Details

analyze1.4s (22.9%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
2.3%	91.3%	6.4%	9
3.5%	87%	9.5%	10
4.1%	86.4%	9.5%	11
18.4%	66.6%	15%	12
20.5%	61.8%	17.7%	13
21.9%	60.4%	17.7%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.8s (46.1%)

Results

1.1s	6342×	body	128	valid
707.0ms	993×	body	1024	valid
287.0ms	596×	body	512	valid
220.0ms	1560×	body	128	invalid
138.0ms	217×	body	1024	invalid
134.0ms	319×	body	256	valid
110.0ms	232×	body	512	invalid
49.0ms	167×	body	256	invalid
8.0ms	6×	body	2048	valid

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess48.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

792×	`times-frac_binary64`
358×	`fma-def_binary64`
193×	`associate-l_binary64`
167×	`associate-r_binary64`
155×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	80
1	62	64
2	94	64
3	194	64
4	482	64
5	1189	64
6	3217	64
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify32.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

522×	`unswap-sqr_binary64`
363×	`fma-def_binary64`
253×	`associate-l_binary64`
215×	`associate-r_binary64`
204×	`div-sub_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	19	16
2	28	16
3	57	16
4	138	16
5	332	16
6	893	16
7	3314	16

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

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

6.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.5b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))

Compiler

Compiled 55 to 31 computations (43.6% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
✓	0.0b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
✓	0.0b	(/.f64 y (+.f64 y z))
✓	7.0b	(pow.f64 (/.f64 y (+.f64 y z)) y)

series169.0ms (2.8%)

Counts

4 → 108

Calls

27 calls:

20.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))	x	0
19.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))	x	inf
14.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))	x	-inf
9.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)	z	-inf
9.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)	y	inf

rewrite70.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

374×	`fma-def_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
198×	`fma-neg_binary64`
187×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	46
1	214	46
2	3333	46

Stop Event

1×	node limit

Counts

4 → 142

simplify111.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

347×	`fma-def_binary64`
340×	`associate-+r+_binary64`
334×	`+-commutative_binary64`
277×	`associate-+l+_binary64`
244×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	362	5179
1	1193	5024
2	4951	5024

Stop Event

1×	node limit

Counts

250 → 265

prune183.0ms (3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	261	4	265
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	262	4	266

Error

0.0b

Counts

266 → 4

Alt Table

Status	Error	Program
	30.4b	(fma.f64 (sqrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (sqrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) x)
	7.7b	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) 3)
	12.6b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
▶	2.3b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 8443 to 3850 computations (54.4% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 1 y))

series4.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

1.0ms	(+.f64 x (/.f64 1 y))	x	0
1.0ms	(+.f64 x (/.f64 1 y))	x	-inf
1.0ms	(+.f64 x (/.f64 1 y))	x	inf
0.0ms	(+.f64 x (/.f64 1 y))	y	0
0.0ms	(+.f64 x (/.f64 1 y))	y	inf

rewrite39.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

620×	`log1p-expm1-u_binary64`
620×	`expm1-log1p-u_binary64`
483×	`prod-diff_binary64`
112×	`log1p-udef_binary64`
64×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	128	7
2	1692	7

Stop Event

1×	node limit

Counts

1 → 35

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	138
1	9	138

Stop Event

1×

saturated

Counts

59 → 38

prune25.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	38	4	42

Error

0.0b

Counts

42 → 4

Alt Table

Status	Error	Program
▶	3.5b	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) 3)
	30.4b	(fma.f64 (sqrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (sqrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) x)
	12.6b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	2.3b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 507 to 319 computations (37.1% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 x (/.f64 1 y))
✓	0.6b	(cbrt.f64 (+.f64 x (/.f64 1 y)))
✓	0.7b	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) 3)

series353.0ms (5.9%)

Counts

2 → 24

Calls

12 calls:

117.0ms	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) 3)	y	-inf
117.0ms	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) 3)	y	inf
92.0ms	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) 3)	x	0
5.0ms	(cbrt.f64 (+.f64 x (/.f64 1 y)))	y	-inf
4.0ms	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) 3)	x	-inf

rewrite50.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

777×	`log1p-expm1-u_binary64`
777×	`expm1-log1p-u_binary64`
483×	`prod-diff_binary64`
82×	`add-sqr-sqrt_binary64`
80×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	188	16
2	2168	16

Stop Event

1×	node limit

Counts

2 → 64

simplify34.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

665×	`times-frac_binary64`
371×	`associate-/r*_binary64`
324×	`cancel-sign-sub-inv_binary64`
310×	`associate-/l*_binary64`
247×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	798
1	191	744
2	558	720
3	2203	717

Stop Event

1×	node limit

Counts

88 → 86

prune71.0ms (1.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	123	5	128

Error

Counts

128 → 5

Alt Table

Status	Error	Program
✓	3.5b	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) 3)
	30.4b	(fma.f64 (sqrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (sqrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) x)
▶	4.4b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 1 y)))) 2) 3) (cbrt.f64 (+.f64 x (/.f64 1 y))))
	12.6b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	2.3b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 2006 to 1446 computations (27.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 (+.f64 x (/.f64 1 y)))
✓	0.6b	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 1 y)))) 2)
✓	0.6b	(cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))))
✓	0.8b	(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 1 y)))) 2) 3)

series85.0ms (1.4%)

Counts

3 → 72

Calls

18 calls:

9.0ms	(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 1 y)))) 2) 3)	x	inf
8.0ms	(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 1 y)))) 2) 3)	x	-inf
7.0ms	(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 1 y)))) 2) 3)	y	0
6.0ms	(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 1 y)))) 2) 3)	y	-inf
6.0ms	(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 1 y)))) 2) 3)	y	inf

rewrite53.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

483×	`prod-diff_binary64`
195×	`fma-def_binary64`
182×	`expm1-udef_binary64`
182×	`log1p-udef_binary64`
169×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	39
1	252	37
2	2840	37

Stop Event

1×	node limit

Counts

3 → 68

simplify84.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

953×	`times-frac_binary64`
707×	`fma-def_binary64`
292×	`cancel-sign-sub-inv_binary64`
137×	`associate-r_binary64`
130×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	3848
1	599	3604
2	2053	3406

Stop Event

1×	node limit

Counts

140 → 140

prune177.0ms (2.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	220	5	225

Error

Counts

225 → 5

Alt Table

Status	Error	Program
✓	3.5b	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) 3)
	30.4b	(fma.f64 (sqrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (sqrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) x)
✓	4.4b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 1 y)))) 2) 3) (cbrt.f64 (+.f64 x (/.f64 1 y))))
	12.6b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	2.3b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 6885 to 5355 computations (22.2% saved)

regimes157.0ms (2.6%)

Accuracy

Total 0.8b remaining (89%)

Threshold costs 0.8b (89%)

Counts

20 → 2

Compiler

Compiled 1669 to 1043 computations (37.5% saved)

bsearch5.0ms (0.1%)

Algorithm

1×	binary-search

Calls

1 calls:

4.0ms

Steps

Iters	Point		Range
7.540237662362719e-24	∈ [	5.434948514041475e-39	,	1.0650454868106292e-8	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	22	24
2	24	24
3	25	24

Stop Event

1×

saturated

end74.0ms (1.2%)

Stop Event

1×

fuel

Compiler

Compiled 113 to 74 computations (34.5% saved)

Details

analyze1.4s (22.9%)

sample2.8s (46.1%)

preprocess48.0ms (0.8%)

simplify32.0ms (0.5%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series169.0ms (2.8%)

rewrite70.0ms (1.2%)

simplify111.0ms (1.8%)

prune183.0ms (3%)

localize3.0ms (0.1%)

series4.0ms (0.1%)

rewrite39.0ms (0.7%)

simplify11.0ms (0.2%)

prune25.0ms (0.4%)

localize5.0ms (0.1%)

series353.0ms (5.9%)

rewrite50.0ms (0.8%)

simplify34.0ms (0.6%)

prune71.0ms (1.2%)

localize11.0ms (0.2%)

series85.0ms (1.4%)

rewrite53.0ms (0.9%)

simplify84.0ms (1.4%)

prune177.0ms (2.9%)

regimes157.0ms (2.6%)

bsearch5.0ms (0.1%)

simplify4.0ms (0.1%)

end74.0ms (1.2%)

Profiling