Use of DSLs and tools like flex and bison makes the implementation a whole lot more reliable (but only if they're used, and some commonly run languages have a very implementation-specific grammar).

consider:

    input:    /* empty string */
            | input line
    ;
    
    line:     '\n'
            | exp '\n'  { printf ("\t%.10g\n", $1); }
    ;
    
    exp:      NUM                { $$ = $1;         }
            | exp '+' exp        { $$ = $1 + $3;    }
            | exp '-' exp        { $$ = $1 - $3;    }
            | exp '*' exp        { $$ = $1 * $3;    }
            | exp '/' exp        { $$ = $1 / $3;    }
            | '-' exp  %prec NEG { $$ = -$2;        }
            | exp '^' exp        { $$ = pow ($1, $3); }
            | '(' exp ')'        { $$ = $2;         }
    ;

http://dinosaur.compilertools.net/bison/bison_5.html#SEC27