Details

analyze2.0s (11.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.6%	98.1%	0.3%	13
2.3%	97.4%	0.3%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample2.0s (11.2%)

Results

1.3s	8256×	body	128	valid
712.0ms	3834×	body	128	invalid

Compiler

Compiled 44 to 28 computations (36.4% saved)

preprocess47.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

1158×	`fma-def_binary64`
334×	`associate-+l+_binary64`
305×	`associate-+r+_binary64`
240×	`+-commutative_binary64`
65×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	86	352
1	249	254
2	785	236
3	1753	236
4	1909	236
5	1931	236
6	1931	208
7	2475	208
8	2475	208
0	6	6

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 21 to 13 computations (38.1% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

89×	`fma-def_binary64`
24×	`associate-+l+_binary64`
21×	`associate-+r+_binary64`
18×	`+-commutative_binary64`
10×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	27	16
2	69	15
3	147	13
4	192	13
5	204	13
6	207	13

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0%)

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
	2.5b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	2.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	0.0b	(+.f64 x (*.f64 y z))
✓	4.7b	(.f64 (.f64 a z) b)

series46.0ms (0.3%)

Counts

3 → 144

Calls

36 calls:

8.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))	a	-inf
4.0ms	(+.f64 x (*.f64 y z))	z	inf
1.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))	x	inf
1.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))	x	-inf
1.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))	x	0

rewrite69.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

296×	`log1p-udef_binary64`
162×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`
154×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	36
1	311	28
2	4617	28

Stop Event

1×	node limit

Counts

3 → 93

simplify36.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

86×	`fma-def_binary64`
16×	`+-commutative_binary64`
16×	`associate-+l+_binary64`
15×	`associate-+r+_binary64`
9×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	1400
1	78	1228
2	145	1226
3	186	1226

Stop Event

1×

saturated

Counts

237 → 117

prune82.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	116	3	119

Error

0.0b

Counts

119 → 3

Alt Table

Status	Error	Program
✓	2.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	17.6b	(fma.f64 z (fma.f64 a b y) x)
▶	2.5b	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))

Compiler

Compiled 2392 to 557 computations (76.7% saved)

localize9.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.4b	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))

series26.0ms (0.1%)

Counts

1 → 72

Calls

18 calls:

4.0ms	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))	z	-inf
1.0ms	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))	b	-inf
1.0ms	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))	a	-inf
1.0ms	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))	x	-inf
1.0ms	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))	t	-inf

rewrite111.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

535×	`log-prod_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
202×	`prod-diff_binary64`
193×	`pow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	217	16
2	2636	16

Stop Event

1×	node limit

Counts

1 → 30

simplify26.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

86×	`fma-def_binary64`
16×	`+-commutative_binary64`
16×	`associate-+l+_binary64`
15×	`associate-+r+_binary64`
10×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	928
1	79	817
2	145	815
3	186	815

Stop Event

1×

saturated

Counts

102 → 55

prune29.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	55	3	58

Error

0.0b

Counts

58 → 3

Alt Table

Status	Error	Program
✓	2.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
▶	17.6b	(fma.f64 z (fma.f64 a b y) x)
✓	2.5b	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))

Compiler

Compiled 844 to 177 computations (79% saved)

localize13.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.1b	(fma.f64 z (fma.f64 a b y) x)

series19.0ms (0.1%)

Counts

1 → 60

Calls

15 calls:

3.0ms	(fma.f64 z (fma.f64 a b y) x)	y	-inf
1.0ms	(fma.f64 z (fma.f64 a b y) x)	z	-inf
1.0ms	(fma.f64 z (fma.f64 a b y) x)	z	inf
1.0ms	(fma.f64 z (fma.f64 a b y) x)	a	-inf
1.0ms	(fma.f64 z (fma.f64 a b y) x)	b	-inf

rewrite35.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`log1p-expm1-u_binary64`
700×	`expm1-log1p-u_binary64`
149×	`expm1-udef_binary64`
149×	`log1p-udef_binary64`
128×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	157	9
2	1879	9

Stop Event

1×	node limit

Counts

1 → 23

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

29×	`fma-def_binary64`
7×	`+-commutative_binary64`
7×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	576
1	47	486
2	70	486
3	75	486

Stop Event

1×

saturated

Counts

83 → 38

prune25.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	37	4	41

Error

Counts

41 → 4

Alt Table

Status	Error	Program
✓	2.5b	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))
▶	18.5b	(pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 a b y) x)) 3)
✓	2.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	17.6b	(fma.f64 z (fma.f64 a b y) x)

Compiler

Compiled 473 to 144 computations (69.6% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (fma.f64 z (fma.f64 a b y) x))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 a b y) x)) 3)
	3.1b	(fma.f64 z (fma.f64 a b y) x)

series12.3s (68.2%)

Counts

2 → 120

Calls

30 calls:

5.8s	(pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 a b y) x)) 3)	b	inf
5.0s	(pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 a b y) x)) 3)	y	-inf
263.0ms	(pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 a b y) x)) 3)	b	0
227.0ms	(pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 a b y) x)) 3)	z	-inf
221.0ms	(pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 a b y) x)) 3)	z	inf

rewrite43.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

868×	`log1p-expm1-u_binary64`
868×	`expm1-log1p-u_binary64`
128×	`prod-diff_binary64`
101×	`add-sqr-sqrt_binary64`
94×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	218	20
2	2380	20

Stop Event

1×	node limit

Counts

2 → 49

simplify173.0ms (1%)

Algorithm

1×	egg-herbie

Rules

494×	`*-commutative_binary64`
271×	`+-commutative_binary64`
221×	`fma-def_binary64`
209×	`associate-r_binary64`
187×	`associate-+r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1136	14327
1	4611	13739

Stop Event

1×	node limit

Counts

169 → 238

prune306.0ms (1.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	276	0	276
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	276	4	280

Error

Counts

280 → 4

Alt Table

Status	Error	Program
✓	2.5b	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))
✓	18.5b	(pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 a b y) x)) 3)
✓	2.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	17.6b	(fma.f64 z (fma.f64 a b y) x)

Compiler

Compiled 19132 to 10756 computations (43.8% saved)

regimes459.0ms (2.5%)

Accuracy

Total 1.4b remaining (99.1%)

Threshold costs 0b (0%)

Counts

56 → 2

Compiler

Compiled 5740 to 3829 computations (33.3% saved)

bsearch7.0ms (0%)

Algorithm

1×	binary-search

Calls

1 calls:

6.0ms

Steps

Iters	Point		Range
1.3279760387023665e-47	∈ [	1.2394964113242515e-47	,	1.4754420843325584e-47	]

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	37
1	22	37

Stop Event

1×

saturated

end81.0ms (0.4%)

Stop Event

1×

done

Compiler

Compiled 134 to 76 computations (43.3% saved)

Details

analyze2.0s (11.3%)

sample2.0s (11.2%)

preprocess47.0ms (0.3%)

simplify8.0ms (0%)

prune3.0ms (0%)

localize13.0ms (0.1%)

series46.0ms (0.3%)

rewrite69.0ms (0.4%)

simplify36.0ms (0.2%)

prune82.0ms (0.5%)

localize9.0ms (0%)

series26.0ms (0.1%)

rewrite111.0ms (0.6%)

simplify26.0ms (0.1%)

prune29.0ms (0.2%)

localize13.0ms (0.1%)

series19.0ms (0.1%)

rewrite35.0ms (0.2%)

simplify18.0ms (0.1%)

prune25.0ms (0.1%)

localize11.0ms (0.1%)

series12.3s (68.2%)

rewrite43.0ms (0.2%)

simplify173.0ms (1%)

prune306.0ms (1.7%)

regimes459.0ms (2.5%)

bsearch7.0ms (0%)

simplify2.0ms (0%)

end81.0ms (0.4%)

Profiling