Details

analyze141.0ms (6.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	62.4%	12.6%	6
25%	46.8%	28.2%	7
31.2%	35.9%	32.9%	8
39%	25%	36%	9
42.9%	18.7%	38.3%	10
47.2%	12.9%	39.9%	11
49.4%	9.6%	41.1%	12
51.6%	6.5%	41.9%	13
52.7%	4.8%	42.4%	14

Compiler

Compiled 16 to 10 computations (37.5% saved)

sample851.0ms (40.1%)

Symmetry

(sort x y)

Results

797.0ms	8256×	body	128	valid
21.0ms	220×	body	128	invalid

Compiler

Compiled 47 to 29 computations (38.3% saved)

simplify9.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

33×	`fma-def_binary64`
8×	`*-commutative_binary64`
7×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	19	14
2	45	12
3	68	12
4	70	12
5	70	12

prune3.0ms (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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 x (fma.f64 2 y x) (*.f64 y y))

Compiler

Compiled 46 to 24 computations (47.8% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (fma.f64 2 y x) (*.f64 y y))

series6.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(fma.f64 x (fma.f64 2 y x) (*.f64 y y))

rewrite101.0ms (4.8%)

Algorithm

2×	batch-egg-rewrite

Rules

581×	`log1p-expm1-u_binary64`
581×	`expm1-log1p-u_binary64`
291×	`log-prod_binary64`
153×	`prod-diff_binary64`
122×	`expm1-udef_binary64`

Counts

1 → 29

Calls

1 calls:

100.0ms

(fma.f64 x (fma.f64 2 y x) (*.f64 y y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	140	12
2	1507	12
3	4949	12
4	4990	12
5	4958	12
0	0	0
1	0	0

simplify159.0ms (7.5%)

Algorithm

1×	egg-herbie

Rules

968×	`sqr-pow_binary64`
615×	`fma-def_binary64`
579×	`fabs-mul_binary64`
537×	`cube-prod_binary64`
464×	`*-commutative_binary64`

Counts

53 → 39

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	294
1	32	267
2	62	222
3	129	216
4	318	216
5	1005	216
6	1665	216
7	1886	216
8	2020	216
9	2235	216
10	2469	216
11	2722	216
12	2890	216
13	3334	216
14	3914	216
15	4267	216
16	4546	216
17	4648	216
18	4677	216
19	4689	216
20	5141	216

prune25.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	37	2	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	3	40

Error

Counts

40 → 3

Alt Table

Status	Error	Program
	0.0b	(fma.f64 y (fma.f64 2 x y) (*.f64 x x))
▶	0.0b	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
✓	0.0b	(fma.f64 x (fma.f64 2 y x) (*.f64 y y))

Compiler

Compiled 588 to 311 computations (47.1% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 y 2) (pow.f64 x 2))
✓	0.0b	(.f64 2 (.f64 y x))
✓	0.0b	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))

series19.0ms (0.9%)

Counts

3 → 18

Calls

3 calls:

7.0ms	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
6.0ms	(+.f64 (pow.f64 y 2) (pow.f64 x 2))
6.0ms	(.f64 2 (.f64 y x))

rewrite78.0ms (3.7%)

Algorithm

2×	batch-egg-rewrite

Rules

576×	`fma-def_binary64`
535×	`log-prod_binary64`
299×	`fma-neg_binary64`
193×	`expm1-udef_binary64`
193×	`log1p-udef_binary64`

Counts

3 → 161

Calls

3 calls:

75.0ms	(+.f64 (pow.f64 y 2) (pow.f64 x 2))
75.0ms	(.f64 2 (.f64 y x))
75.0ms	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	34
1	228	28
2	2814	28
3	5702	28
0	0	0
1	0	0

simplify157.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

968×	`sqr-pow_binary64`
579×	`fabs-mul_binary64`
537×	`cube-prod_binary64`
474×	`fma-def_binary64`
464×	`*-commutative_binary64`

Counts

179 → 169

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	10	114
1	26	111
2	49	102
3	110	96
4	284	96
5	949	96
6	1558	96
7	1753	96
8	1887	96
9	2102	96
10	2336	96
11	2597	96
12	2773	96
13	3216	96
14	3796	96
15	4149	96
16	4428	96
17	4530	96
18	4559	96
19	4571	96
20	5023	96

prune102.0ms (4.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	169	3	172

Error

Counts

172 → 3

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 y (fma.f64 2 x y) (*.f64 x x))
✓	0.0b	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
✓	0.0b	(fma.f64 x (fma.f64 2 y x) (*.f64 y y))

Compiler

Compiled 3002 to 1518 computations (49.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (fma.f64 2 x y) (*.f64 x x))

series6.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(fma.f64 y (fma.f64 2 x y) (*.f64 x x))

rewrite99.0ms (4.7%)

Algorithm

2×	batch-egg-rewrite

Rules

581×	`log1p-expm1-u_binary64`
581×	`expm1-log1p-u_binary64`
291×	`log-prod_binary64`
153×	`prod-diff_binary64`
122×	`expm1-udef_binary64`

Counts

1 → 29

Calls

1 calls:

98.0ms

(fma.f64 y (fma.f64 2 x y) (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	140	12
2	1507	12
3	4949	12
4	4990	12
5	4958	12
0	0	0
1	0	0

simplify159.0ms (7.5%)

Algorithm

1×	egg-herbie

Rules

968×	`sqr-pow_binary64`
615×	`fma-def_binary64`
579×	`fabs-mul_binary64`
537×	`cube-prod_binary64`
464×	`*-commutative_binary64`

Counts

53 → 39

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	294
1	32	267
2	62	222
3	129	216
4	318	216
5	1005	216
6	1665	216
7	1886	216
8	2020	216
9	2235	216
10	2469	216
11	2722	216
12	2890	216
13	3334	216
14	3914	216
15	4267	216
16	4546	216
17	4648	216
18	4677	216
19	4689	216
20	5141	216

prune23.0ms (1.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	39	3	42

Error

Counts

42 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 y (fma.f64 2 x y) (*.f64 x x))
✓	0.0b	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
✓	0.0b	(fma.f64 x (fma.f64 2 y x) (*.f64 y y))

Compiler

Compiled 562 to 294 computations (47.7% saved)

regimes78.0ms (3.7%)

Accuracy

Total 0.0b remaining (67.3%)

Threshold costs 0.0b (67.3%)

Counts

19 → 1

Compiler

Compiled 630 to 383 computations (39.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	9	15
2	9	15

end86.0ms (4%)

Remove: (sort x y)
Compiler: Compiled 89 to 51 computations (42.7% saved)

Details

analyze141.0ms (6.6%)

sample851.0ms (40.1%)

simplify9.0ms (0.4%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite101.0ms (4.8%)

simplify159.0ms (7.5%)

prune25.0ms (1.2%)

localize7.0ms (0.3%)

series19.0ms (0.9%)

rewrite78.0ms (3.7%)

simplify157.0ms (7.4%)

prune102.0ms (4.8%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite99.0ms (4.7%)

simplify159.0ms (7.5%)

prune23.0ms (1.1%)

regimes78.0ms (3.7%)

simplify2.0ms (0.1%)

end86.0ms (4%)

Profiling