Variables not updating in recursive descent parser

I'm writing a recursive descent parser that recognizes this language:

<expr> ::= <term> | <term> "+" <expr> | <variable> "=" <expr>
<term> ::= <factor> | <term> "*" <factor>
<factor> ::= <constant> | <variable> | "(" <expr> ")"
<variable> ::= "x" | "y" | "z"
<constant> ::= <digit> | <digit> <constant>
<digit> ::= "0"|"1"|"2"|"3"|"4"|"5"|"6"|"7"|"8"|"9"

I'm assigning a variable a value works, but when I try to assign a variable to an expression containing a variable, it assigns the value 0 to both variables.

For example, I have an input expression y=3+3, which does indeed evaluate to y=6. If I try to write x=y+1, both x and y go to 0. I have a std::map<char, double> vars = {{'x', 0}, {'y', 0}, {'z', 0}};

My parse tree for x=y+1 should be

                           <expr>
                         /    |    \
                      <var>  '='   <expr>
                       /           /  |  \
                   vars['x']  <term> '+'  <expr>
                                |           |
                              <fact>      <term>
                                |           |
                              <var>       <fact>
                                |           |
                              vars['y']   <cons>
                                            |
                                          <digit>
                                            |
                                            1

To save from posting a lot of code, it can be found on my GitHub.

If needed, I can post my code, but it's over 300 lines of code. How can I fix this assignment?

Thanks, erip