Details

analyze170.0ms (2.9%)

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
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 34 to 22 computations (35.3% saved)

sample76.0ms (1.3%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify60.0ms (1%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-def_binary64`
669×	`unsub-neg_binary64`
596×	`cancel-sign-sub-inv_binary64`
340×	`+-commutative_binary64`
277×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	63	40
2	170	36
3	542	36
4	1867	32
5	3281	32
6	4881	32
7	4958	32

prune5.0ms (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
▶	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Status

Error

Program

0.2b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)

▶

0.0b

(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 172 to 108 computations (37.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a -3 1)
✓	0.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
✓	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.1b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series69.0ms (1.2%)

Counts

4 → 84

Calls

4 calls:

36.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
20.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
12.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
2.0ms	(fma.f64 a -3 1)

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`fma-udef_binary64`

Counts

4 → 53

Calls

4 calls:

8.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
0.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
0.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
0.0ms	(fma.f64 a -3 1)

simplify100.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
528×	`fma-neg_binary64`
415×	`associate-+l+_binary64`
313×	`cancel-sign-sub-inv_binary64`
229×	`associate-+r+_binary64`

Counts

137 → 125

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	2754
1	318	2352
2	969	2192
3	3184	2169
4	4818	2143
5	4983	2143

prune168.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	121	6	127

Error

Counts

127 → 6

Alt Table

Status	Error	Program
	0.2b	(+.f64 (.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)
	15.2b	(+.f64 (*.f64 (pow.f64 a 3) (+.f64 4 a)) -1)
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
▶	0.0b	(+.f64 (fma.f64 4 (.f64 (.f64 (cbrt.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))) (cbrt.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))) (cbrt.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
	0.1b	(+.f64 (+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))) (pow.f64 a 4)) -1)

Compiler

Compiled 3824 to 2141 computations (44% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (.f64 b b) (fma.f64 a -3 1))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))) (cbrt.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))) (cbrt.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))))
✓	0.4b	(.f64 (cbrt.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))) (cbrt.f64 (fma.f64 a (fma.f64 a a a) (.f64 (*.f64 b b) (fma.f64 a -3 1)))))
✓	8.9b	(cbrt.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))

series351.0ms (5.9%)

Counts

3 → 72

Calls

3 calls:

242.0ms

(*.f64 (cbrt.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))) (cbrt.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))))

85.0ms

(cbrt.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))))

23.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))) (cbrt.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))))) (cbrt.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

7.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))) (cbrt.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))))) (cbrt.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))) (cbrt.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))))

1.0ms

(cbrt.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))))

simplify178.0ms (3%)

Algorithm

1×	egg-herbie

Rules

711×	`fma-def_binary64`
575×	`times-frac_binary64`
456×	`associate-/l*_binary64`
246×	`*-commutative_binary64`
166×	`+-commutative_binary64`

Counts

165 → 204

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	684	12643
1	2343	11183
2	5117	11183

prune1.2s (20.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	439	0	439
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	439	6	445

Error

Counts

445 → 6

Alt Table

Status	Error	Program
	0.2b	(+.f64 (.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)
	15.2b	(+.f64 (*.f64 (pow.f64 a 3) (+.f64 4 a)) -1)
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.0b	(+.f64 (fma.f64 4 (.f64 (.f64 (cbrt.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))) (cbrt.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))) (cbrt.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
▶	0.1b	(+.f64 (+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))) (pow.f64 a 4)) -1)

Compiler

Compiled 40966 to 25739 computations (37.2% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))) (pow.f64 a 4))
✓	0.0b	(*.f64 a (fma.f64 a 2 -12))
✓	0.0b	(fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12)))))
✓	0.7b	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))

series76.0ms (1.3%)

Counts

4 → 84

Calls

4 calls:

28.0ms	(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))) (pow.f64 a 4))
23.0ms	(fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12)))))
22.0ms	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))
3.0ms	(*.f64 a (fma.f64 a 2 -12))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`
10×	`*-un-lft-identity_binary64`

Counts

4 → 75

Calls

4 calls:

6.0ms	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))
3.0ms	(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))) (pow.f64 a 4))
3.0ms	(*.f64 a (fma.f64 a 2 -12))
0.0ms	(fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12)))))

simplify108.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

662×	`fma-neg_binary64`
633×	`associate-+l+_binary64`
400×	`*-commutative_binary64`
389×	`associate-+r+_binary64`
354×	`exp-sum_binary64`

Counts

159 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	4633
1	490	3460
2	1724	3385
3	3782	3385
4	5068	3385

prune260.0ms (4.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	2	3
Picked	1	0	1
Done	1	1	2
Total	167	4	171

Error

Counts

171 → 4

Alt Table

Status	Error	Program
	0.2b	(+.f64 (.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)
▶	0.1b	(+.f64 (+.f64 (.f64 b (.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4)))) (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (pow.f64 a 4))) -1)
	15.2b	(+.f64 (*.f64 (pow.f64 a 3) (+.f64 4 a)) -1)
✓	0.0b	(+.f64 (fma.f64 4 (.f64 (.f64 (cbrt.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))) (cbrt.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))) (cbrt.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 6353 to 4134 computations (34.9% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))
✓	0.0b	(fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (pow.f64 a 4))
✓	0.1b	(.f64 b (.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))
✓	0.1b	(*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4)))

series92.0ms (1.5%)

Counts

4 → 84

Calls

4 calls:

62.0ms	(.f64 b (.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))
17.0ms	(*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4)))
9.0ms	(fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))
4.0ms	(fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (pow.f64 a 4))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`fma-udef_binary64`

Counts

4 → 66

Calls

4 calls:

4.0ms	(.f64 b (.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))
3.0ms	(*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4)))
0.0ms	(fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))
0.0ms	(fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (pow.f64 a 4))

simplify112.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

556×	`distribute-rgt-in_binary64`
538×	`distribute-lft-in_binary64`
462×	`fma-def_binary64`
349×	`exp-prod_binary64`
266×	`*-commutative_binary64`

Counts

150 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	3357
1	299	2612
2	929	2369
3	3583	2367
4	4741	2367
5	4977	2367

prune253.0ms (4.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	128	4	132

Error

Counts

132 → 4

Alt Table

Status	Error	Program
	0.2b	(+.f64 (.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)
✓	0.1b	(+.f64 (+.f64 (.f64 b (.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4)))) (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (pow.f64 a 4))) -1)
	1.4b	(+.f64 (+.f64 (.f64 b (.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4)))) (*.f64 (pow.f64 a 3) (+.f64 4 a))) -1)
✓	0.0b	(+.f64 (fma.f64 4 (.f64 (.f64 (cbrt.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))) (cbrt.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))) (cbrt.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 4241 to 2767 computations (34.8% saved)

regimes1.5s (25%)

Accuracy

Total 0.0b remaining (49.8%)

Threshold costs 0.0b (49.8%)

Counts

190 → 1

Compiler

Compiled 31396 to 20807 computations (33.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	47
1	26	47
2	26	47

end1.0ms (0%)

Compiler: Compiled 35 to 23 computations (34.3% saved)

sample1.0s (17.6%)

Algorithm

1×

intervals

Results

675.0ms	8000×	body	128	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 234 to 144 computations (38.5% saved)

Details

analyze170.0ms (2.9%)

sample76.0ms (1.3%)

simplify60.0ms (1%)

prune5.0ms (0.1%)

localize13.0ms (0.2%)

series69.0ms (1.2%)

rewrite12.0ms (0.2%)

simplify100.0ms (1.7%)

prune168.0ms (2.8%)

localize18.0ms (0.3%)

series351.0ms (5.9%)

rewrite26.0ms (0.4%)

simplify178.0ms (3%)

prune1.2s (20.3%)

localize18.0ms (0.3%)

series76.0ms (1.3%)

rewrite17.0ms (0.3%)

simplify108.0ms (1.8%)

prune260.0ms (4.4%)

localize17.0ms (0.3%)

series92.0ms (1.5%)

rewrite10.0ms (0.2%)

simplify112.0ms (1.9%)

prune253.0ms (4.2%)

regimes1.5s (25%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.0s (17.6%)

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