Details

analyze129.0ms (4.8%)

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)

sample40.0ms (1.5%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
1.0ms	14×	body	128	nan

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify12.0ms (0.5%)

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))

series21.0ms (0.8%)

Counts

1 → 8

Calls

1 calls:

20.0ms

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

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`sqrt-prod_binary64`
2×	`sqrt-div_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 19

Calls

1 calls:

5.0ms

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

simplify121.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

917×	`fma-neg_binary64`
656×	`associate-l_binary64`
406×	`distribute-rgt-neg-in_binary64`
392×	`distribute-lft-neg-in_binary64`
370×	`hypot-def_binary64`

Counts

27 → 41

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	80	388
1	187	383
2	446	375
3	1235	372
4	2724	370
5	4709	370
6	4967	370

prune45.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	3	42

Error

Counts

42 → 3

Alt Table

Status	Error	Program
▶	0.4b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x y))) (sqrt.f64 (sqrt.f64 (+.f64 x y))))
	6.7b	(+.f64 (sqrt.f64 y) (.f64 x (fma.f64 1/2 (sqrt.f64 (/.f64 1 y)) (.f64 x (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8)))))
✓	0.0b	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 606 to 342 computations (43.6% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 x y))
✓	0.1b	(sqrt.f64 (sqrt.f64 (+.f64 x y)))
✓	0.5b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x y))) (sqrt.f64 (sqrt.f64 (+.f64 x y))))

series76.0ms (2.8%)

Counts

2 → 32

Calls

2 calls:

38.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x y))) (sqrt.f64 (sqrt.f64 (+.f64 x y))))
38.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x y)))

rewrite56.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`sqrt-prod_binary64`
64×	`add-sqr-sqrt_binary64`
36×	`sqrt-pow1_binary64`
32×	`*-un-lft-identity_binary64`
28×	`sqrt-div_binary64`

Counts

2 → 122

Calls

2 calls:

26.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x y))) (sqrt.f64 (sqrt.f64 (+.f64 x y))))
6.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x y)))

simplify181.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

521×	`fma-def_binary64`
414×	`fma-neg_binary64`
358×	`*-commutative_binary64`
348×	`times-frac_binary64`
243×	`associate-/l*_binary64`

Counts

154 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	220	2687
1	515	2544
2	1538	2377
3	4306	2272
4	4902	2272
5	4962	2272

prune184.0ms (6.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	317	0	317
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	317	3	320

Error

Counts

320 → 3

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x y))) (sqrt.f64 (sqrt.f64 (+.f64 x y))))
▶	6.7b	(+.f64 (sqrt.f64 y) (.f64 x (fma.f64 1/2 (sqrt.f64 (/.f64 1 y)) (.f64 x (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8)))))
✓	0.0b	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 6715 to 2842 computations (57.7% saved)

localize37.0ms (1.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 x (fma.f64 1/2 (sqrt.f64 (/.f64 1 y)) (.f64 x (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8))))
✓	0.3b	(/.f64 1 (pow.f64 y 3))
✓	5.3b	(.f64 x (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8))
✓	21.7b	(sqrt.f64 (/.f64 1 (pow.f64 y 3)))

series213.0ms (7.9%)

Counts

4 → 24

Calls

4 calls:

101.0ms	(.f64 x (fma.f64 1/2 (sqrt.f64 (/.f64 1 y)) (.f64 x (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8))))
96.0ms	(.f64 x (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8))
11.0ms	(sqrt.f64 (/.f64 1 (pow.f64 y 3)))
5.0ms	(/.f64 1 (pow.f64 y 3))

rewrite69.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`times-frac_binary64`
67×	`add-sqr-sqrt_binary64`
58×	`*-un-lft-identity_binary64`
54×	`add-cube-cbrt_binary64`
40×	`sqrt-prod_binary64`

Counts

4 → 181

Calls

4 calls:

22.0ms	(.f64 x (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8))
10.0ms	(sqrt.f64 (/.f64 1 (pow.f64 y 3)))
8.0ms	(/.f64 1 (pow.f64 y 3))
5.0ms	(.f64 x (fma.f64 1/2 (sqrt.f64 (/.f64 1 y)) (.f64 x (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8))))

simplify271.0ms (10%)

Algorithm

1×	egg-herbie

Rules

746×	`times-frac_binary64`
551×	`unswap-sqr_binary64`
391×	`fma-def_binary64`
284×	`*-commutative_binary64`
249×	`associate-/r*_binary64`

Counts

205 → 201

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	164	3203
1	289	2957
2	892	2955
3	3418	2851
4	4802	2851
5	4992	2851
6	4900	2851

prune346.0ms (12.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	201	3	204

Error

Counts

204 → 3

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x y))) (sqrt.f64 (sqrt.f64 (+.f64 x y))))
✓	6.7b	(+.f64 (sqrt.f64 y) (.f64 x (fma.f64 1/2 (sqrt.f64 (/.f64 1 y)) (.f64 x (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8)))))
✓	0.0b	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 5700 to 4187 computations (26.5% saved)

regimes124.0ms (4.6%)

Accuracy

Total 0.0b remaining (38.6%)

Threshold costs 0.0b (38.6%)

Counts

20 → 1

Compiler

Compiled 1230 to 874 computations (28.9% saved)

simplify4.0ms (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

end12.0ms (0.4%)

Remove: (sort x y)
Compiler: Compiled 18 to 12 computations (33.3% saved)

sample748.0ms (27.6%)

Algorithm

1×

intervals

Results

342.0ms	8000×	body	128	valid
8.0ms	234×	body	128	nan

Compiler

Compiled 57 to 39 computations (31.6% saved)

Details

analyze129.0ms (4.8%)

sample40.0ms (1.5%)

simplify12.0ms (0.5%)

prune1.0ms (0.1%)

localize3.0ms (0.1%)

series21.0ms (0.8%)

rewrite7.0ms (0.2%)

simplify121.0ms (4.5%)

prune45.0ms (1.7%)

localize9.0ms (0.3%)

series76.0ms (2.8%)

rewrite56.0ms (2.1%)

simplify181.0ms (6.7%)

prune184.0ms (6.8%)

localize37.0ms (1.4%)

series213.0ms (7.9%)

rewrite69.0ms (2.5%)

simplify271.0ms (10%)

prune346.0ms (12.8%)

regimes124.0ms (4.6%)

simplify4.0ms (0.1%)

end12.0ms (0.4%)

sample748.0ms (27.6%)

Profiling