Greetings tybalt89

I wanted to see if I could make yours work with mine, and with a minor tweak, I did. I prefer to use assignment with s///, as in:

   (my $tybalt89 = $str) =~ s/...

You did not; to each his own, but to make yours work in my preferred model I removed the /r from the outer regex expression. Once I did that I was able to replace my CODE statement with yours, as a drop-in. I teach math to undergrads with Perl, Python and R, and I have to be able to answer their questions, so I had to understand exactly what is going on here. I also added an extra digit, to see multiple ',' insertions and put the real number into a string. TMTOWTDI, works great, as in:

use 5.20.0;
use strict;

my $n = 4;
my $raw  = (1234567.56567);
my $orig = (1234567.56567 * $n);
say "raw real number:   $raw";
say "factored real nbr: $orig";
my $str = "This is a real number ${\($raw * $n)}.";
say $str;

(my $tybalt89 = $str) =~ s{ \d+ }{ $& =~ s/ \B (?= (?:\d{3})+ $ ) /,/x
+rg }xe;
say "tybalt89's with assignment and \\r tweak => \'$tybalt89\'";

(my $perlboy = (($raw) =~ s{ \d+\.?\d* }{ $& * 4 }erx )) =~ s{ \d+ }{
    $& =~ s/ (?<=\d) (?= (?:\d{3} )+ (?!\d) ) /,/xrg; }ex;
say "perlboy's => \'$perlboy\'";

(my $mixed = (($raw) =~ s{ \d+\.?\d* }{ $& * 4 }erx )) =~ s{ \d+ }{
    $& =~ s/ \B (?= (?:\d{3})+ $ ) /,/xrg }xe;
say "perboy's w/tybalt89's drop-in with \\r tweak => \'$mixed\'";

say "tybalt89's original regex, without assignment => ", ($str) =~ s{ 
+\d+ }{ $& =~ s/ \B (?= (?:\d{3})+ $ ) /,/xgr }xer;

say "tybalt89's original regex, without assignment => ", (1234567.5656
+7 * 4) =~ s{ \d+ }{ $& =~ s/ \B (?= (?:\d{3})+ $ ) /,/xgr }xer;

exit(0)
__END__
[download]

which when run yields:

   raw real number:   1234567.56567
   factored real nbr: 4938270.26268
   This is a real number 4938270.26268.
   tybalt89's with assignment and \r tweak => 'This is a real number 4,938,270.26268.'
   perlboy's => '4,938,270.26268'
   perboy's w/tybalt89's drop-in with \r tweak => '4,938,270.26268'
   tybalt89's original regex, without assignment => This is a real number 4,938,270.26268.
   tybalt89's original regex, without assignment => 4,938,270.26268

As I said, the only change to yours was to remove /r from the outer s///. To verify it would insert multiple ',', I added an extra digit and interpolated the real number into a string. So, that \B assertion works, and by removing two look-arounds, probably runs faster than mine.

UPDATE 9/17/2023

   Running timethese(-10, {...));
   Benchmark: running perlboy, tybalt89 for at least 10 CPU seconds...
   perlboy: 10 wallclock secs (10.52 usr +  0.00 sys = 10.52 CPU) @ 25551.33/s (n=268800)
  tybalt89: 11 wallclock secs (10.45 usr +  0.00 sys = 10.45 CPU) @ 27807.18/s (n=290585)

   Running cmpthese(-10, {...});
               Rate  perlboy tybalt89
   perlboy  25623/s       --      -8%
   tybalt89 27900/s       9%       --

Cheers, and happy perl-ing