Details

analyze166.0ms (9.9%)

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)

sample1.0s (60.2%)

Symmetry

(sort x y)

Results

883.0ms	8256×	body	128	valid
47.0ms	491×	body	128	invalid

Compiler

Compiled 38 to 29 computations (23.7% saved)

simplify28.0ms (1.7%)

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 (0.2%)

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)

localize6.0ms (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)

series14.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

9.0ms	(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))
4.0ms	(/.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))

simplify66.0ms (4%)

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

prune35.0ms (2.1%)

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))
▶	0.1b	(fma.f64 z -1/8 (/.f64 x (/.f64 2 y)))

Compiler

Compiled 766 to 473 computations (38.3% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z -1/8 (/.f64 x (/.f64 2 y)))
✓	0.2b	(/.f64 x (/.f64 2 y))

series11.0ms (0.7%)

Counts

2 → 60

Calls

2 calls:

7.0ms	(fma.f64 z -1/8 (/.f64 x (/.f64 2 y)))
4.0ms	(/.f64 x (/.f64 2 y))

rewrite11.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
44×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
44×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64`

Counts

2 → 82

Calls

2 calls:

4.0ms	(/.f64 x (/.f64 2 y))
0.0ms	(fma.f64 z -1/8 (/.f64 x (/.f64 2 y)))

simplify148.0ms (8.8%)

Algorithm

1×	egg-herbie

Rules

622×	`fma-def_binary64`
506×	`*-commutative_binary64`
463×	`distribute-rgt-in_binary64`
331×	`associate-/r/_binary64`
299×	`associate-/l/_binary64`

Counts

142 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	169	1984
1	336	1847
2	944	1846
3	2170	1846
4	2928	1846
5	4851	1846
6	4996	1846
7	5000	1846
8	4912	1846

prune69.0ms (4.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	132	2	134

Error

Counts

134 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))
✓	0.1b	(fma.f64 z -1/8 (/.f64 x (/.f64 2 y)))

Compiler

Compiled 2104 to 1268 computations (39.7% saved)

regimes50.0ms (3%)

Accuracy

Total 0.0b remaining (86.9%)

Threshold costs 0.0b (86.9%)

Counts

5 → 1

Compiler

Compiled 410 to 311 computations (24.1% 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

end46.0ms (2.7%)

Remove: (sort x y)
Compiler: Compiled 66 to 48 computations (27.3% 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

analyze166.0ms (9.9%)

sample1.0s (60.2%)

simplify28.0ms (1.7%)

prune3.0ms (0.2%)

localize6.0ms (0.3%)

series14.0ms (0.8%)

rewrite5.0ms (0.3%)

simplify66.0ms (4%)

prune35.0ms (2.1%)

localize6.0ms (0.3%)

series11.0ms (0.7%)

rewrite11.0ms (0.7%)

simplify148.0ms (8.8%)

prune69.0ms (4.1%)

regimes50.0ms (3%)

simplify2.0ms (0.1%)

end46.0ms (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