An iterative method for computing π by argument reduction of the tangent function

In this work, we develop a new iterative method for computing digits of π by argument reduction of the tangent function. This method combines a modified version of the iterative formula for π with squared convergence that we found in our previous work and a leading arctangent term from the Machin-like formula. The computational test we performed shows that algorithmic implementation can provide more than 17 digits of π per increment. Mathematica codes, showing the convergence rate in computing digits of π, are presented.