The representation of pi with the arctan function at small values, is efficient for the calculation of pi, because many series such as the taylor series for the arctan function: $arctan(x)=x-x^3/3+x^5/5-x^7/7+x^9/9...$ converge faster, for smaller values of x, and if one has a unit fraction 1/k, they only have to calculate powers of k, sense 1 raised to any power is 1, as apposed to a non unit fraction a/b, where powers of both a, and b, have to be calculated. Sense it is also easy to multiply real numbers with integers haveing pi in the form $\pi=Karctan(1/p)+Barctan(1/q)...$ allows one to reduce the value of the argument in arctan(x), and therefore be able to use smaller values, which converge faster in many arctan series, for example although $\pi/4=arctan(1)=1-1/3+1/5-1/7+1/9..$, this series converges slowly, while $\pi/4=4(1/5-1/375+1/15625...)-(1/239-1/40955757..)$, converges much faster, thus making machin's formula more efficient.