Suggestions on syntax to express mathematical formula concisely

Question

I am developing functional domain specific embedded language within C++ to translate formulas into working code as concisely and accurately as possible.

I posted a proto

Answer 1

I am not sure how complicated those formulas will be, but if get to the point when your API looks more like that math domain than standard C++ (which is using operator overloading and template metaprogramming done quite easily), I would guess you should consider developing a Domain Specific Language (DSL). When you are trying to do it in a language (like in your case) it is called internal DSL and although it has some advantages, it has many disadvantages. You should know your requirements best, however I want to suggest you looking at tools for external DSLs, which are small external languages specialized for certain domain. Look at Jetbrains MPS and Eclipse Xtext, those are two open source tools, which can be used for rapid external DSL development.