Initial Query

Given this BNF-style grammar write a Python function `evaluate(str)` that evaluates the expression <expression> ::= <term> | <expression> '+' <term> | <expression> '-' <term> <term> ::= <factor> | <term> '*' <factor> | <term> '/' <factor> <factor> ::= <number> | '(' <expression> ')' | <prefix-op> <factor> <prefix-op> ::= 'sin' | 'cos' <number> ::= <digit> | <number> <digit> <digit> ::= '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9' For example you can evaluate this sin(3 + 2 * 4) - cos(15) = -0.240302

LLM Generation

Query

Given this BNF-style grammar write a Python function `evaluate(str)` that evaluates the expression <expression> ::= <term> | <expression> '+' <term> | <expression> '-' <term> <term> ::= <factor> | <term> '*' <factor> | <term> '/' <factor> <factor> ::= <number> | '(' <expression> ')' | <prefix-op> <factor> <prefix-op> ::= 'sin' | 'cos' <number> ::= <digit> | <number> <digit> <digit> ::= '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9' For example you can evaluate this sin(3 + 2 * 4) - cos(15) = -0.240302

Output

**Evaluating Mathematical Expressions** ===================================== We will implement a recursive descent parser to evaluate the given mathematical expressions. The parser will use a top-down approach to parse the input string and evaluate the expression. **Code** -------- 

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import math

def evaluate(str):
    """
    Evaluates a mathematical expression.

    Args:
        str (str): The mathematical expression to evaluate.

    Returns:
        float: The result of the evaluation.
    """
    pos = 0

    def parse_expression():
        nonlocal pos
        result = parse_term()
        while pos < len(str) and str[pos] in '+-':
            if str[pos] == '+':
                pos += 1
                result += parse_term()
            elif str[pos] == '-':
                pos += 1
                result -= parse_term()
        return result

    def parse_term():
        nonlocal pos
        result = parse_factor()
        while pos < len(str) and str[pos] in '*/':
            if str[pos] == '*':
                pos += 1
                result *= parse_factor()
            elif str[pos] == '/':
                pos += 1
                result /= parse_factor()
        return result

    def parse_factor():
        nonlocal pos
        if str[pos].isdigit():
            return parse_number()
        elif str[pos] == '(':
            pos += 1
            result = parse_expression()
            pos += 1  # consume ')'
            return result
        elif str[pos:pos+3] == 'sin':
            pos += 3
            result = math.sin(parse_factor())
            return result
        elif str[pos:pos+3] == 'cos':
            pos += 3
            result = math.cos(parse_factor())
            return result
        else:
            raise ValueError("Invalid character")

    def parse_number():
        nonlocal pos
        result = 0
        while pos < len(str) and str[pos].isdigit():
            result = result * 10 + int(str[pos])
            pos += 1
        return result

    return parse_expression()


# Example usage
if __name__ == "__main__":
    print(evaluate("sin(3 + 2 * 4) - cos(15)"))
**Explanation** --------------- * The `evaluate` function takes a string as input and returns the result of the evaluation. * The `parse_expression`, `parse_term`, and `parse_factor` functions implement the recursive descent parser. They use a `nonlocal` variable `pos` to keep track of the current position in the input string. * The `parse_number` function parses a number from the input string. * The parser uses a top-down approach, where it first tries to parse an expression, then a term, and finally a factor. * The parser supports the `sin` and `cos` prefix operators, as well as the `+`, `-`, `*`, and `/` operators. * The example usage demonstrates how to use the `evaluate` function to evaluate a mathematical expression.

Extract Code

I extracted the following code from that output: 

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import math

def evaluate(str):
    """
    Evaluates a mathematical expression.

    Args:
        str (str): The mathematical expression to evaluate.

    Returns:
        float: The result of the evaluation.
    """
    pos = 0

    def parse_expression():
        nonlocal pos
        result = parse_term()
        while pos < len(str) and str[pos] in '+-':
            if str[pos] == '+':
                pos += 1
                result += parse_term()
            elif str[pos] == '-':
                pos += 1
                result -= parse_term()
        return result

    def parse_term():
        nonlocal pos
        result = parse_factor()
        while pos < len(str) and str[pos] in '*/':
            if str[pos] == '*':
                pos += 1
                result *= parse_factor()
            elif str[pos] == '/':
                pos += 1
                result /= parse_factor()
        return result

    def parse_factor():
        nonlocal pos
        if str[pos].isdigit():
            return parse_number()
        elif str[pos] == '(':
            pos += 1
            result = parse_expression()
            pos += 1  # consume ')'
            return result
        elif str[pos:pos+3] == 'sin':
            pos += 3
            result = math.sin(parse_factor())
            return result
        elif str[pos:pos+3] == 'cos':
            pos += 3
            result = math.cos(parse_factor())
            return result
        else:
            raise ValueError("Invalid character")

    def parse_number():
        nonlocal pos
        result = 0
        while pos < len(str) and str[pos].isdigit():
            result = result * 10 + int(str[pos])
            pos += 1
        return result

    return parse_expression()


# Example usage
if __name__ == "__main__":
    print(evaluate("sin(3 + 2 * 4) - cos(15)"))

Run Code Interpreter

Running the following program: 

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import math

def evaluate(str):
    """
    Evaluates a mathematical expression.

    Args:
        str (str): The mathematical expression to evaluate.

    Returns:
        float: The result of the evaluation.
    """
    pos = 0

    def parse_expression():
        nonlocal pos
        result = parse_term()
        while pos < len(str) and str[pos] in '+-':
            if str[pos] == '+':
                pos += 1
                result += parse_term()
            elif str[pos] == '-':
                pos += 1
                result -= parse_term()
        return result

    def parse_term():
        nonlocal pos
        result = parse_factor()
        while pos < len(str) and str[pos] in '*/':
            if str[pos] == '*':
                pos += 1
                result *= parse_factor()
            elif str[pos] == '/':
                pos += 1
                result /= parse_factor()
        return result

    def parse_factor():
        nonlocal pos
        if str[pos].isdigit():
            return parse_number()
        elif str[pos] == '(':
            pos += 1
            result = parse_expression()
            pos += 1  # consume ')'
            return result
        elif str[pos:pos+3] == 'sin':
            pos += 3
            result = math.sin(parse_factor())
            return result
        elif str[pos:pos+3] == 'cos':
            pos += 3
            result = math.cos(parse_factor())
            return result
        else:
            raise ValueError("Invalid character")

    def parse_number():
        nonlocal pos
        result = 0
        while pos < len(str) and str[pos].isdigit():
            result = result * 10 + int(str[pos])
            pos += 1
        return result

    return parse_expression()


# Example usage
if __name__ == "__main__":
    print(evaluate("sin(3 + 2 * 4) - cos(15)"))





answer = round(evaluate('sin(35+2*4)-cos(15)'), 5)
expected = -0.07209
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: Traceback (most recent call last): File "/usr/src/app/main.py", line 73, in <module> print(evaluate("sin(3 + 2 * 4) - cos(15)")) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "/usr/src/app/main.py", line 68, in evaluate return parse_expression() ^^^^^^^^^^^^^^^^^^ File "/usr/src/app/main.py", line 22, in parse_expression result += parse_term() ^^^^^^^^^^^^ File "/usr/src/app/main.py", line 30, in parse_term result = parse_factor() ^^^^^^^^^^^^^^ File "/usr/src/app/main.py", line 58, in parse_factor raise ValueError("Invalid character") ValueError: Invalid character

Substring Evaluation

Testing if the previous output contains the string All tests passed: False