Details

analyze3.6s

Algorithm

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%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
1.2%	98.6%	0.2%	11
1.4%	98.4%	0.2%	12
10.8%	88.9%	0.2%	13
10.8%	88.9%	0.2%	14

sample285.0ms

Algorithm

intervals

Results

175.0ms	100×	body	1280	valid
60.0ms	56×	body	640	valid
15.0ms	22×	body	320	valid
12.0ms	64×	body	80	valid
6.0ms	14×	body	160	valid

simplify76.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	464	55
1	464	55

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 0.1b

Counts

2 → 1

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 theta) (sin.f64 delta))
0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.4b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
4×	`insert-posit16`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sin-mult_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `asin-acos_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64`

Counts

4 → 61

Calls

4 calls:

7.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
7.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
2.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
5.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))

series214.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
54.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
52.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
58.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	49	9
1	49	9
0	49	9
1	49	9
0	1	3
1	1	3
0	55	9
1	55	9
0	55	9
1	55	9
0	1	3
1	1	3
0	88	9
1	88	9
0	88	9
1	88	9
0	1	3
1	1	3

simplify172.0ms

Counts

73 → 73

Iterations

Useful iterations: 0 (140.0ms)

Iter	Nodes	Cost
0	5288	1916

prune127.0ms

Filtered

58 candidates to 73 candidates (-25.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	65	8	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	8	74

Merged error: 0.0b

Counts

74 → 8

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.3b	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.4b	(pow.f64 (cos.f64 delta) 3)
0.4b	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
6×	`pow-unpow_binary64`
4×	`add-log-exp_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `insert-posit16`
3×	`pow-pow_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`
2×	`pow-to-exp_binary64` `asin-acos_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `cube-div_binary64` `prod-exp_binary64` `sin-mult_binary64`

Counts

4 → 66

Calls

4 calls:

2.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
2.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
3.0ms	(pow.f64 (cos.f64 delta) 3)
8.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3)

series1.1s

Counts

4 → 12

Calls

4 calls:

53.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
55.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
967.0ms	(pow.f64 (cos.f64 delta) 3)
54.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	59	9
1	59	9
0	59	9
1	59	9
0	1	3
1	1	3
0	18791	9
1	18791	9
0	18791	9
1	18791	9
0	1	3
1	1	3
0	49	9
1	49	9
0	49	9
1	49	9
0	1	3
1	1	3
0	49	9
1	49	9
0	49	9
1	49	9
0	1	3
1	1	3

simplify85.0ms

Counts

78 → 78

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5157	1535

prune151.0ms

Filtered

53 candidates to 78 candidates (-47.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	79	7	86

Merged error: 0.0b

Counts

86 → 7

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3) 3)
0.4b	(pow.f64 (cos.f64 delta) 3)
0.4b	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3)
7.0b	(cbrt.f64 (pow.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3) 3))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

24×	`unpow-prod-down_binary64` `cube-prod_binary64`
22×	`cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`add-exp-log_binary64`
9×	`pow-unpow_binary64` `add-cbrt-cube_binary64` `pow-exp_binary64`
8×	`pow1_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
5×	`cube-div_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `insert-posit16`
3×	`sin-mult_binary64`
2×	`prod-exp_binary64`
1×	`cbrt-div_binary64` `pow-prod-down_binary64` `rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `pow1/3_binary64`

Counts

4 → 119

Calls

4 calls:

8.0ms	(pow.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3) 3)
3.0ms	(pow.f64 (cos.f64 delta) 3)
8.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3)
7.0ms	(cbrt.f64 (pow.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3) 3))

series1.2s

Counts

4 → 12

Calls

4 calls:

57.0ms	(pow.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3) 3)
1.1s	(pow.f64 (cos.f64 delta) 3)
56.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3)
57.0ms	(cbrt.f64 (pow.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3) 3))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	65	9
1	65	9
0	65	9
1	65	9
0	1	3
1	1	3
0	59	9
1	59	9
0	59	9
1	59	9
0	1	3
1	1	3
0	18791	9
1	18791	9
0	18791	9
1	18791	9
0	1	3
1	1	3
0	62	9
1	62	9
0	62	9
1	62	9
0	1	3
1	1	3

simplify99.0ms

Counts

131 → 131

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5781	4447

prune178.0ms

Filtered

65 candidates to 131 candidates (-101.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	131	7	138

Merged error: 0.0b

Counts

138 → 7

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.4b	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3)
0.4b	(-.f64 (cos.f64 delta) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3)))
18.6b	(cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
10×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
7×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
4×	`insert-posit16`
3×	`pow-unpow_binary64` `sqr-pow_binary64` `difference-of-squares_binary64`
2×	`pow-pow_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64` `unpow-prod-down_binary64` `sin-mult_binary64` `cube-prod_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `pow-prod-down_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `asin-acos_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 68

Calls

4 calls:

2.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
7.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3)
8.0ms	(-.f64 (cos.f64 delta) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3)))
4.0ms	(cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3))

series220.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
55.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3)
55.0ms	(-.f64 (cos.f64 delta) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3)))
54.0ms	(cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	62	9
1	62	9
0	62	9
1	62	9
0	1	3
1	1	3
0	74	9
1	74	9
0	74	9
1	74	9
0	1	3
1	1	3
0	59	9
1	59	9
0	59	9
1	59	9
0	1	3
1	1	3
0	49	9
1	49	9
0	49	9
1	49	9
0	1	3
1	1	3

simplify153.0ms

Counts

80 → 80

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	5084	2832

prune85.0ms

Filtered

60 candidates to 80 candidates (-33.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	80	7	87

Merged error: 0.0b

Counts

87 → 7

regimes156.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	54	149
1	54	149

end0.0ms

sample9.0s

Algorithm

intervals

Results

5.7s	3135×	body	1280	valid
1.9s	1830×	body	640	valid
504.0ms	730×	body	320	valid
385.0ms	1974×	body	80	valid
151.0ms	331×	body	160	valid

Iter	Nodes	Cost
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	49	9
1	49	9
0	49	9
1	49	9
0	1	3
1	1	3
0	55	9
1	55	9
0	55	9
1	55	9
0	1	3
1	1	3
0	88	9
1	88	9
0	88	9
1	88	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	62	9
1	62	9
0	62	9
1	62	9
0	1	3
1	1	3
0	74	9
1	74	9
0	74	9
1	74	9
0	1	3
1	1	3
0	59	9
1	59	9
0	59	9
1	59	9
0	1	3
1	1	3
0	49	9
1	49	9
0	49	9
1	49	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	49	9
1	49	9
0	49	9
1	49	9
0	1	3
1	1	3
0	55	9
1	55	9
0	55	9
1	55	9
0	1	3
1	1	3
0	88	9
1	88	9
0	88	9
1	88	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	62	9
1	62	9
0	62	9
1	62	9
0	1	3
1	1	3
0	74	9
1	74	9
0	74	9
1	74	9
0	1	3
1	1	3
0	59	9
1	59	9
0	59	9
1	59	9
0	1	3
1	1	3
0	49	9
1	49	9
0	49	9
1	49	9
0	1	3
1	1	3

Details

analyze3.6s

sample285.0ms

simplify76.0ms

prune5.0ms

localize37.0ms

rewrite23.0ms

series214.0ms

simplify172.0ms

prune127.0ms

localize45.0ms

rewrite17.0ms

series1.1s

simplify85.0ms

prune151.0ms

localize53.0ms

rewrite30.0ms

series1.2s

simplify99.0ms

prune178.0ms

localize33.0ms

rewrite23.0ms

series220.0ms

simplify153.0ms

prune85.0ms

regimes156.0ms

bsearch0.0ms

simplify7.0ms

end0.0ms

sample9.0s

Profiling

Iter	Nodes	Cost
0	67	9
1	67	9
0	67	9
1	67	9
0	1	3
1	1	3
0	49	9
1	49	9
0	49	9
1	49	9
0	1	3
1	1	3
0	55	9
1	55	9
0	55	9
1	55	9
0	1	3
1	1	3
0	88	9
1	88	9
0	88	9
1	88	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	62	9
1	62	9
0	62	9
1	62	9
0	1	3
1	1	3
0	74	9
1	74	9
0	74	9
1	74	9
0	1	3
1	1	3
0	59	9
1	59	9
0	59	9
1	59	9
0	1	3
1	1	3
0	49	9
1	49	9
0	49	9
1	49	9
0	1	3
1	1	3