Details

analyze434.0ms (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%	74.9%	25.1%	3
0%	74.9%	25.1%	4
0%	74.9%	25.1%	5
0%	62.4%	37.6%	6
0%	31.2%	68.8%	7
0%	31.2%	68.8%	8
0%	31.2%	68.8%	9
0%	28.1%	71.9%	10
4.7%	21.8%	73.5%	11
4.7%	21.8%	73.5%	12
7%	19.5%	73.5%	13
8.2%	17.5%	74.3%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample2.3s (31%)

Results

968.0ms	5963×	body	128	valid
531.0ms	672×	body	1024	valid
445.0ms	908×	body	512	valid
202.0ms	695×	body	256	valid
61.0ms	323×	body	128	invalid
26.0ms	18×	body	2048	valid

Compiler

Compiled 36 to 26 computations (27.8% saved)

preprocess70.0ms (1%)

Algorithm

2×	egg-herbie

Rules

535×	`fma-neg_binary64`
351×	`cancel-sign-sub-inv_binary64`
301×	`sub-neg_binary64`
265×	`distribute-rgt-in_binary64`
256×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	126
1	101	119
2	216	119
3	382	119
4	662	119
5	1095	119
6	2181	119
7	3682	119
8	4434	119
9	4693	119
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify39.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-neg_binary64`
312×	`fma-def_binary64`
173×	`distribute-rgt-in_binary64`
132×	`unsub-neg_binary64`
123×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	18
1	25	17
2	46	17
3	75	17
4	123	17
5	201	17
6	379	17
7	721	17
8	1279	17
9	2012	17
10	2697	17
11	2973	17
12	2989	17
13	2989	17

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)

Compiler

Compiled 58 to 37 computations (36.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (neg.f64 y))
✓	0.0b	(-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)
✓	0.0b	(*.f64 z (log1p.f64 (neg.f64 y)))
✓	0.2b	(fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y))))

series630.0ms (8.7%)

Counts

4 → 120

Calls

30 calls:

109.0ms	(*.f64 z (log1p.f64 (neg.f64 y)))	z	0
55.0ms	(*.f64 z (log1p.f64 (neg.f64 y)))	z	-inf
54.0ms	(*.f64 z (log1p.f64 (neg.f64 y)))	z	inf
49.0ms	(-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)	z	inf
44.0ms	(-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 (neg.f64 y)))) t)	t	0

rewrite66.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

714×	`prod-diff_binary64`
274×	`fma-def_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
149×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	227	36
2	2944	36

Stop Event

1×	node limit

Counts

4 → 143

simplify56.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

671×	`associate--r+_binary64`
460×	`distribute-neg-in_binary64`
315×	`distribute-rgt-in_binary64`
304×	`sub-neg_binary64`
212×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	2192
1	595	2027
2	1942	1970

Stop Event

1×	node limit

Counts

263 → 246

prune223.0ms (3.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	238	8	246
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	239	8	247

Error

0.0b

Counts

247 → 8

Alt Table

Status	Error	Program
	27.1b	(fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (log.f64 y)) (-.f64 (*.f64 z (log1p.f64 y)) t))
	0.4b	(-.f64 (fma.f64 x (log.f64 y) (neg.f64 (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) z)) (+.f64 (.f64 y z) (+.f64 (.f64 1/4 (.f64 (pow.f64 y 4) z)) (.f64 1/3 (*.f64 (pow.f64 y 3) z))))))) t)
	36.5b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 y)) (-.f64 (.f64 z (log1p.f64 y)) t))
	13.1b	(pow.f64 (cbrt.f64 (-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 y))) t)) 3)
	0.7b	(-.f64 (*.f64 (log.f64 y) x) (fma.f64 y z t))
	12.6b	(fma.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (-.f64 (.f64 z (log1p.f64 y)) t))
▶	0.1b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (*.f64 (log.f64 y) x)) t)
	39.2b	(-.f64 (pow.f64 (sqrt.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 y)))) 2) t)

Compiler

Compiled 5078 to 1985 computations (60.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 (neg.f64 y))
✓	0.0b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (*.f64 (log.f64 y) x)) t)
✓	0.0b	(fma.f64 (log1p.f64 (neg.f64 y)) z (*.f64 (log.f64 y) x))
✓	0.3b	(*.f64 (log.f64 y) x)

series612.0ms (8.4%)

Counts

3 → 92

Calls

27 calls:

72.0ms	(*.f64 (log.f64 y) x)	x	0
50.0ms	(*.f64 (log.f64 y) x)	x	inf
48.0ms	(*.f64 (log.f64 y) x)	x	-inf
41.0ms	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (*.f64 (log.f64 y) x)) t)	z	0
37.0ms	(*.f64 (log.f64 y) x)	y	0

rewrite62.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

714×	`prod-diff_binary64`
284×	`fma-def_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
149×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	227	33
2	2943	33

Stop Event

1×	node limit

Counts

3 → 127

simplify51.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

533×	`associate-+l+_binary64`
491×	`associate--r+_binary64`
489×	`fma-def_binary64`
303×	`distribute-neg-in_binary64`
293×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	1681
1	394	1585
2	1252	1454

Stop Event

1×	node limit

Counts

219 → 187

prune153.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	228	7	235

Error

0.0b

Counts

235 → 7

Alt Table

Status	Error	Program
	36.5b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 y)) (-.f64 (.f64 z (log1p.f64 y)) t))
	13.1b	(pow.f64 (cbrt.f64 (-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 y))) t)) 3)
✓	0.1b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (*.f64 (log.f64 y) x)) t)
	27.1b	(fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (log.f64 y)) (-.f64 (*.f64 z (log1p.f64 y)) t))
	39.2b	(-.f64 (pow.f64 (sqrt.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 y)))) 2) t)
▶	0.4b	(-.f64 (.f64 x (log.f64 y)) (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (*.f64 z (pow.f64 y 3)) t)))
	12.6b	(fma.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (-.f64 (.f64 z (log1p.f64 y)) t))

Compiler

Compiled 4552 to 1634 computations (64.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x (log.f64 y)) (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (*.f64 z (pow.f64 y 3)) t)))
✓	0.1b	(fma.f64 1/3 (*.f64 z (pow.f64 y 3)) t)
✓	0.3b	(*.f64 x (log.f64 y))
✓	4.5b	(*.f64 z (pow.f64 y 3))

series349.0ms (4.8%)

Counts

4 → 132

Calls

33 calls:

60.0ms	(*.f64 x (log.f64 y))	x	0
52.0ms	(*.f64 x (log.f64 y))	x	-inf
48.0ms	(*.f64 x (log.f64 y))	x	inf
16.0ms	(-.f64 (.f64 x (log.f64 y)) (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (*.f64 z (pow.f64 y 3)) t)))	z	0
16.0ms	(-.f64 (.f64 x (log.f64 y)) (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (*.f64 z (pow.f64 y 3)) t)))	t	0

rewrite91.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

956×	`prod-diff_binary64`
172×	`add-sqr-sqrt_binary64`
164×	`log1p-expm1-u_binary64`
164×	`expm1-log1p-u_binary64`
163×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	54
1	354	54
2	4244	54

Stop Event

1×	node limit

Counts

4 → 142

simplify56.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

373×	`fma-def_binary64`
242×	`distribute-rgt-in_binary64`
235×	`sub-neg_binary64`
198×	`associate--l+_binary64`
194×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	2068
1	206	1795
2	681	1725
3	2780	1716

Stop Event

1×	node limit

Counts

274 → 175

prune216.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	170	5	175
Fresh	4	1	5
Picked	1	0	1
Done	0	1	1
Total	175	7	182

Error

0.0b

Counts

182 → 7

Alt Table

Status	Error	Program
	15.9b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 x (log.f64 y)) 2)) (cbrt.f64 (.f64 x (log.f64 y))) (neg.f64 (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (.f64 z (pow.f64 y 3)) t))))
	29.9b	(+.f64 (fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 y)) (neg.f64 (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (.f64 z (pow.f64 y 3)) t)))) (fma.f64 -1 (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (.f64 z (pow.f64 y 3)) t)) (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (*.f64 z (pow.f64 y 3)) t))))
✓	0.1b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (*.f64 (log.f64 y) x)) t)
	34.6b	(fma.f64 (sqrt.f64 (.f64 x (log.f64 y))) (sqrt.f64 (.f64 x (log.f64 y))) (neg.f64 (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (.f64 z (pow.f64 y 3)) t))))
	0.9b	(+.f64 (fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (log.f64 y)) (neg.f64 (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (.f64 z (pow.f64 y 3)) t)))) (fma.f64 -1 (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (.f64 z (pow.f64 y 3)) t)) (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (*.f64 z (pow.f64 y 3)) t))))
▶	0.6b	(+.f64 (fma.f64 (cbrt.f64 (pow.f64 (log.f64 y) 2)) (.f64 (cbrt.f64 (log.f64 y)) x) (neg.f64 (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (.f64 z (pow.f64 y 3)) t)))) (fma.f64 -1 (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (.f64 z (pow.f64 y 3)) t)) (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (*.f64 z (pow.f64 y 3)) t))))
	13.1b	(pow.f64 (cbrt.f64 (-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 y))) t)) 3)

Compiler

Compiled 7778 to 4033 computations (48.1% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (log.f64 y) 2)
✓	0.5b	(cbrt.f64 (log.f64 y))
✓	0.5b	(cbrt.f64 (pow.f64 (log.f64 y) 2))
	4.5b	(*.f64 z (pow.f64 y 3))

series257.0ms (3.5%)

Counts

3 → 32

Calls

9 calls:

85.0ms	(cbrt.f64 (log.f64 y))	y	inf
37.0ms	(cbrt.f64 (pow.f64 (log.f64 y) 2))	y	-inf
32.0ms	(cbrt.f64 (pow.f64 (log.f64 y) 2))	y	inf
32.0ms	(cbrt.f64 (pow.f64 (log.f64 y) 2))	y	0
25.0ms	(cbrt.f64 (log.f64 y))	y	-inf

rewrite43.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

459×	`log1p-expm1-u_binary64`
459×	`expm1-log1p-u_binary64`
341×	`unpow-prod-down_binary64`
239×	`log-prod_binary64`
141×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	134	19
2	1376	19

Stop Event

1×	node limit

Counts

3 → 135

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

428×	`fma-def_binary64`
384×	`unswap-sqr_binary64`
268×	`unsub-neg_binary64`
267×	`fma-neg_binary64`
222×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	248
1	63	232
2	107	232
3	293	232
4	993	232
5	2984	232

Stop Event

1×	node limit

Counts

167 → 145

prune452.0ms (6.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	191	2	193
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	193	7	200

Error

0.0b

Counts

200 → 7

Alt Table

Status	Error	Program
	13.1b	(pow.f64 (cbrt.f64 (-.f64 (fma.f64 x (log.f64 y) (*.f64 z (log1p.f64 y))) t)) 3)
	0.6b	(+.f64 (fma.f64 (cbrt.f64 (pow.f64 (log.f64 y) 2)) (.f64 (.f64 (cbrt.f64 -1) (pow.f64 (log.f64 (/.f64 1 y)) 1/3)) x) (neg.f64 (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (.f64 z (pow.f64 y 3)) t)))) (fma.f64 -1 (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (.f64 z (pow.f64 y 3)) t)) (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (.f64 z (pow.f64 y 3)) t))))
✓	0.1b	(-.f64 (fma.f64 (log1p.f64 (neg.f64 y)) z (*.f64 (log.f64 y) x)) t)
	34.6b	(fma.f64 (sqrt.f64 (.f64 x (log.f64 y))) (sqrt.f64 (.f64 x (log.f64 y))) (neg.f64 (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (.f64 z (pow.f64 y 3)) t))))
	29.9b	(+.f64 (fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 y)) (neg.f64 (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (.f64 z (pow.f64 y 3)) t)))) (fma.f64 -1 (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (.f64 z (pow.f64 y 3)) t)) (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (*.f64 z (pow.f64 y 3)) t))))
	0.7b	(+.f64 (fma.f64 (cbrt.f64 (-.f64 (exp.f64 (log1p.f64 (pow.f64 (log.f64 y) 2))) 1)) (.f64 (cbrt.f64 (log.f64 y)) x) (neg.f64 (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (.f64 z (pow.f64 y 3)) t)))) (fma.f64 -1 (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (.f64 z (pow.f64 y 3)) t)) (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (*.f64 z (pow.f64 y 3)) t))))
✓	0.6b	(+.f64 (fma.f64 (cbrt.f64 (pow.f64 (log.f64 y) 2)) (.f64 (cbrt.f64 (log.f64 y)) x) (neg.f64 (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (.f64 z (pow.f64 y 3)) t)))) (fma.f64 -1 (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (.f64 z (pow.f64 y 3)) t)) (fma.f64 z (fma.f64 1/2 (.f64 y y) y) (fma.f64 1/3 (*.f64 z (pow.f64 y 3)) t))))

Compiler

Compiled 13513 to 7081 computations (47.6% saved)

regimes851.0ms (11.7%)

Accuracy

Total 0.1b remaining (73.8%)

Threshold costs 0.1b (73.8%)

Counts

105 → 1

Compiler

Compiled 23594 to 14181 computations (39.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	18	17
2	23	17
3	26	17
4	27	17

Stop Event

1×

saturated

end201.0ms (2.8%)

Stop Event

1×

fuel

Compiler

Compiled 369 to 228 computations (38.2% saved)

Details

analyze434.0ms (6%)

sample2.3s (31%)

preprocess70.0ms (1%)

simplify39.0ms (0.5%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series630.0ms (8.7%)

rewrite66.0ms (0.9%)

simplify56.0ms (0.8%)

prune223.0ms (3.1%)

localize9.0ms (0.1%)

series612.0ms (8.4%)

rewrite62.0ms (0.9%)

simplify51.0ms (0.7%)

prune153.0ms (2.1%)

localize15.0ms (0.2%)

series349.0ms (4.8%)

rewrite91.0ms (1.3%)

simplify56.0ms (0.8%)

prune216.0ms (3%)

localize26.0ms (0.4%)

series257.0ms (3.5%)

rewrite43.0ms (0.6%)

simplify34.0ms (0.5%)

prune452.0ms (6.2%)

regimes851.0ms (11.7%)

simplify2.0ms (0%)

end201.0ms (2.8%)

Profiling