As others have pointed out, the correct code for sub2 is something like this:

sub sub2 {
  my ($self) = @_;
  $self->_sub1;
}
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In this particular case, because sub2 isn't actually doing anything, other than passing straight through to _sub1, there are a couple of other options which perform better, CPU and memory wise:

# Use goto because that automatically passes on @_ to the
# next function.
sub sub2 {
    goto \&_sub1;
}
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or:

# Just make one sub into an alias for the other...
*sub2 = \&_sub1;
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There are considerations to make regarding things like inheritance though, so while each of these are faster, the first example is in many ways "better".