Does Anticavalry unit deals extra damage to Mobile Ranged units like Horse Archers?

[Lonecat Nekophrodite]

Does Anticavalry unit deals extra damage to Mobile Ranged units like Horse Archers? Is there any combat resolving calculations comparable with Melee, Light and Heavy Cavalry of the same class and same era as Horse Archers being attackers yield the same or similar damage values?
From my raw experiences, a warrior can still kill a Barbarian Horse Archer easily, dealing significant damage. Providing that warrior can corner Horse Archer AND survive a strong hit and run attacks (and earned Tortoise Promotion).