====================
parses numbers
===================
5
---
(number)

===================
parses variables
===================
x
---
(variable)

===================
parses products
===================
x * x
---
(product (variable) (variable))

===================
parses sums
===================
x + x
---
(sum (variable) (variable))

===============================================
binds multiplication more tightly than addition
===============================================
a * b + c * d
---
(sum
    (product (variable) (variable))
    (product (variable) (variable)))

============================
parses exponents
============================
x + y * z^(a + b)
---
(sum
    (variable)
    (product
        (variable)
        (exponent
            (variable)
            (group (sum (variable) (variable))))))