Newton's method

newton.js

// Newton's method as explained here: https://youtu.be/U0xlKuFqCuI?t=290
// To be used in the console of http://linalg.novidee.com or any environment with mathjs

function deriv(fcode, a, step = 0.01) {
  return (fcode.eval({ x: a + step }) - fcode.eval({ x: a })) / step;
}

function newton(f, precision, seed = 0) {
  const fcode = math.parse(f).compile();

  // This is not optimal as we evaluate twice the function at seed here and in deriv
  const fa = fcode.eval({ x: seed });
  const dfdx = deriv(fcode, seed);

  const res = -fa / dfdx + seed;
  if (Math.abs(fcode.eval({ x: res })) > precision) {
    return newton(f, precision, res);
  }
  return res;
}