Details

analyze2.1s (40.1%)

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)

sample1.8s (34.6%)

Results

1.2s	8256×	body	128	valid
552.0ms	3883×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

89×	`fma-def_binary64`
24×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
19×	`+-commutative_binary64`
10×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	27	16
2	66	15
3	122	13
4	157	13
5	164	13
6	167	13
7	167	13

prune3.0ms (0.1%)

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
	3.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	2.8b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
✓	0.0b	(+.f64 x (*.f64 y z))
✓	0.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	5.6b	(.f64 (.f64 a z) b)

series57.0ms (1.1%)

Counts

4 → 204

Calls

4 calls:

24.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
13.0ms	(.f64 (.f64 a z) b)
12.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
8.0ms	(+.f64 x (*.f64 y z))

rewrite93.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

4 → 135

Calls

4 calls:

89.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
89.0ms	(+.f64 x (*.f64 y z))
89.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
89.0ms	(.f64 (.f64 a z) b)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	49
1	311	37
2	4341	37
3	5237	37
0	0	0
1	0	0

simplify74.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

339 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	1867
1	72	1695
2	129	1693
3	168	1693
4	167	1693

prune120.0ms (2.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	159	4	163

Error

Counts

163 → 4

Alt Table

Status	Error	Program
	3.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	2.7b	(fma.f64 (*.f64 a z) b (fma.f64 a t (fma.f64 z y x)))
	23.5b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (pow.f64 (sqrt.f64 (.f64 (.f64 a z) b)) 2))
	3.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 3383 to 807 computations (76.1% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.6b	(fma.f64 (*.f64 a z) b (fma.f64 a t (fma.f64 z y x)))

series25.0ms (0.5%)

Counts

1 → 72

Calls

1 calls:

25.0ms

(fma.f64 (*.f64 a z) b (fma.f64 a t (fma.f64 z y x)))

rewrite84.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

1 → 30

Calls

1 calls:

83.0ms

(fma.f64 (*.f64 a z) b (fma.f64 a t (fma.f64 z y x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	217	16
2	2540	16
3	4850	16
4	5003	16
0	0	0
1	0	0

simplify24.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

102 → 54

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	988
1	75	815
2	138	815
3	169	815
4	167	815

prune29.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	54	4	58

Error

Counts

58 → 4

Alt Table

Status	Error	Program
	3.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.7b	(fma.f64 (*.f64 a z) b (fma.f64 a t (fma.f64 z y x)))
	23.5b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (pow.f64 (sqrt.f64 (.f64 (.f64 a z) b)) 2))
▶	3.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 902 to 215 computations (76.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	2.9b	(fma.f64 z (fma.f64 a b y) x)

series40.0ms (0.8%)

Counts

2 → 132

Calls

2 calls:

22.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
18.0ms	(fma.f64 z (fma.f64 a b y) x)

rewrite51.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

889×	`log1p-expm1-u_binary64`
889×	`expm1-log1p-u_binary64`
192×	`prod-diff_binary64`
103×	`add-sqr-sqrt_binary64`
94×	`add-log-exp_binary64`

Counts

2 → 47

Calls

2 calls:

50.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
50.0ms	(fma.f64 z (fma.f64 a b y) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	197	22
2	2289	22
3	5801	22
0	0	0
1	0	0

simplify37.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

87×	`fma-def_binary64`
17×	`+-commutative_binary64`
14×	`associate-+l+_binary64`
12×	`associate-+r+_binary64`
10×	`*-commutative_binary64`

Counts

179 → 77

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	1564
1	80	1301
2	142	1301
3	169	1301
4	167	1301

prune48.0ms (0.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	77	4	81

Error

Counts

81 → 4

Alt Table

Status	Error	Program
▶	3.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.7b	(fma.f64 (*.f64 a z) b (fma.f64 a t (fma.f64 z y x)))
	23.5b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (pow.f64 (sqrt.f64 (.f64 (.f64 a z) b)) 2))
✓	3.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 1131 to 284 computations (74.9% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.6b	(fma.f64 a (fma.f64 z b t) x)

series18.0ms (0.4%)

Counts

1 → 60

Calls

1 calls:

18.0ms

(fma.f64 a (fma.f64 z b t) x)

rewrite40.0ms (0.8%)

Algorithm

2×	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`

Counts

1 → 23

Calls

1 calls:

39.0ms

(fma.f64 a (fma.f64 z b t) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	157	9
2	1811	9
3	4988	9
0	0	0
1	0	0

simplify18.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

29×	`fma-def_binary64`
10×	`*-commutative_binary64`
8×	`+-commutative_binary64`
2×	`associate-+r+_binary64`
2×	`associate-r_binary64`

Counts

83 → 38

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	627
1	37	486
2	59	486
3	65	486
4	64	486

prune27.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	38	4	42

Error

Counts

42 → 4

Alt Table

Status	Error	Program
✓	3.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.7b	(fma.f64 (*.f64 a z) b (fma.f64 a t (fma.f64 z y x)))
	23.5b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (pow.f64 (sqrt.f64 (.f64 (.f64 a z) b)) 2))
✓	3.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 581 to 176 computations (69.7% saved)

regimes381.0ms (7.4%)

Accuracy

Total 1.4b remaining (99.4%)

Threshold costs 0b (0%)

Counts

48 → 2

Compiler

Compiled 4760 to 3101 computations (34.9% saved)

bsearch1.0ms (0%)

Compiler: Compiled 21 to 13 computations (38.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	56
1	31	56
2	31	56

end84.0ms (1.6%)

Compiler: Compiled 166 to 88 computations (47% saved)

Details

analyze2.1s (40.1%)

sample1.8s (34.6%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series57.0ms (1.1%)

rewrite93.0ms (1.8%)

simplify74.0ms (1.4%)

prune120.0ms (2.3%)

localize8.0ms (0.2%)

series25.0ms (0.5%)

rewrite84.0ms (1.6%)

simplify24.0ms (0.5%)

prune29.0ms (0.6%)

localize7.0ms (0.1%)

series40.0ms (0.8%)

rewrite51.0ms (1%)

simplify37.0ms (0.7%)

prune48.0ms (0.9%)

localize7.0ms (0.1%)

series18.0ms (0.4%)

rewrite40.0ms (0.8%)

simplify18.0ms (0.4%)

prune27.0ms (0.5%)

regimes381.0ms (7.4%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end84.0ms (1.6%)

Profiling