Just FYI, FWIW, the .. operator has a couple of features that can replace the duplicated regex matching.

First, the value of .. isn't just FALSE or TRUE, it's also a line number relative to the start of the range. Before the start, the value is 0 (aka FALSE). When the start of the range is matched, the value is 1. this number increments until the end of the range. So, you can:

my $rln = /$start_re/ .. /$end_re/;
if $rln == 1
{
    # open output file
    next;
}
if $rln > 1
{
   print $out_fh $_;
}
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Second, when the range ends, the number has 'E0' appended. So, you can:

if rindex($rln, 'E0')
{
    close $out_fh;
    next;
}
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rindex is a simple string search that works backwards, so has much less overhead than another regex match. And appending 'E0' to a string of digits is still a valid number - numerically equal to the number without the 'E0'.