def problem460():
    """


    On the Euclidean plane, an ant travels from point A(0, 1) to point B(d, 1)
       for an integer d.

       In each step, the ant at point (x[0], y[0]) chooses one of the lattice
       points (x[1], y[1]) which satisfy x[1] ≥ 0 and y[1] ≥ 1 and goes straight
       to (x[1], y[1]) at a constant velocity v. The value of v depends on y[0]
       and y[1] as follows:

         • If y[0] = y[1], the value of v equals y[0].
         • If y[0] ≠ y[1], the value of v equals (y[1] - y[0]) / (ln(y[1]) -
           ln(y[0])).

       The left image is one of the possible paths for d = 4. First the ant goes
       from A(0, 1) to P[1](1, 3) at velocity (3 - 1) / (ln(3) - ln(1)) ≈ 1.8205.
       Then the required time is sqrt(5) / 1.8205 ≈ 1.2283.
       From P[1](1, 3) to P[2](3, 3) the ant travels at velocity 3 so the
       required time is 2 / 3 ≈ 0.6667. From P[2](3, 3) to B(4, 1) the ant
       travels at velocity (1 - 3) / (ln(1) - ln(3)) ≈ 1.8205 so the required
       time is sqrt(5) / 1.8205 ≈ 1.2283.
       Thus the total required time is 1.2283 + 0.6667 + 1.2283 = 3.1233.

       The right image is another path. The total required time is calculated as
       0.98026 + 1 + 0.98026 = 2.96052. It can be shown that this is the quickest
       path for d = 4.

       Let F(d) be the total required time if the ant chooses the quickest path.
       For example, F(4) ≈ 2.960516287.
       We can verify that F(10) ≈ 4.668187834 and F(100) ≈ 9.217221972.

       Find F(10000). Give your answer rounded to nine decimal places.
    """

    pass
