Details

analyze111.0ms (1.8%)

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
50%	50%	0.1%	6
56.2%	37.5%	6.3%	7
68.7%	25%	6.3%	8
71.8%	18.7%	9.5%	9
78%	12.5%	9.5%	10
79.6%	9.4%	11%	11
82.7%	6.2%	11%	12
83.5%	4.7%	11.8%	13
85.1%	3.1%	11.8%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample820.0ms (13.4%)

Results

800.0ms	8256×	body	128	valid
7.0ms	77×	body	128	invalid

Compiler

Compiled 28 to 22 computations (21.4% saved)

preprocess66.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

1297×	`fma-neg_binary64`
333×	`cancel-sign-sub-inv_binary64`
300×	`fma-def_binary64`
262×	`sub-neg_binary64`
200×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	44	28
2	106	24
3	247	24
4	557	22
5	1221	22
6	2255	22
7	3430	22
8	3826	22
9	3844	22
10	3844	22
11	4502	22
12	4502	22
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify30.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-neg_binary64`
578×	`fma-def_binary64`
222×	`cancel-sign-sub-inv_binary64`
114×	`sub-neg_binary64`
81×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	27	14
2	62	12
3	129	12
4	268	11
5	580	11
6	1075	11
7	1794	11
8	2581	11
9	2752	11
10	2779	11

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
▶	0.0b	(-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)

Compiler

Compiled 67 to 49 computations (26.9% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
✓	0.0b	(-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)

series9.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

1.0ms	(-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)	x	-inf
1.0ms	(-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)	x	inf
1.0ms	(-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)	y	-inf
1.0ms	(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)	x	inf
1.0ms	(-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)	y	inf

rewrite54.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

431×	`prod-diff_binary64`
379×	`log-prod_binary64`
268×	`fma-def_binary64`
168×	`expm1-udef_binary64`
168×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	182	19
2	2394	19

Stop Event

1×	node limit

Counts

2 → 139

simplify52.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

613×	`fma-neg_binary64`
468×	`fma-def_binary64`
122×	`sub-neg_binary64`
109×	`cancel-sign-sub-inv_binary64`
79×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	483
1	67	465
2	157	443
3	343	407
4	734	407
5	1355	407
6	1942	407
7	2195	407
8	2322	407
9	2341	407

Stop Event

1×

saturated

Counts

187 → 155

prune88.0ms (1.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	155	2	157

Error

Counts

157 → 2

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 y (+.f64 x -1/2) (-.f64 918938533204673/1000000000000000 x))
	0.8b	(pow.f64 (cbrt.f64 (-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)) 3)

Compiler

Compiled 2514 to 1635 computations (35% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 918938533204673/1000000000000000 x)
✓	0.0b	(fma.f64 y (+.f64 x -1/2) (-.f64 918938533204673/1000000000000000 x))

series7.0ms (0.1%)

Counts

2 → 27

Calls

9 calls:

1.0ms	(fma.f64 y (+.f64 x -1/2) (-.f64 918938533204673/1000000000000000 x))	x	0
1.0ms	(fma.f64 y (+.f64 x -1/2) (-.f64 918938533204673/1000000000000000 x))	x	-inf
1.0ms	(fma.f64 y (+.f64 x -1/2) (-.f64 918938533204673/1000000000000000 x))	x	inf
1.0ms	(fma.f64 y (+.f64 x -1/2) (-.f64 918938533204673/1000000000000000 x))	y	-inf
1.0ms	(fma.f64 y (+.f64 x -1/2) (-.f64 918938533204673/1000000000000000 x))	y	inf

rewrite45.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

371×	`log-prod_binary64`
241×	`pow2_binary64`
209×	`prod-diff_binary64`
168×	`expm1-udef_binary64`
168×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	182	15
2	2324	15

Stop Event

1×	node limit

Counts

2 → 74

simplify45.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

596×	`fma-neg_binary64`
435×	`fma-def_binary64`
120×	`sub-neg_binary64`
95×	`cancel-sign-sub-inv_binary64`
83×	`associate--r+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	262
1	66	262
2	147	260
3	326	242
4	694	242
5	1289	242
6	1872	242
7	2129	242
8	2252	242
9	2273	242

Stop Event

1×

saturated

Counts

101 → 87

prune49.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	87	2	89

Error

Counts

89 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 y (+.f64 x -1/2) (-.f64 918938533204673/1000000000000000 x))
▶	0.8b	(pow.f64 (cbrt.f64 (-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)) 3)

Compiler

Compiled 1125 to 780 computations (30.7% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)
	0.0b	(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
✓	0.3b	(cbrt.f64 (-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x))
✓	0.5b	(pow.f64 (cbrt.f64 (-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)) 3)

series4.2s (69.1%)

Counts

2 → 16

Calls

12 calls:

2.2s	(pow.f64 (cbrt.f64 (-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)) 3)	x	0
2.0s	(pow.f64 (cbrt.f64 (-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)) 3)	y	0
10.0ms	(cbrt.f64 (-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x))	x	0
9.0ms	(cbrt.f64 (-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x))	y	0
4.0ms	(cbrt.f64 (-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x))	y	-inf

rewrite66.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

431×	`prod-diff_binary64`
299×	`fma-def_binary64`
197×	`expm1-udef_binary64`
197×	`log1p-udef_binary64`
162×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	242	24
2	2872	24

Stop Event

1×	node limit

Counts

2 → 162

simplify43.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

386×	`associate-+l+_binary64`
367×	`associate--r+_binary64`
340×	`cancel-sign-sub-inv_binary64`
327×	`associate--l+_binary64`
235×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	1674
1	456	1591
2	1754	1271

Stop Event

1×	node limit

Counts

178 → 185

prune224.0ms (3.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	340	0	340
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	340	2	342

Error

Counts

342 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 y (+.f64 x -1/2) (-.f64 918938533204673/1000000000000000 x))
✓	0.8b	(pow.f64 (cbrt.f64 (-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)) 3)

Compiler

Compiled 7764 to 5448 computations (29.8% saved)

regimes119.0ms (1.9%)

Accuracy

Total 0.0b remaining (21.7%)

Threshold costs 0.0b (21.7%)

Counts

30 → 1

Compiler

Compiled 1124 to 852 computations (24.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	11	11
2	16	11
3	18	11
4	19	11

Stop Event

1×

saturated

end43.0ms (0.7%)

Stop Event

1×

done

Compiler

Compiled 43 to 31 computations (27.9% saved)

Details

analyze111.0ms (1.8%)

sample820.0ms (13.4%)

preprocess66.0ms (1.1%)

simplify30.0ms (0.5%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series9.0ms (0.1%)

rewrite54.0ms (0.9%)

simplify52.0ms (0.9%)

prune88.0ms (1.4%)

localize5.0ms (0.1%)

series7.0ms (0.1%)

rewrite45.0ms (0.7%)

simplify45.0ms (0.7%)

prune49.0ms (0.8%)

localize7.0ms (0.1%)

series4.2s (69.1%)

rewrite66.0ms (1.1%)

simplify43.0ms (0.7%)

prune224.0ms (3.6%)

regimes119.0ms (1.9%)

simplify2.0ms (0%)

end43.0ms (0.7%)

Profiling