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)

sample748.0ms (29.5%)

Symmetry

(sort x y)

Results

714.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify11.0ms (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)))

rewrite4.0ms (0.2%)

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 (2.2%)

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

prune10.0ms (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

0.0b

Counts

28 → 2

Alt Table

Status	Error	Program
▶	39.1b	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)))) (sqrt.f64 (fabs.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 x y))))))
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 367 to 146 computations (60.2% saved)

localize15.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.0b	(-.f64 (pow.f64 x 3) (pow.f64 y 3))
✓	18.0b	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)))) (sqrt.f64 (fabs.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 x y))))))
✓	19.0b	(sqrt.f64 (fabs.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3))))
✓	26.5b	(sqrt.f64 (fabs.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 x y)))))

series242.0ms (9.5%)

Counts

4 → 54

Calls

4 calls:

191.0ms	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)))) (sqrt.f64 (fabs.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 x y))))))
21.0ms	(sqrt.f64 (fabs.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 x y)))))
19.0ms	(sqrt.f64 (fabs.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3))))
11.0ms	(-.f64 (pow.f64 x 3) (pow.f64 y 3))

rewrite216.0ms (8.5%)

Algorithm

1×	rewrite-expression-head

Rules

600×	`add-sqr-sqrt_binary64`
586×	`sqrt-prod_binary64`
410×	`fabs-mul_binary64`
348×	`*-un-lft-identity_binary64`
320×	`times-frac_binary64`

Counts

4 → 661

Calls

4 calls:

27.0ms	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)))) (sqrt.f64 (fabs.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 x y))))))
16.0ms	(-.f64 (pow.f64 x 3) (pow.f64 y 3))
11.0ms	(sqrt.f64 (fabs.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3))))
7.0ms	(sqrt.f64 (fabs.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 x y)))))

simplify744.0ms (29.3%)

Algorithm

1×	egg-herbie

Rules

1003×	`fma-neg_binary64`
582×	`cancel-sign-sub-inv_binary64`
328×	`exp-prod_binary64`
286×	`distribute-rgt-neg-in_binary64`
162×	`associate-l_binary64`

Counts

715 → 560

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	587	29902
1	807	27947
2	2314	27083
3	4245	25867
4	4733	25867
5	4855	25867

prune374.0ms (14.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	560	0	560
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	560	2	562

Error

0.0b

Counts

562 → 2

Alt Table

Status	Error	Program
✓	39.1b	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)))) (sqrt.f64 (fabs.f64 (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 x y))))))
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 24179 to 10050 computations (58.4% saved)

regimes54.0ms (2.1%)

Accuracy

Total 0.0b remaining (7.4%)

Threshold costs 0.0b (7.4%)

Counts

8 → 1

Compiler

Compiled 878 to 607 computations (30.9% 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

end48.0ms (1.9%)

Remove: (sort x y)
Compiler: Compiled 60 to 42 computations (30% saved)

Details

analyze1.0ms (0.1%)

sample748.0ms (29.5%)

simplify11.0ms (0.4%)

prune1.0ms (0.1%)

localize4.0ms (0.1%)

series6.0ms (0.2%)

rewrite4.0ms (0.2%)

simplify57.0ms (2.2%)

prune10.0ms (0.4%)

localize15.0ms (0.6%)

series242.0ms (9.5%)

rewrite216.0ms (8.5%)

simplify744.0ms (29.3%)

prune374.0ms (14.7%)

regimes54.0ms (2.1%)

simplify2.0ms (0.1%)

end48.0ms (1.9%)

Profiling