gistfile1.jl

julia> quality(x,a::Rational) = log(den(a),1/abs(x-a))

julia> function maxquality(x,n)
           Q = -Inf
           for k = 1:n
               a = rational(x,1/2^k)
               if a == x break end
               q = quality(x,a)
               if isfinite(q) && Q < q
                   Q = q
               end
           end
           return Q
       end

julia> maxquality(pi,10)
3.429288337281781

julia> median(map(x->maxquality(x,10),rand(100000)))
3.189712422680679