Details

analyze97.0ms (6%)

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
25%	56.2%	18.8%	6
25%	40.6%	34.4%	7
31.2%	31.2%	37.6%	8
39%	21.1%	39.9%	9
42.9%	16%	41.1%	10
47.2%	10.7%	42%	11
49.4%	8.1%	42.5%	12
51.6%	5.4%	43%	13
52.7%	4.1%	43.2%	14

Compiler

Compiled 10 to 5 computations (50% saved)

sample658.0ms (40.8%)

Symmetry

(sort x y)

Results

617.0ms	8256×	body	128	valid
8.0ms	108×	body	128	invalid

Compiler

Compiled 29 to 14 computations (51.7% saved)

simplify12.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

70×	`fma-def_binary64`
24×	`associate-+l+_binary64`
18×	`associate-+r+_binary64`
10×	`distribute-rgt-in_binary64`
8×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	12	10
2	29	10
3	67	10
4	110	10
5	140	10
6	160	10
7	177	10
8	179	10

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (+.f64 x y) (+.f64 x y))

Compiler

Compiled 27 to 12 computations (55.6% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 x y))

series5.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

5.0ms

(*.f64 (+.f64 x y) (+.f64 x y))

rewrite36.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

682×	`prod-diff_binary64`
618×	`log1p-expm1-u_binary64`
618×	`expm1-log1p-u_binary64`
60×	`add-sqr-sqrt_binary64`
58×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	115	7
2	1719	7

Stop Event

1×	node limit

Counts

1 → 29

Calls

1 calls:

35.0ms

(*.f64 (+.f64 x y) (+.f64 x y))

simplify69.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

613×	`fma-def_binary64`
391×	`sqr-pow_binary64`
374×	`*-commutative_binary64`
372×	`unswap-sqr_binary64`
362×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	294
1	32	267
2	69	222
3	151	216
4	412	216
5	1498	216
6	2779	216
7	3051	216
8	3237	216
9	3481	216
10	3784	216
11	4175	216
12	4682	216

Stop Event

1×	node limit

Counts

53 → 39

prune28.0ms (1.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	37	2	39
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	2	40

Error

Counts

40 → 2

Alt Table

Status	Error	Program
	0.0b	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
▶	0.0b	(fma.f64 x (+.f64 x y) (*.f64 y (+.f64 x y)))

Compiler

Compiled 550 to 210 computations (61.8% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (+.f64 x y) (*.f64 y (+.f64 x y)))
✓	0.0b	(*.f64 y (+.f64 x y))

series13.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

7.0ms	(*.f64 y (+.f64 x y))
6.0ms	(fma.f64 x (+.f64 x y) (*.f64 y (+.f64 x y)))

rewrite46.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

808×	`prod-diff_binary64`
690×	`log1p-expm1-u_binary64`
690×	`expm1-log1p-u_binary64`
69×	`add-sqr-sqrt_binary64`
65×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	21
1	133	14
2	1927	14

Stop Event

1×	node limit

Counts

2 → 62

Calls

2 calls:

44.0ms	(fma.f64 x (+.f64 x y) (*.f64 y (+.f64 x y)))
44.0ms	(*.f64 y (+.f64 x y))

simplify68.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

822×	`fma-def_binary64`
391×	`sqr-pow_binary64`
379×	`associate-l_binary64`
372×	`unswap-sqr_binary64`
308×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	462
1	35	417
2	79	372
3	169	366
4	461	366
5	1649	366
6	3082	366
7	3426	366
8	3616	366
9	3864	366
10	4168	366
11	4561	366

Stop Event

1×	node limit

Counts

110 → 75

prune38.0ms (2.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	75	2	77

Error

Counts

77 → 2

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 y y (*.f64 x (fma.f64 y 2 x)))
✓	0.0b	(fma.f64 x (+.f64 x y) (*.f64 y (+.f64 x y)))

Compiler

Compiled 1065 to 357 computations (66.5% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y y (*.f64 x (fma.f64 y 2 x)))
✓	0.0b	(*.f64 x (fma.f64 y 2 x))

series11.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

6.0ms	(fma.f64 y y (*.f64 x (fma.f64 y 2 x)))
5.0ms	(*.f64 x (fma.f64 y 2 x))

rewrite40.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

600×	`log1p-expm1-u_binary64`
600×	`expm1-log1p-u_binary64`
312×	`log-prod_binary64`
180×	`prod-diff_binary64`
126×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	140	20
2	1617	20

Stop Event

1×	node limit

Counts

2 → 51

Calls

2 calls:

39.0ms	(fma.f64 y y (*.f64 x (fma.f64 y 2 x)))
39.0ms	(*.f64 x (fma.f64 y 2 x))

simplify77.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

613×	`fma-def_binary64`
391×	`sqr-pow_binary64`
372×	`unswap-sqr_binary64`
366×	`*-commutative_binary64`
362×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	525
1	32	480
2	69	399
3	151	393
4	414	393
5	1499	393
6	2775	393
7	3047	393
8	3232	393
9	3476	393
10	3777	393
11	4170	393
12	4677	393

Stop Event

1×	node limit

Counts

99 → 63

prune37.0ms (2.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	63	2	65

Error

Counts

65 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 y y (*.f64 x (fma.f64 y 2 x)))
✓	0.0b	(fma.f64 x (+.f64 x y) (*.f64 y (+.f64 x y)))

Compiler

Compiled 867 to 451 computations (48% saved)

regimes180.0ms (11.1%)

Accuracy

Total 0.0b remaining (83.1%)

Threshold costs 0.0b (83.1%)

Counts

49 → 1

Compiler

Compiled 2016 to 1389 computations (31.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	14
1	8	14

Stop Event

1×

saturated

end184.0ms (11.4%)

Compiler: Compiled 71 to 31 computations (56.3% saved)

Details

analyze97.0ms (6%)

sample658.0ms (40.8%)

simplify12.0ms (0.7%)

prune1.0ms (0.1%)

localize3.0ms (0.2%)

series5.0ms (0.3%)

rewrite36.0ms (2.2%)

simplify69.0ms (4.3%)

prune28.0ms (1.8%)

localize5.0ms (0.3%)

series13.0ms (0.8%)

rewrite46.0ms (2.8%)

simplify68.0ms (4.2%)

prune38.0ms (2.3%)

localize7.0ms (0.4%)

series11.0ms (0.7%)

rewrite40.0ms (2.5%)

simplify77.0ms (4.8%)

prune37.0ms (2.3%)

regimes180.0ms (11.1%)

simplify2.0ms (0.1%)

end184.0ms (11.4%)

Profiling