Build me a compiler

My request is to make a compiler that transforms an expression like "add(5, mul(3, sub(10, pow(6, 4))))", in a equivalent mathematical expression, "5 + 3 * (10 - 6^4)" in this case. Functions: add(x, y) (addition), sub(x, y) (subtraction), mul(x, y) (multiplication), div(x, y) (division), mod(x, y) (modulo), pow (x, y) (power), where x, y are operands Operand: a number conforming to the following grammar: <number> ::= <optional-sign> <digit-sequence> <optional-fraction> <optional-exponent> <optional-sign> ::= "" | "+" | "-" <optional-fraction> ::= "" | "." <digit-sequence> <optional-exponent> ::= "" | "e" <optional-sign> <digit-sequence> <digit-sequence> ::= <digit> | <digit> <digit-sequence> <digit> ::= "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" Other elements: brackets ( and ) and whitespace (in the evaluated expression, there can be any number of whitespace characters, like spaces) Desired result: A mathematical expression equivalent to the specified composition of functions. Make sure the order of operation application stays the same. Unnecessary brackets should be omitted. The operator precedence has three levels, from lowest to highest: 1: +, - 2: *, /, % 3: ^ The ^ operator is right associative, other operators are left associative. Implementation language: C, C++ or Java For lexical analysis, use regular expressions and finite automata; for syntax analysis, use context-free grammars and precedence-based parsing ALL PARTS OF THE CODE MUST BE LARGELY COMMENTED!