Details

analyze599.0ms (17.1%)

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
0%	99.9%	0.1%	5
21.8%	78%	0.1%	6
26.5%	73.3%	0.1%	7
32%	67.9%	0.1%	8
46.4%	52.7%	0.9%	9
50.9%	47.2%	1.9%	10
54.3%	43.3%	2.4%	11
62.1%	32.5%	5.4%	12
64.3%	28.1%	7.6%	13
66.3%	24.6%	9.2%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample30.0ms (0.8%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
2.0ms	37×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify64.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1167×	`fma-def_binary64`
1073×	`fma-neg_binary64`
225×	`cancel-sign-sub-inv_binary64`
222×	`distribute-rgt-in_binary64`
163×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	22	18
2	43	18
3	75	18
4	123	16
5	213	16
6	302	16
7	472	16
8	1009	13
9	1328	13
10	1542	13
11	1559	13
12	1556	13
13	1556	13
14	1453	13

prune3.0ms (0.1%)

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
	4.3b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
▶	2.0b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 78 to 51 computations (34.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 4) y)
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
✓	3.1b	(*.f64 (/.f64 x y) z)

series42.0ms (1.2%)

Counts

3 → 96

Calls

3 calls:

20.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
14.0ms	(*.f64 (/.f64 x y) z)
7.0ms	(/.f64 (+.f64 x 4) y)

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
46×	`times-frac_binary64`
41×	`add-sqr-sqrt_binary64`
36×	`add-cube-cbrt_binary64`
16×	`fma-neg_binary64`

Counts

3 → 117

Calls

3 calls:

8.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
5.0ms	(*.f64 (/.f64 x y) z)
4.0ms	(/.f64 (+.f64 x 4) y)

simplify121.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

450×	`associate-l_binary64`
381×	`fma-def_binary64`
379×	`associate-*l/_binary64`
369×	`associate-r_binary64`
310×	`fma-neg_binary64`

Counts

213 → 177

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	187	3147
1	457	2896
2	1229	2394
3	3977	2382
4	4927	2330
5	4911	2330

prune118.0ms (3.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	175	4	179

Error

Counts

179 → 4

Alt Table

Status	Error	Program
	4.3b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
▶	3.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
✓	2.0b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	4.3b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))

Compiler

Compiled 3593 to 1689 computations (53% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 x 4) y)
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y)))
✓	6.1b	(*.f64 x (/.f64 z y))

series36.0ms (1%)

Counts

2 → 72

Calls

2 calls:

21.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y)))
15.0ms	(*.f64 x (/.f64 z y))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
31×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
16×	`fma-neg_binary64`

Counts

2 → 82

Calls

2 calls:

8.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y)))
5.0ms	(*.f64 x (/.f64 z y))

simplify110.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

381×	`associate-r_binary64`
373×	`associate-*r/_binary64`
365×	`associate-*l/_binary64`
350×	`fma-def_binary64`
341×	`fma-neg_binary64`

Counts

154 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	2478
1	386	2346
2	1212	1703
3	3481	1689
4	4636	1689
5	4914	1689

prune110.0ms (3.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	171	4	175

Error

Counts

175 → 4

Alt Table

Status	Error	Program
▶	4.3b	(fabs.f64 (/.f64 (fma.f64 x (-.f64 1 z) 4) y))
✓	3.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
✓	2.0b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	4.3b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))

Compiler

Compiled 3421 to 1631 computations (52.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 1 z) 4)
✓	4.1b	(/.f64 (fma.f64 x (-.f64 1 z) 4) y)

series21.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

17.0ms	(/.f64 (fma.f64 x (-.f64 1 z) 4) y)
4.0ms	(fma.f64 x (-.f64 1 z) 4)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

2.0ms	(/.f64 (fma.f64 x (-.f64 1 z) 4) y)
0.0ms	(fma.f64 x (-.f64 1 z) 4)

simplify76.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

488×	`unsub-neg_binary64`
437×	`fma-neg_binary64`
317×	`times-frac_binary64`
313×	`distribute-rgt-in_binary64`
302×	`distribute-lft-in_binary64`

Counts

99 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	1544
1	172	1481
2	394	1286
3	824	1193
4	3792	1193
5	5192	1193

prune46.0ms (1.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	67	3	70

Error

Counts

70 → 3

Alt Table

Status	Error	Program
▶	4.3b	(fabs.f64 (*.f64 1 (-.f64 (/.f64 x y) (/.f64 (fma.f64 x z -4) y))))
✓	3.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
✓	2.0b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 999 to 664 computations (33.5% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x y) (/.f64 (fma.f64 x z -4) y))
✓	4.1b	(/.f64 (fma.f64 x z -4) y)

series31.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

18.0ms	(-.f64 (/.f64 x y) (/.f64 (fma.f64 x z -4) y))
13.0ms	(/.f64 (fma.f64 x z -4) y)

rewrite57.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

271×	`times-frac_binary64`
220×	`add-sqr-sqrt_binary64`
216×	`*-un-lft-identity_binary64`
208×	`add-cube-cbrt_binary64`
169×	`prod-diff_binary64`

Counts

2 → 248

Calls

2 calls:

15.0ms	(-.f64 (/.f64 x y) (/.f64 (fma.f64 x z -4) y))
2.0ms	(/.f64 (fma.f64 x z -4) y)

simplify244.0ms (7%)

Algorithm

1×	egg-herbie

Rules

397×	`distribute-rgt-in_binary64`
383×	`distribute-lft-in_binary64`
313×	`fma-neg_binary64`
192×	`cancel-sign-sub-inv_binary64`
189×	`exp-prod_binary64`

Counts

320 → 345

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	354	12450
1	792	8092
2	1712	5749
3	4473	5749
4	4792	5749

prune287.0ms (8.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	345	0	345
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	345	3	348

Error

Counts

348 → 3

Alt Table

Status	Error	Program
✓	4.3b	(fabs.f64 (*.f64 1 (-.f64 (/.f64 x y) (/.f64 (fma.f64 x z -4) y))))
✓	3.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
✓	2.0b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 14802 to 7998 computations (46% saved)

regimes469.0ms (13.4%)

Accuracy

Total 0.1b remaining (85.6%)

Threshold costs 0.1b (85.6%)

Counts

67 → 3

Compiler

Compiled 4727 to 3421 computations (27.6% saved)

bsearch31.0ms (0.9%)

Steps

Iters	Range		Point
5	6.104887814344928e-75	1.6618560111820844e-74	8.95711979789483e-75
9	-6.323451006006471e-6	-1.8014106467941592e-12	-5.654014599181771e-9

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary64`
13×	`sub-neg_binary64`
11×	`*-commutative_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	64
1	53	64
2	80	64
3	99	64
4	114	64
5	119	64
6	120	64
7	117	64

end1.0ms (0%)

Compiler: Compiled 46 to 31 computations (32.6% saved)

sample915.0ms (26.2%)

Algorithm

1×

intervals

Results

506.0ms	8000×	body	128	valid
59.0ms	1196×	body	128	invalid

Compiler

Compiled 111 to 76 computations (31.5% saved)

Details

analyze599.0ms (17.1%)

sample30.0ms (0.8%)

simplify64.0ms (1.8%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series42.0ms (1.2%)

rewrite26.0ms (0.7%)

simplify121.0ms (3.5%)

prune118.0ms (3.4%)

localize8.0ms (0.2%)

series36.0ms (1%)

rewrite19.0ms (0.5%)

simplify110.0ms (3.2%)

prune110.0ms (3.1%)

localize6.0ms (0.2%)

series21.0ms (0.6%)

rewrite4.0ms (0.1%)

simplify76.0ms (2.2%)

prune46.0ms (1.3%)

localize8.0ms (0.2%)

series31.0ms (0.9%)

rewrite57.0ms (1.6%)

simplify244.0ms (7%)

prune287.0ms (8.2%)

regimes469.0ms (13.4%)

bsearch31.0ms (0.9%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample915.0ms (26.2%)

Profiling