class Minitest::Benchmark

def fit_logarithmic xs, ys
  n     = xs.size
  xys   = xs.zip(ys)
  slnx2 = sigma(xys) { |x, _| Math.log(x) ** 2 }
  slnx  = sigma(xys) { |x, _| Math.log(x)      }
  sylnx = sigma(xys) { |x, y| y * Math.log(x)  }
  sy    = sigma(xys) { |_, y| y                }
  c = n * slnx2 - slnx ** 2
  b = ( n * sylnx - sy * slnx ) / c
  a = (sy - b * slnx) / n
  return a, b, fit_error(xys) { |x| a + b * Math.log(x) }
end