Term for "functions that have a closed-form expression in terms of base functions $B$"? Suppose we have a set of "basic" functions $B=\{+,-,\cdot,/,\exp,\log,\sin \}$, and we want to define: 

The set of functions $F_B$ which can be defined as $f(x)=\textit{application of elements of }B$.  

Is there a term for this? I originally thought that "algebraic functions" referred to the set $F_B$ for $B=\{+,-,\cdot,/,\text{power}_{q\in\mathbb Q}\}$, until I found out about the Abel-Ruffini theorem. 
I'd like a general natural language term for $F$. Does it exist?

I would call them $B$-based or $B$-generated functions.
