[Malleys]

function goldenRatioMinimum(fn, a, b, ε) {
	ε = ε || 1e-8;

	var φ = (-1 + Math.sqrt(5)) / 2;

	var x1 = a + (1 - φ) * (b - a);
	var x2 = b - (1 - φ) * (b - a);

	var A = fn(x1);
	var B = fn(x2);

	while(b - a > ε) {
		if(A < B) {
			b = x2;
			x2 = x1;
			B = A;
			x1 = a + (1 - φ) * (b - a);
			A = fn(x1);
		} else {
			a = x1;
			x1 = x2;
			A = B;
			x2 = b - (1 - φ) * (b - a);
			B = fn(x2);
		}
	}

	var x = (a + b) / 2;
	x = Math.abs(x) < 1e-6 ? 0 : x;

	return {
		x: x,
		y: fn(x)
	}
}

// Пример
var result = goldenRatioMinimum(function(x) { return x * x - 4 }, 0, 1);
alert("Минимум функции f(x) = x² - 4 на отрезке [-1; 1] находится в точке x = " + result.x + " и f(" + result.x + ") = " + result.y);