E(X & R) = E(X)/2
E(X | R) = (E(X)+1)/2

##</code><code>##

#! /usr/bin/perl

use strict;
use warnings;

my $bits = shift;
my $den = 2**$bits;
foreach my $num (1 .. $den-1) {
        my $str = sprintf "%0${bits}b", $num;
        $str =~ s/0*$//;
        my $len = length $str;
        $str =~ s/0/R & (/g;
        $str =~ s/1/R | (/g;
        $str .= ")" x $len;
        $str =~ s/ \| \(\)//;
        $str =~ s/\(R\)/R/;
        print "E($num/$den) = $str\n";
}

##</code><code>##

E(1/32) = R & (R & (R & (R & R)))
E(2/32) = R & (R & (R & R))
E(3/32) = R & (R & (R & (R | R)))
E(4/32) = R & (R & R)
E(5/32) = R & (R & (R | (R & R)))
E(6/32) = R & (R & (R | R))
E(7/32) = R & (R & (R | (R | R)))
E(8/32) = R & R
E(9/32) = R & (R | (R & (R & R)))
E(10/32) = R & (R | (R & R))
E(11/32) = R & (R | (R & (R | R)))
E(12/32) = R & (R | R)
E(13/32) = R & (R | (R | (R & R)))
E(14/32) = R & (R | (R | R))
E(15/32) = R & (R | (R | (R | R)))
E(16/32) = R
E(17/32) = R | (R & (R & (R & R)))
E(18/32) = R | (R & (R & R))
E(19/32) = R | (R & (R & (R | R)))
E(20/32) = R | (R & R)
E(21/32) = R | (R & (R | (R & R)))
E(22/32) = R | (R & (R | R))
E(23/32) = R | (R & (R | (R | R)))
E(24/32) = R | R
E(25/32) = R | (R | (R & (R & R)))
E(26/32) = R | (R | (R & R))
E(27/32) = R | (R | (R & (R | R)))
E(28/32) = R | (R | R)
E(29/32) = R | (R | (R | (R & R)))
E(30/32) = R | (R | (R | R))
E(31/32) = R | (R | (R | (R | R)))