To add a little more context than Hippo's answer: Because you have a variable substitution on the pattern, perl can't pre-compile the regex and so each time it hits that line it performs two regex compiles and two regex comparisons. While in this case "index" will be the ideal approach, if you ever have a similar case where you do need a regex, I recommend this:

if ($subpath =~ m:^\Q$target\E(/|$):) {
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The \Q and \E perform escaping of the $target so that regex special characters in $target don't get interpreted as regex structure, I used m:...: instead of /.../ because you have a literal / in the pattern and this way you don't need to escape it, and the alternation ending of / or $ lets you match with a single regex.