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

#! /usr/bin/perl

...
        $str =~ s/\(R\)/R/;
        print "E($num/$den) = $str\n";
}

E(1/32) = R & (R & (R & (R & R)))
E(2/32) = R & (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)))