  We present a simple recurrent formula to generate the Machin-like expression
for calculating $\pi/4$. The method works for any denominator in the starting
term and always provides a finite decomposition. We show that the terms in the
Machin-like formula decrease so rapidly that the Lehmer's measure can be made
arbitrarily small only by selecting the first term. We introduce the concept of
the partial Machin-like formula. While the growth of the integer numbers may
quickly render the computer implementation impractical, the same reason
restricts the total contribution of the high terms. If the required precision
is known in advance, the subset of the expression may be selected to satisfy
it. We also present the Python program to compute the terms of the Machin-like
formula (full and partial), and its Lehmer's measure.
