Details

analyze44.0ms (3.5%)

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)

sample708.0ms (56.5%)

Symmetry

(sort x y)

Results

662.0ms	8256×	body	128	valid
17.0ms	269×	body	128	invalid

Compiler

Compiled 20 to 14 computations (30% saved)

simplify26.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6

Stop Event

1×

saturated

Counts

1 → 1

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 (0.2%)

Local error

Found 1 expressions with local error:

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

series13.0ms (1%)

Counts

1 → 8

Calls

1 calls:

13.0ms

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

rewrite32.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

553×	`log1p-expm1-u_binary64`
553×	`expm1-log1p-u_binary64`
455×	`prod-diff_binary64`
160×	`fma-def_binary64`
99×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	109	6
2	1479	6

Stop Event

1×	node limit

Counts

1 → 27

Calls

1 calls:

31.0ms

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

simplify28.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-neg_binary64`
844×	`fma-def_binary64`
541×	`associate-l_binary64`
416×	`associate-r_binary64`
224×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	51	212
1	137	212
2	378	204
3	1199	198
4	4325	197

Stop Event

1×	node limit

Counts

35 → 41

prune20.0ms (1.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	2	42

Error

Counts

42 → 2

Alt Table

Status	Error	Program
▶	30.8b	(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x y) 2))) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
✓	0.0b	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 529 to 315 computations (40.5% saved)

localize8.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (+.f64 x y)))
✓	0.4b	(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x y) 2))) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
✓	0.6b	(cbrt.f64 (+.f64 x y))
✓	29.5b	(cbrt.f64 (pow.f64 (+.f64 x y) 2))

series63.0ms (5%)

Counts

4 → 80

Calls

4 calls:

18.0ms	(cbrt.f64 (pow.f64 (+.f64 x y) 2))
15.0ms	(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x y) 2))) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
15.0ms	(sqrt.f64 (cbrt.f64 (+.f64 x y)))
14.0ms	(cbrt.f64 (+.f64 x y))

rewrite62.0ms (5%)

Algorithm

1×	batch-egg-rewrite

Rules

839×	`log1p-expm1-u_binary64`
839×	`expm1-log1p-u_binary64`
455×	`prod-diff_binary64`
103×	`egg-rr`
98×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	42
1	228	28
2	2576	28

Stop Event

1×	node limit

Counts

4 → 103

Calls

4 calls:

60.0ms	(sqrt.f64 (cbrt.f64 (+.f64 x y)))
60.0ms	(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x y) 2))) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
60.0ms	(cbrt.f64 (+.f64 x y))
60.0ms	(cbrt.f64 (pow.f64 (+.f64 x y) 2))

simplify63.0ms (5%)

Algorithm

1×	egg-herbie

Rules

698×	`times-frac_binary64`
340×	`cancel-sign-sub-inv_binary64`
211×	`associate-r_binary64`
192×	`unswap-sqr_binary64`
175×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	2866
1	733	2828
2	2494	2576

Stop Event

1×	node limit

Counts

183 → 195

prune105.0ms (8.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	195	2	197

Error

Counts

197 → 2

Alt Table

Status	Error	Program
✓	30.8b	(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x y) 2))) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
✓	0.0b	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 4620 to 2948 computations (36.2% saved)

regimes29.0ms (2.3%)

Accuracy

Total 0.0b remaining (14%)

Threshold costs 0.0b (14%)

Counts

4 → 1

Compiler

Compiled 202 to 138 computations (31.7% 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

Stop Event

1×

saturated

end44.0ms (3.5%)

Remove: (sort x y)
Compiler: Compiled 45 to 30 computations (33.3% saved)

Details

analyze44.0ms (3.5%)

sample708.0ms (56.5%)

simplify26.0ms (2.1%)

prune1.0ms (0.1%)

localize3.0ms (0.2%)

series13.0ms (1%)

rewrite32.0ms (2.6%)

simplify28.0ms (2.3%)

prune20.0ms (1.6%)

localize8.0ms (0.7%)

series63.0ms (5%)

rewrite62.0ms (5%)

simplify63.0ms (5%)

prune105.0ms (8.4%)

regimes29.0ms (2.3%)

simplify2.0ms (0.1%)

end44.0ms (3.5%)

Profiling