Taylor Series Approximation for Pi

pi.js

const pi = (iterations=10_000_000) => {
  let π = 0.0; 

  for (let i = 0; i < iterations; i++) {
    let numerator = parseFloat(Math.pow(-1, i + 1));
    let denominator = parseFloat(((2 * i) + 1));

    π += parseFloat(numerator / denominator);

  }
  
  return {
    output: Math.abs(parseFloat(π * 4.0)),
    degrees: iterations * 2
  }
}

(() => {
  let benchmark1 = Date.now();
  let calculatedPi = pi(1_000_000_000); // number of approximations made
  let benchmark2 = Date.now();

  console.log(`Maclaurin Series for π (${calculatedPi.toString().length.toLocaleString()} digits):
  • Stored Pi: ${Math.PI}
  • Calculated Pi: ${calculatedPi.output}
  ------
  • Degrees: ${calculatedPi.degrees.toLocaleString()}
  • Approximation: ${(calculatedPi.degrees / 2).toLocaleString()} points
  • Benchmark: ${(benchmark2 - benchmark1)} ms
  • Accuracy: ${((1 - parseFloat(Math.PI - calculatedPi.output)) * 100)}%
  `);
})();

Not the most efficient, but gets the job done.

The script essentially uses the Maclaurin arctan series where x is 1 and n is the defined number in the pi() function.