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a distance less than 36 is impossible in robocode, but a correct formula should give correct result in this case. So I prefer the atan approach.

asin approach is incorrect by geometry as well.

however trigs are always expensive, so using 18 / distance is acceptable since it gives similar result.

I haven't checked it in Java but asin(positive infinity) results in positive infinity which is true for the bot width formula if we assume that the bullet starts from the robot location. The same case also happens with Traditional MEA when bullet speed is 0.

Wrong. Infinity means nothing in radians. Valid values are 0~2pi or -pi~pi or so.

An angle should never be infinty radians.

If it means nothing can't we assume that the traditional formula is completely wrong since with a bullet velocity of 0, it will return positive infinity.

Bullet velocity = 0 is another geometrical situation. But in this case, distance < 36 should still fit in to your image. Or, it must be wrong.l