Details

analyze179.0ms (9.6%)

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
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
81.1%	18.7%	0.1%	9
81.1%	18.7%	0.1%	10
81.1%	15.6%	3.3%	11
84.3%	10.9%	4.8%	12
84.3%	10.9%	4.8%	13
84.3%	8.6%	7.2%	14

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample972.0ms (52.1%)

Symmetry

(sort x y)

Results

845.0ms	8255×	body	128	valid
49.0ms	509×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 38 to 29 computations (23.7% saved)

simplify25.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

209×	`fma-def_binary64`
157×	`fma-neg_binary64`
56×	`cancel-sign-sub-inv_binary64`
42×	`distribute-rgt-neg-in_binary64`
36×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	15	13
2	26	13
3	39	13
4	66	11
5	109	11
6	198	11
7	307	11
8	429	11
9	522	11
10	578	11
11	593	11
12	596	11
13	513	11

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 z -1/8 (/.f64 (*.f64 x y) 2))

Compiler

Compiled 42 to 29 computations (31% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))
✓	0.0b	(/.f64 (*.f64 x y) 2)

series12.0ms (0.7%)

Counts

2 → 60

Calls

2 calls:

7.0ms	(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))
5.0ms	(/.f64 (*.f64 x y) 2)

rewrite5.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 33

Calls

2 calls:

3.0ms	(/.f64 (*.f64 x y) 2)
0.0ms	(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))

simplify73.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

753×	`distribute-rgt-in_binary64`
565×	`associate-/r/_binary64`
449×	`associate-l_binary64`
391×	`associate-/r*_binary64`
388×	`associate-*r/_binary64`

Counts

93 → 59

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	74	985
1	140	863
2	382	863
3	1101	863
4	3121	863
5	5499	863

prune30.0ms (1.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	2	60

Error

Counts

60 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))
▶	0.3b	(fma.f64 z -1/8 (*.f64 (/.f64 x (sqrt.f64 2)) (/.f64 y (sqrt.f64 2))))

Compiler

Compiled 774 to 481 computations (37.9% saved)

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z -1/8 (*.f64 (/.f64 x (sqrt.f64 2)) (/.f64 y (sqrt.f64 2))))
✓	0.3b	(*.f64 (/.f64 x (sqrt.f64 2)) (/.f64 y (sqrt.f64 2)))
✓	0.4b	(/.f64 x (sqrt.f64 2))
✓	0.5b	(/.f64 y (sqrt.f64 2))

series135.0ms (7.2%)

Counts

4 → 60

Calls

4 calls:

62.0ms	(*.f64 (/.f64 x (sqrt.f64 2)) (/.f64 y (sqrt.f64 2)))
58.0ms	(fma.f64 z -1/8 (*.f64 (/.f64 x (sqrt.f64 2)) (/.f64 y (sqrt.f64 2))))
8.0ms	(/.f64 x (sqrt.f64 2))
6.0ms	(/.f64 y (sqrt.f64 2))

rewrite30.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`add-sqr-sqrt_binary64`
84×	`times-frac_binary64`
60×	`*-un-lft-identity_binary64`
60×	`add-cube-cbrt_binary64`
48×	`sqrt-prod_binary64`

Counts

4 → 167

Calls

4 calls:

12.0ms	(*.f64 (/.f64 x (sqrt.f64 2)) (/.f64 y (sqrt.f64 2)))
5.0ms	(/.f64 y (sqrt.f64 2))
3.0ms	(/.f64 x (sqrt.f64 2))
0.0ms	(fma.f64 z -1/8 (*.f64 (/.f64 x (sqrt.f64 2)) (/.f64 y (sqrt.f64 2))))

simplify121.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

797×	`fma-def_binary64`
677×	`associate-/l*_binary64`
429×	`times-frac_binary64`
381×	`associate-/l/_binary64`
297×	`*-commutative_binary64`

Counts

227 → 220

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	3439
1	424	2952
2	1320	2844
3	3309	2796
4	4249	2796
5	4959	2796

prune139.0ms (7.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	220	2	222

Error

Counts

222 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))
✓	0.3b	(fma.f64 z -1/8 (*.f64 (/.f64 x (sqrt.f64 2)) (/.f64 y (sqrt.f64 2))))

Compiler

Compiled 4203 to 3089 computations (26.5% saved)

regimes74.0ms (4%)

Accuracy

Total -0.0b remaining (-4175.5%)

Threshold costs -0.0b (-4175.5%)

Counts

7 → 1

Compiler

Compiled 711 to 546 computations (23.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	10	11
2	10	11

end51.0ms (2.7%)

Remove: (sort x y)
Compiler: Compiled 70 to 52 computations (25.7% saved)

Iter	Nodes	Cost
0	10	13
1	15	13
2	26	13
3	39	13
4	66	11
5	109	11
6	198	11
7	307	11
8	429	11
9	522	11
10	578	11
11	593	11
12	596	11
13	513	11

Iter	Nodes	Cost
0	10	13
1	15	13
2	26	13
3	39	13
4	66	11
5	109	11
6	198	11
7	307	11
8	429	11
9	522	11
10	578	11
11	593	11
12	596	11
13	513	11

Details

analyze179.0ms (9.6%)

sample972.0ms (52.1%)

simplify25.0ms (1.4%)

prune3.0ms (0.1%)

localize5.0ms (0.3%)

series12.0ms (0.7%)

rewrite5.0ms (0.3%)

simplify73.0ms (3.9%)

prune30.0ms (1.6%)

localize9.0ms (0.5%)

series135.0ms (7.2%)

rewrite30.0ms (1.6%)

simplify121.0ms (6.5%)

prune139.0ms (7.5%)

regimes74.0ms (4%)

simplify2.0ms (0.1%)

end51.0ms (2.7%)

Profiling

Iter	Nodes	Cost
0	10	13
1	15	13
2	26	13
3	39	13
4	66	11
5	109	11
6	198	11
7	307	11
8	429	11
9	522	11
10	578	11
11	593	11
12	596	11
13	513	11