Details

analyze90.0ms (5.2%)

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)

sample680.0ms (39.1%)

Results

661.0ms	8256×	body	128	valid
6.0ms	88×	body	128	invalid

Compiler

Compiled 20 to 10 computations (50% saved)

preprocess25.0ms (1.5%)

Algorithm

2×	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	7	20
1	23	20
2	43	20
3	79	20
4	122	20
5	152	20
6	172	20
7	189	20
8	191	20
0	2	2
1	2	2

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort x y)

Compiler

Compiled 9 to 4 computations (55.6% saved)

simplify11.0ms (0.6%)

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

6 calls:

1.0ms	(*.f64 (+.f64 x y) (+.f64 x y))	x	0
1.0ms	(*.f64 (+.f64 x y) (+.f64 x y))	x	inf
1.0ms	(*.f64 (+.f64 x y) (+.f64 x y))	y	-inf
1.0ms	(*.f64 (+.f64 x y) (+.f64 x y))	x	-inf
1.0ms	(*.f64 (+.f64 x y) (+.f64 x y))	y	inf

rewrite36.0ms (2.1%)

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

simplify67.0ms (3.8%)

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

prune25.0ms (1.4%)

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

0.0b

Counts

40 → 2

Alt Table

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

Compiler

Compiled 542 to 200 computations (63.1% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.4%)

Counts

1 → 24

Calls

6 calls:

2.0ms	(fma.f64 x (fma.f64 y 2 x) (*.f64 y y))	y	-inf
1.0ms	(fma.f64 x (fma.f64 y 2 x) (*.f64 y y))	x	0
1.0ms	(fma.f64 x (fma.f64 y 2 x) (*.f64 y y))	x	-inf
1.0ms	(fma.f64 x (fma.f64 y 2 x) (*.f64 y y))	x	inf
1.0ms	(fma.f64 x (fma.f64 y 2 x) (*.f64 y y))	y	inf

rewrite35.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

581×	`log1p-expm1-u_binary64`
581×	`expm1-log1p-u_binary64`
291×	`log-prod_binary64`
153×	`prod-diff_binary64`
122×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	140	12
2	1603	12

Stop Event

1×	node limit

Counts

1 → 29

simplify66.0ms (3.8%)

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

prune18.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	39	2	41

Error

0.0b

Counts

41 → 2

Alt Table

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

Compiler

Compiled 560 to 287 computations (48.8% saved)

localize4.0ms (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))

series10.0ms (0.6%)

Counts

2 → 48

Calls

12 calls:

1.0ms	(fma.f64 x (+.f64 x y) (*.f64 y (+.f64 x y)))	y	-inf
1.0ms	(fma.f64 x (+.f64 x y) (*.f64 y (+.f64 x y)))	x	-inf
1.0ms	(fma.f64 x (+.f64 x y) (*.f64 y (+.f64 x y)))	x	inf
1.0ms	(fma.f64 x (+.f64 x y) (*.f64 y (+.f64 x y)))	y	inf
1.0ms	(*.f64 y (+.f64 x y))	y	-inf

rewrite42.0ms (2.4%)

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

simplify68.0ms (3.9%)

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

prune39.0ms (2.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
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 (fma.f64 y 2 x) (*.f64 y y))

Compiler

Compiled 1064 to 358 computations (66.4% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

series11.0ms (0.6%)

Counts

2 → 48

Calls

12 calls:

1.0ms	(*.f64 x (fma.f64 y 2 x))	x	-inf
1.0ms	(fma.f64 y y (*.f64 x (fma.f64 y 2 x)))	x	-inf
1.0ms	(fma.f64 y y (*.f64 x (fma.f64 y 2 x)))	y	-inf
1.0ms	(fma.f64 y y (*.f64 x (fma.f64 y 2 x)))	x	inf
1.0ms	(fma.f64 y y (*.f64 x (fma.f64 y 2 x)))	y	inf

rewrite42.0ms (2.4%)

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

simplify78.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

613×	`fma-def_binary64`
391×	`sqr-pow_binary64`
374×	`*-commutative_binary64`
372×	`unswap-sqr_binary64`
361×	`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	1495	393
6	2776	393
7	3048	393
8	3234	393
9	3478	393
10	3781	393
11	4172	393
12	4679	393

Stop Event

1×	node limit

Counts

99 → 63

prune30.0ms (1.7%)

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

Compiler

Compiled 854 to 443 computations (48.1% saved)

regimes151.0ms (8.7%)

Accuracy

Total 0.0b remaining (29.9%)

Threshold costs 0.0b (29.9%)

Counts

42 → 1

Compiler

Compiled 1676 to 1137 computations (32.2% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	8	12

Stop Event

1×

saturated

end180.0ms (10.4%)

Stop Event

1×

done

Compiler

Compiled 66 to 36 computations (45.5% saved)

Details

analyze90.0ms (5.2%)

sample680.0ms (39.1%)

preprocess25.0ms (1.5%)

simplify11.0ms (0.6%)

prune1.0ms (0.1%)

localize3.0ms (0.2%)

series5.0ms (0.3%)

rewrite36.0ms (2.1%)

simplify67.0ms (3.8%)

prune25.0ms (1.4%)

localize5.0ms (0.3%)

series7.0ms (0.4%)

rewrite35.0ms (2%)

simplify66.0ms (3.8%)

prune18.0ms (1%)

localize4.0ms (0.3%)

series10.0ms (0.6%)

rewrite42.0ms (2.4%)

simplify68.0ms (3.9%)

prune39.0ms (2.2%)

localize7.0ms (0.4%)

series11.0ms (0.6%)

rewrite42.0ms (2.4%)

simplify78.0ms (4.5%)

prune30.0ms (1.7%)

regimes151.0ms (8.7%)

simplify3.0ms (0.2%)

end180.0ms (10.4%)

Profiling