This is not just a "lex"-like scanner as noted in perlre, but a fully recursive parser (note the calls to expr() inside some of the actions). It will properly handle multiple levels of parentheses.

The advice I would give is to instrument it up with debug prints to see what's happening, also adding a recursion level counter to track recursive calls.

It is loosely based on this expression parser I wrote a while ago:

#!/usr/bin/perl

use strict;   # mini.pl - modified Pratt parser by tybalt89
use warnings; # https://en.wikipedia.org/wiki/Pratt_parser
sub error { die "ERROR  ", s/\G/ <@_> /r, "\n" }

sub expr # two statement parser - precedences: (3 **) (2 * /) (1 + -)
  {
  my $answer =
    /\G\s* ((?:\d+(?:\.\d*)?|\.\d+)(e[+-]?\d+)?) /gcxi ? $1 :
    /\G\s*\(/gc ? (expr(0), /\G\s*\)/gc || error 'missing )')[0] :
    /\G\s* - /gcx ? -expr(3) :  # unary minus
    /\G\s* \+ /gcx ? +expr(3) :  # unary plus
    error 'bad operand';
  $answer =
    $_[0] <= 3 && /\G\s* \*\* /gcx ? $answer ** expr(3) :
    $_[0] <= 2 && /\G\s* \* /gcx   ? $answer * expr(3)  :
    $_[0] <= 2 && /\G\s* \/ /gcx   ? $answer / expr(3)  :
    $_[0] <= 1 && /\G\s* \+ /gcx   ? $answer + expr(2)  :
    $_[0] <= 1 && /\G\s* \- /gcx   ? $answer - expr(2)  :
    return $answer while 1;
  }

for ( @ARGV ? @ARGV : scalar <> ) # source as commandline args or stdi
+n
  {
  my $answer = expr(0);
  /\G\s*\z/gc ? print s/\s*\z/ = $answer\n/r : error 'incomplete parse
+';
  }
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which was also the basis for this Re: Parsing Boolean expressions

but it doesn't need the precedence stuff.