Your OP code is slow:

my %freq;
for my $i ( 1 .. @data ) {
    $freq{ $1 }[ $-[0] ] += 1/@data while $data[ $i-1 ] =~ /(.)/g;
}
[download]

For several reasons (in roughly scale of penalty):

1. It starts the regex engine for every line.
   1. Just starting the regex engine, even with a simple pattern, is expensive.
   2. I'm not sure whether that simple pattern get re-parsed each time; or if the parsing is cached, but its still parsing.
   3. It uses capture brackets, which means that not only does $1 have to be populated, but also @+, @-, $&, $`, $' and possibly %+ ...
2. It performs the same invariant calculation (1/@data) for every line.

   Moving that out of the loop and adding the invariant is simple and effective.

3. It does a completely unnecessary calculation ($i-1) for every line.

   Changing the loop parameters to for my $i ( 0 .. $#data ) avoids that repeated subtraction.

4. It indexes into @data for every line.

   Why generate a list of integers, and then use those integers to index into the array, when you can access the array elements directly?

Most of those can be avoided like this:

my $inc = 1 / @data;                                       ## do the i
+nvariant once:
for ( @data ) {                                            ## $_ alias
+es each line in turn avoids both the $i-1 and indexing the array
    $freq{ $1 }[ $-[0] ] += $inc while /(.)/g;             ## the rege
+x engine operates directly on the $_ alias.
}
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But that still incurs the penalty of the regex engine to get the chars 1 at a time. A naive alternative is ... for split //; but that still involves the regex engine, albeit in a faster mode.

The regex can be avoided completely using ... for unpack '(a1)*', $_;, but that template still requires parsing, albeit a simpler language; but the big penalty here is the construction of a long list of single chars, each in its own scalar that each require over 100 bytes of memory. That is a costly process.

Contrast that with the substr version $freq{ substr $data, $_, 1 }[ $_ ] += $inc for 0 .. length( $d )-1;. That numerical iterator costs only ~20 bytes regardless of the length of the string.

My other version trades the (fairly expensive) call to substr and the iterator, for a very cheap operation chop and an increment. And a little obscurity.

It can however be made to be the fastest of the lot with a couple of simple changes:

for( @data ) {                                 ## use $_ to alias the 
+lines
    my $p = -1;                                ## Allow pre-increment 
+which is more efficient
    $freq{ chop() }[ ++$p ] += $inc while $_;  ## implicit arg for cho
+p; avoid call to length.
}
[download]

That might see you over the 6X mark. Or not.

The chop version is wrong, it's trimming chars from the end, but counting them from zero. This fixes that:

for( @data ) {                                 ## use $_ to alias the 
+lines
    my $p = length();                          ## Allow pre-decrement 
+and count backwards
    $freq{ chop() }[ --$p ] += $inc while $p;  ## implicit arg for cho
+p; avoid call to length.
}
[download]

---

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Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

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1/@data
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substr and chop do only one thing, which means they're much faster than regex engine

Also while...=~/(.)/g; is fastest written as  for  split '',...;,

For a sea of benchmarks/topic/"explanations" about these tricks see Re: How to make this substitutions without splitting the strings? (compute not reckon)