Details

analyze1.2s (23.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	99.9%	0.1%	10
0%	99.9%	0.1%	11
0%	99.9%	0.1%	12
0%	99.9%	0.1%	13
0%	99.9%	0.1%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample795.0ms (15.2%)

Symmetry

(sort x y)

Results

752.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify10.0ms (0.2%)

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%)

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)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

6.0ms

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

rewrite4.0ms (0.1%)

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)))

simplify106.0ms (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

prune10.0ms (0.2%)

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
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))
▶	30.1b	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y)))) (sqrt.f64 (fabs.f64 (+.f64 x y))))

Compiler

Compiled 351 to 134 computations (61.8% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (+.f64 x y)))
✓	0.4b	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y)))) (sqrt.f64 (fabs.f64 (+.f64 x y))))
✓	3.1b	(-.f64 (.f64 x x) (.f64 y y))
✓	28.0b	(sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y))))

series86.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

52.0ms	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y)))) (sqrt.f64 (fabs.f64 (+.f64 x y))))
16.0ms	(sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y))))
11.0ms	(-.f64 (.f64 x x) (.f64 y y))
6.0ms	(sqrt.f64 (fabs.f64 (+.f64 x y)))

rewrite52.0ms (1%)

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:

11.0ms	(/.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))))
3.0ms	(sqrt.f64 (fabs.f64 (+.f64 x y)))
3.0ms	(-.f64 (.f64 x x) (.f64 y y))

simplify312.0ms (6%)

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

prune95.0ms (1.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	268	1	269
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	268	3	271

Error

0.0b

Counts

271 → 3

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))
✓	30.1b	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (.f64 x x) (.f64 y y)))) (sqrt.f64 (fabs.f64 (+.f64 x y))))
▶	0.1b	(/.f64 (*.f64 (sqrt.f64 (fabs.f64 (+.f64 x y))) (sqrt.f64 (fabs.f64 (-.f64 x y)))) (sqrt.f64 (fabs.f64 (+.f64 x y))))

Compiler

Compiled 7308 to 1063 computations (85.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series22.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(*.f64 (sqrt.f64 (fabs.f64 (+.f64 x y))) (sqrt.f64 (fabs.f64 (-.f64 x y))))
6.0ms	(/.f64 (*.f64 (sqrt.f64 (fabs.f64 (+.f64 x y))) (sqrt.f64 (fabs.f64 (-.f64 x y)))) (sqrt.f64 (fabs.f64 (+.f64 x y))))

rewrite49.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

151×	`add-sqr-sqrt_binary64`
99×	`rem-sqrt-square_binary64`
58×	`fabs-mul_binary64`
57×	`sqrt-prod_binary64`
45×	`fabs-sqr_binary64`

Counts

2 → 149

Calls

2 calls:

14.0ms	(/.f64 (*.f64 (sqrt.f64 (fabs.f64 (+.f64 x y))) (sqrt.f64 (fabs.f64 (-.f64 x y)))) (sqrt.f64 (fabs.f64 (+.f64 x y))))
13.0ms	(*.f64 (sqrt.f64 (fabs.f64 (+.f64 x y))) (sqrt.f64 (fabs.f64 (-.f64 x y))))

simplify190.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

398×	`fma-def_binary64`
386×	`associate-/l/_binary64`
364×	`associate-/r/_binary64`
318×	`fma-neg_binary64`
238×	`associate-*l/_binary64`

Counts

197 → 213

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	212	4765
1	423	4069
2	1285	3875
3	2366	3858
4	3061	3848
5	4487	3848
6	4957	3848

prune149.0ms (2.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	294	2	296
Fresh	0	0	0
Picked	1	0	1
Done	1	1	2
Total	296	3	299

Error

Counts

299 → 3

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))
▶	0.5b	(/.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y))))) (sqrt.f64 (fabs.f64 (-.f64 x y)))) (sqrt.f64 (fabs.f64 (+.f64 x y))))
	0.5b	(/.f64 (.f64 (.f64 (sqrt.f64 (fabs.f64 (+.f64 x y))) (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))))) (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))))) (sqrt.f64 (fabs.f64 (+.f64 x y))))

Compiler

Compiled 7095 to 1135 computations (84% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y))))
✓	0.4b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y))))) (sqrt.f64 (fabs.f64 (-.f64 x y))))
✓	0.4b	(/.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y))))) (sqrt.f64 (fabs.f64 (-.f64 x 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)))))

series609.0ms (11.6%)

Counts

4 → 96

Calls

4 calls:

581.0ms	(sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y))))
14.0ms	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y))))) (sqrt.f64 (fabs.f64 (-.f64 x y))))
8.0ms	(/.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y))))) (sqrt.f64 (fabs.f64 (-.f64 x y)))) (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)))))

rewrite232.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Rules

876×	`add-sqr-sqrt_binary64`
768×	`rem-sqrt-square_binary64`
536×	`sqrt-prod_binary64`
400×	`mul-fabs_binary64`
267×	`fabs-mul_binary64`

Counts

4 → 494

Calls

4 calls:

36.0ms	(/.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y))))) (sqrt.f64 (fabs.f64 (-.f64 x y)))) (sqrt.f64 (fabs.f64 (+.f64 x y))))
25.0ms	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y))))) (sqrt.f64 (fabs.f64 (-.f64 x y))))
17.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y)))))
4.0ms	(sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y))))

simplify365.0ms (7%)

Algorithm

1×	egg-herbie

Rules

614×	`times-frac_binary64`
492×	`associate-/l*_binary64`
457×	`associate-l_binary64`
330×	`associate-r_binary64`
244×	`fma-def_binary64`

Counts

590 → 529

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	413	14640
1	755	12536
2	3181	11912
3	4141	11898
4	4956	11898

prune279.0ms (5.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	571	0	571
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	571	3	574

Error

Counts

574 → 3

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))
✓	0.5b	(/.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (+.f64 x y))))) (sqrt.f64 (fabs.f64 (-.f64 x y)))) (sqrt.f64 (fabs.f64 (+.f64 x y))))
	0.5b	(/.f64 (.f64 (.f64 (sqrt.f64 (fabs.f64 (+.f64 x y))) (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))))) (sqrt.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))))) (sqrt.f64 (fabs.f64 (+.f64 x y))))

Compiler

Compiled 18644 to 2998 computations (83.9% saved)

regimes541.0ms (10.3%)

Accuracy

Total 0.0b remaining (29.8%)

Threshold costs 0.0b (29.8%)

Counts

106 → 1

Compiler

Compiled 12158 to 7027 computations (42.2% saved)

simplify2.0ms (0%)

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

end56.0ms (1.1%)

Remove: (sort x y)
Compiler: Compiled 89 to 49 computations (44.9% saved)

Details

analyze1.2s (23.3%)

sample795.0ms (15.2%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series7.0ms (0.1%)

rewrite4.0ms (0.1%)

simplify106.0ms (2%)

prune10.0ms (0.2%)

localize14.0ms (0.3%)

series86.0ms (1.6%)

rewrite52.0ms (1%)

simplify312.0ms (6%)

prune95.0ms (1.8%)

localize8.0ms (0.2%)

series22.0ms (0.4%)

rewrite49.0ms (0.9%)

simplify190.0ms (3.6%)

prune149.0ms (2.9%)

localize10.0ms (0.2%)

series609.0ms (11.6%)

rewrite232.0ms (4.4%)

simplify365.0ms (7%)

prune279.0ms (5.3%)

regimes541.0ms (10.3%)

simplify2.0ms (0%)

end56.0ms (1.1%)

Profiling