Details

analyze3.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 8 to 6 computations (25% saved)

sample733.0ms (50.5%)

Symmetry

(sort x y)

Results

697.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify10.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-neg_binary64`
17×	`sub-neg_binary64`
17×	`fma-def_binary64`
16×	`cancel-sign-sub-inv_binary64`
9×	`fabs-sub_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	10	8
2	17	8
3	26	8
4	42	8
5	76	8
6	88	8
7	108	8
8	124	8
9	129	8
10	113	8

prune3.0ms (0.2%)

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 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.4%)

Counts

1 → 0

Calls

1 calls:

6.0ms

(sqrt.f64 (fabs.f64 (-.f64 x y)))

rewrite4.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`sqrt-prod_binary64`
9×	`add-sqr-sqrt_binary64`
6×	`fabs-mul_binary64`
5×	`*-un-lft-identity_binary64`
3×	`rem-sqrt-square_binary64`

Counts

1 → 25

Calls

1 calls:

3.0ms

(sqrt.f64 (fabs.f64 (-.f64 x y)))

simplify57.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

572×	`distribute-rgt-in_binary64`
512×	`distribute-lft-in_binary64`
468×	`cancel-sign-sub-inv_binary64`
435×	`unsub-neg_binary64`
349×	`fma-neg_binary64`

Counts

25 → 27

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	62	313
1	107	300
2	187	300
3	319	300
4	655	300
5	1903	300
6	4539	300
7	5093	300

prune12.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	2	28

Error

Counts

28 → 2

Alt Table

Status	Error	Program
▶	32.3b	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y)))) (sqrt.f64 (fabs.f64 (+.f64 x y))))
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 351 to 134 computations (61.8% saved)

localize11.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (+.f64 x y)))
✓	0.5b	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y)))) (sqrt.f64 (fabs.f64 (+.f64 x y))))
✓	3.3b	(-.f64 (.f64 x x) (.f64 y y))
✓	30.1b	(sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y))))

series79.0ms (5.4%)

Counts

4 → 96

Calls

4 calls:

49.0ms	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y)))) (sqrt.f64 (fabs.f64 (+.f64 x y))))
17.0ms	(sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y))))
7.0ms	(-.f64 (.f64 x x) (.f64 y y))
6.0ms	(sqrt.f64 (fabs.f64 (+.f64 x y)))

rewrite50.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

208×	`sqrt-prod_binary64`
130×	`add-sqr-sqrt_binary64`
121×	`times-frac_binary64`
112×	`fabs-mul_binary64`
106×	`*-un-lft-identity_binary64`

Counts

4 → 236

Calls

4 calls:

12.0ms	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y)))) (sqrt.f64 (fabs.f64 (+.f64 x y))))
3.0ms	(sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y))))
3.0ms	(sqrt.f64 (fabs.f64 (+.f64 x y)))
3.0ms	(-.f64 (.f64 x x) (.f64 y y))

simplify304.0ms (20.9%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-def_binary64`
727×	`times-frac_binary64`
283×	`fma-neg_binary64`
224×	`cancel-sign-sub-inv_binary64`
215×	`unswap-sqr_binary64`

Counts

332 → 269

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	263	9438
1	404	8989
2	890	8983
3	2162	8409
4	4533	8409
5	4973	8409
6	4901	8409

prune82.0ms (5.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	269	0	269
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	269	2	271

Error

Counts

271 → 2

Alt Table

Status	Error	Program
✓	32.3b	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y)))) (sqrt.f64 (fabs.f64 (+.f64 x y))))
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 7270 to 1043 computations (85.7% saved)

regimes47.0ms (3.2%)

Accuracy

Total 0.0b remaining (17.2%)

Threshold costs 0.0b (17.2%)

Counts

6 → 1

Compiler

Compiled 533 to 367 computations (31.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	10	8
2	17	8
3	22	8
4	25	8
5	26	8
6	26	8

end47.0ms (3.2%)

Remove: (sort x y)
Compiler: Compiled 52 to 36 computations (30.8% saved)

Details

analyze3.0ms (0.2%)

sample733.0ms (50.5%)

simplify10.0ms (0.7%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

series6.0ms (0.4%)

rewrite4.0ms (0.3%)

simplify57.0ms (3.9%)

prune12.0ms (0.8%)

localize11.0ms (0.7%)

series79.0ms (5.4%)

rewrite50.0ms (3.4%)

simplify304.0ms (20.9%)

prune82.0ms (5.7%)

regimes47.0ms (3.2%)

simplify2.0ms (0.1%)

end47.0ms (3.2%)

Profiling