Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25.7%	74.3%	0
25.7%	0%	74.3%	1

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample1.5s (32.9%)

Results

922.0ms	6817×	body	128	valid
254.0ms	565×	body	1024	valid
192.0ms	549×	body	512	valid
75.0ms	312×	body	256	valid
9.0ms	13×	body	2048	valid

Compiler

Compiled 52 to 38 computations (26.9% saved)

preprocess28.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

718×	`fma-def_binary64`
450×	`distribute-rgt-in_binary64`
422×	`distribute-lft-in_binary64`
275×	`associate-l_binary64`
248×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	29	26
2	62	26
3	136	26
4	395	26
5	1607	26
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify21.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

436×	`unswap-sqr_binary64`
376×	`fma-def_binary64`
252×	`distribute-rgt-neg-in_binary64`
235×	`distribute-rgt-in_binary64`
219×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	38	13
3	80	13
4	228	13
5	912	13
6	2927	13

Stop Event

1×	node limit

Counts

1 → 1

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

6.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	6.7b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))

Compiler

Compiled 33 to 24 computations (27.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 x eps) 5)
✓	1.1b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))

series27.0ms (0.6%)

Counts

2 → 48

Calls

12 calls:

5.0ms	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))	x	0
3.0ms	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))	eps	0
3.0ms	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))	x	-inf
2.0ms	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))	x	inf
2.0ms	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))	eps	-inf

rewrite59.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

907×	`prod-diff_binary64`
171×	`expm1-udef_binary64`
171×	`log1p-udef_binary64`
101×	`add-sqr-sqrt_binary64`
98×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	190	20
2	2667	20

Stop Event

1×	node limit

Counts

2 → 87

simplify77.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

849×	`distribute-lft-out_binary64`
481×	`*-commutative_binary64`
377×	`distribute-rgt-out_binary64`
345×	`associate-+l+_binary64`
323×	`fma-def_binary64`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	39	1152
1	125	1083
2	360	1062
3	1317	993
4	2443	972
5	3481	972
6	4326	960
7	4967	960

Stop Event

1×	node limit

Counts

135 → 109

prune126.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	6	110

Error

0.0b

Counts

110 → 6

Alt Table

Status	Error	Program
	11.9b	(.f64 eps (+.f64 (.f64 (.f64 5 x) (+.f64 (pow.f64 eps 3) (pow.f64 x 3))) (.f64 (.f64 eps 10) (.f64 x (*.f64 x (+.f64 eps x))))))
	11.9b	(+.f64 (.f64 5 (.f64 eps (pow.f64 x 4))) (+.f64 (.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2))) (+.f64 (.f64 5 (.f64 (pow.f64 eps 4) x)) (.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
	11.9b	(.f64 eps (+.f64 (.f64 5 (pow.f64 x 4)) (.f64 10 (.f64 eps (.f64 x (.f64 x (+.f64 eps x)))))))
✓	6.7b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))
	56.9b	(.f64 (-.f64 (pow.f64 (+.f64 x eps) 15) (pow.f64 x 15)) (/.f64 1 (+.f64 (pow.f64 (+.f64 x eps) 10) (+.f64 (pow.f64 x 10) (pow.f64 (.f64 (+.f64 x eps) x) 5)))))
▶	6.9b	(*.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) (pow.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) 2))

Compiler

Compiled 2632 to 1706 computations (35.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) (pow.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) 2))
✓	0.2b	(pow.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) 2)
	1.1b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))
✓	19.1b	(cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5)))

series94.0ms (2.1%)

Counts

3 → 32

Calls

18 calls:

10.0ms	(pow.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) 2)	x	0
8.0ms	(pow.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) 2)	eps	inf
7.0ms	(pow.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) 2)	x	inf
7.0ms	(pow.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) 2)	x	-inf
7.0ms	(cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5)))	x	0

rewrite58.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

907×	`prod-diff_binary64`
127×	`add-sqr-sqrt_binary64`
123×	`pow1_binary64`
122×	`add-log-exp_binary64`
122×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	272	46
2	3263	46

Stop Event

1×	node limit

Counts

3 → 110

simplify35.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

721×	`fma-def_binary64`
671×	`associate-l_binary64`
664×	`associate-r_binary64`
300×	`associate-+l+_binary64`
196×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	1075
1	370	1043
2	1278	1014

Stop Event

1×	node limit

Counts

142 → 141

prune641.0ms (14.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	345	1	346
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	345	7	352

Error

0.0b

Counts

352 → 7

Alt Table

Status	Error	Program
	11.9b	(.f64 eps (+.f64 (.f64 (.f64 5 x) (+.f64 (pow.f64 eps 3) (pow.f64 x 3))) (.f64 (.f64 eps 10) (.f64 x (*.f64 x (+.f64 eps x))))))
	11.9b	(+.f64 (.f64 5 (.f64 eps (pow.f64 x 4))) (+.f64 (.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2))) (+.f64 (.f64 5 (.f64 (pow.f64 eps 4) x)) (.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
	11.9b	(.f64 eps (+.f64 (.f64 5 (pow.f64 x 4)) (.f64 10 (.f64 eps (.f64 x (.f64 x (+.f64 eps x)))))))
✓	6.7b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))
▶	7.1b	(*.f64 (cbrt.f64 (+.f64 (fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x eps)) 2) 5) (pow.f64 (cbrt.f64 (+.f64 x eps)) 5) (neg.f64 (pow.f64 x 5))) (fma.f64 -1 (pow.f64 x 5) (pow.f64 x 5)))) (pow.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) 2))
	56.9b	(.f64 (-.f64 (pow.f64 (+.f64 x eps) 15) (pow.f64 x 15)) (/.f64 1 (+.f64 (pow.f64 (+.f64 x eps) 10) (+.f64 (pow.f64 x 10) (pow.f64 (.f64 (+.f64 x eps) x) 5)))))
✓	6.9b	(*.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) (pow.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) 2))

Compiler

Compiled 11827 to 7985 computations (32.5% saved)

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.1b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))
✓	10.1b	(fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x eps)) 2) 5) (pow.f64 (cbrt.f64 (+.f64 x eps)) 5) (neg.f64 (pow.f64 x 5)))
	19.1b	(cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5)))
✓	29.4b	(cbrt.f64 (+.f64 (fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x eps)) 2) 5) (pow.f64 (cbrt.f64 (+.f64 x eps)) 5) (neg.f64 (pow.f64 x 5))) (fma.f64 -1 (pow.f64 x 5) (pow.f64 x 5))))

series310.0ms (7%)

Counts

2 → 32

Calls

12 calls:

90.0ms	(cbrt.f64 (+.f64 (fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x eps)) 2) 5) (pow.f64 (cbrt.f64 (+.f64 x eps)) 5) (neg.f64 (pow.f64 x 5))) (fma.f64 -1 (pow.f64 x 5) (pow.f64 x 5))))	eps	inf
75.0ms	(cbrt.f64 (+.f64 (fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x eps)) 2) 5) (pow.f64 (cbrt.f64 (+.f64 x eps)) 5) (neg.f64 (pow.f64 x 5))) (fma.f64 -1 (pow.f64 x 5) (pow.f64 x 5))))	eps	-inf
65.0ms	(cbrt.f64 (+.f64 (fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x eps)) 2) 5) (pow.f64 (cbrt.f64 (+.f64 x eps)) 5) (neg.f64 (pow.f64 x 5))) (fma.f64 -1 (pow.f64 x 5) (pow.f64 x 5))))	eps	0
19.0ms	(fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x eps)) 2) 5) (pow.f64 (cbrt.f64 (+.f64 x eps)) 5) (neg.f64 (pow.f64 x 5)))	eps	0
17.0ms	(cbrt.f64 (+.f64 (fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x eps)) 2) 5) (pow.f64 (cbrt.f64 (+.f64 x eps)) 5) (neg.f64 (pow.f64 x 5))) (fma.f64 -1 (pow.f64 x 5) (pow.f64 x 5))))	x	0

rewrite56.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

279×	`log1p-udef_binary64`
182×	`add-sqr-sqrt_binary64`
176×	`pow1_binary64`
172×	`*-un-lft-identity_binary64`
172×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	67
1	372	37
2	4647	37

Stop Event

1×	node limit

Counts

2 → 48

simplify42.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

668×	`unswap-sqr_binary64`
548×	`fma-def_binary64`
495×	`associate-l_binary64`
484×	`fma-neg_binary64`
482×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	707
1	300	694
2	971	676
3	4194	673

Stop Event

1×	node limit

Counts

80 → 75

prune415.0ms (9.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	194	7	201

Error

0.0b

Counts

201 → 7

Alt Table

Status	Error	Program
▶	11.9b	(.f64 eps (+.f64 (.f64 (.f64 5 x) (+.f64 (pow.f64 eps 3) (pow.f64 x 3))) (.f64 (.f64 eps 10) (.f64 x (*.f64 x (+.f64 eps x))))))
	11.9b	(+.f64 (.f64 5 (.f64 eps (pow.f64 x 4))) (+.f64 (.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2))) (+.f64 (.f64 5 (.f64 (pow.f64 eps 4) x)) (.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
	11.9b	(.f64 eps (+.f64 (.f64 5 (pow.f64 x 4)) (.f64 10 (.f64 eps (.f64 x (.f64 x (+.f64 eps x)))))))
✓	6.7b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))
✓	7.1b	(*.f64 (cbrt.f64 (+.f64 (fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x eps)) 2) 5) (pow.f64 (cbrt.f64 (+.f64 x eps)) 5) (neg.f64 (pow.f64 x 5))) (fma.f64 -1 (pow.f64 x 5) (pow.f64 x 5)))) (pow.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) 2))
	56.9b	(.f64 (-.f64 (pow.f64 (+.f64 x eps) 15) (pow.f64 x 15)) (/.f64 1 (+.f64 (pow.f64 (+.f64 x eps) 10) (+.f64 (pow.f64 x 10) (pow.f64 (.f64 (+.f64 x eps) x) 5)))))
✓	6.9b	(*.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) (pow.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) 2))

Compiler

Compiled 9891 to 6778 computations (31.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 eps 10) (.f64 x (.f64 x (+.f64 eps x))))
✓	0.1b	(.f64 eps (+.f64 (.f64 (.f64 5 x) (+.f64 (pow.f64 eps 3) (pow.f64 x 3))) (.f64 (.f64 eps 10) (.f64 x (*.f64 x (+.f64 eps x))))))
✓	0.1b	(.f64 x (.f64 x (+.f64 eps x)))
✓	0.1b	(.f64 (.f64 5 x) (+.f64 (pow.f64 eps 3) (pow.f64 x 3)))

series59.0ms (1.3%)

Counts

4 → 96

Calls

24 calls:

6.0ms	(.f64 (.f64 eps 10) (.f64 x (.f64 x (+.f64 eps x))))	eps	-inf
5.0ms	(.f64 x (.f64 x (+.f64 eps x)))	eps	inf
3.0ms	(.f64 eps (+.f64 (.f64 (.f64 5 x) (+.f64 (pow.f64 eps 3) (pow.f64 x 3))) (.f64 (.f64 eps 10) (.f64 x (*.f64 x (+.f64 eps x))))))	eps	0
3.0ms	(.f64 (.f64 eps 10) (.f64 x (.f64 x (+.f64 eps x))))	eps	inf
3.0ms	(.f64 (.f64 eps 10) (.f64 x (.f64 x (+.f64 eps x))))	eps	0

rewrite37.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

208×	`add-sqr-sqrt_binary64`
202×	`pow1_binary64`
200×	`*-un-lft-identity_binary64`
196×	`add-log-exp_binary64`
196×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	77
1	425	77

Stop Event

1×	node limit

Counts

4 → 72

simplify101.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

666×	`distribute-lft-out_binary64`
446×	`distribute-rgt-in_binary64`
364×	`distribute-rgt-out_binary64`
334×	`*-commutative_binary64`
276×	`unswap-sqr_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	40	1722
1	122	1653
2	352	1476
3	1336	1455
4	2557	1425
5	3107	1419
6	3718	1419
7	4254	1419
8	4821	1419

Stop Event

1×	node limit

Counts

168 → 101

prune141.0ms (3.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	1	2	3
Picked	1	0	1
Done	0	3	3
Total	101	7	108

Error

0.0b

Counts

108 → 7

Alt Table

Status	Error	Program
	11.9b	(+.f64 (.f64 5 (.f64 eps (pow.f64 x 4))) (+.f64 (.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2))) (+.f64 (.f64 5 (.f64 (pow.f64 eps 4) x)) (.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
	11.9b	(.f64 eps (.f64 x (+.f64 (.f64 x (.f64 (.f64 eps 10) (+.f64 eps x))) (.f64 5 (+.f64 (pow.f64 eps 3) (pow.f64 x 3))))))
✓	6.7b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))
✓	7.1b	(*.f64 (cbrt.f64 (+.f64 (fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x eps)) 2) 5) (pow.f64 (cbrt.f64 (+.f64 x eps)) 5) (neg.f64 (pow.f64 x 5))) (fma.f64 -1 (pow.f64 x 5) (pow.f64 x 5)))) (pow.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) 2))
	56.9b	(.f64 (-.f64 (pow.f64 (+.f64 x eps) 15) (pow.f64 x 15)) (/.f64 1 (+.f64 (pow.f64 (+.f64 x eps) 10) (+.f64 (pow.f64 x 10) (pow.f64 (.f64 (+.f64 x eps) x) 5)))))
✓	6.9b	(*.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) (pow.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))) 2))
	12.0b	(.f64 eps (+.f64 (expm1.f64 (log1p.f64 (.f64 5 (.f64 x (+.f64 (pow.f64 eps 3) (pow.f64 x 3)))))) (.f64 (.f64 eps 10) (.f64 x (*.f64 x (+.f64 eps x))))))

Compiler

Compiled 3250 to 1949 computations (40% saved)

regimes409.0ms (9.2%)

Accuracy

Total 0.8b remaining (96.5%)

Threshold costs 0.8b (96.5%)

Counts

78 → 3

Compiler

Compiled 6178 to 4358 computations (29.5% saved)

bsearch4.0ms (0.1%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))
0.0ms	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))

Steps

Iters	Point		Range
0.0	∈ [	0.0	,	3.6e-322	]
-1.9715732985220083e-294	∈ [	-1.9715732985220083e-294	,	0.0	]

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
7×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	133
1	62	133
2	66	133
3	68	133
4	69	133

Stop Event

1×

saturated

end193.0ms (4.3%)

Stop Event

1×

fuel

Compiler

Compiled 386 to 269 computations (30.3% saved)

Details

analyze2.0ms (0%)

sample1.5s (32.9%)

preprocess28.0ms (0.6%)

simplify21.0ms (0.5%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series27.0ms (0.6%)

rewrite59.0ms (1.3%)

simplify77.0ms (1.7%)

prune126.0ms (2.8%)

localize8.0ms (0.2%)

series94.0ms (2.1%)

rewrite58.0ms (1.3%)

simplify35.0ms (0.8%)

prune641.0ms (14.4%)

localize21.0ms (0.5%)

series310.0ms (7%)

rewrite56.0ms (1.3%)

simplify42.0ms (0.9%)

prune415.0ms (9.3%)

localize15.0ms (0.3%)

series59.0ms (1.3%)

rewrite37.0ms (0.8%)

simplify101.0ms (2.3%)

prune141.0ms (3.2%)

regimes409.0ms (9.2%)

bsearch4.0ms (0.1%)

simplify5.0ms (0.1%)

end193.0ms (4.3%)

Profiling