Building a decision tree to approximate a known function (not to learn an unknown function)
For bitstring to boolean functions, people usually build binary decision diagrams instead of decision trees to represent functions compactly. If you want to find a small BDD and are willing to sacrifice correctness on a few inputs (as your question implies) then you might want to look into approximate BDDs as studied in the following two papers:

Hinsberger, U., Kolla, R., and Kunjan, T. [1997] "Approximative Representation of boolean Functions by size controllable ROBDD's"

Ravi, K., McMillan, K.L., Shiple, T.R., and Somenzi, F. [1998] "Approximation and decomposition of binary decision diagrams"

I am not sure if there is work that generalizes this for $\mathbb{R}^d \supset \mathbb{D}  \rightarrow \{0,1\}$ functions, but I would use those papers as a starting point and do a forward-reference search.