With trees and symbols, we can often simplify the expression with more ease when compared to the previous approach. Is there a logic towards selecting one approach over another? Maybe if the expression is reused more often, or if it is possible to simplify at all..

Why are current systems not great with vectors/3D? Are there obstacles that make generalizing to higher dimensions especially difficult?

Can Automatic differentiation be seen as a simplified, dynamic version of symbolic differentiation?

I'm also wondering why the current system is not great with vectors. Can't we just perform the same operations element-wise?

What prevents current systems from further simplifying their complex formulae?

I don't really understand this method; would you still be applying it to functions and derivatives in parallel?

How do current symbolic differentiation systems simplify expressions? It seems quite expensive to search through the entire expression tree for common subexpressions that could be pulled out or terms that could be factored since there are an exponential number of ways to arrange each expression due to commutativity and associativity rules