perl -MYAPE::Regex::Explain -e "my $rex = qr(s/.*\/(.*).lib/$1/); print YAPE::Regex::Explain->new($rex)->explain"
The regular expression:

(?-imsx:s/.*\/(.*).lib//)

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/'
----------------------------------------------------------------------
  .*                       any character except \n (0 or more times
                           (matching the most amount possible))
----------------------------------------------------------------------
  \/                       '/'
----------------------------------------------------------------------
  (                        group and capture to \1:
----------------------------------------------------------------------
    .*                       any character except \n (0 or more times
                             (matching the most amount possible))
----------------------------------------------------------------------
  )                        end of \1
----------------------------------------------------------------------
  .                        any character except \n
----------------------------------------------------------------------
  lib//                    'lib//'
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------

##</code><code>##

perl -MYAPE::Regex::Explain -e "print YAPE::Regex::Explain->new('.*\/(.*).lib')->explain"
The regular expression:

(?-imsx:.*\/(.*).lib)

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):
----------------------------------------------------------------------
  .*                       any character except \n (0 or more times
                           (matching the most amount possible))
----------------------------------------------------------------------
  \/                       '/'
----------------------------------------------------------------------
  (                        group and capture to \1:
----------------------------------------------------------------------
    .*                       any character except \n (0 or more times
                             (matching the most amount possible))
----------------------------------------------------------------------
  )                        end of \1
----------------------------------------------------------------------
  .                        any character except \n
----------------------------------------------------------------------
  lib                      'lib'
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------