use strict;
my $str = 'y ~ 1 + a + (b | c) + (d^2) + e + (1 | f) + g
y~1+a+(b|c)+(d^2)+e+ (1|f)+g
(b | c) + y ~ 1 + a + (d^2) + e + (1 | f) + g
y ~ 1 + a + (d^2) + e + (1 | f) + g + (b | c)
(h|i) + y ~ 1 + a + (b | c) + (d^2) + e + (1 | f) + g +(j+k| m)';
my $regex = qr/^\([^|)]+\|[^)]+\) *\+ ?| \+? *\([^|)]+\|[^)]+\)/mp;
my $subst = '';
my $result = $str =~ s/$regex/$subst/rg;
print "The result of the substitution is' $result\n";
Please keep in mind that these code samples are automatically generated and are not guaranteed to work. If you find any syntax errors, feel free to submit a bug report. For a full regex reference for Perl, please visit: http://perldoc.perl.org/perlre.html