The additive Chernoff Bound says for $X_i \in \{0,1\}$ that satisfies $\mathbb{E}[X_i] = p,$ $$ \mathbb P\left(\sum_{i=1}^nX_i \geq np+n\epsilon \right) \leq \exp\left(-\frac{(n\epsilon)^2}{2(np+\frac{n\epsilon}{3})}\right) .$$ This inequality given by my advisor. I don't understand what kind of additive chernoff? I don't see anywhere in the Wikipedia.

I know only this, the additive version says that $$ \mathbb P\left(\sum_{i=1}^nX_i \geq np+n\epsilon \right) \leq e^{-2n\epsilon^2}.$$

Anybody help me how to get my advisor chernoff version.