Details

analyze1.3s (29.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
2.3%	97.4%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
29.7%	70%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.1s (26.6%)

Results

1.0s	8255×	body	128	valid
92.0ms	759×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess43.0ms (1%)

Algorithm

2×	egg-herbie

Rules

932×	`div-sub_binary64`
494×	`fma-def_binary64`
327×	`fma-neg_binary64`
303×	`distribute-rgt-in_binary64`
262×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	176
1	109	176
2	250	154
3	611	154
4	1514	154
5	4194	154
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify23.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

734×	`fma-def_binary64`
533×	`div-sub_binary64`
511×	`fma-neg_binary64`
499×	`times-frac_binary64`
213×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	19	16
2	40	14
3	85	14
4	194	14
5	394	14
6	832	14
7	2375	14

Stop Event

1×	node limit

Counts

1 → 2

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	11.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	1.0b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series47.0ms (1.1%)

Counts

2 → 96

Calls

24 calls:

3.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)	a	inf
3.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)	a	0
3.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)	z	0
2.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)	z	-inf
2.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)	z	inf

rewrite54.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

365×	`fma-def_binary64`
224×	`expm1-udef_binary64`
224×	`log1p-udef_binary64`
200×	`fma-neg_binary64`
193×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	227	24
2	3413	24

Stop Event

1×	node limit

Counts

2 → 77

simplify57.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

774×	`fma-def_binary64`
656×	`times-frac_binary64`
494×	`cancel-sign-sub-inv_binary64`
325×	`sub-neg_binary64`
153×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	2936
1	568	2936
2	1962	2292

Stop Event

1×	node limit

Counts

173 → 153

prune126.0ms (2.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	148	5	153
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	150	5	155

Error

Counts

155 → 5

Alt Table

Status	Error	Program
▶	0.6b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
	2.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
	21.4b	(-.f64 (+.f64 x y) (/.f64 t (/.f64 z y)))
	1.1b	(*.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x) 1)
	11.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))

Compiler

Compiled 3492 to 1229 computations (64.8% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
✓	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	1.2b	(/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))

series91.0ms (2.1%)

Counts

3 → 144

Calls

36 calls:

7.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))	y	0
6.0ms	(/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))	t	-inf
4.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))	a	inf
3.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))	z	0
3.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))	a	0

rewrite68.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

260×	`expm1-udef_binary64`
260×	`log1p-udef_binary64`
142×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	264	37
2	4345	37

Stop Event

1×	node limit

Counts

3 → 118

simplify81.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

820×	`times-frac_binary64`
711×	`cancel-sign-sub-inv_binary64`
436×	`sub-neg_binary64`
210×	`associate--l+_binary64`
182×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	215	4438
1	702	4195
2	2428	4075

Stop Event

1×	node limit

Counts

262 → 230

prune170.0ms (3.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	227	3	230
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	230	5	235

Error

Counts

235 → 5

Alt Table

Status	Error	Program
	21.4b	(-.f64 (+.f64 x y) (/.f64 t (/.f64 z y)))
▶	1.1b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	0.6b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
	2.9b	(fma.f64 (/.f64 y (-.f64 z a)) (-.f64 z t) x)
	11.3b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))

Compiler

Compiled 5732 to 1908 computations (66.7% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	1.6b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

series79.0ms (1.8%)

Counts

2 → 108

Calls

27 calls:

8.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))	z	0
6.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))	a	-inf
5.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))	z	inf
5.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))	a	0
3.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))	z	0

rewrite61.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

280×	`fma-neg_binary64`
254×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`
138×	`add-sqr-sqrt_binary64`
133×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	258	27
2	4066	27

Stop Event

1×	node limit

Counts

2 → 59

simplify63.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
539×	`times-frac_binary64`
519×	`cancel-sign-sub-inv_binary64`
469×	`associate-/l*_binary64`
269×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	3341
1	486	3098
2	1619	2588

Stop Event

1×	node limit

Counts

167 → 138

prune150.0ms (3.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	222	5	227

Error

Counts

227 → 5

Alt Table

Status	Error	Program
	21.4b	(-.f64 (+.f64 x y) (/.f64 t (/.f64 z y)))
✓	1.1b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	0.6b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
▶	2.9b	(fma.f64 (/.f64 y (-.f64 z a)) (-.f64 z t) x)
	11.3b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))

Compiler

Compiled 5375 to 1853 computations (65.5% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 z a))
✓	2.8b	(fma.f64 (/.f64 y (-.f64 z a)) (-.f64 z t) x)

series44.0ms (1%)

Counts

2 → 84

Calls

24 calls:

3.0ms	(fma.f64 (/.f64 y (-.f64 z a)) (-.f64 z t) x)	z	0
3.0ms	(fma.f64 (/.f64 y (-.f64 z a)) (-.f64 z t) x)	a	0
3.0ms	(fma.f64 (/.f64 y (-.f64 z a)) (-.f64 z t) x)	t	inf
2.0ms	(fma.f64 (/.f64 y (-.f64 z a)) (-.f64 z t) x)	z	-inf
2.0ms	(fma.f64 (/.f64 y (-.f64 z a)) (-.f64 z t) x)	z	inf

rewrite56.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

805×	`prod-diff_binary64`
220×	`log1p-udef_binary64`
120×	`add-sqr-sqrt_binary64`
114×	`log1p-expm1-u_binary64`
114×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	224	21
2	3280	21

Stop Event

1×	node limit

Counts

2 → 58

simplify47.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

685×	`times-frac_binary64`
669×	`fma-def_binary64`
558×	`associate-/l*_binary64`
338×	`cancel-sign-sub-inv_binary64`
306×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	2442
1	510	2442
2	1573	1848

Stop Event

1×	node limit

Counts

142 → 123

prune77.0ms (1.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	123	5	128

Error

Counts

128 → 5

Alt Table

Status	Error	Program
	21.4b	(-.f64 (+.f64 x y) (/.f64 t (/.f64 z y)))
✓	1.1b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	0.6b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
✓	2.9b	(fma.f64 (/.f64 y (-.f64 z a)) (-.f64 z t) x)
	11.3b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))

Compiler

Compiled 2614 to 859 computations (67.1% saved)

regimes455.0ms (10.5%)

Accuracy

Total 1.3b remaining (99.2%)

Threshold costs 0b (0%)

Counts

74 → 1

Compiler

Compiled 7765 to 4986 computations (35.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	16	16
2	24	16
3	28	16
4	30	16

Stop Event

1×

saturated

end64.0ms (1.5%)

Stop Event

1×

fuel

Compiler

Compiled 109 to 68 computations (37.6% saved)

Details

analyze1.3s (29.6%)

sample1.1s (26.6%)

preprocess43.0ms (1%)

simplify23.0ms (0.5%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series47.0ms (1.1%)

rewrite54.0ms (1.2%)

simplify57.0ms (1.3%)

prune126.0ms (2.9%)

localize10.0ms (0.2%)

series91.0ms (2.1%)

rewrite68.0ms (1.6%)

simplify81.0ms (1.9%)

prune170.0ms (3.9%)

localize7.0ms (0.2%)

series79.0ms (1.8%)

rewrite61.0ms (1.4%)

simplify63.0ms (1.5%)

prune150.0ms (3.5%)

localize7.0ms (0.2%)

series44.0ms (1%)

rewrite56.0ms (1.3%)

simplify47.0ms (1.1%)

prune77.0ms (1.8%)

regimes455.0ms (10.5%)

simplify3.0ms (0.1%)

end64.0ms (1.5%)

Profiling