Details

analyze132.0ms (9.4%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
56.2%	43.7%	0.1%	7
65.6%	34.3%	0.1%	8
76.5%	23.4%	0.1%	9
82%	18%	0.1%	10
87.8%	12.1%	0.1%	11
90.7%	9.2%	0.1%	12
93.8%	6.1%	0.1%	13
95.3%	4.6%	0.1%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample832.0ms (59.7%)

Symmetry

(sort x y)

Results

800.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify7.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

2×	`hypot-def_binary64`
2×	`fma-def_binary64`
1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	10	4
2	12	4
3	12	4

prune3.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(hypot.f64 x y)
	34.2b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 43 to 25 computations (41.9% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series11.0ms (0.8%)

Counts

1 → 24

Calls

1 calls:

11.0ms

(hypot.f64 x y)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(hypot.f64 x y)

simplify53.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

755×	`fma-neg_binary64`
537×	`cancel-sign-sub-inv_binary64`
354×	`neg-mul-1_binary64`
312×	`distribute-rgt-neg-in_binary64`
310×	`distribute-lft-neg-in_binary64`

Counts

34 → 42

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	63	568
1	174	541
2	511	525
3	2175	525
4	4416	525
5	5032	525

prune22.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	41	3	44

Error

Counts

44 → 3

Alt Table

Status	Error	Program
▶	34.2b	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	0.0b	(hypot.f64 x y)
	37.2b	(neg.f64 (fma.f64 1/2 (/.f64 (*.f64 y y) x) x))

Compiler

Compiled 585 to 351 computations (40% saved)

localize4.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y y (*.f64 x x))
✓	32.1b	(sqrt.f64 (fma.f64 y y (*.f64 x x)))

series18.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
7.0ms	(fma.f64 y y (*.f64 x x))

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt_binary64`
3×	`*-un-lft-identity_binary64`
3×	`sqrt-prod_binary64`
3×	`add-cube-cbrt_binary64`
3×	`pow1_binary64`

Counts

2 → 26

Calls

2 calls:

1.0ms	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
0.0ms	(fma.f64 y y (*.f64 x x))

simplify61.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

747×	`fma-neg_binary64`
537×	`cancel-sign-sub-inv_binary64`
354×	`neg-mul-1_binary64`
312×	`distribute-rgt-neg-in_binary64`
310×	`distribute-lft-neg-in_binary64`

Counts

74 → 77

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	77	970
1	189	838
2	565	817
3	2335	817
4	4350	791
5	5023	791

prune31.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	77	3	80

Error

Counts

80 → 3

Alt Table

Status	Error	Program
✓	34.2b	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	0.0b	(hypot.f64 x y)
▶	37.2b	(neg.f64 (fma.f64 1/2 (/.f64 (*.f64 y y) x) x))

Compiler

Compiled 966 to 465 computations (51.9% saved)

localize5.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	7.5b	(/.f64 (*.f64 y y) x)

series10.0ms (0.8%)

Counts

1 → 24

Calls

1 calls:

10.0ms

(/.f64 (*.f64 y y) x)

rewrite4.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
3×	`associate-/r*_binary64`
3×	`*-un-lft-identity_binary64`
3×	`times-frac_binary64`

Counts

1 → 23

Calls

1 calls:

3.0ms

(/.f64 (*.f64 y y) x)

simplify69.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

544×	`associate-/r/_binary64`
390×	`associate-*r/_binary64`
327×	`div-sub_binary64`
320×	`associate-r_binary64`
295×	`unswap-sqr_binary64`

Counts

47 → 29

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	429
1	102	384
2	283	384
3	934	384
4	2005	384
5	2978	384
6	4495	384
7	4955	384

prune12.0ms (0.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	29	3	32

Error

Counts

32 → 3

Alt Table

Status	Error	Program
✓	34.2b	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	0.0b	(hypot.f64 x y)
✓	37.2b	(neg.f64 (fma.f64 1/2 (/.f64 (*.f64 y y) x) x))

Compiler

Compiled 415 to 185 computations (55.4% saved)

regimes65.0ms (4.7%)

Accuracy

Total 0.0b remaining (14.8%)

Threshold costs 0.0b (14.8%)

Counts

7 → 1

Compiler

Compiled 461 to 293 computations (36.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	4	4

end47.0ms (3.3%)

Remove: (sort x y)
Compiler: Compiled 45 to 27 computations (40% saved)

Details

analyze132.0ms (9.4%)

sample832.0ms (59.7%)

simplify7.0ms (0.5%)

prune3.0ms (0.2%)

localize2.0ms (0.1%)

series11.0ms (0.8%)

rewrite1.0ms (0%)

simplify53.0ms (3.8%)

prune22.0ms (1.6%)

localize4.0ms (0.3%)

series18.0ms (1.3%)

rewrite2.0ms (0.1%)

simplify61.0ms (4.3%)

prune31.0ms (2.2%)

localize5.0ms (0.4%)

series10.0ms (0.8%)

rewrite4.0ms (0.3%)

simplify69.0ms (4.9%)

prune12.0ms (0.9%)

regimes65.0ms (4.7%)

simplify2.0ms (0.1%)

end47.0ms (3.3%)

Profiling