  In this work, we consider the properties of the two-term Machin-like formula
and develop an algorithm for computing digits of $\pi$ by using its rational
approximation. In this approximation, both terms are constructed by using a
representation of $1/\pi$ in the binary form. This approach provides the
squared convergence in computing digits of $\pi$ without any trigonometric
functions and surd numbers. The Mathematica codes showing some examples are
presented.
