What is the first algorithm to compute digits in the decimal expansion of π?

The first algorithm to compute digits in the decimal expansion of π was developed by the mathematician William Shanks in the 19th century. However, Shanks' algorithm was later found to be flawed and produced incorrect digits after a certain point. Today, there are more advanced algorithms and methods, such as the Bailey–Borwein–Plouffe formula and the Chudnovsky algorithm, that are used to compute digits of π with high accuracy.

Machin-like formula