Just for future reference, here's a solution (proper one), that uses XML::Rules.

use strict;
use warnings;
use XML::Rules;

my $rules =XML::Rules->new(
    style => 'parser',
    rules => {
        'inline-formula'  => sub {
            # (tag, attrs, context, parents, parser)
            open my $OUT, '>:utf8', $_[1]{id} . ".xml"; # open file na
+med after the contents of the id attribute
            print $OUT $_[4]->toXML($_[0], $_[1]); # serialize the tag
+ with attributes
            close $OUT;
        },
        '_default' => 'raw', # make sure we keep everything else intac
+t
    }
);

$rules->parse( *DATA );

__DATA__
<data>
<inline-formula id="ieqn-1"><alternatives><mml:math display="inline"><
+mml:mi>&#964;</mml:mi></mml:math></alternatives></inline-formula>

<inline-formula id="ieqn-2"><alternatives><mml:math display="inline"><
+mml:mi>&#964;</mml:mi></mml:math></alternatives></inline-formula>

<inline-formula id="ieqn-3"><alternatives><mml:math display="inline"><
+mml:mi>&#964;</mml:mi></mml:math></alternatives></inline-formula>
</data>
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