Details

analyze1.0ms (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)

sample707.0ms (54.4%)

Symmetry

(sort x y)

Results

669.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify9.0ms (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

prune2.0ms (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 (0.3%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.7%)

Counts

1 → 0

Calls

1 calls:

9.0ms

(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)))

simplify60.0ms (4.6%)

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

prune14.0ms (1.1%)

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
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))
▶	0.9b	(*.f64 (fabs.f64 (cbrt.f64 (-.f64 x y))) (sqrt.f64 (fabs.f64 (cbrt.f64 (-.f64 x y)))))

Compiler

Compiled 345 to 126 computations (63.5% saved)

localize6.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (fabs.f64 (cbrt.f64 (-.f64 x y))))
✓	0.4b	(*.f64 (fabs.f64 (cbrt.f64 (-.f64 x y))) (sqrt.f64 (fabs.f64 (cbrt.f64 (-.f64 x y)))))
✓	0.6b	(cbrt.f64 (-.f64 x y))

series86.0ms (6.6%)

Counts

3 → 72

Calls

3 calls:

49.0ms	(*.f64 (fabs.f64 (cbrt.f64 (-.f64 x y))) (sqrt.f64 (fabs.f64 (cbrt.f64 (-.f64 x y)))))
24.0ms	(cbrt.f64 (-.f64 x y))
12.0ms	(sqrt.f64 (fabs.f64 (cbrt.f64 (-.f64 x y))))

rewrite33.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`add-sqr-sqrt_binary64`
51×	`sqrt-prod_binary64`
50×	`fabs-mul_binary64`
49×	`cbrt-prod_binary64`
32×	`fabs-sqr_binary64`

Counts

3 → 136

Calls

3 calls:

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

simplify147.0ms (11.3%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-neg_binary64`
454×	`*-commutative_binary64`
387×	`fma-def_binary64`
293×	`cancel-sign-sub-inv_binary64`
203×	`times-frac_binary64`

Counts

208 → 222

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	4691
1	601	3930
2	1540	3655
3	3974	3074
4	4948	3074
5	4934	3074

prune104.0ms (8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	274	2	276

Error

Counts

276 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))
✓	0.9b	(*.f64 (fabs.f64 (cbrt.f64 (-.f64 x y))) (sqrt.f64 (fabs.f64 (cbrt.f64 (-.f64 x y)))))

Compiler

Compiled 6293 to 2159 computations (65.7% saved)

regimes68.0ms (5.2%)

Accuracy

Total 0.0b remaining (23.9%)

Threshold costs 0.0b (23.9%)

Counts

11 → 1

Compiler

Compiled 773 to 487 computations (37% 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

end46.0ms (3.5%)

Remove: (sort x y)
Compiler: Compiled 49 to 32 computations (34.7% saved)

Details

analyze1.0ms (0.1%)

sample707.0ms (54.4%)

simplify9.0ms (0.7%)

prune2.0ms (0.1%)

localize4.0ms (0.3%)

series9.0ms (0.7%)

rewrite4.0ms (0.3%)

simplify60.0ms (4.6%)

prune14.0ms (1.1%)

localize6.0ms (0.4%)

series86.0ms (6.6%)

rewrite33.0ms (2.5%)

simplify147.0ms (11.3%)

prune104.0ms (8%)

regimes68.0ms (5.2%)

simplify2.0ms (0.2%)

end46.0ms (3.5%)

Profiling