Details

analyze54.0ms (3.9%)

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
50%	50%	0.1%	4
50%	50%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
87.4%	12.5%	0.1%	8
87.4%	12.5%	0.1%	9
93.7%	6.2%	0.1%	10
93.7%	6.2%	0.1%	11
96.8%	3.1%	0.1%	12
96.8%	3.1%	0.1%	13
99.1%	0.8%	0.1%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample837.0ms (60.3%)

Results

716.0ms	7975×	body	128	valid
28.0ms	98×	body	1024	valid
22.0ms	67×	body	2048	valid
14.0ms	70×	body	512	valid
7.0ms	46×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify16.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

97×	`fma-neg_binary64`
32×	`cancel-sign-sub-inv_binary64`
30×	`fma-def_binary64`
29×	`sub-neg_binary64`
17×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	12
2	20	12
3	29	12
4	45	12
5	79	12
6	97	12
7	123	12
8	174	10
9	188	10
10	229	10
11	263	10
12	283	10
13	291	10
14	296	10
15	256	10

prune4.0ms (0.3%)

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)

Compiler

Compiled 35 to 21 computations (40% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)

rewrite42.0ms (3%)

Algorithm

2×	batch-egg-rewrite

Rules

725×	`log1p-expm1-u_binary64`
725×	`expm1-log1p-u_binary64`
615×	`prod-diff_binary64`
80×	`add-sqr-sqrt_binary64`
75×	`add-log-exp_binary64`

Counts

1 → 24

Calls

1 calls:

41.0ms

(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	155	8
2	1768	8
3	5462	8
0	0	0
1	0	0

simplify28.0ms (2%)

Algorithm

1×	egg-herbie

Rules

97×	`fma-neg_binary64`
46×	`fma-def_binary64`
34×	`cancel-sign-sub-inv_binary64`
28×	`sub-neg_binary64`
19×	`distribute-rgt-neg-in_binary64`

Counts

48 → 28

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	221
1	15	221
2	23	221
3	32	221
4	48	221
5	82	221
6	100	221
7	128	221
8	191	221
9	204	221
10	242	221
11	257	221
12	263	221
13	268	221
14	238	221

prune13.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	2	29

Error

0.1b

Counts

29 → 2

Alt Table

Status	Error	Program
▶	52.0b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 y x) 1/2 x) 3))
✓	0.1b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)

Compiler

Compiled 323 to 172 computations (46.7% saved)

localize6.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (-.f64 y x) 1/2 x)
✓	0.0b	(pow.f64 (fma.f64 (-.f64 y x) 1/2 x) 3)
✓	39.4b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 y x) 1/2 x) 3))

series35.0ms (2.5%)

Counts

3 → 72

Calls

3 calls:

22.0ms	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 y x) 1/2 x) 3))
9.0ms	(pow.f64 (fma.f64 (-.f64 y x) 1/2 x) 3)
4.0ms	(fma.f64 (-.f64 y x) 1/2 x)

rewrite51.0ms (3.7%)

Algorithm

2×	batch-egg-rewrite

Rules

823×	`log1p-expm1-u_binary64`
823×	`expm1-log1p-u_binary64`
408×	`prod-diff_binary64`
86×	`add-sqr-sqrt_binary64`
82×	`add-log-exp_binary64`

Counts

3 → 81

Calls

3 calls:

49.0ms	(fma.f64 (-.f64 y x) 1/2 x)
49.0ms	(pow.f64 (fma.f64 (-.f64 y x) 1/2 x) 3)
49.0ms	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 y x) 1/2 x) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	178	27
2	2058	27
3	5651	27
0	0	0
1	0	0

simplify165.0ms (11.9%)

Algorithm

1×	egg-herbie

Rules

783×	`*-commutative_binary64`
758×	`sqr-pow_binary64`
555×	`fma-def_binary64`
356×	`unswap-sqr_binary64`
332×	`associate-l_binary64`

Counts

153 → 69

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	807
1	78	774
2	188	750
3	530	702
4	1509	702
5	2256	702
6	2383	702
7	2598	702
8	2977	702
9	3384	702
10	3900	702
11	3690	702
12	4116	702
13	4751	702
14	4963	702

prune34.0ms (2.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	69	2	71

Error

0.1b

Counts

71 → 2

Alt Table

Status	Error	Program
✓	52.0b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 y x) 1/2 x) 3))
✓	0.1b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)

Compiler

Compiled 972 to 581 computations (40.2% saved)

regimes41.0ms (3%)

Accuracy

Total 0.0b remaining (1.6%)

Threshold costs 0.0b (1.6%)

Counts

11 → 1

Compiler

Compiled 296 to 220 computations (25.7% saved)

simplify2.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	11	10
2	18	10
3	23	10
4	26	10
5	27	10
6	27	10

end51.0ms (3.7%)

Compiler: Compiled 38 to 26 computations (31.6% saved)

Iter	Nodes	Cost
0	8	12
1	13	12
2	20	12
3	29	12
4	45	12
5	79	12
6	97	12
7	123	12
8	174	10
9	188	10
10	229	10
11	263	10
12	283	10
13	291	10
14	296	10
15	256	10

Iter	Nodes	Cost
0	8	221
1	15	221
2	23	221
3	32	221
4	48	221
5	82	221
6	100	221
7	128	221
8	191	221
9	204	221
10	242	221
11	257	221
12	263	221
13	268	221
14	238	221

Iter	Nodes	Cost
0	8	12
1	13	12
2	20	12
3	29	12
4	45	12
5	79	12
6	97	12
7	123	12
8	174	10
9	188	10
10	229	10
11	263	10
12	283	10
13	291	10
14	296	10
15	256	10

Iter	Nodes	Cost
0	8	221
1	15	221
2	23	221
3	32	221
4	48	221
5	82	221
6	100	221
7	128	221
8	191	221
9	204	221
10	242	221
11	257	221
12	263	221
13	268	221
14	238	221

Details

analyze54.0ms (3.9%)

sample837.0ms (60.3%)

simplify16.0ms (1.2%)

prune4.0ms (0.3%)

localize5.0ms (0.3%)

series6.0ms (0.4%)

rewrite42.0ms (3%)

simplify28.0ms (2%)

prune13.0ms (0.9%)

localize6.0ms (0.4%)

series35.0ms (2.5%)

rewrite51.0ms (3.7%)

simplify165.0ms (11.9%)

prune34.0ms (2.4%)

regimes41.0ms (3%)

simplify2.0ms (0.2%)

end51.0ms (3.7%)

Profiling

Iter	Nodes	Cost
0	8	12
1	13	12
2	20	12
3	29	12
4	45	12
5	79	12
6	97	12
7	123	12
8	174	10
9	188	10
10	229	10
11	263	10
12	283	10
13	291	10
14	296	10
15	256	10

Iter	Nodes	Cost
0	8	221
1	15	221
2	23	221
3	32	221
4	48	221
5	82	221
6	100	221
7	128	221
8	191	221
9	204	221
10	242	221
11	257	221
12	263	221
13	268	221
14	238	221