Details

analyze425.0ms (21.6%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
31.2%	68.6%	0.1%	9
35.9%	55.4%	8.7%	10
42.9%	47.6%	9.5%	11
51.5%	38.4%	10.1%	12
55%	30.3%	14.7%	13
59.5%	25.4%	15.1%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample797.0ms (40.5%)

Results

729.0ms	8252×	body	128	valid
52.0ms	603×	body	128	invalid
0.0ms	2×	body	1024	valid
0.0ms	2×	body	512	valid

Compiler

Compiled 22 to 16 computations (27.3% saved)

preprocess28.0ms (1.4%)

Algorithm

2×	egg-herbie

Rules

522×	`fma-def_binary64`
100×	`distribute-rgt-in_binary64`
78×	`associate-+l+_binary64`
66×	`associate-+r+_binary64`
64×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
1	53	40
2	137	40
3	334	40
4	694	40
5	1078	40
6	1144	40
7	1150	40
0	3	3
1	3	3

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort x y)

Compiler

Compiled 10 to 7 computations (30% saved)

simplify9.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

186×	`fma-def_binary64`
33×	`distribute-rgt-in_binary64`
26×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
21×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	19	10
2	51	10
3	120	10
4	249	10
5	389	10
6	411	10
7	413	10

Stop Event

1×

saturated

Counts

1 → 1

prune2.0ms (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 z 1))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))

series8.0ms (0.4%)

Counts

1 → 36

Calls

9 calls:

2.0ms	(*.f64 (+.f64 x y) (+.f64 z 1))	x	-inf
1.0ms	(*.f64 (+.f64 x y) (+.f64 z 1))	x	inf
1.0ms	(*.f64 (+.f64 x y) (+.f64 z 1))	y	-inf
1.0ms	(*.f64 (+.f64 x y) (+.f64 z 1))	y	0
1.0ms	(*.f64 (+.f64 x y) (+.f64 z 1))	y	inf

rewrite44.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

676×	`prod-diff_binary64`
324×	`fma-def_binary64`
172×	`fma-neg_binary64`
154×	`log1p-udef_binary64`
153×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	176	10
2	2483	10

Stop Event

1×	node limit

Counts

1 → 74

simplify18.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

174×	`fma-def_binary64`
24×	`associate-+l+_binary64`
22×	`distribute-rgt-in_binary64`
20×	`associate-+r+_binary64`
13×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	378
1	41	351
2	76	318
3	155	318
4	246	318
5	294	318
6	329	318
7	335	318

Stop Event

1×

saturated

Counts

110 → 83

prune42.0ms (2.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	2	84

Error

0.0b

Counts

84 → 2

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 (+.f64 x y) z (+.f64 x y))
	0.0b	(fma.f64 x (+.f64 z 1) (*.f64 y (+.f64 z 1)))

Compiler

Compiled 1173 to 455 computations (61.2% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.4%)

Counts

1 → 36

Calls

9 calls:

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

rewrite37.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

675×	`log1p-expm1-u_binary64`
675×	`expm1-log1p-u_binary64`
539×	`prod-diff_binary64`
68×	`add-sqr-sqrt_binary64`
64×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	129	11
2	1763	11

Stop Event

1×	node limit

Counts

1 → 25

simplify19.0ms (1%)

Algorithm

1×	egg-herbie

Rules

200×	`fma-def_binary64`
30×	`distribute-rgt-in_binary64`
24×	`associate-+l+_binary64`
20×	`associate-+r+_binary64`
13×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	378
1	37	345
2	78	318
3	141	318
4	215	318
5	309	318
6	359	318
7	372	318

Stop Event

1×

saturated

Counts

61 → 35

prune14.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	35	2	37

Error

0.0b

Counts

37 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (+.f64 x y) z (+.f64 x y))
▶	0.0b	(fma.f64 x (+.f64 z 1) (*.f64 y (+.f64 z 1)))

Compiler

Compiled 432 to 120 computations (72.2% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (+.f64 z 1))
✓	0.0b	(fma.f64 x (+.f64 z 1) (*.f64 y (+.f64 z 1)))

series13.0ms (0.7%)

Counts

2 → 60

Calls

15 calls:

2.0ms	(*.f64 y (+.f64 z 1))	y	-inf
1.0ms	(fma.f64 x (+.f64 z 1) (*.f64 y (+.f64 z 1)))	y	-inf
1.0ms	(fma.f64 x (+.f64 z 1) (*.f64 y (+.f64 z 1)))	x	-inf
1.0ms	(fma.f64 x (+.f64 z 1) (*.f64 y (+.f64 z 1)))	x	inf
1.0ms	(fma.f64 x (+.f64 z 1) (*.f64 y (+.f64 z 1)))	x	0

rewrite43.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

784×	`log1p-expm1-u_binary64`
784×	`expm1-log1p-u_binary64`
367×	`prod-diff_binary64`
84×	`add-sqr-sqrt_binary64`
78×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	167	15
2	2149	15

Stop Event

1×	node limit

Counts

2 → 51

simplify30.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

200×	`fma-def_binary64`
30×	`distribute-rgt-in_binary64`
24×	`associate-+l+_binary64`
20×	`associate-+r+_binary64`
13×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	534
1	37	459
2	78	432
3	141	432
4	215	432
5	309	432
6	359	432
7	372	432

Stop Event

1×

saturated

Counts

111 → 62

prune36.0ms (1.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	61	3	64

Error

Counts

64 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (+.f64 x y) z (+.f64 x y))
✓	0.0b	(fma.f64 x (+.f64 z 1) (*.f64 y (+.f64 z 1)))
▶	27.7b	(fma.f64 x (+.f64 z 1) (cbrt.f64 (pow.f64 (fma.f64 z y y) 3)))

Compiler

Compiled 798 to 386 computations (51.6% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (+.f64 z 1) (cbrt.f64 (pow.f64 (fma.f64 z y y) 3)))
✓	0.1b	(pow.f64 (fma.f64 z y y) 3)
✓	38.6b	(cbrt.f64 (pow.f64 (fma.f64 z y y) 3))

series27.0ms (1.3%)

Counts

3 → 84

Calls

21 calls:

3.0ms	(pow.f64 (fma.f64 z y y) 3)	z	0
2.0ms	(pow.f64 (fma.f64 z y y) 3)	y	-inf
2.0ms	(pow.f64 (fma.f64 z y y) 3)	y	inf
2.0ms	(pow.f64 (fma.f64 z y y) 3)	y	0
2.0ms	(pow.f64 (fma.f64 z y y) 3)	z	-inf

rewrite48.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

912×	`log1p-expm1-u_binary64`
912×	`expm1-log1p-u_binary64`
260×	`prod-diff_binary64`
100×	`add-sqr-sqrt_binary64`
95×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	223	25
2	2484	25

Stop Event

1×	node limit

Counts

3 → 77

simplify44.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

632×	`unswap-sqr_binary64`
600×	`distribute-rgt-out_binary64`
419×	`associate-+l+_binary64`
278×	`fma-def_binary64`
254×	`*-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	34	982
1	102	861
2	334	804
3	1465	778
4	3367	775

Stop Event

1×	node limit

Counts

161 → 104

prune58.0ms (2.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	104	3	107

Error

Counts

107 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (+.f64 x y) z (+.f64 x y))
✓	0.0b	(fma.f64 x (+.f64 z 1) (*.f64 y (+.f64 z 1)))
✓	27.7b	(fma.f64 x (+.f64 z 1) (cbrt.f64 (pow.f64 (fma.f64 z y y) 3)))

Compiler

Compiled 1615 to 827 computations (48.8% saved)

regimes131.0ms (6.7%)

Accuracy

Total 0.0b remaining (64.2%)

Threshold costs 0.0b (64.2%)

Counts

24 → 1

Compiler

Compiled 1812 to 1093 computations (39.7% saved)

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	7	11

Stop Event

1×

saturated

end55.0ms (2.8%)

Stop Event

1×

done

Remove

(sort x y)

Compiler

Compiled 83 to 44 computations (47% saved)

Details

analyze425.0ms (21.6%)

sample797.0ms (40.5%)

preprocess28.0ms (1.4%)

simplify9.0ms (0.5%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series8.0ms (0.4%)

rewrite44.0ms (2.2%)

simplify18.0ms (0.9%)

prune42.0ms (2.1%)

localize5.0ms (0.3%)

series7.0ms (0.4%)

rewrite37.0ms (1.9%)

simplify19.0ms (1%)

prune14.0ms (0.7%)

localize7.0ms (0.3%)

series13.0ms (0.7%)

rewrite43.0ms (2.2%)

simplify30.0ms (1.5%)

prune36.0ms (1.8%)

localize8.0ms (0.4%)

series27.0ms (1.3%)

rewrite48.0ms (2.4%)

simplify44.0ms (2.2%)

prune58.0ms (2.9%)

regimes131.0ms (6.7%)

simplify7.0ms (0.4%)

end55.0ms (2.8%)

Profiling