)

Counts

4 → 148

Calls

39 calls:

78.0ms	(/.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)))	kx	inf
78.0ms	(/.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)))	kx	-inf
73.0ms	(/.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)))	ky	-inf
73.0ms	(/.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)))	ky	inf
34.0ms	(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))	Om	inf

rewrite84.0ms (0.5%)

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

simplify170.0ms (1%)

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	4886	10261

Stop Event

1×	node limit

Counts

241 → 221

prune343.0ms (2.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	217	4	221
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	218	4	222

Error

0.5b

Counts

222 → 4

Alt Table

Status	Error	Program
	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 4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)))))
▶	2.0b	(sqrt.f64 (+.f64 1/2 (-.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1))))) 1)))
	34.9b	(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))))))
	24.4b	(sqrt.f64 (+.f64 1/2 1/2))

Compiler

Compiled 12390 to 8574 computations (30.8% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2)
✓	2.8b	(fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1)
✓	3.6b	(-.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1))))) 1)
✓	7.3b	(sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1))

series3.7s (22.1%)

Counts

4 → 168

Calls

42 calls:

764.0ms	(-.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1))))) 1)	kx	-inf
716.0ms	(-.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1))))) 1)	kx	inf
681.0ms	(-.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1))))) 1)	ky	-inf
679.0ms	(-.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1))))) 1)	ky	inf
75.0ms	(-.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1))))) 1)	ky	0

rewrite48.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

203×	`add-sqr-sqrt_binary64`
198×	`expm1-log1p-u_binary64`
197×	`log1p-expm1-u_binary64`
192×	`add-cbrt-cube_binary64`
192×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	90
1	438	90

Stop Event

1×	node limit

Counts

4 → 114

simplify144.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

423×	`fma-def_binary64`
361×	`times-frac_binary64`
297×	`associate-/l*_binary64`
286×	`associate-/r*_binary64`
264×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	441	13088
1	1537	12417

Stop Event

1×	node limit

Counts

282 → 248

prune463.0ms (2.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	248	4	252

Error

0.5b

Counts

252 → 4

Alt Table

Status	Error	Program
	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 4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)))))
✓	2.0b	(sqrt.f64 (+.f64 1/2 (-.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1))))) 1)))
	34.9b	(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))))))
▶	24.4b	(sqrt.f64 (+.f64 1/2 1/2))

Compiler

Compiled 16385 to 11373 computations (30.6% saved)

localize2.0ms (0%)

prune6.0ms (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

0.5b

Counts

4 → 4

Alt Table

Status	Error	Program
▶	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 4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)))))
✓	2.0b	(sqrt.f64 (+.f64 1/2 (-.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1))))) 1)))
	34.9b	(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))))))
✓	24.4b	(sqrt.f64 (+.f64 1/2 1/2))

Compiler

Compiled 242 to 174 computations (28.1% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.3b	(.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
✓	3.5b	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
✓	26.8b	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
✓	27.2b	(sqrt.f64 (.f64 4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series578.0ms (3.5%)

Counts

4 → 156

Calls

39 calls:

31.0ms	(.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))	kx	-inf
29.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))	l	-inf
28.0ms	(.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))	ky	inf
28.0ms	(.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))	l	inf
27.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))	kx	inf

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

simplify89.0ms (0.5%)

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

prune358.0ms (2.2%)

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

0.5b

Counts

238 → 4

Alt Table

Status	Error	Program
✓	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 4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) Om)))))
✓	2.0b	(sqrt.f64 (+.f64 1/2 (-.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 (*.f64 4 (pow.f64 (/.f64 l Om) 2)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 2) 1))))) 1)))
	34.9b	(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))))))
✓	24.4b	(sqrt.f64 (+.f64 1/2 1/2))

Compiler

Compiled 11690 to 7151 computations (38.8% saved)

regimes4.9s (29.5%)

Accuracy

Total 0.7b remaining (78.1%)

Threshold costs 0.7b (78.1%)

Counts

196 → 1

Compiler

Compiled 143359 to 111803 computations (22% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	41
1	31	41
2	32	41

Stop Event

1×

saturated

end129.0ms (0.8%)

Stop Event

1×

fuel

Remove

(sort kx ky)

Compiler

Compiled 260 to 208 computations (20% saved)

Details

analyze833.0ms (5%)

sample3.9s (23.3%)

preprocess41.0ms (0.2%)

simplify22.0ms (0.1%)

prune4.0ms (0%)

localize20.0ms (0.1%)

series752.0ms (4.5%)

rewrite84.0ms (0.5%)

simplify170.0ms (1%)

prune343.0ms (2.1%)

localize21.0ms (0.1%)

series3.7s (22.1%)

rewrite48.0ms (0.3%)

simplify144.0ms (0.9%)

prune463.0ms (2.8%)

localize2.0ms (0%)

prune6.0ms (0%)

localize22.0ms (0.1%)

series578.0ms (3.5%)

rewrite42.0ms (0.3%)

simplify89.0ms (0.5%)

prune358.0ms (2.2%)

regimes4.9s (29.5%)

simplify2.0ms (0%)

end129.0ms (0.8%)

Profiling