Details

analyze1.8s (28.6%)

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 (28.4%)

Results

1.2s	8256×	body	128	valid
527.0ms	3909×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify9.0ms (0.1%)

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
	4.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	0.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize11.0ms (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 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	0.0b	(+.f64 x (*.f64 y z))
✓	4.2b	(.f64 (.f64 a z) b)

series50.0ms (0.8%)

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 x (.f64 y z)) (.f64 t a))
8.0ms	(.f64 (.f64 a z) b)
5.0ms	(+.f64 x (*.f64 y z))

rewrite92.0ms (1.5%)

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 → 136

Calls

4 calls:

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

simplify48.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Counts

340 → 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

prune114.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	157	4	161
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	158	5	163

Error

0.0b

Counts

163 → 5

Alt Table

Status	Error	Program
✓	0.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	4.3b	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))
▶	3.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	44.3b	(/.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 a t (fma.f64 z y x)) 2) (.f64 (.f64 (.f64 a z) b) (-.f64 (.f64 (.f64 a z) b) (fma.f64 a t (fma.f64 z y x))))) (+.f64 (pow.f64 (.f64 (*.f64 a z) b) 3) (pow.f64 (fma.f64 a t (fma.f64 z y x)) 3))))
	33.9b	(.f64 (-.f64 (pow.f64 (fma.f64 a t (fma.f64 z y x)) 2) (pow.f64 (.f64 (.f64 a z) b) 2)) (/.f64 1 (-.f64 (fma.f64 a t (fma.f64 z y x)) (.f64 (*.f64 a z) b))))

Compiler

Compiled 3564 to 863 computations (75.8% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series16.0ms (0.3%)

Counts

1 → 60

Calls

1 calls:

16.0ms

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

rewrite46.0ms (0.7%)

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 → 24

Calls

1 calls:

45.0ms

(fma.f64 z (fma.f64 a b y) 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 (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

84 → 38

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	576
1	40	486
2	60	486
3	65	486
4	64	486

prune28.0ms (0.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	38	5	43

Error

0.0b

Counts

43 → 5

Alt Table

Status	Error	Program
✓	0.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
▶	4.3b	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))
✓	3.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	44.3b	(/.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 a t (fma.f64 z y x)) 2) (.f64 (.f64 (.f64 a z) b) (-.f64 (.f64 (.f64 a z) b) (fma.f64 a t (fma.f64 z y x))))) (+.f64 (pow.f64 (.f64 (*.f64 a z) b) 3) (pow.f64 (fma.f64 a t (fma.f64 z y x)) 3))))
	33.9b	(.f64 (-.f64 (pow.f64 (fma.f64 a t (fma.f64 z y x)) 2) (pow.f64 (.f64 (.f64 a z) b) 2)) (/.f64 1 (-.f64 (fma.f64 a t (fma.f64 z y x)) (.f64 (*.f64 a z) b))))

Compiler

Compiled 764 to 255 computations (66.6% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.1b	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))

series23.0ms (0.4%)

Counts

1 → 72

Calls

1 calls:

23.0ms

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

rewrite78.0ms (1.3%)

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 → 31

Calls

1 calls:

77.0ms

(fma.f64 a (*.f64 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

simplify23.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

103 → 56

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	928
1	72	817
2	128	815
3	169	815
4	167	815

prune32.0ms (0.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	56	5	61

Error

0.0b

Counts

61 → 5

Alt Table

Status	Error	Program
✓	0.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	4.3b	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))
✓	3.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	44.3b	(/.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 a t (fma.f64 z y x)) 2) (.f64 (.f64 (.f64 a z) b) (-.f64 (.f64 (.f64 a z) b) (fma.f64 a t (fma.f64 z y x))))) (+.f64 (pow.f64 (.f64 (*.f64 a z) b) 3) (pow.f64 (fma.f64 a t (fma.f64 z y x)) 3))))
▶	33.9b	(.f64 (-.f64 (pow.f64 (fma.f64 a t (fma.f64 z y x)) 2) (pow.f64 (.f64 (.f64 a z) b) 2)) (/.f64 1 (-.f64 (fma.f64 a t (fma.f64 z y x)) (.f64 (*.f64 a z) b))))

Compiler

Compiled 1034 to 252 computations (75.6% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (.f64 (.f64 a z) b) 2)
	4.2b	(.f64 (.f64 a z) b)
✓	4.6b	(-.f64 (pow.f64 (fma.f64 a t (fma.f64 z y x)) 2) (pow.f64 (.f64 (.f64 a z) b) 2))
✓	31.5b	(.f64 (-.f64 (pow.f64 (fma.f64 a t (fma.f64 z y x)) 2) (pow.f64 (.f64 (.f64 a z) b) 2)) (/.f64 1 (-.f64 (fma.f64 a t (fma.f64 z y x)) (.f64 (*.f64 a z) b))))

series624.0ms (10%)

Counts

3 → 180

Calls

3 calls:

509.0ms

(*.f64 (-.f64 (pow.f64 (fma.f64 a t (fma.f64 z y x)) 2) (pow.f64 (*.f64 (*.f64 a z) b) 2)) (/.f64 1 (-.f64 (fma.f64 a t (fma.f64 z y x)) (*.f64 (*.f64 a z) b))))

97.0ms

(-.f64 (pow.f64 (fma.f64 a t (fma.f64 z y x)) 2) (pow.f64 (*.f64 (*.f64 a z) b) 2))

16.0ms

(pow.f64 (*.f64 (*.f64 a z) b) 2)

rewrite106.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

810×	`prod-diff_binary64`
201×	`add-sqr-sqrt_binary64`
195×	`log1p-expm1-u_binary64`
195×	`expm1-log1p-u_binary64`
188×	`add-cbrt-cube_binary64`

Counts

3 → 176

Calls

3 calls:

99.0ms

(pow.f64 (*.f64 (*.f64 a z) b) 2)

99.0ms

(-.f64 (pow.f64 (fma.f64 a t (fma.f64 z y x)) 2) (pow.f64 (*.f64 (*.f64 a z) b) 2))

99.0ms

(*.f64 (-.f64 (pow.f64 (fma.f64 a t (fma.f64 z y x)) 2) (pow.f64 (*.f64 (*.f64 a z) b) 2)) (/.f64 1 (-.f64 (fma.f64 a t (fma.f64 z y x)) (*.f64 (*.f64 a z) b))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	78
1	412	52
2	4664	52
3	6277	52
0	0	0
1	0	0

simplify233.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

587×	`associate-+r+_binary64`
411×	`associate-/l*_binary64`
314×	`associate-r_binary64`
309×	`fma-def_binary64`
216×	`associate-*r/_binary64`

Counts

356 → 342

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1840	25251
1	5704	25251

prune517.0ms (8.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	373	1	374
Fresh	1	0	1
Picked	0	1	1
Done	0	3	3
Total	374	5	379

Error

0.0b

Counts

379 → 5

Alt Table

Status	Error	Program
	34.6b	(.f64 (-.f64 (pow.f64 (fma.f64 a t (fma.f64 z y x)) 2) (.f64 (.f64 a z) (.f64 b (.f64 (.f64 a z) b)))) (/.f64 1 (-.f64 (fma.f64 a t (fma.f64 z y x)) (.f64 (.f64 a z) b))))
✓	4.3b	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))
✓	0.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	3.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	33.9b	(.f64 (-.f64 (pow.f64 (fma.f64 a t (fma.f64 z y x)) 2) (pow.f64 (.f64 (.f64 a z) b) 2)) (/.f64 1 (-.f64 (fma.f64 a t (fma.f64 z y x)) (.f64 (*.f64 a z) b))))

Compiler

Compiled 42311 to 14152 computations (66.6% saved)

regimes480.0ms (7.7%)

Accuracy

Total 2.0b remaining (99.5%)

Threshold costs 0b (0%)

Counts

60 → 1

Compiler

Compiled 7644 to 4599 computations (39.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	12	16
2	12	16

end87.0ms (1.4%)

Compiler: Compiled 173 to 90 computations (48% saved)

Details

analyze1.8s (28.6%)

sample1.8s (28.4%)

simplify9.0ms (0.1%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

series50.0ms (0.8%)

rewrite92.0ms (1.5%)

simplify48.0ms (0.8%)

prune114.0ms (1.8%)

localize8.0ms (0.1%)

series16.0ms (0.3%)

rewrite46.0ms (0.7%)

simplify18.0ms (0.3%)

prune28.0ms (0.5%)

localize9.0ms (0.1%)

series23.0ms (0.4%)

rewrite78.0ms (1.3%)

simplify23.0ms (0.4%)

prune32.0ms (0.5%)

localize17.0ms (0.3%)

series624.0ms (10%)

rewrite106.0ms (1.7%)

simplify233.0ms (3.8%)

prune517.0ms (8.3%)

regimes480.0ms (7.7%)

simplify2.0ms (0%)

end87.0ms (1.4%)

Profiling