Details

analyze2.0ms (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)

sample37.0ms (3.4%)

Algorithm

1×

intervals

Symmetry

(sort x y)

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 17 to 13 computations (23.5% saved)

simplify9.0ms (0.9%)

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 (0.4%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.7%)

Counts

1 → 0

Calls

1 calls:

7.0ms

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

rewrite4.0ms (0.4%)

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 (5.3%)

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 (1%)

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
▶	50.3b	(*.f64 (sqrt.f64 (fabs.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (fabs.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 y)))))
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 351 to 134 computations (61.8% saved)

localize9.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

series41.0ms (3.8%)

Counts

4 → 50

Calls

4 calls:

17.0ms	(*.f64 (sqrt.f64 (fabs.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (fabs.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 y)))))
11.0ms	(+.f64 (sqrt.f64 x) (sqrt.f64 y))
6.0ms	(sqrt.f64 (fabs.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
6.0ms	(sqrt.f64 (fabs.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 y))))

rewrite45.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`add-sqr-sqrt_binary64`
89×	`sqrt-prod_binary64`
44×	`fabs-mul_binary64`
36×	`*-un-lft-identity_binary64`
24×	`rem-sqrt-square_binary64`

Counts

4 → 152

Calls

4 calls:

17.0ms	(*.f64 (sqrt.f64 (fabs.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (fabs.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 y)))))
5.0ms	(sqrt.f64 (fabs.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 y))))
4.0ms	(sqrt.f64 (fabs.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
4.0ms	(+.f64 (sqrt.f64 x) (sqrt.f64 y))

simplify281.0ms (26.1%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
869×	`fma-neg_binary64`
458×	`associate-+l+_binary64`
364×	`cancel-sign-sub-inv_binary64`
331×	`associate-+r+_binary64`

Counts

202 → 191

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	166	4714
1	292	3977
2	570	3761
3	848	3761
4	1716	3761
5	3817	3761
6	4496	3761
7	4956	3761
8	5000	3761
9	4874	3761

prune51.0ms (4.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	191	2	193

Error

Counts

193 → 2

Alt Table

Status	Error	Program
✓	50.3b	(*.f64 (sqrt.f64 (fabs.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (fabs.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 y)))))
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 4414 to 683 computations (84.5% saved)

regimes29.0ms (2.7%)

Accuracy

Total 0.0b remaining (12.5%)

Threshold costs 0.0b (12.5%)

Counts

3 → 1

Compiler

Compiled 228 to 142 computations (37.7% saved)

simplify2.0ms (0.2%)

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

end6.0ms (0.6%)

Remove: (sort x y)
Compiler: Compiled 21 to 15 computations (28.6% saved)

sample479.0ms (44.5%)

Algorithm

1×

intervals

Results

257.0ms

8000×

body

128

valid

Compiler

Compiled 41 to 29 computations (29.3% saved)

Details

analyze2.0ms (0.2%)

sample37.0ms (3.4%)

simplify9.0ms (0.9%)

prune1.0ms (0.1%)

localize4.0ms (0.4%)

series7.0ms (0.7%)

rewrite4.0ms (0.4%)

simplify57.0ms (5.3%)

prune11.0ms (1%)

localize9.0ms (0.8%)

series41.0ms (3.8%)

rewrite45.0ms (4.2%)

simplify281.0ms (26.1%)

prune51.0ms (4.7%)

regimes29.0ms (2.7%)

simplify2.0ms (0.2%)

end6.0ms (0.6%)

sample479.0ms (44.5%)

Profiling