Details

analyze817.0ms (7%)

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 (32.8%)

Results

2.0s	6557×	body	128	valid
1.1s	800×	body	1024	valid
530.0ms	581×	body	512	valid
201.0ms	318×	body	256	valid

Compiler

Compiled 68 to 60 computations (11.8% saved)

preprocess39.0ms (0.3%)

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 (0.2%)

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

1.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.2b	(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)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (sin.f64 kx) 2)
✓	0.5b	(/.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)))
✓	1.9b	(fma.f64 (pow.f64 (*.f64 2 (/.f64 l Om)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) 1)
✓	8.4b	(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))

series650.0ms (5.6%)

Counts

4 → 148

Calls

39 calls:

72.0ms	(/.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
72.0ms	(/.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
69.0ms	(/.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
67.0ms	(/.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
27.0ms	(/.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	0

rewrite77.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

653×	`prod-diff_binary64`
197×	`add-sqr-sqrt_binary64`
193×	`pow1_binary64`
190×	`*-un-lft-identity_binary64`
184×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	94
1	405	85
2	4925	85

Stop Event

1×	node limit

Counts

4 → 93

simplify179.0ms (1.5%)

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

prune345.0ms (3%)

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

Counts

222 → 4

Alt Table

Status	Error	Program
	29.3b	(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)))))
	32.3b	(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))))))
✓	1.2b	(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)))))
▶	10.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (.f64 (/.f64 (.f64 l l) Om) (/.f64 (pow.f64 (sin.f64 ky) 2) Om)) 4 1)))))

Compiler

Compiled 12392 to 8571 computations (30.8% saved)

localize35.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.6b	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
✓	5.9b	(sqrt.f64 (fma.f64 (.f64 (/.f64 (.f64 l l) Om) (/.f64 (pow.f64 (sin.f64 ky) 2) Om)) 4 1))
✓	6.5b	(.f64 (/.f64 (.f64 l l) Om) (/.f64 (pow.f64 (sin.f64 ky) 2) Om))
✓	7.0b	(/.f64 (*.f64 l l) Om)

series163.0ms (1.4%)

Counts

4 → 100

Calls

30 calls:

22.0ms	(.f64 (/.f64 (.f64 l l) Om) (/.f64 (pow.f64 (sin.f64 ky) 2) Om))	l	-inf
16.0ms	(sqrt.f64 (fma.f64 (.f64 (/.f64 (.f64 l l) Om) (/.f64 (pow.f64 (sin.f64 ky) 2) Om)) 4 1))	ky	-inf
14.0ms	(sqrt.f64 (fma.f64 (.f64 (/.f64 (.f64 l l) Om) (/.f64 (pow.f64 (sin.f64 ky) 2) Om)) 4 1))	ky	inf
10.0ms	(.f64 (/.f64 (.f64 l l) Om) (/.f64 (pow.f64 (sin.f64 ky) 2) Om))	ky	-inf
9.0ms	(.f64 (/.f64 (.f64 l l) Om) (/.f64 (pow.f64 (sin.f64 ky) 2) Om))	l	0

rewrite65.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

248×	`expm1-udef_binary64`
248×	`log1p-udef_binary64`
147×	`add-sqr-sqrt_binary64`
144×	`pow1_binary64`
143×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	58
1	310	52
2	3866	52

Stop Event

1×	node limit

Counts

4 → 148

simplify49.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

744×	`associate-/l*_binary64`
573×	`associate-/r*_binary64`
255×	`fma-def_binary64`
207×	`associate-*l/_binary64`
178×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	127	2317
1	395	2267
2	1498	2234

Stop Event

1×	node limit

Counts

248 → 198

prune225.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	199	3	202

Error

Counts

202 → 3

Alt Table

Status	Error	Program
	16.1b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (.f64 (/.f64 (.f64 l l) Om) (*.f64 (/.f64 ky Om) ky)) 4 1)))))
✓	1.2b	(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)))))
▶	5.3b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om) Om) 4 1)))))

Compiler

Compiled 5372 to 3515 computations (34.6% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1/2 (sqrt.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om) Om) 4 1)))
✓	2.9b	(/.f64 (/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om) Om)
✓	4.9b	(/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om)
✓	5.9b	(sqrt.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om) Om) 4 1))

series301.0ms (2.6%)

Counts

4 → 144

Calls

36 calls:

43.0ms	(/.f64 1/2 (sqrt.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om) Om) 4 1)))	ky	inf
42.0ms	(/.f64 1/2 (sqrt.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om) Om) 4 1)))	ky	-inf
15.0ms	(sqrt.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om) Om) 4 1))	ky	inf
15.0ms	(sqrt.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om) Om) 4 1))	ky	-inf
12.0ms	(/.f64 (/.f64 (pow.f64 (*.f64 l (sin.f64 ky)) 2) Om) Om)	ky	inf

rewrite73.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

269×	`expm1-udef_binary64`
269×	`log1p-udef_binary64`
158×	`add-sqr-sqrt_binary64`
153×	`pow1_binary64`
152×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	72
1	334	63
2	4009	63

Stop Event

1×	node limit

Counts

4 → 122

simplify76.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

876×	`associate-/l*_binary64`
447×	`fma-def_binary64`
322×	`cancel-sign-sub-inv_binary64`
254×	`associate-/r/_binary64`
184×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	4069
1	555	3983
2	2109	3938

Stop Event

1×	node limit

Counts

266 → 204

prune230.0ms (2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	205	2	207

Error

Counts

207 → 2

Alt Table

Status	Error	Program
▶	3.6b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (log.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1)))))))
✓	1.2b	(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)))))

Status

Error

Program

▶

3.6b

(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (log.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1)))))))

✓

1.2b

(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 5719 to 3776 computations (34% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2)
✓	0.7b	(log.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1))))
✓	2.7b	(/.f64 (*.f64 l (sin.f64 ky)) Om)
✓	5.9b	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1))

series140.0ms (1.2%)

Counts

4 → 112

Calls

36 calls:

9.0ms	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1))	ky	-inf
9.0ms	(log.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1))))	ky	inf
9.0ms	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1))	ky	inf
8.0ms	(log.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1))))	ky	-inf
7.0ms	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1))	ky	0

rewrite68.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

610×	`log-prod_binary64`
224×	`expm1-udef_binary64`
224×	`log1p-udef_binary64`
195×	`log-pow_binary64`
131×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	57
1	284	57
2	3219	57

Stop Event

1×	node limit

Counts

4 → 160

simplify64.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

809×	`associate-/l*_binary64`
613×	`associate-/r*_binary64`
271×	`fma-def_binary64`
206×	`associate-/r/_binary64`
162×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	3450
1	430	3362
2	1596	3304

Stop Event

1×	node limit

Counts

272 → 179

prune177.0ms (1.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	179	2	181

Error

Counts

181 → 2

Alt Table

Status

Error

Program

✓

3.6b

(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (log.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (*.f64 l (sin.f64 ky)) Om) 2) 4 1)))))))

✓

1.2b

(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 5065 to 3330 computations (34.3% saved)

regimes3.9s (33.1%)

Accuracy

Total 0.7b remaining (83.3%)

Threshold costs 0.7b (83.3%)

Counts

151 → 3

Compiler

Compiled 78770 to 64717 computations (17.8% saved)

bsearch6.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(sin.f64 kx)
0.0ms	(sin.f64 kx)

Steps

Iters	Point		Range
-5.174496557575073e-305	∈ [	-5.174496557575073e-305	,	9.61966246705209e-291	]
-5.98664871367318e-76	∈ [	-5.98664871367318e-76	,	-4.7307516232512617e-76	]

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	114
1	45	114

Stop Event

1×

saturated

end108.0ms (0.9%)

Stop Event

1×

done

Remove

(sort kx ky)

Compiler

Compiled 359 to 272 computations (24.2% saved)

Details

analyze817.0ms (7%)

sample3.8s (32.8%)

preprocess39.0ms (0.3%)

simplify22.0ms (0.2%)

prune4.0ms (0%)

localize17.0ms (0.1%)

series650.0ms (5.6%)

rewrite77.0ms (0.7%)

simplify179.0ms (1.5%)

prune345.0ms (3%)

localize35.0ms (0.3%)

series163.0ms (1.4%)

rewrite65.0ms (0.6%)

simplify49.0ms (0.4%)

prune225.0ms (1.9%)

localize21.0ms (0.2%)

series301.0ms (2.6%)

rewrite73.0ms (0.6%)

simplify76.0ms (0.7%)

prune230.0ms (2%)

localize18.0ms (0.2%)

series140.0ms (1.2%)

rewrite68.0ms (0.6%)

simplify64.0ms (0.5%)

prune177.0ms (1.5%)

regimes3.9s (33.1%)

bsearch6.0ms (0%)

simplify7.0ms (0.1%)

end108.0ms (0.9%)

Profiling