Although use re 'debug'; is available, YAPE::Regex::Explain is a fair amount more detailed in its output when explaining a regex:

use warnings;
use strict;

use YAPE::Regex::Explain;

my $re = 's/ ^\w*\K\n(?=\w*\n) | ^.*\..*\K\n(?=.*\.) //mx';

print YAPE::Regex::Explain->new($re)->explain;
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Output:

The regular expression:

(?-imsx:s/ ^\w*\K\n(?=\w*\n) | ^.*\..*\K\n(?=.*\.) //mx)

matches as follows:

NODE                     EXPLANATION
----------------------------------------------------------------------
(?-imsx:                 group, but do not capture (case-sensitive)
                         (with ^ and $ matching normally) (with . not
                         matching \n) (matching whitespace and #
                         normally):
----------------------------------------------------------------------
  s/                       's/ '
----------------------------------------------------------------------
  ^                        the beginning of the string
----------------------------------------------------------------------
  \w*                      word characters (a-z, A-Z, 0-9, _) (0 or
                           more times (matching the most amount
                           possible))
----------------------------------------------------------------------
  \K                       'K'
----------------------------------------------------------------------
  \n                       '\n' (newline)
----------------------------------------------------------------------
  (?=                      look ahead to see if there is:
----------------------------------------------------------------------
    \w*                      word characters (a-z, A-Z, 0-9, _) (0 or
                             more times (matching the most amount
                             possible))
----------------------------------------------------------------------
    \n                       '\n' (newline)
----------------------------------------------------------------------
  )                        end of look-ahead
----------------------------------------------------------------------
                           ' '
----------------------------------------------------------------------
 |                        OR
----------------------------------------------------------------------
                           ' '
----------------------------------------------------------------------
  ^                        the beginning of the string
----------------------------------------------------------------------
  .*                       any character except \n (0 or more times
                           (matching the most amount possible))
----------------------------------------------------------------------
  \.                       '.'
----------------------------------------------------------------------
  .*                       any character except \n (0 or more times
                           (matching the most amount possible))
----------------------------------------------------------------------
  \K                       'K'
----------------------------------------------------------------------
  \n                       '\n' (newline)
----------------------------------------------------------------------
  (?=                      look ahead to see if there is:
----------------------------------------------------------------------
    .*                       any character except \n (0 or more times
                             (matching the most amount possible))
----------------------------------------------------------------------
    \.                       '.'
----------------------------------------------------------------------
  )                        end of look-ahead
----------------------------------------------------------------------
   //mx                    ' //mx'
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------
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For the items that still may not be clear, see perlre.