To go from ε-DP to ρ-zCDP, we can use the optimal formula proven here instead of the one from the original Bun & Steinke paper.

To go from ρ-zCDP to (ε,δ)-DP, there are better formulas than the one we use; getting an optimal conversion however is likely to be a huge pain, see details inside the "more info" thingy in this blog post.