Details

analyze2.0ms (0.1%)

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)

sample782.0ms (31.6%)

Symmetry

(sort x y)

Results

741.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify9.0ms (0.4%)

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

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

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.2%)

Counts

1 → 0

Calls

1 calls:

6.0ms

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

rewrite7.0ms (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:

6.0ms

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

simplify61.0ms (2.5%)

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

prune11.0ms (0.4%)

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
▶	0.4b	(*.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y)))))
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 347 to 126 computations (63.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series1.2s (47.4%)

Counts

2 → 48

Calls

2 calls:

1.2s	(sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))))
6.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y)))))

rewrite41.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

230×	`sqrt-prod_binary64`
146×	`add-sqr-sqrt_binary64`
50×	`fabs-mul_binary64`
48×	`rem-sqrt-square_binary64`
37×	`*-un-lft-identity_binary64`

Counts

2 → 174

Calls

2 calls:

14.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y)))))
3.0ms	(sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))))

simplify190.0ms (7.7%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-neg_binary64`
395×	`fma-def_binary64`
274×	`*-commutative_binary64`
266×	`unsub-neg_binary64`
246×	`sqr-pow_binary64`

Counts

222 → 163

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	157	3471
1	230	3272
2	531	3245
3	1084	3154
4	1858	3154
5	3292	3105
6	4048	3099
7	4854	3099
8	4892	3099

prune89.0ms (3.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	250	0	250
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	250	2	252

Error

Counts

252 → 2

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y)))))
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 4937 to 885 computations (82.1% saved)

regimes49.0ms (2%)

Accuracy

Total 0.0b remaining (32.2%)

Threshold costs 0.0b (32.2%)

Counts

8 → 1

Compiler

Compiled 578 to 347 computations (40% 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

end42.0ms (1.7%)

Remove: (sort x y)
Compiler: Compiled 50 to 32 computations (36% saved)

Details

analyze2.0ms (0.1%)

sample782.0ms (31.6%)

simplify9.0ms (0.4%)

prune1.0ms (0.1%)

localize4.0ms (0.1%)

series6.0ms (0.2%)

rewrite7.0ms (0.3%)

simplify61.0ms (2.5%)

prune11.0ms (0.4%)

localize6.0ms (0.2%)

series1.2s (47.4%)

rewrite41.0ms (1.6%)

simplify190.0ms (7.7%)

prune89.0ms (3.6%)

regimes49.0ms (2%)

simplify2.0ms (0.1%)

end42.0ms (1.7%)

Profiling