Is there a standard name for this property of ordered pairs of binary operations?

Question

I know that the distributive property of ordered pairs of binary operations is well-known. However, I have thought of a new property of ordered pairs of binary operations. Let $+$ and $*$ be the binary operations on a set $S$, which are arbitrary. (So, for example, don't confuse $+$ with addition). I define $(+,*)$ to be switchable iff for all $x,y,z$ in $S$, $(x+(y*z))=((x+y)*z)$. So, for example, $(+,-)$, where $+$ represents addition on the reals and $-$ represents binary subtraction on the reals, is a switchable pair of binary operations. Also, an operation $*$ is associative iff the pair $(*,*)$ is switchable. Is there a standard name for this property? Also, has any book or paper defined this property?

Answer 1

This is an equation in the term algebra of signature $\{+, *\}$, but I don't think this specific equation has an accepted name.