use strict;
...
sub compare {
$a =~ /(\d{2})\/(\d{2})\/(\d{4})/;
$c = $3 . $1 . $2;

$b =~ /(\d{2})\/(\d{2})\/(\d{4})/;
$c = $3 . $1 . $2;

$c <=> $d;
}
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The fact that you assign the two compound numbers to the same variable may be your issue, use warnings; would have noted this.