Details

analyze572.0ms (17.8%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
23.8%	74.5%	1.7%	9
40%	56.4%	3.7%	10
46.9%	48.7%	4.4%	11
48%	45.8%	6.2%	12
58.1%	32.2%	9.7%	13
62.1%	27.2%	10.6%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.1s (34.2%)

Results

881.0ms	8256×	body	128	valid
111.0ms	1083×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify55.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

823×	`div-sub_binary64`
529×	`fma-neg_binary64`
475×	`distribute-rgt-in_binary64`
409×	`fma-def_binary64`
380×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	50	11
3	156	11
4	331	11
5	666	11
6	1744	11
7	3988	11
8	4953	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

9.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.6b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

Compiler

Compiled 42 to 22 computations (47.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 y z) x)
✓	8.9b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

series23.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

13.0ms	(/.f64 (fma.f64 x (-.f64 y z) x) z)
9.0ms	(fma.f64 x (-.f64 y z) x)

rewrite50.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

857×	`log1p-expm1-u_binary64`
857×	`expm1-log1p-u_binary64`
441×	`prod-diff_binary64`
82×	`add-sqr-sqrt_binary64`
76×	`add-log-exp_binary64`

Counts

2 → 56

Calls

2 calls:

49.0ms	(fma.f64 x (-.f64 y z) x)
49.0ms	(/.f64 (fma.f64 x (-.f64 y z) x) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	155	19
2	2114	19
3	6096	19
0	0	0
1	0	0

simplify84.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

606×	`fma-def_binary64`
383×	`associate-/l*_binary64`
340×	`neg-sub0_binary64`
339×	`neg-mul-1_binary64`
328×	`distribute-rgt-out--_binary64`

Counts

128 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	760
1	75	760
2	166	697
3	366	637
4	1205	637
5	3037	637
6	4643	637
7	5092	637

prune60.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	69	8	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	8	78

Error

1.9b

Counts

78 → 8

Alt Table

Status	Error	Program
	31.7b	(.f64 (/.f64 1 (cbrt.f64 (.f64 z z))) (/.f64 (fma.f64 x (-.f64 y z) x) (cbrt.f64 z)))
	26.8b	(/.f64 (-.f64 x (*.f64 z x)) z)
▶	3.8b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
	19.2b	(-.f64 (/.f64 x z) x)
	40.8b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z) 3))
	9.7b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))
	9.8b	(pow.f64 (/.f64 z (fma.f64 x (-.f64 y z) x)) -1)
	38.3b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 x (-.f64 y z) x) 3)) z)

Compiler

Compiled 1140 to 384 computations (66.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z))
✓	0.0b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
✓	8.1b	(/.f64 (*.f64 y x) z)

series43.0ms (1.3%)

Counts

3 → 45

Calls

3 calls:

17.0ms	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
15.0ms	(+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z))
11.0ms	(/.f64 (*.f64 y x) z)

rewrite101.0ms (3.1%)

Algorithm

2×	batch-egg-rewrite

Rules

862×	`fma-def_binary64`
420×	`fma-neg_binary64`
307×	`egg-rr`
208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`

Counts

3 → 307

Calls

3 calls:

93.0ms	(+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z))
93.0ms	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
93.0ms	(/.f64 (*.f64 y x) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	215	36
2	3429	32
3	5337	32
0	0	0
1	0	0

simplify74.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

884×	`fma-def_binary64`
554×	`fma-neg_binary64`
153×	`distribute-rgt-in_binary64`
120×	`distribute-lft-in_binary64`
118×	`unsub-neg_binary64`

Counts

352 → 319

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	437
1	49	437
2	110	413
3	228	413
4	559	377
5	922	377
6	1330	377
7	1390	377
8	1402	377
9	1402	377
10	1323	377

prune172.0ms (5.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	316	3	319
Fresh	7	0	7
Picked	0	1	1
Done	0	0	0
Total	323	4	327

Error

0.0b

Counts

327 → 4

Alt Table

Status	Error	Program
	3.9b	(fma.f64 (/.f64 1 z) (fma.f64 y x x) (neg.f64 x))
▶	1.6b	(fma.f64 y (/.f64 x z) (-.f64 (/.f64 x z) x))
✓	3.8b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
	4.8b	(fma.f64 (/.f64 y z) x (-.f64 (/.f64 x z) x))

Compiler

Compiled 5891 to 1466 computations (75.1% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x z) x)
✓	1.6b	(fma.f64 y (/.f64 x z) (-.f64 (/.f64 x z) x))

series24.0ms (0.7%)

Counts

2 → 51

Calls

2 calls:

18.0ms	(fma.f64 y (/.f64 x z) (-.f64 (/.f64 x z) x))
6.0ms	(-.f64 (/.f64 x z) x)

rewrite59.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

850×	`expm1-log1p-u_binary64`
695×	`prod-diff_binary64`
130×	`egg-rr`
82×	`add-sqr-sqrt_binary64`
78×	`log1p-expm1-u_binary64`

Counts

2 → 130

Calls

2 calls:

56.0ms	(-.f64 (/.f64 x z) x)
56.0ms	(fma.f64 y (/.f64 x z) (-.f64 (/.f64 x z) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	21
1	155	21
2	2115	21
3	4965	21
0	0	0
1	0	0

simplify78.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

637×	`fma-def_binary64`
603×	`fma-neg_binary64`
152×	`distribute-rgt-in_binary64`
127×	`unsub-neg_binary64`
121×	`distribute-lft-in_binary64`

Counts

181 → 144

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	28	609
1	64	609
2	150	549
3	294	549
4	618	459
5	995	459
6	1317	459
7	1389	459
8	1408	459
9	1408	459
10	1329	459

prune70.0ms (2.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	144	4	148

Error

0.0b

Counts

148 → 4

Alt Table

Status	Error	Program
▶	3.9b	(fma.f64 (/.f64 1 z) (fma.f64 y x x) (neg.f64 x))
✓	1.6b	(fma.f64 y (/.f64 x z) (-.f64 (/.f64 x z) x))
✓	3.8b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
	4.8b	(fma.f64 (/.f64 y z) x (-.f64 (/.f64 x z) x))

Compiler

Compiled 2894 to 723 computations (75% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.8b	(fma.f64 (/.f64 1 z) (fma.f64 y x x) (neg.f64 x))

series15.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

15.0ms

(fma.f64 (/.f64 1 z) (fma.f64 y x x) (neg.f64 x))

rewrite103.0ms (3.2%)

Algorithm

2×	batch-egg-rewrite

Rules

702×	`log1p-expm1-u_binary64`
702×	`expm1-log1p-u_binary64`
292×	`prod-diff_binary64`
155×	`fma-udef_binary64`
154×	`fma-def_binary64`

Counts

1 → 33

Calls

1 calls:

102.0ms

(fma.f64 (/.f64 1 z) (fma.f64 y x x) (neg.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	179	11
2	1831	11
3	4997	11
4	4794	11
5	4987	11
0	0	0
1	0	0

simplify72.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-def_binary64`
572×	`fma-neg_binary64`
166×	`distribute-rgt-in_binary64`
145×	`distribute-lft-in_binary64`
129×	`associate-l_binary64`

Counts

69 → 42

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	23	515
1	52	515
2	116	455
3	251	455
4	564	365
5	917	365
6	1311	365
7	1390	365
8	1402	365
9	1402	365
10	1323	365

prune24.0ms (0.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	42	4	46

Error

0.0b

Counts

46 → 4

Alt Table

Status	Error	Program
✓	3.9b	(fma.f64 (/.f64 1 z) (fma.f64 y x x) (neg.f64 x))
✓	1.6b	(fma.f64 y (/.f64 x z) (-.f64 (/.f64 x z) x))
✓	3.8b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
	4.8b	(fma.f64 (/.f64 y z) x (-.f64 (/.f64 x z) x))

Compiler

Compiled 649 to 177 computations (72.7% saved)

regimes339.0ms (10.6%)

Accuracy

Total 0.1b remaining (86.1%)

Threshold costs 0.1b (86.1%)

Counts

61 → 3

Compiler

Compiled 3396 to 1966 computations (42.1% saved)

bsearch2.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	75
1	33	75
2	41	75
3	45	75
4	47	75
5	46	75

end64.0ms (2%)

Compiler: Compiled 163 to 77 computations (52.8% saved)

Details

analyze572.0ms (17.8%)

sample1.1s (34.2%)

simplify55.0ms (1.7%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series23.0ms (0.7%)

rewrite50.0ms (1.6%)

simplify84.0ms (2.6%)

prune60.0ms (1.9%)

localize7.0ms (0.2%)

series43.0ms (1.3%)

rewrite101.0ms (3.1%)

simplify74.0ms (2.3%)

prune172.0ms (5.4%)

localize5.0ms (0.2%)

series24.0ms (0.7%)

rewrite59.0ms (1.8%)

simplify78.0ms (2.4%)

prune70.0ms (2.2%)

localize7.0ms (0.2%)

series15.0ms (0.5%)

rewrite103.0ms (3.2%)

simplify72.0ms (2.2%)

prune24.0ms (0.7%)

regimes339.0ms (10.6%)

bsearch2.0ms (0%)

simplify5.0ms (0.2%)

end64.0ms (2%)

Profiling