Details

analyze2.4s (11.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	98.2%	1.8%	7
0%	92%	8%	8
0%	91.2%	8.8%	9
0.4%	89.3%	10.3%	10
7.1%	79.2%	13.6%	11
11.9%	70.2%	17.9%	12
13.8%	67.4%	18.7%	13
16.6%	63.3%	20.1%	14

Compiler

Compiled 41 to 33 computations (19.5% saved)

sample132.0ms (0.7%)

Algorithm

1×

intervals

Results

27.0ms	171×	body	128	valid
15.0ms	22×	body	2048	valid
15.0ms	22×	body	2048	nan
13.0ms	26×	body	1024	valid
13.0ms	26×	body	1024	nan
10.0ms	81×	body	128	nan
9.0ms	24×	body	512	valid
5.0ms	12×	body	512	nan
3.0ms	13×	body	256	valid
2.0ms	7×	body	256	nan

Compiler

Compiled 81 to 69 computations (14.8% saved)

simplify149.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5390	61

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

52.5b

Counts

2 → 1

Compiler

Compiled 80 to 59 computations (26.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.6b	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
13.4b	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
17.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
33.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

rewrite104.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`sqrt-div_binary64_2482`
40×	`associate-*r/_binary64_2407`
39×	`*-un-lft-identity_binary64_2465`
36×	`times-frac_binary64_2471`
35×	`add-sqr-sqrt_binary64_2487`
34×	`associate-*l/_binary64_2408`
32×	`add-cube-cbrt_binary64_2500`
25×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
24×	`frac-times_binary64_2475` `frac-sub_binary64_2474`
22×	`flip--_binary64_2440` `flip3--_binary64_2469`
20×	`associate-/l/_binary64_2412` `distribute-neg-frac_binary64_2429`
17×	`pow1_binary64_2526`
16×	`distribute-lft-neg-in_binary64_2422` `distribute-rgt-neg-in_binary64_2423`
15×	`sqrt-prod_binary64_2481`
12×	`associate-/l*_binary64_2410`
8×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
7×	`pow-prod-down_binary64_2536`
5×	`sqrt-pow1_binary64_2483`
4×	`add-log-exp_binary64_2504` `unpow-prod-down_binary64_2544` `neg-mul-1_binary64_2461`
3×	`associate-/r_binary64_2409` `associate-r_binary64_2405` `distribute-lft-out_binary64_2416` `associate-l*_binary64_2406`
2×	`pow1/2_binary64_2545` `associate-/r/_binary64_2411`
1×	`*-commutative_binary64_2396` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-sub_binary64_2470` `distribute-lft-out--_binary64_2417` `unswap-sqr_binary64_2433` `div-exp_binary64_2516` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `prod-exp_binary64_2514` `frac-2neg_binary64_2476` `distribute-frac-neg_binary64_2428` `neg-sub0_binary64_2460` `cbrt-unprod_binary64_2498`

Counts

4 → 158

Calls

4 calls:

34.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
18.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
12.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
8.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

series860.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

370.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
369.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
62.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
59.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

simplify152.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4948	11070
1	4948	11070

prune615.0ms (3.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	152	18	170
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	153	18	171

Error

45.7b

Counts

171 → 18

Compiler

Compiled 12101 to 6880 computations (43.1% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.6b	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
13.4b	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
17.6b	(.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (/.f64 1 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4)))))
33.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

rewrite113.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`sqrt-div_binary64_2482`
70×	`associate-*l/_binary64_2408`
61×	`associate-*r/_binary64_2407`
56×	`frac-times_binary64_2475`
40×	`distribute-neg-frac_binary64_2429`
37×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
36×	`frac-sub_binary64_2474`
32×	`flip--_binary64_2440` `flip3--_binary64_2469`
27×	`add-sqr-sqrt_binary64_2487`
25×	`*-un-lft-identity_binary64_2465`
19×	`pow1_binary64_2526`
18×	`associate-r_binary64_2405`
17×	`add-cube-cbrt_binary64_2500`
15×	`add-exp-log_binary64_2503` `associate-l_binary64_2406`
11×	`times-frac_binary64_2471` `add-cbrt-cube_binary64_2501`
9×	`sqrt-prod_binary64_2481`
8×	`pow-prod-down_binary64_2536`
5×	`prod-exp_binary64_2514` `sqrt-pow1_binary64_2483`
4×	`distribute-lft-neg-in_binary64_2422` `add-log-exp_binary64_2504` `distribute-rgt-neg-in_binary64_2423` `unswap-sqr_binary64_2433` `unpow-prod-down_binary64_2544`
3×	`distribute-lft-out_binary64_2416` `cbrt-unprod_binary64_2498`
2×	`*-commutative_binary64_2396` `pow1/2_binary64_2545` `div-exp_binary64_2516` `associate-/r/_binary64_2411`
1×	`rec-exp_binary64_2515` `distribute-lft-neg-out_binary64_2424` `cbrt-undiv_binary64_2499` `distribute-lft-out--_binary64_2417` `un-div-inv_binary64_2463` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `neg-mul-1_binary64_2461` `1-exp_binary64_2509`

Counts

4 → 159

Calls

4 calls:

35.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
24.0ms	(.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (/.f64 1 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4)))))
11.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
9.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

series857.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

370.0ms	(.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (/.f64 1 (-.f64 (.f64 B B) (.f64 C (*.f64 A 4)))))
358.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
70.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
59.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

simplify163.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4961	11422
1	4961	11422

prune555.0ms (2.8%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	165	6	171
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	169	20	189

Error

45.7b

Counts

189 → 20

Compiler

Compiled 12431 to 6914 computations (44.4% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

15.5b	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))))))
18.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
33.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
33.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite152.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

404×	`sqrt-div_binary64_2482`
136×	`associate-*r/_binary64_2407`
122×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
120×	`frac-times_binary64_2475`
104×	`associate-*l/_binary64_2408`
96×	`frac-sub_binary64_2474`
56×	`associate-/l/_binary64_2412` `distribute-neg-frac_binary64_2429`
45×	`flip--_binary64_2440` `flip3--_binary64_2469`
36×	`times-frac_binary64_2471`
33×	`add-sqr-sqrt_binary64_2487`
31×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
16×	`distribute-lft-neg-in_binary64_2422` `distribute-rgt-neg-in_binary64_2423` `pow1_binary64_2526`
15×	`sqrt-prod_binary64_2481`
12×	`associate-/l*_binary64_2410`
6×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow-prod-down_binary64_2536` `sqrt-pow1_binary64_2483`
4×	`add-log-exp_binary64_2504` `neg-mul-1_binary64_2461`
3×	`associate-/r*_binary64_2409` `pow1/2_binary64_2545`
2×	`rem-sqrt-square_binary64_2478` `associate-/r/_binary64_2411`
1×	`clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-sub_binary64_2470` `div-exp_binary64_2516` `div-inv_binary64_2462` `frac-2neg_binary64_2476` `distribute-frac-neg_binary64_2428` `neg-sub0_binary64_2460`

Counts

4 → 222

Calls

4 calls:

29.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
25.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

series881.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

377.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
373.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))))))
69.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
62.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify202.0ms (1%)

Algorithm

1×	egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5558	20240

prune1.4s (7.1%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	222	12	234
Fresh	6	13	19
Picked	1	0	1
Done	0	0	0
Total	229	25	254

Error

45.6b

Counts

254 → 25

Compiler

Compiled 23939 to 12804 computations (46.5% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

33.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
33.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
33.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
33.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite45.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`sqrt-prod_binary64_2481` `add-sqr-sqrt_binary64_2487`
8×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `pow1_binary64_2526` `sqrt-div_binary64_2482`
4×	`flip3-+_binary64_2468` `add-log-exp_binary64_2504` `pow1/2_binary64_2545` `flip-+_binary64_2439` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`

Counts

4 → 60

Calls

4 calls:

9.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

series279.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
71.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
69.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
63.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify76.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5058	1232

prune263.0ms (1.3%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	1	23	24
Picked	1	0	1
Done	0	0	0
Total	70	27	97

Error

45.6b

Counts

97 → 27

Compiler

Compiled 5972 to 3402 computations (43% saved)

regimes2.4s (12.1%)

Accuracy

Total 2.6b remaining (5.2%)

Threshold costs 0b (0%)

Compiler

Compiled 39802 to 25524 computations (35.9% saved)

bsearch11.0ms (0.1%)

Compiler: Compiled 40 to 32 computations (20% saved)

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	463	259
1	463	259

end0.0ms (0%)

sample8.0s (40.1%)

Algorithm

1×

intervals

Results

748.0ms	5424×	body	128	valid
492.0ms	703×	body	2048	valid
485.0ms	882×	body	1024	valid
451.0ms	831×	body	1024	nan
405.0ms	587×	body	2048	nan
360.0ms	2587×	body	128	nan
245.0ms	617×	body	512	valid
231.0ms	579×	body	512	nan
108.0ms	373×	body	256	valid
89.0ms	333×	body	256	nan
1.0ms	1×	body	4096	valid

Compiler

Compiled 6829 to 4391 computations (35.7% saved)

Details

analyze2.4s (11.9%)

sample132.0ms (0.7%)

simplify149.0ms (0.7%)

prune4.0ms (0%)

localize21.0ms (0.1%)

rewrite104.0ms (0.5%)

series860.0ms (4.3%)

simplify152.0ms (0.8%)

prune615.0ms (3.1%)

localize26.0ms (0.1%)

rewrite113.0ms (0.6%)

series857.0ms (4.3%)

simplify163.0ms (0.8%)

prune555.0ms (2.8%)

localize28.0ms (0.1%)

rewrite152.0ms (0.8%)

series881.0ms (4.4%)

simplify202.0ms (1%)

prune1.4s (7.1%)

localize34.0ms (0.2%)

rewrite45.0ms (0.2%)

series279.0ms (1.4%)

simplify76.0ms (0.4%)

prune263.0ms (1.3%)

regimes2.4s (12.1%)

bsearch11.0ms (0.1%)

simplify18.0ms (0.1%)

end0.0ms (0%)

sample8.0s (40.1%)

Profiling