# 黄金分割法による極値の探索
awk '
BEGIN {
  print find_min(0, 1)
  exit 0
}
# 区間 a <= x <= b で meas(x) の極小値を探す
function find_min(a, b,  c, d, fc, fd, i, r) {
  r = (sqrt(5.0) - 1.0) * 0.5	# golden ratio
  c = r * a + (1.0 - r) * b;
  d = (1.0 - r) * a + r * b;
  fc = meas(c)
  fd = meas(d)
   for (i = 0; ((d - c) / (c + d) > eps) && i < 100; i++)  {
	if ((b - a) / (a + b) <= 5e-3)
		break	# 誤差 0.5 % 以内に追い込んで終り
#	if (fc > fd) {	# 極大値を探す場合
	if (fc < fd) {	# 極小値を探す場合
		b = d
		d = c
		fd = fc
		c = r * a + (1.0 - r) * b; fc = meas(c)
	}
	else {
		a = c
		c = d; fc = fd
		d = (1.0 - r) * a + r * b; fd = meas(d)
	}
  }
  if (i == 100)
	print "Warning: find_min() retry over." >/dev/stderr
  if (fc < fd)
	return (c + r*a + (1.0 - r)*b) * 0.5
  return (d + (1.0 - r)*a + r*b) * 0.5
}
# 変数 x に対する測定値
function meas(x) {
  return (x - 0.8)^2
}
'