(ok, yea, square root is just a specific exponent)

Small: (8 + skill_lvl * 0.2) ^ (HP / Max_HP) - (8 + skill_lvl *0.2) ^ 0.5
Medium: (12 + skill_lvl * 0.2) ^ (HP / Max_HP) - (12 + skill_lvl *0.2) ^ 0.5
Large: (16 + skill_lvl * 0.2) ^ (HP / Max_HP) - (16 + skill_lvl *0.2) ^ 0.5

The short of it is, the bonus comes out to 0 when your HP is at half or less.
And it degrades fast. According to the table, medium lv 20 starts at +12% at 100% HP, but hits +4% at 75% HP.