How to calculate the ideal hit of arrow?

Question

I am trying to make the AI shoot an arrow and always hit the target. Assuming that the target is within his range I am stuck what the correct way is to do this. I search and found some solutions but they do not seem to work 100% perfectly in my code (How can I shoot an arrow if I know the shot power and target?).

My code is (target is the prefab I want the AI to hit):

arrow.GetComponent<Rigidbody>().AddForce (Aim()*speed, ForceMode.VelocityChange);

private Vector3 Aim()
{
    float xAim = target.transform.position.x - transform.position.x;

    float yAim = Mathf.Rad2Deg * Mathf.Atan((speed*speed + Mathf.Sqrt(speed*speed*speed*speed) - (-Physics.gravity.y) * (-Physics.gravity.y * HorizontalDistance()*HorizontalDistance()) + 2 * VerticalDistance() * speed*speed / -Physics.gravity.y * HorizontalDistance()));
    float zAim = target.transform.position.z - transform.position.z;
    Vector3 aim = new Vector3(xAim, yAim, zAim).normalized;     
    return aim;
}
private float HorizontalDistance()
{
    float xDistance = target.transform.position.x - transform.position.x;

   // float zDistance = target.transform.position.z - transform.position.z;
    float distance = Mathf.Sqrt(xDistance*xDistance);// + (zDistance*zDistance));

    return distance;
}
private float VerticalDistance()
{
    return Mathf.Abs(target.transform.position.y - transform.position.y);
}

Answer 1

Thanks wondra, solved the issue by splitting everything and to translate the formula to C#:

where posX and posY is the target x and y where g is de phycics gravity where speed is the value I want to fill in.

Now I have the angleZ to put in my arrow Vector3

float s = Mathf.Sqrt((speed * speed * speed * speed) - g * (g * (posX * posX) + 2 * posY * (speed * speed)));
float angleZ = Mathf.Atan(((speed * speed) + s) / (g * posX))*Mathf.Rad2Deg;

I only still have the problem when y is not 0. The formula I now used only works if y=0. Have not found the correct formula so I can get the correct angle even when y is different from eachother.