Details

analyze1.9s (12.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
1.1%	98.6%	0.3%	12
1.9%	97.8%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 28 to 17 computations (39.3% saved)

sample97.0ms (0.6%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

128

valid

Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify93.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

765×	`sub-neg_binary64`
731×	`fma-neg_binary64`
652×	`neg-mul-1_binary64`
505×	`fma-def_binary64`
495×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	37	29
2	85	29
3	194	27
4	486	27
5	1003	27
6	1920	27
7	3406	27
8	4078	27
9	4431	27
10	4919	27
11	5085	27

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

25.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	25.2b	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))

Compiler

Compiled 96 to 51 computations (46.9% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 (+.f64 x y) z (*.f64 t a))
✓	1.0b	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
✓	23.6b	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))

series187.0ms (1.2%)

Counts

3 → 204

Calls

3 calls:

147.0ms	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))
26.0ms	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
14.0ms	(fma.f64 (+.f64 x y) z (*.f64 t a))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out_binary64`

Counts

3 → 59

Calls

3 calls:

5.0ms	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))
0.0ms	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
0.0ms	(fma.f64 (+.f64 x y) z (*.f64 t a))

simplify151.0ms (1%)

Algorithm

1×	egg-herbie

Rules

591×	`associate-/l*_binary64`
378×	`associate-/r*_binary64`
286×	`+-commutative_binary64`
241×	`associate-+r+_binary64`
237×	`associate--l+_binary64`

Counts

263 → 200

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	673	11356
1	1961	11106
2	5078	11106

prune197.0ms (1.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	189	11	200
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	190	11	201

Error

2.3b

Counts

201 → 11

Alt Table

Status	Error	Program
	25.3b	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
	43.4b	(cbrt.f64 (.f64 (.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t))) (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))) (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
▶	25.3b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
	42.3b	a
	28.1b	(-.f64 (+.f64 a z) b)
	42.3b	z
	48.4b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 y t) 3))) (+.f64 (.f64 x x) (-.f64 (.f64 (+.f64 y t) (+.f64 y t)) (*.f64 x (+.f64 y t)))))
	41.0b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
	50.2b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) 3)) (+.f64 x (+.f64 y t)))
	45.3b	(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (sqrt.f64 (+.f64 x (+.f64 y t)))) (sqrt.f64 (+.f64 x (+.f64 y t))))
	26.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t)))) (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t))))) (/.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (+.f64 (+.f64 t x) y)))

Compiler

Compiled 10707 to 3161 computations (70.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
	0.3b	(fma.f64 (+.f64 x y) z (*.f64 t a))
	1.0b	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
✓	23.7b	(/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))

series1.7s (10.7%)

Counts

2 → 144

Calls

2 calls:

1.5s	(/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))
132.0ms	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))

rewrite36.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64`
132×	`times-frac_binary64`
68×	`add-sqr-sqrt_binary64`
68×	`add-cube-cbrt_binary64`
48×	`distribute-lft-out_binary64`

Counts

2 → 141

Calls

2 calls:

7.0ms	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
5.0ms	(/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))

simplify375.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

600×	`associate-/l*_binary64`
436×	`times-frac_binary64`
336×	`fma-def_binary64`
77×	`sub-neg_binary64`
46×	`sqr-pow_binary64`

Counts

285 → 297

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2784	46779
1	5617	46779

prune623.0ms (4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	370	2	372
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	371	12	383

Error

2.3b

Counts

383 → 12

Alt Table

Status	Error	Program
	48.4b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 y t) 3))) (+.f64 (.f64 x x) (-.f64 (.f64 (+.f64 y t) (+.f64 y t)) (*.f64 x (+.f64 y t)))))
	25.4b	(/.f64 1 (.f64 (+.f64 x (+.f64 y t)) (/.f64 1 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))))))
▶	25.3b	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
	43.4b	(cbrt.f64 (.f64 (.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t))) (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))) (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
✓	25.3b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
	42.3b	a
	41.0b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
	28.2b	(/.f64 1 (/.f64 1 (-.f64 (+.f64 a z) b)))
	28.1b	(-.f64 (+.f64 a z) b)
	42.3b	z
	45.3b	(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (sqrt.f64 (+.f64 x (+.f64 y t)))) (sqrt.f64 (+.f64 x (+.f64 y t))))
	26.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t)))) (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t))))) (/.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (+.f64 (+.f64 t x) y)))

Compiler

Compiled 54814 to 20837 computations (62% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x (+.f64 y t)))
	0.3b	(fma.f64 (+.f64 x y) z (*.f64 t a))
	1.0b	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
✓	23.8b	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))

series154.0ms (1%)

Counts

2 → 108

Calls

2 calls:

127.0ms	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
27.0ms	(/.f64 1 (+.f64 x (+.f64 y t)))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
29×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
21×	`distribute-lft-out_binary64`

Counts

2 → 89

Calls

2 calls:

8.0ms	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
5.0ms	(/.f64 1 (+.f64 x (+.f64 y t)))

simplify148.0ms (1%)

Algorithm

1×	egg-herbie

Rules

671×	`associate-/l*_binary64`
456×	`associate-/r*_binary64`
306×	`+-commutative_binary64`
245×	`associate-+r+_binary64`
176×	`fma-def_binary64`

Counts

197 → 229

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	745	11101
1	2289	10838
2	5016	10838

prune222.0ms (1.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	304	0	304
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	304	12	316

Error

2.3b

Counts

316 → 12

Alt Table

Status	Error	Program
	48.4b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 y t) 3))) (+.f64 (.f64 x x) (-.f64 (.f64 (+.f64 y t) (+.f64 y t)) (*.f64 x (+.f64 y t)))))
▶	25.4b	(/.f64 1 (.f64 (+.f64 x (+.f64 y t)) (/.f64 1 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))))))
✓	25.3b	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
	43.4b	(cbrt.f64 (.f64 (.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t))) (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))) (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
✓	25.3b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
	42.3b	a
	41.0b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
	28.2b	(/.f64 1 (/.f64 1 (-.f64 (+.f64 a z) b)))
	28.1b	(-.f64 (+.f64 a z) b)
	42.3b	z
	45.3b	(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (sqrt.f64 (+.f64 x (+.f64 y t)))) (sqrt.f64 (+.f64 x (+.f64 y t))))
	26.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t)))) (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t))))) (/.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (+.f64 (+.f64 t x) y)))

Compiler

Compiled 14398 to 4568 computations (68.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(fma.f64 (+.f64 x y) z (*.f64 t a))
	1.0b	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
✓	1.4b	(/.f64 1 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))
✓	22.0b	(.f64 (+.f64 x (+.f64 y t)) (/.f64 1 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a)))))

series2.0s (13.2%)

Counts

2 → 144

Calls

2 calls:

1.5s	(.f64 (+.f64 x (+.f64 y t)) (/.f64 1 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a)))))
562.0ms	(/.f64 1 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
18×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

2 → 77

Calls

2 calls:

8.0ms	(.f64 (+.f64 x (+.f64 y t)) (/.f64 1 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a)))))
2.0ms	(/.f64 1 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))))

simplify567.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

655×	`times-frac_binary64`
485×	`fma-def_binary64`
21×	`unpow2_binary64`
11×	`cube-mult_binary64`
11×	`unpow3_binary64`

Counts

221 → 309

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3203	51683
1	4999	51683
2	4994	51683

prune818.0ms (5.3%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	384	0	384
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	384	12	396

Error

2.3b

Counts

396 → 12

Alt Table

Status	Error	Program
	48.4b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 y t) 3))) (+.f64 (.f64 x x) (-.f64 (.f64 (+.f64 y t) (+.f64 y t)) (*.f64 x (+.f64 y t)))))
✓	25.4b	(/.f64 1 (.f64 (+.f64 x (+.f64 y t)) (/.f64 1 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))))))
✓	25.3b	(.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (/.f64 1 (+.f64 x (+.f64 y t))))
	43.4b	(cbrt.f64 (.f64 (.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t))) (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))) (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
✓	25.3b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))))
	42.3b	a
	41.0b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
	28.2b	(/.f64 1 (/.f64 1 (-.f64 (+.f64 a z) b)))
	28.1b	(-.f64 (+.f64 a z) b)
	42.3b	z
	45.3b	(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (sqrt.f64 (+.f64 x (+.f64 y t)))) (sqrt.f64 (+.f64 x (+.f64 y t))))
	26.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t)))) (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t))))) (/.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (+.f64 (+.f64 t x) y)))

Compiler

Compiled 67895 to 27999 computations (58.8% saved)

regimes5.0s (32.6%)

Accuracy

Total 4.4b remaining (59.1%)

Threshold costs 0b (0%)

Counts

228 → 3

Compiler

Compiled 44350 to 25395 computations (42.7% saved)

bsearch9.0ms (0.1%)

Compiler: Compiled 27 to 16 computations (40.7% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
6×	`*-commutative_binary64`
5×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	112
1	45	112
2	57	112
3	63	112
4	66	112
5	66	112

end1.0ms (0%)

Compiler: Compiled 81 to 25 computations (69.1% saved)

sample1.0s (6.6%)

Algorithm

1×

intervals

Results

538.0ms	7999×	body	128	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 457 to 215 computations (53% saved)

Details

analyze1.9s (12.3%)

sample97.0ms (0.6%)

simplify93.0ms (0.6%)

prune4.0ms (0%)

localize16.0ms (0.1%)

series187.0ms (1.2%)

rewrite12.0ms (0.1%)

simplify151.0ms (1%)

prune197.0ms (1.3%)

localize14.0ms (0.1%)

series1.7s (10.7%)

rewrite36.0ms (0.2%)

simplify375.0ms (2.4%)

prune623.0ms (4%)

localize12.0ms (0.1%)

series154.0ms (1%)

rewrite20.0ms (0.1%)

simplify148.0ms (1%)

prune222.0ms (1.4%)

localize13.0ms (0.1%)

series2.0s (13.2%)

rewrite16.0ms (0.1%)

simplify567.0ms (3.7%)

prune818.0ms (5.3%)

regimes5.0s (32.6%)

bsearch9.0ms (0.1%)

simplify5.0ms (0%)

end1.0ms (0%)

sample1.0s (6.6%)

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