Details

analyze36.0ms (0.9%)

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)

sample36.0ms (1%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 17 to 13 computations (23.5% saved)

simplify18.0ms (0.5%)

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

prune5.0ms (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)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series12.0ms (0.3%)

Counts

1 → 0

Calls

1 calls:

12.0ms

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

rewrite8.0ms (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:

6.0ms

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

simplify76.0ms (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

prune16.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	25	3	28

Error

Counts

28 → 3

Alt Table

Status	Error	Program
	31.6b	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y)))) (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)))))
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 381 to 148 computations (61.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))
✓	0.2b	(sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))))
✓	0.6b	(*.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y)))))

series1.0s (27%)

Counts

2 → 48

Calls

2 calls:

1.0s	(sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))))
10.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y)))))

rewrite97.0ms (2.6%)

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:

37.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y)))))
8.0ms	(sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))))

simplify380.0ms (10.2%)

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

prune162.0ms (4.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	250	0	250
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	250	3	253

Error

Counts

253 → 3

Alt Table

Status	Error	Program
▶	31.6b	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y)))) (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)))))
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 4971 to 907 computations (81.8% saved)

localize21.0ms (0.6%)

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))))
✓	1.5b	(-.f64 (.f64 x x) (.f64 y y))
✓	29.4b	(sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y))))

series144.0ms (3.9%)

Counts

4 → 96

Calls

4 calls:

90.0ms	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y)))) (sqrt.f64 (fabs.f64 (+.f64 x y))))
31.0ms	(sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y))))
13.0ms	(-.f64 (.f64 x x) (.f64 y y))
10.0ms	(sqrt.f64 (fabs.f64 (+.f64 x y)))

rewrite239.0ms (6.4%)

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:

19.0ms	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y)))) (sqrt.f64 (fabs.f64 (+.f64 x y))))
6.0ms	(sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y))))
5.0ms	(sqrt.f64 (fabs.f64 (+.f64 x y)))
5.0ms	(-.f64 (.f64 x x) (.f64 y y))

simplify485.0ms (13%)

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

prune145.0ms (3.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	269	0	269
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	269	3	272

Error

Counts

272 → 3

Alt Table

Status	Error	Program
✓	31.6b	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y)))) (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)))))
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 7285 to 1050 computations (85.6% saved)

regimes120.0ms (3.2%)

Accuracy

Total 0.0b remaining (42.9%)

Threshold costs 0.0b (42.9%)

Counts

12 → 1

Compiler

Compiled 838 to 562 computations (32.9% saved)

simplify4.0ms (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

end10.0ms (0.3%)

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

sample702.0ms (18.8%)

Algorithm

1×

intervals

Results

359.0ms

8000×

body

128

valid

Compiler

Compiled 56 to 36 computations (35.7% saved)

Details

analyze36.0ms (0.9%)

sample36.0ms (1%)

simplify18.0ms (0.5%)

prune5.0ms (0.1%)

localize7.0ms (0.2%)

series12.0ms (0.3%)

rewrite8.0ms (0.2%)

simplify76.0ms (2%)

prune16.0ms (0.4%)

localize8.0ms (0.2%)

series1.0s (27%)

rewrite97.0ms (2.6%)

simplify380.0ms (10.2%)

prune162.0ms (4.3%)

localize21.0ms (0.6%)

series144.0ms (3.9%)

rewrite239.0ms (6.4%)

simplify485.0ms (13%)

prune145.0ms (3.9%)

regimes120.0ms (3.2%)

simplify4.0ms (0.1%)

end10.0ms (0.3%)

sample702.0ms (18.8%)

Profiling