Details

analyze83.0ms (2.9%)

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
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)

sample33.0ms (1.2%)

Algorithm

1×

intervals

Symmetry

(sort x y)

Results

7.0ms	256×	body	128	valid
0.0ms	19×	body	128	nan

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify6.0ms (0.2%)

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))

series20.0ms (0.7%)

Counts

1 → 8

Calls

1 calls:

20.0ms

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

rewrite3.0ms (0.1%)

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:

3.0ms

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

simplify66.0ms (2.3%)

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

prune23.0ms (0.8%)

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

0.0b

Counts

42 → 3

Alt Table

Status	Error	Program
▶	0.6b	(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))
✓	0.0b	(sqrt.f64 (+.f64 x y))
	0.8b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 y x))) (sqrt.f64 (cbrt.f64 (+.f64 y x))))

Compiler

Compiled 584 to 326 computations (44.2% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))
✓	0.1b	(sqrt.f64 (/.f64 1 y))
✓	0.2b	(*.f64 (sqrt.f64 (/.f64 1 y)) x)

series39.0ms (1.4%)

Counts

3 → 12

Calls

3 calls:

19.0ms	(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))
14.0ms	(*.f64 (sqrt.f64 (/.f64 1 y)) x)
5.0ms	(sqrt.f64 (/.f64 1 y))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
29×	`sqrt-prod_binary64`
22×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`

Counts

3 → 77

Calls

3 calls:

6.0ms	(*.f64 (sqrt.f64 (/.f64 1 y)) x)
5.0ms	(sqrt.f64 (/.f64 1 y))
0.0ms	(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))

simplify94.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

883×	`fma-def_binary64`
585×	`times-frac_binary64`
466×	`distribute-rgt-in_binary64`
458×	`distribute-lft-in_binary64`
297×	`associate-l_binary64`

Counts

89 → 93

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	1114
1	120	1062
2	280	1062
3	442	1062
4	1037	1062
5	3164	1062
6	4743	1062
7	4945	1062

prune63.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	93	3	96

Error

0.0b

Counts

96 → 3

Alt Table

Status	Error	Program
✓	0.6b	(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))
✓	0.0b	(sqrt.f64 (+.f64 x y))
▶	0.8b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 y x))) (sqrt.f64 (cbrt.f64 (+.f64 y x))))

Compiler

Compiled 1571 to 1021 computations (35% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (+.f64 y x)))
✓	0.3b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 y x))) (sqrt.f64 (cbrt.f64 (+.f64 y x))))
✓	0.5b	(cbrt.f64 (+.f64 y x))

series109.0ms (3.8%)

Counts

3 → 72

Calls

3 calls:

65.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 y x))) (sqrt.f64 (cbrt.f64 (+.f64 y x))))
22.0ms	(sqrt.f64 (cbrt.f64 (+.f64 y x)))
22.0ms	(cbrt.f64 (+.f64 y x))

rewrite28.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64`
30×	`cbrt-prod_binary64`
24×	`sqrt-prod_binary64`
20×	`*-un-lft-identity_binary64`
16×	`cbrt-div_binary64`

Counts

3 → 100

Calls

3 calls:

15.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 y x))) (sqrt.f64 (cbrt.f64 (+.f64 y x))))
3.0ms	(sqrt.f64 (cbrt.f64 (+.f64 y x)))
2.0ms	(cbrt.f64 (+.f64 y x))

simplify182.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

351×	`fma-neg_binary64`
340×	`associate-r_binary64`
339×	`cancel-sign-sub-inv_binary64`
288×	`associate-/r/_binary64`
261×	`associate-l_binary64`

Counts

172 → 238

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	336	5529
1	905	5131
2	2926	4485
3	4806	4291
4	4997	4291
5	4939	4291

prune206.0ms (7.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	294	1	295
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	294	4	298

Error

Counts

298 → 4

Alt Table

Status	Error	Program
▶	1.0b	(.f64 (sqrt.f64 (cbrt.f64 (+.f64 y x))) (.f64 (sqrt.f64 (cbrt.f64 (+.f64 y x))) (sqrt.f64 (cbrt.f64 (+.f64 y x)))))
✓	0.6b	(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))
✓	0.0b	(sqrt.f64 (+.f64 x y))
✓	0.8b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 y x))) (sqrt.f64 (cbrt.f64 (+.f64 y x))))

Compiler

Compiled 7576 to 3480 computations (54.1% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (cbrt.f64 (+.f64 y x)))
✓	0.3b	(.f64 (sqrt.f64 (cbrt.f64 (+.f64 y x))) (.f64 (sqrt.f64 (cbrt.f64 (+.f64 y x))) (sqrt.f64 (cbrt.f64 (+.f64 y x)))))
	0.5b	(cbrt.f64 (+.f64 y x))
✓	0.5b	(*.f64 (sqrt.f64 (cbrt.f64 (+.f64 y x))) (sqrt.f64 (cbrt.f64 (+.f64 y x))))

series44.0ms (1.5%)

Counts

2 → 32

Calls

2 calls:

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

rewrite59.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64`
66×	`sqrt-div_binary64`
66×	`cbrt-div_binary64`
55×	`sqrt-prod_binary64`
52×	`pow1_binary64`

Counts

2 → 175

Calls

2 calls:

20.0ms	(.f64 (sqrt.f64 (cbrt.f64 (+.f64 y x))) (.f64 (sqrt.f64 (cbrt.f64 (+.f64 y x))) (sqrt.f64 (cbrt.f64 (+.f64 y x)))))
11.0ms	(*.f64 (sqrt.f64 (cbrt.f64 (+.f64 y x))) (sqrt.f64 (cbrt.f64 (+.f64 y x))))

simplify130.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

549×	`fma-def_binary64`
348×	`times-frac_binary64`
253×	`associate-r_binary64`
247×	`associate-/l*_binary64`
203×	`unswap-sqr_binary64`

Counts

207 → 265

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	287	3920
1	623	3748
2	1870	3440
3	4691	3325
4	4933	3325

prune1.0s (35.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	625	0	625
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	625	4	629

Error

Counts

629 → 4

Alt Table

Status	Error	Program
✓	1.0b	(.f64 (sqrt.f64 (cbrt.f64 (+.f64 y x))) (.f64 (sqrt.f64 (cbrt.f64 (+.f64 y x))) (sqrt.f64 (cbrt.f64 (+.f64 y x)))))
✓	0.6b	(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))
✓	0.0b	(sqrt.f64 (+.f64 x y))
✓	0.8b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 y x))) (sqrt.f64 (cbrt.f64 (+.f64 y x))))

Compiler

Compiled 17911 to 6697 computations (62.6% saved)

regimes132.0ms (4.6%)

Accuracy

Total 0.0b remaining (33.3%)

Threshold costs 0.0b (33.3%)

Counts

28 → 1

Compiler

Compiled 1510 to 930 computations (38.4% 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

end8.0ms (0.3%)

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

sample469.0ms (16.3%)

Algorithm

1×

intervals

Results

211.0ms	8000×	body	128	valid
9.0ms	230×	body	128	nan

Compiler

Compiled 65 to 38 computations (41.5% saved)

Details

analyze83.0ms (2.9%)

sample33.0ms (1.2%)

simplify6.0ms (0.2%)

prune1.0ms (0.1%)

localize3.0ms (0.1%)

series20.0ms (0.7%)

rewrite3.0ms (0.1%)

simplify66.0ms (2.3%)

prune23.0ms (0.8%)

localize8.0ms (0.3%)

series39.0ms (1.4%)

rewrite15.0ms (0.5%)

simplify94.0ms (3.3%)

prune63.0ms (2.2%)

localize8.0ms (0.3%)

series109.0ms (3.8%)

rewrite28.0ms (1%)

simplify182.0ms (6.3%)

prune206.0ms (7.1%)

localize10.0ms (0.4%)

series44.0ms (1.5%)

rewrite59.0ms (2.1%)

simplify130.0ms (4.5%)

prune1.0s (35.8%)

regimes132.0ms (4.6%)

simplify2.0ms (0.1%)

end8.0ms (0.3%)

sample469.0ms (16.3%)

Profiling