Details

analyze73.0ms (3.7%)

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
25%	74.9%	0.1%	3
25%	62.4%	12.6%	4
37.5%	43.7%	18.8%	5
37.5%	34.3%	28.2%	6
43.7%	23.4%	32.9%	7
43.7%	18%	38.3%	8
46.8%	12.1%	41.1%	9
46.8%	9.2%	44%	10
48.4%	6.1%	45.5%	11
48.4%	4.6%	47%	12
49.2%	3.1%	47.7%	13
49.2%	2.3%	48.5%	14

Compiler

Compiled 7 to 5 computations (28.6% saved)

sample807.0ms (41.2%)

Symmetry

(sort x y)

Results

748.0ms	8256×	body	128	valid
20.0ms	255×	body	128	invalid

Compiler

Compiled 20 to 14 computations (30% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6
2	6	6

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series18.0ms (0.9%)

Counts

1 → 8

Calls

1 calls:

18.0ms

(sqrt.f64 (+.f64 x y))

rewrite128.0ms (6.5%)

Algorithm

2×	batch-egg-rewrite

Rules

553×	`log1p-expm1-u_binary64`
553×	`expm1-log1p-u_binary64`
464×	`prod-diff_binary64`
352×	`fma-udef_binary64`
223×	`fma-def_binary64`

Counts

1 → 26

Calls

1 calls:

127.0ms

(sqrt.f64 (+.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	108	6
2	1381	6
3	4863	6
4	4852	6
5	4970	6
0	0	0
1	0	0

simplify55.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

873×	`fma-neg_binary64`
845×	`fma-def_binary64`
562×	`associate-l_binary64`
465×	`distribute-rgt-neg-in_binary64`
431×	`distribute-lft-neg-in_binary64`

Counts

34 → 40

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	51	212
1	135	212
2	345	204
3	984	198
4	2981	196
5	4841	196
6	5010	196

prune24.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	4	41

Error

Counts

41 → 4

Alt Table

Status	Error	Program
▶	0.5b	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
✓	0.0b	(sqrt.f64 (+.f64 x y))
	19.8b	(cbrt.f64 (pow.f64 (+.f64 x y) 3/2))
	0.8b	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (sqrt.f64 (+.f64 x y))))

Compiler

Compiled 545 to 326 computations (40.2% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 x y) 1/4)
✓	0.5b	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)

series47.0ms (2.4%)

Counts

2 → 48

Calls

2 calls:

25.0ms	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
21.0ms	(pow.f64 (+.f64 x y) 1/4)

rewrite51.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

751×	`log1p-expm1-u_binary64`
751×	`expm1-log1p-u_binary64`
455×	`prod-diff_binary64`
80×	`add-sqr-sqrt_binary64`
79×	`add-cbrt-cube_binary64`

Counts

2 → 47

Calls

2 calls:

50.0ms	(pow.f64 (+.f64 x y) 1/4)
50.0ms	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	181	13
2	1906	13
3	5305	13
0	0	0
1	0	0

simplify54.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

834×	`times-frac_binary64`
561×	`fma-def_binary64`
523×	`associate-/l*_binary64`
387×	`associate-/r*_binary64`
197×	`cancel-sign-sub-inv_binary64`

Counts

95 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	162	1962
1	480	1934
2	1572	1608
3	5144	1608

prune76.0ms (3.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	107	4	111

Error

Counts

111 → 4

Alt Table

Status	Error	Program
✓	0.5b	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
✓	0.0b	(sqrt.f64 (+.f64 x y))
	19.8b	(cbrt.f64 (pow.f64 (+.f64 x y) 3/2))
▶	0.8b	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (sqrt.f64 (+.f64 x y))))

Compiler

Compiled 2335 to 1639 computations (29.8% saved)

localize6.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 x y))
✓	0.3b	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (sqrt.f64 (+.f64 x y))))
✓	0.5b	(cbrt.f64 (+.f64 x y))
✓	0.6b	(cbrt.f64 (sqrt.f64 (+.f64 x y)))

series56.0ms (2.8%)

Counts

3 → 56

Calls

3 calls:

22.0ms	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (sqrt.f64 (+.f64 x y))))
18.0ms	(cbrt.f64 (sqrt.f64 (+.f64 x y)))
15.0ms	(cbrt.f64 (+.f64 x y))

rewrite50.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

666×	`log1p-expm1-u_binary64`
666×	`expm1-log1p-u_binary64`
455×	`prod-diff_binary64`
120×	`log1p-udef_binary64`
72×	`egg-rr`

Counts

3 → 72

Calls

3 calls:

48.0ms	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (sqrt.f64 (+.f64 x y))))
48.0ms	(cbrt.f64 (+.f64 x y))
48.0ms	(cbrt.f64 (sqrt.f64 (+.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	145	19
2	1691	19
3	5108	19
0	0	0
1	0	0

simplify63.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-def_binary64`
698×	`times-frac_binary64`
441×	`associate-/l*_binary64`
267×	`cancel-sign-sub-inv_binary64`
164×	`associate-r_binary64`

Counts

128 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	2158
1	604	2120
2	1942	1828
3	5179	1828

prune122.0ms (6.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	188	4	192

Error

Counts

192 → 4

Alt Table

Status	Error	Program
✓	0.5b	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
✓	0.0b	(sqrt.f64 (+.f64 x y))
▶	19.8b	(cbrt.f64 (pow.f64 (+.f64 x y) 3/2))
✓	0.8b	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (sqrt.f64 (+.f64 x y))))

Compiler

Compiled 4010 to 2226 computations (44.5% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 x y) 3/2)
✓	19.0b	(cbrt.f64 (pow.f64 (+.f64 x y) 3/2))

series37.0ms (1.9%)

Counts

2 → 32

Calls

2 calls:

21.0ms	(cbrt.f64 (pow.f64 (+.f64 x y) 3/2))
16.0ms	(pow.f64 (+.f64 x y) 3/2)

rewrite42.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

698×	`log1p-expm1-u_binary64`
698×	`expm1-log1p-u_binary64`
455×	`prod-diff_binary64`
73×	`add-sqr-sqrt_binary64`
71×	`add-cube-cbrt_binary64`

Counts

2 → 47

Calls

2 calls:

41.0ms	(pow.f64 (+.f64 x y) 3/2)
41.0ms	(cbrt.f64 (pow.f64 (+.f64 x y) 3/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	153	13
2	1749	13
3	4998	13
0	0	0
1	0	0

simplify72.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-neg_binary64`
382×	`associate-r_binary64`
371×	`times-frac_binary64`
348×	`fma-def_binary64`
325×	`associate-l_binary64`

Counts

79 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1106
1	314	1092
2	979	926
3	4246	845
4	4967	845
5	4967	845

prune51.0ms (2.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	93	4	97

Error

Counts

97 → 4

Alt Table

Status	Error	Program
✓	0.5b	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
✓	0.0b	(sqrt.f64 (+.f64 x y))
✓	19.8b	(cbrt.f64 (pow.f64 (+.f64 x y) 3/2))
✓	0.8b	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (sqrt.f64 (+.f64 x y))))

Compiler

Compiled 1535 to 1008 computations (34.3% saved)

regimes41.0ms (2.1%)

Accuracy

Total 0.0b remaining (66.7%)

Threshold costs 0.0b (66.7%)

Counts

8 → 1

Compiler

Compiled 306 to 214 computations (30.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6
2	6	6

end61.0ms (3.1%)

Remove: (sort x y)
Compiler: Compiled 59 to 40 computations (32.2% saved)

Details

analyze73.0ms (3.7%)

sample807.0ms (41.2%)

simplify6.0ms (0.3%)

prune1.0ms (0.1%)

localize3.0ms (0.1%)

series18.0ms (0.9%)

rewrite128.0ms (6.5%)

simplify55.0ms (2.8%)

prune24.0ms (1.2%)

localize6.0ms (0.3%)

series47.0ms (2.4%)

rewrite51.0ms (2.6%)

simplify54.0ms (2.7%)

prune76.0ms (3.9%)

localize6.0ms (0.3%)

series56.0ms (2.8%)

rewrite50.0ms (2.5%)

simplify63.0ms (3.2%)

prune122.0ms (6.2%)

localize6.0ms (0.3%)

series37.0ms (1.9%)

rewrite42.0ms (2.2%)

simplify72.0ms (3.7%)

prune51.0ms (2.6%)

regimes41.0ms (2.1%)

simplify2.0ms (0.1%)

end61.0ms (3.1%)

Profiling