Details

analyze1.2s (10.1%)

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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample5.1s (43.3%)

Symmetry

(sort a1 a2)

Results

1.4s	1825×	body	1024	valid
1.3s	1627×	body	1024	invalid
952.0ms	5077×	body	128	valid
469.0ms	921×	body	512	valid
445.0ms	858×	body	512	invalid
189.0ms	426×	body	256	valid
162.0ms	408×	body	256	invalid
120.0ms	636×	body	128	invalid
7.0ms	7×	body	2048	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
23×	`*-commutative_binary64`
20×	`associate-/l*_binary64`
11×	`associate-/r/_binary64`
9×	`associate-*r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	27	18
2	53	18
3	76	18
4	103	18
5	117	18
6	132	18
7	134	18
8	136	18
9	136	18

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
✓	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series85.0ms (0.7%)

Counts

2 → 60

Calls

2 calls:

57.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
28.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
31×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64`

Counts

2 → 85

Calls

2 calls:

7.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
5.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

simplify111.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

456×	`associate-l_binary64`
410×	`associate-r_binary64`
396×	`fma-neg_binary64`
332×	`associate-/l*_binary64`
299×	`sub-neg_binary64`

Counts

145 → 151

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	3315
1	365	3012
2	1289	2968
3	4359	2968
4	5076	2968

prune165.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	144	7	151
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	144	9	153

Error

Counts

153 → 9

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.7b	(.f64 (.f64 (cos.f64 th) (/.f64 1 (sqrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
▶	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
	0.7b	(.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) (.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))
	1.2b	(.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2)))) (/.f64 (sqrt.f64 2) (cbrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))))))
	0.7b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))))
	0.5b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))))

Compiler

Compiled 3820 to 1798 computations (52.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
✓	0.2b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
✓	0.2b	(/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))
✓	0.3b	(.f64 (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))

series295.0ms (2.5%)

Counts

4 → 108

Calls

4 calls:

114.0ms	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
69.0ms	(.f64 (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))
69.0ms	(/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
42.0ms	(/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))

rewrite58.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
70×	`times-frac_binary64`
61×	`add-exp-log_binary64`
50×	`*-un-lft-identity_binary64`
50×	`add-cube-cbrt_binary64`

Counts

4 → 181

Calls

4 calls:

17.0ms	(.f64 (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))
12.0ms	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
7.0ms	(/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
3.0ms	(/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))

simplify185.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

517×	`cancel-sign-sub-inv_binary64`
363×	`fma-neg_binary64`
266×	`associate-r_binary64`
250×	`associate-l_binary64`
250×	`associate-*r/_binary64`

Counts

289 → 309

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	347	9877
1	938	7509
2	3617	7422
3	5079	7422

prune362.0ms (3.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	308	1	309
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	310	8	318

Error

Counts

318 → 8

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.7b	(.f64 (.f64 (cos.f64 th) (/.f64 1 (sqrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
▶	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.7b	(.f64 (cos.f64 th) (.f64 (/.f64 (sqrt.f64 (hypot.f64 a2 a1)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (/.f64 (sqrt.f64 (hypot.f64 a2 a1)) (cbrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
	0.7b	(.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) (.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))
	0.5b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))))

Compiler

Compiled 10549 to 6907 computations (34.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
✓	0.3b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
✓	0.4b	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2))
✓	6.5b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series271.0ms (2.3%)

Counts

4 → 120

Calls

4 calls:

200.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
36.0ms	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
21.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2))
14.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite37.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`sqrt-prod_binary64`
72×	`times-frac_binary64`
65×	`add-sqr-sqrt_binary64`
60×	`*-un-lft-identity_binary64`
60×	`add-cube-cbrt_binary64`

Counts

4 → 162

Calls

4 calls:

10.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
5.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2))
4.0ms	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
1.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

simplify221.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

621×	`fma-def_binary64`
376×	`cancel-sign-sub-inv_binary64`
345×	`associate-l_binary64`
317×	`sub-neg_binary64`
308×	`fma-neg_binary64`

Counts

282 → 332

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	347	7564
1	936	6108
2	3364	6008
3	4799	6003
4	4932	6003
5	5038	6003

prune284.0ms (2.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	331	1	332
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	333	7	340

Error

Counts

340 → 7

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
▶	0.3b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
	0.7b	(.f64 (cos.f64 th) (.f64 (/.f64 (sqrt.f64 (hypot.f64 a2 a1)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (/.f64 (sqrt.f64 (hypot.f64 a2 a1)) (cbrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
	0.7b	(.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) (.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))
	0.7b	(.f64 (.f64 (cos.f64 th) (/.f64 1 (sqrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))))

Compiler

Compiled 9352 to 3959 computations (57.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)
	0.2b	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
✓	0.3b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
✓	6.6b	(sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2))

series124.0ms (1.1%)

Counts

3 → 84

Calls

3 calls:

92.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
21.0ms	(sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2))
11.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
28×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64`
26×	`sqrt-prod_binary64`
26×	`add-cube-cbrt_binary64`

Counts

3 → 90

Calls

3 calls:

8.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
2.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)
2.0ms	(sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2))

simplify134.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

767×	`times-frac_binary64`
619×	`fma-neg_binary64`
488×	`cancel-sign-sub-inv_binary64`
293×	`associate-r_binary64`
260×	`associate-l_binary64`

Counts

174 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	293	5151
1	752	4553
2	2741	3865
3	5000	3865
4	5283	3865

prune279.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	277	2	279
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	280	6	286

Error

Counts

286 → 6

Alt Table

Status	Error	Program
	0.7b	(.f64 (cos.f64 th) (.f64 (/.f64 (sqrt.f64 (hypot.f64 a2 a1)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (/.f64 (sqrt.f64 (hypot.f64 a2 a1)) (cbrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))))
	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 2 (hypot.f64 a2 a1)))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
✓	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.7b	(.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) (.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))
	0.5b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))

Compiler

Compiled 7728 to 3423 computations (55.7% saved)

regimes2.6s (22.5%)

Accuracy

Total 0.3b remaining (89%)

Threshold costs 0.3b (89%)

Counts

271 → 1

Compiler

Compiled 48425 to 32382 computations (33.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	20	24
2	19	24

end119.0ms (1%)

Remove: (sort a1 a2)
Compiler: Compiled 210 to 135 computations (35.7% saved)

Details

analyze1.2s (10.1%)

sample5.1s (43.3%)

simplify9.0ms (0.1%)

prune5.0ms (0%)

localize9.0ms (0.1%)

series85.0ms (0.7%)

rewrite20.0ms (0.2%)

simplify111.0ms (0.9%)

prune165.0ms (1.4%)

localize13.0ms (0.1%)

series295.0ms (2.5%)

rewrite58.0ms (0.5%)

simplify185.0ms (1.6%)

prune362.0ms (3.1%)

localize13.0ms (0.1%)

series271.0ms (2.3%)

rewrite37.0ms (0.3%)

simplify221.0ms (1.9%)

prune284.0ms (2.4%)

localize11.0ms (0.1%)

series124.0ms (1.1%)

rewrite18.0ms (0.2%)

simplify134.0ms (1.1%)

prune279.0ms (2.4%)

regimes2.6s (22.5%)

simplify2.0ms (0%)

end119.0ms (1%)

Profiling