Details

analyze270.0ms (7.9%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
50%	46.8%	3.2%	7
56.2%	37.5%	6.3%	8
62.4%	25.8%	11.8%	9
65.6%	20.3%	14.1%	10
68.7%	13.5%	17.9%	11
70.2%	10.5%	19.2%	12
71.8%	6.9%	21.3%	13
72.6%	5.4%	22%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample999.0ms (29.2%)

Results

945.0ms	8256×	body	128	valid
32.0ms	352×	body	128	invalid

Compiler

Compiled 28 to 22 computations (21.4% saved)

preprocess33.0ms (1%)

Algorithm

2×	egg-herbie

Rules

620×	`fma-def_binary64`
514×	`distribute-rgt-in_binary64`
475×	`distribute-lft-in_binary64`
190×	`div-sub_binary64`
178×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	41	32
2	133	32
3	395	32
4	1406	32
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify28.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

417×	`unsub-neg_binary64`
308×	`fma-def_binary64`
306×	`fma-neg_binary64`
269×	`times-frac_binary64`
261×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	24	16
2	71	16
3	204	16
4	733	16
5	3250	16

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
▶	0.4b	(.f64 (-.f64 1 x) (.f64 (-.f64 3 x) (/.f64 1/3 y)))
	4.5b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

Compiler

Compiled 76 to 58 computations (23.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (-.f64 1 x) (.f64 (-.f64 3 x) (/.f64 1/3 y)))
✓	0.3b	(*.f64 (-.f64 3 x) (/.f64 1/3 y))
✓	0.3b	(/.f64 1/3 y)

series24.0ms (0.7%)

Counts

3 → 48

Calls

15 calls:

5.0ms	(.f64 (-.f64 1 x) (.f64 (-.f64 3 x) (/.f64 1/3 y)))	y	-inf
4.0ms	(*.f64 (-.f64 3 x) (/.f64 1/3 y))	x	-inf
2.0ms	(.f64 (-.f64 1 x) (.f64 (-.f64 3 x) (/.f64 1/3 y)))	y	inf
2.0ms	(.f64 (-.f64 1 x) (.f64 (-.f64 3 x) (/.f64 1/3 y)))	y	0
2.0ms	(.f64 (-.f64 1 x) (.f64 (-.f64 3 x) (/.f64 1/3 y)))	x	inf

rewrite68.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

214×	`expm1-udef_binary64`
213×	`log1p-udef_binary64`
194×	`prod-diff_binary64`
179×	`fma-def_binary64`
174×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	244	30
2	3181	30

Stop Event

1×	node limit

Counts

3 → 137

simplify38.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

479×	`distribute-rgt-in_binary64`
453×	`cancel-sign-sub-inv_binary64`
402×	`fma-neg_binary64`
234×	`fma-def_binary64`
156×	`unsub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	44	717
1	127	685
2	289	521
3	742	474
4	2423	464

Stop Event

1×	node limit

Counts

185 → 157

prune147.0ms (4.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	154	3	157
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	154	5	159

Error

0.0b

Counts

159 → 5

Alt Table

Status	Error	Program
	0.4b	(*.f64 (/.f64 (-.f64 3 x) y) (fma.f64 x -1/3 1/3))
▶	0.2b	(.f64 (-.f64 1 x) (-.f64 (/.f64 1 y) (.f64 1/3 (/.f64 x y))))
✓	0.4b	(.f64 (-.f64 1 x) (.f64 (-.f64 3 x) (/.f64 1/3 y)))
	4.5b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
	0.2b	(*.f64 (-.f64 1 x) (/.f64 (fma.f64 x -1/3 1) y))

Compiler

Compiled 2704 to 1950 computations (27.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 y) (*.f64 1/3 (/.f64 x y)))
✓	0.1b	(.f64 (-.f64 1 x) (-.f64 (/.f64 1 y) (.f64 1/3 (/.f64 x y))))
✓	0.3b	(*.f64 1/3 (/.f64 x y))

series27.0ms (0.8%)

Counts

3 → 39

Calls

18 calls:

5.0ms	(.f64 (-.f64 1 x) (-.f64 (/.f64 1 y) (.f64 1/3 (/.f64 x y))))	y	0
2.0ms	(.f64 (-.f64 1 x) (-.f64 (/.f64 1 y) (.f64 1/3 (/.f64 x y))))	y	inf
2.0ms	(.f64 (-.f64 1 x) (-.f64 (/.f64 1 y) (.f64 1/3 (/.f64 x y))))	y	-inf
2.0ms	(.f64 (-.f64 1 x) (-.f64 (/.f64 1 y) (.f64 1/3 (/.f64 x y))))	x	-inf
2.0ms	(.f64 (-.f64 1 x) (-.f64 (/.f64 1 y) (.f64 1/3 (/.f64 x y))))	x	inf

rewrite89.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

877×	`prod-diff_binary64`
200×	`egg-rr`
124×	`add-sqr-sqrt_binary64`
118×	`add-cbrt-cube_binary64`
118×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	250	33
2	3470	33

Stop Event

1×	node limit

Counts

3 → 200

simplify37.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

505×	`cancel-sign-sub-inv_binary64`
464×	`fma-neg_binary64`
304×	`distribute-rgt-in_binary64`
222×	`distribute-lft-in_binary64`
204×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	627
1	106	595
2	246	449
3	682	402
4	2303	392

Stop Event

1×	node limit

Counts

239 → 217

prune297.0ms (8.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	217	5	222

Error

0.0b

Counts

222 → 5

Alt Table

Status	Error	Program
	0.4b	(*.f64 (/.f64 (-.f64 3 x) y) (fma.f64 x -1/3 1/3))
✓	0.2b	(.f64 (-.f64 1 x) (-.f64 (/.f64 1 y) (.f64 1/3 (/.f64 x y))))
✓	0.4b	(.f64 (-.f64 1 x) (.f64 (-.f64 3 x) (/.f64 1/3 y)))
	4.5b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
▶	0.2b	(*.f64 (-.f64 1 x) (/.f64 (fma.f64 x -1/3 1) y))

Compiler

Compiled 6387 to 3791 computations (40.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (-.f64 1 x) (/.f64 (fma.f64 x -1/3 1) y))
✓	0.1b	(/.f64 (fma.f64 x -1/3 1) y)
✓	0.1b	(fma.f64 x -1/3 1)

series25.0ms (0.7%)

Counts

3 → 60

Calls

15 calls:

5.0ms	(*.f64 (-.f64 1 x) (/.f64 (fma.f64 x -1/3 1) y))	y	inf
3.0ms	(*.f64 (-.f64 1 x) (/.f64 (fma.f64 x -1/3 1) y))	y	-inf
2.0ms	(*.f64 (-.f64 1 x) (/.f64 (fma.f64 x -1/3 1) y))	y	0
1.0ms	(/.f64 (fma.f64 x -1/3 1) y)	y	-inf
1.0ms	(*.f64 (-.f64 1 x) (/.f64 (fma.f64 x -1/3 1) y))	x	inf

rewrite61.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

455×	`log-prod_binary64`
176×	`pow1/3_binary64`
171×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`
161×	`pow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	193	27
2	2531	27

Stop Event

1×	node limit

Counts

3 → 146

simplify39.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

505×	`cancel-sign-sub-inv_binary64`
471×	`fma-neg_binary64`
304×	`distribute-rgt-in_binary64`
222×	`distribute-lft-in_binary64`
215×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	789
1	114	757
2	262	575
3	702	528
4	2336	518

Stop Event

1×	node limit

Counts

206 → 170

prune133.0ms (3.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	0	2	2
Picked	0	1	1
Done	1	1	2
Total	170	5	175

Error

Counts

175 → 5

Alt Table

Status	Error	Program
	0.4b	(*.f64 (/.f64 (-.f64 3 x) y) (fma.f64 x -1/3 1/3))
✓	0.2b	(.f64 (-.f64 1 x) (-.f64 (/.f64 1 y) (.f64 1/3 (/.f64 x y))))
▶	0.2b	(/.f64 (-.f64 1 x) (/.f64 y (fma.f64 x -1/3 1)))
	4.5b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
✓	0.2b	(*.f64 (-.f64 1 x) (/.f64 (fma.f64 x -1/3 1) y))

Compiler

Compiled 2884 to 2043 computations (29.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 y (fma.f64 x -1/3 1))
✓	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (fma.f64 x -1/3 1)))
	0.1b	(fma.f64 x -1/3 1)

series27.0ms (0.8%)

Counts

2 → 48

Calls

12 calls:

6.0ms	(/.f64 y (fma.f64 x -1/3 1))	y	0
3.0ms	(/.f64 y (fma.f64 x -1/3 1))	y	-inf
3.0ms	(/.f64 y (fma.f64 x -1/3 1))	y	inf
3.0ms	(/.f64 (-.f64 1 x) (/.f64 y (fma.f64 x -1/3 1)))	y	-inf
2.0ms	(/.f64 (-.f64 1 x) (/.f64 y (fma.f64 x -1/3 1)))	y	inf

rewrite165.0ms (4.8%)

Algorithm

1×	batch-egg-rewrite

Rules

456×	`prod-diff_binary64`
322×	`egg-rr`
179×	`expm1-udef_binary64`
178×	`log1p-udef_binary64`
165×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	201	22
2	2844	22

Stop Event

1×	node limit

Counts

2 → 322

simplify48.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

401×	`associate-l_binary64`
306×	`fma-neg_binary64`
268×	`cancel-sign-sub-inv_binary64`
249×	`fma-def_binary64`
213×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	856
1	207	822
2	560	646
3	1783	608

Stop Event

1×	node limit

Counts

370 → 350

prune492.0ms (14.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	381	0	381
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	381	5	386

Error

Counts

386 → 5

Alt Table

Status	Error	Program
	0.4b	(*.f64 (/.f64 (-.f64 3 x) y) (fma.f64 x -1/3 1/3))
✓	0.2b	(.f64 (-.f64 1 x) (-.f64 (/.f64 1 y) (.f64 1/3 (/.f64 x y))))
✓	0.2b	(/.f64 (-.f64 1 x) (/.f64 y (fma.f64 x -1/3 1)))
	4.5b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
✓	0.2b	(*.f64 (-.f64 1 x) (/.f64 (fma.f64 x -1/3 1) y))

Compiler

Compiled 17392 to 12019 computations (30.9% saved)

regimes202.0ms (5.9%)

Accuracy

Total 0.1b remaining (82.9%)

Threshold costs 0.1b (82.9%)

Counts

38 → 1

Compiler

Compiled 2187 to 1628 computations (25.6% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	13	14
2	17	14
3	19	14
4	20	14

Stop Event

1×

saturated

end141.0ms (4.1%)

Stop Event

1×

fuel

Compiler

Compiled 88 to 66 computations (25% saved)

Details

analyze270.0ms (7.9%)

sample999.0ms (29.2%)

preprocess33.0ms (1%)

simplify28.0ms (0.8%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series24.0ms (0.7%)

rewrite68.0ms (2%)

simplify38.0ms (1.1%)

prune147.0ms (4.3%)

localize7.0ms (0.2%)

series27.0ms (0.8%)

rewrite89.0ms (2.6%)

simplify37.0ms (1.1%)

prune297.0ms (8.7%)

localize6.0ms (0.2%)

series25.0ms (0.7%)

rewrite61.0ms (1.8%)

simplify39.0ms (1.1%)

prune133.0ms (3.9%)

localize9.0ms (0.2%)

series27.0ms (0.8%)

rewrite165.0ms (4.8%)

simplify48.0ms (1.4%)

prune492.0ms (14.4%)

regimes202.0ms (5.9%)

simplify6.0ms (0.2%)

end141.0ms (4.1%)

Profiling