I've been told, but haven't been able to verify when this change took place, that the latest versions of Perl won't recompile a regular expression using interpolation if the variable hasn't changed.

I didn't find any mention of this in perl56delta, perl561delta, the Changes file for 5.6.0, or the Changes file for 5.6.1.

However, it's easy to verify whether a given version has the optimization or not. Since at least 5.6.0,

use re 'debug';

for (1..2) {
   $re_str = $_;
   print("***** $_ *****\n");
   /$re_str/;
}

$re_str = "\\d";
for (3..4) {
   print("***** $_ *****\n");
   /$re_str/;
}
[download]

outputs

***** 1 *****
Compiling REx `1'
Guessing start of match, REx "1" against "1"...

***** 2 *****
Compiling REx `2'
Guessing start of match, REx "2" against "2"...

***** 3 *****
Compiling REx `\d'
Matching REx "\d" against "3"

***** 4 *****
Matching REx "\d" against "4"     <--- No "Compiling" before this.
[download]

(irrelevant lines omitted).

I've personally tested this with 5.6.0, 5.6.1, 5.8.0 and 5.8.8.