At the equinox I would expect the Sun to be at roughly due-east and due-west when it intersects the true horizon itself, rather than when it reaches a depth of 34 arcminutes below the horizon on each side of the sky. To reach that point of depression below the horizon, the center of the Sun will have to travel farther — which means in both cases that you are asking about a point father north and farther below the horizon than the actual points that are due east and due west.
Since we do not have access to your code itself, could you try re-running it with horizon set to zero and see if you get points closer to east and west?