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

To evaluate the given BNF-style grammar in Python, we need to parse and evaluate mathematical expressions that may include operations like addition, subtraction, multiplication, division, and trigonometric functions `sin` and `cos`. Here's how you can define the `evaluate` function using Python's `re` module for parsing and the `math` module for trigonometric operations. Here's the implementation: 

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import re
import math

def evaluate(expression):
    def parse_expression(expression):
        tokens = tokenize(expression)
        return parse_expr(tokens, 0)[0]
    
    def tokenize(expression):
        token_specification = [
            ('NUMBER',   r'\d+(\.\d*)?'),  # Integer or decimal number
            ('PLUS',     r'\+'),           # Addition operator
            ('MINUS',    r'-'),            # Subtraction operator
            ('TIMES',    r'\*'),           # Multiplication operator
            ('DIVIDE',   r'/'),            # Division operator
            ('LPAREN',   r'\('),           # Left parenthesis
            ('RPAREN',   r'\)'),           # Right parenthesis
            ('SIN',      r'sin'),          # Sine function
            ('COS',      r'cos'),          # Cosine function
            ('WS',       r'\s+'),          # Whitespace
        ]
        
        token_regex = '|'.join('(?P<%s>%s)' % pair for pair in token_specification)
        get_token = re.compile(token_regex).match
        line = expression
        pos = 0
        tokens = []
        match = get_token(line)
        while match is not None:
            typ = match.lastgroup
            if typ != 'WS':  # Ignore whitespace
                tokens.append((typ, match.group(typ)))
            pos = match.end()
            match = get_token(line, pos)
        return tokens

    def parse_expr(tokens, pos):
        lhs, pos = parse_term(tokens, pos)
        while pos < len(tokens) and tokens[pos][0] in ('PLUS', 'MINUS'):
            op = tokens[pos][0]
            pos += 1
            rhs, pos = parse_term(tokens, pos)
            if op == 'PLUS':
                lhs += rhs
            elif op == 'MINUS':
                lhs -= rhs
        return lhs, pos

    def parse_term(tokens, pos):
        lhs, pos = parse_factor(tokens, pos)
        while pos < len(tokens) and tokens[pos][0] in ('TIMES', 'DIVIDE'):
            op = tokens[pos][0]
            pos += 1
            rhs, pos = parse_factor(tokens, pos)
            if op == 'TIMES':
                lhs *= rhs
            elif op == 'DIVIDE':
                lhs /= rhs
        return lhs, pos

    def parse_factor(tokens, pos):
        if tokens[pos][0] == 'NUMBER':
            value = float(tokens[pos][1])
            pos += 1
            return value, pos
        elif tokens[pos][0] == 'LPAREN':
            pos += 1
            value, pos = parse_expr(tokens, pos)
            if tokens[pos][0] != 'RPAREN':
                raise SyntaxError("Missing closing parenthesis")
            pos += 1
            return value, pos
        elif tokens[pos][0] in ('SIN', 'COS'):
            func = tokens[pos][0]
            pos += 1
            if tokens[pos][0] != 'LPAREN':
                raise SyntaxError("Expected '(' after " + func)
            pos += 1
            value, pos = parse_expr(tokens, pos)
            if tokens[pos][0] != 'RPAREN':
                raise SyntaxError("Missing closing parenthesis")
            pos += 1
            if func == 'SIN':
                return math.sin(value), pos
            elif func == 'COS':
                return math.cos(value), pos
        else:
            raise SyntaxError("Unexpected token: " + tokens[pos][1])

    result, pos = parse_expression(expression)
    if pos != len(expression):
        raise SyntaxError("Unexpected input at end of expression")
    return result

# Test the evaluate function
expression = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expression)
print(f"{expression} = {result:.6f}")
This code defines a `evaluate` function that can parse and evaluate the given mathematical expression using the specified BNF grammar. It uses a tokenizer to convert the input string into tokens, and then recursively parses these tokens according to the grammar rules. The result is then computed and returned. For the given example `sin(3 + 2 * 4) - cos(15)`, the function should output approximately `-0.240302`.

Extract Code

I extracted the following code from that output: 

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import re
import math

def evaluate(expression):
    def parse_expression(expression):
        tokens = tokenize(expression)
        return parse_expr(tokens, 0)[0]
    
    def tokenize(expression):
        token_specification = [
            ('NUMBER',   r'\d+(\.\d*)?'),  # Integer or decimal number
            ('PLUS',     r'\+'),           # Addition operator
            ('MINUS',    r'-'),            # Subtraction operator
            ('TIMES',    r'\*'),           # Multiplication operator
            ('DIVIDE',   r'/'),            # Division operator
            ('LPAREN',   r'\('),           # Left parenthesis
            ('RPAREN',   r'\)'),           # Right parenthesis
            ('SIN',      r'sin'),          # Sine function
            ('COS',      r'cos'),          # Cosine function
            ('WS',       r'\s+'),          # Whitespace
        ]
        
        token_regex = '|'.join('(?P<%s>%s)' % pair for pair in token_specification)
        get_token = re.compile(token_regex).match
        line = expression
        pos = 0
        tokens = []
        match = get_token(line)
        while match is not None:
            typ = match.lastgroup
            if typ != 'WS':  # Ignore whitespace
                tokens.append((typ, match.group(typ)))
            pos = match.end()
            match = get_token(line, pos)
        return tokens

    def parse_expr(tokens, pos):
        lhs, pos = parse_term(tokens, pos)
        while pos < len(tokens) and tokens[pos][0] in ('PLUS', 'MINUS'):
            op = tokens[pos][0]
            pos += 1
            rhs, pos = parse_term(tokens, pos)
            if op == 'PLUS':
                lhs += rhs
            elif op == 'MINUS':
                lhs -= rhs
        return lhs, pos

    def parse_term(tokens, pos):
        lhs, pos = parse_factor(tokens, pos)
        while pos < len(tokens) and tokens[pos][0] in ('TIMES', 'DIVIDE'):
            op = tokens[pos][0]
            pos += 1
            rhs, pos = parse_factor(tokens, pos)
            if op == 'TIMES':
                lhs *= rhs
            elif op == 'DIVIDE':
                lhs /= rhs
        return lhs, pos

    def parse_factor(tokens, pos):
        if tokens[pos][0] == 'NUMBER':
            value = float(tokens[pos][1])
            pos += 1
            return value, pos
        elif tokens[pos][0] == 'LPAREN':
            pos += 1
            value, pos = parse_expr(tokens, pos)
            if tokens[pos][0] != 'RPAREN':
                raise SyntaxError("Missing closing parenthesis")
            pos += 1
            return value, pos
        elif tokens[pos][0] in ('SIN', 'COS'):
            func = tokens[pos][0]
            pos += 1
            if tokens[pos][0] != 'LPAREN':
                raise SyntaxError("Expected '(' after " + func)
            pos += 1
            value, pos = parse_expr(tokens, pos)
            if tokens[pos][0] != 'RPAREN':
                raise SyntaxError("Missing closing parenthesis")
            pos += 1
            if func == 'SIN':
                return math.sin(value), pos
            elif func == 'COS':
                return math.cos(value), pos
        else:
            raise SyntaxError("Unexpected token: " + tokens[pos][1])

    result, pos = parse_expression(expression)
    if pos != len(expression):
        raise SyntaxError("Unexpected input at end of expression")
    return result

# Test the evaluate function
expression = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expression)
print(f"{expression} = {result:.6f}")

Run Code Interpreter

Running the following program: 

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import re
import math

def evaluate(expression):
    def parse_expression(expression):
        tokens = tokenize(expression)
        return parse_expr(tokens, 0)[0]
    
    def tokenize(expression):
        token_specification = [
            ('NUMBER',   r'\d+(\.\d*)?'),  # Integer or decimal number
            ('PLUS',     r'\+'),           # Addition operator
            ('MINUS',    r'-'),            # Subtraction operator
            ('TIMES',    r'\*'),           # Multiplication operator
            ('DIVIDE',   r'/'),            # Division operator
            ('LPAREN',   r'\('),           # Left parenthesis
            ('RPAREN',   r'\)'),           # Right parenthesis
            ('SIN',      r'sin'),          # Sine function
            ('COS',      r'cos'),          # Cosine function
            ('WS',       r'\s+'),          # Whitespace
        ]
        
        token_regex = '|'.join('(?P<%s>%s)' % pair for pair in token_specification)
        get_token = re.compile(token_regex).match
        line = expression
        pos = 0
        tokens = []
        match = get_token(line)
        while match is not None:
            typ = match.lastgroup
            if typ != 'WS':  # Ignore whitespace
                tokens.append((typ, match.group(typ)))
            pos = match.end()
            match = get_token(line, pos)
        return tokens

    def parse_expr(tokens, pos):
        lhs, pos = parse_term(tokens, pos)
        while pos < len(tokens) and tokens[pos][0] in ('PLUS', 'MINUS'):
            op = tokens[pos][0]
            pos += 1
            rhs, pos = parse_term(tokens, pos)
            if op == 'PLUS':
                lhs += rhs
            elif op == 'MINUS':
                lhs -= rhs
        return lhs, pos

    def parse_term(tokens, pos):
        lhs, pos = parse_factor(tokens, pos)
        while pos < len(tokens) and tokens[pos][0] in ('TIMES', 'DIVIDE'):
            op = tokens[pos][0]
            pos += 1
            rhs, pos = parse_factor(tokens, pos)
            if op == 'TIMES':
                lhs *= rhs
            elif op == 'DIVIDE':
                lhs /= rhs
        return lhs, pos

    def parse_factor(tokens, pos):
        if tokens[pos][0] == 'NUMBER':
            value = float(tokens[pos][1])
            pos += 1
            return value, pos
        elif tokens[pos][0] == 'LPAREN':
            pos += 1
            value, pos = parse_expr(tokens, pos)
            if tokens[pos][0] != 'RPAREN':
                raise SyntaxError("Missing closing parenthesis")
            pos += 1
            return value, pos
        elif tokens[pos][0] in ('SIN', 'COS'):
            func = tokens[pos][0]
            pos += 1
            if tokens[pos][0] != 'LPAREN':
                raise SyntaxError("Expected '(' after " + func)
            pos += 1
            value, pos = parse_expr(tokens, pos)
            if tokens[pos][0] != 'RPAREN':
                raise SyntaxError("Missing closing parenthesis")
            pos += 1
            if func == 'SIN':
                return math.sin(value), pos
            elif func == 'COS':
                return math.cos(value), pos
        else:
            raise SyntaxError("Unexpected token: " + tokens[pos][1])

    result, pos = parse_expression(expression)
    if pos != len(expression):
        raise SyntaxError("Unexpected input at end of expression")
    return result

# Test the evaluate function
expression = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expression)
print(f"{expression} = {result:.6f}")





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 98, in <module> result = evaluate(expression) File "/usr/src/app/main.py", line 91, in evaluate result, pos = parse_expression(expression) TypeError: cannot unpack non-iterable float object

Substring Evaluation

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

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

To evaluate expressions given in the specified BNF-style grammar, we need to parse the input string and compute the result while adhering to the grammar rules. Here is a Python function that accomplishes this using recursive descent parsing: 

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import math
import re

def evaluate(expression: str) -> float:
    tokens = tokenize(expression)
    return parse_expression(tokens)

def tokenize(expression: str):
    token_specification = [
        ('NUMBER',   r'\d+(\.\d*)?'), # Integer or decimal number
        ('PLUS',     r'\+'),          # Addition operator
        ('MINUS',    r'-'),           # Subtraction operator
        ('TIMES',    r'\*'),          # Multiplication operator
        ('DIVIDE',   r'/'),           # Division operator
        ('LPAREN',   r'\('),          # Left parenthesis
        ('RPAREN',   r'\)'),          # Right parenthesis
        ('SIN',      r'sin'),         # Sine function
        ('COS',      r'cos'),         # Cosine function
        ('SKIP',     r'[ \t]+'),      # Skip over spaces and tabs
        ('MISMATCH', r'.'),           # Any other character
    ]
    token_regex = '|'.join('(?P<%s>%s)' % pair for pair in token_specification)
    get_token = re.compile(token_regex).match
    line = expression
    pos = 0
    tokens = []
    mo = get_token(line)
    while mo is not None:
        kind = mo.lastgroup
        value = mo.group(kind)
        if kind == 'NUMBER':
            value = float(value) if '.' in value else int(value)
            tokens.append((kind, value))
        elif kind in ('PLUS', 'MINUS', 'TIMES', 'DIVIDE', 'LPAREN', 'RPAREN', 'SIN', 'COS'):
            tokens.append((kind, value))
        elif kind == 'SKIP':
            pass
        else:
            raise RuntimeError(f'{value}: unexpected character')
        pos = mo.end()
        mo = get_token(line, pos)
    tokens.append(('EOF', None))
    return tokens

class Parser:
    def __init__(self, tokens):
        self.tokens = tokens
        self.pos = 0

    def consume(self, expected_type=None):
        token = self.tokens[self.pos]
        if expected_type and token[0] != expected_type:
            raise RuntimeError(f'Expected {expected_type} but got {token[0]}')
        self.pos += 1
        return token

    def parse_expression(self):
        result = self.parse_term()
        while self.tokens[self.pos][0] in ('PLUS', 'MINUS'):
            if self.tokens[self.pos][0] == 'PLUS':
                self.consume('PLUS')
                result += self.parse_term()
            elif self.tokens[self.pos][0] == 'MINUS':
                self.consume('MINUS')
                result -= self.parse_term()
        return result

    def parse_term(self):
        result = self.parse_factor()
        while self.tokens[self.pos][0] in ('TIMES', 'DIVIDE'):
            if self.tokens[self.pos][0] == 'TIMES':
                self.consume('TIMES')
                result *= self.parse_factor()
            elif self.tokens[self.pos][0] == 'DIVIDE':
                self.consume('DIVIDE')
                result /= self.parse_factor()
        return result

    def parse_factor(self):
        token = self.tokens[self.pos]
        if token[0] == 'NUMBER':
            self.consume('NUMBER')
            return token[1]
        elif token[0] == 'LPAREN':
            self.consume('LPAREN')
            result = self.parse_expression()
            self.consume('RPAREN')
            return result
        elif token[0] in ('SIN', 'COS'):
            func = token[0]
            self.consume(func)
            self.consume('LPAREN')
            result = self.parse_expression()
            self.consume('RPAREN')
            if func == 'SIN':
                return math.sin(result)
            elif func == 'COS':
                return math.cos(result)
        else:
            raise RuntimeError(f'Unexpected token: {token}')

def parse_expression(tokens):
    parser = Parser(tokens)
    return parser.parse_expression()

# Example usage
expr = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expr)
print(f"{expr} = {result:.6f}")
This code first tokenizes the input string using regular expressions and then uses a recursive descent parser to evaluate the expression according to the grammar rules. The `Parser` class contains methods to parse each component of the grammar (`expression`, `term`, and `factor`). The `evaluate` function ties everything together, calling the tokenizer and the parser to compute the result.

Extract Code

I extracted the following code from that output: 

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import math
import re

def evaluate(expression: str) -> float:
    tokens = tokenize(expression)
    return parse_expression(tokens)

def tokenize(expression: str):
    token_specification = [
        ('NUMBER',   r'\d+(\.\d*)?'), # Integer or decimal number
        ('PLUS',     r'\+'),          # Addition operator
        ('MINUS',    r'-'),           # Subtraction operator
        ('TIMES',    r'\*'),          # Multiplication operator
        ('DIVIDE',   r'/'),           # Division operator
        ('LPAREN',   r'\('),          # Left parenthesis
        ('RPAREN',   r'\)'),          # Right parenthesis
        ('SIN',      r'sin'),         # Sine function
        ('COS',      r'cos'),         # Cosine function
        ('SKIP',     r'[ \t]+'),      # Skip over spaces and tabs
        ('MISMATCH', r'.'),           # Any other character
    ]
    token_regex = '|'.join('(?P<%s>%s)' % pair for pair in token_specification)
    get_token = re.compile(token_regex).match
    line = expression
    pos = 0
    tokens = []
    mo = get_token(line)
    while mo is not None:
        kind = mo.lastgroup
        value = mo.group(kind)
        if kind == 'NUMBER':
            value = float(value) if '.' in value else int(value)
            tokens.append((kind, value))
        elif kind in ('PLUS', 'MINUS', 'TIMES', 'DIVIDE', 'LPAREN', 'RPAREN', 'SIN', 'COS'):
            tokens.append((kind, value))
        elif kind == 'SKIP':
            pass
        else:
            raise RuntimeError(f'{value}: unexpected character')
        pos = mo.end()
        mo = get_token(line, pos)
    tokens.append(('EOF', None))
    return tokens

class Parser:
    def __init__(self, tokens):
        self.tokens = tokens
        self.pos = 0

    def consume(self, expected_type=None):
        token = self.tokens[self.pos]
        if expected_type and token[0] != expected_type:
            raise RuntimeError(f'Expected {expected_type} but got {token[0]}')
        self.pos += 1
        return token

    def parse_expression(self):
        result = self.parse_term()
        while self.tokens[self.pos][0] in ('PLUS', 'MINUS'):
            if self.tokens[self.pos][0] == 'PLUS':
                self.consume('PLUS')
                result += self.parse_term()
            elif self.tokens[self.pos][0] == 'MINUS':
                self.consume('MINUS')
                result -= self.parse_term()
        return result

    def parse_term(self):
        result = self.parse_factor()
        while self.tokens[self.pos][0] in ('TIMES', 'DIVIDE'):
            if self.tokens[self.pos][0] == 'TIMES':
                self.consume('TIMES')
                result *= self.parse_factor()
            elif self.tokens[self.pos][0] == 'DIVIDE':
                self.consume('DIVIDE')
                result /= self.parse_factor()
        return result

    def parse_factor(self):
        token = self.tokens[self.pos]
        if token[0] == 'NUMBER':
            self.consume('NUMBER')
            return token[1]
        elif token[0] == 'LPAREN':
            self.consume('LPAREN')
            result = self.parse_expression()
            self.consume('RPAREN')
            return result
        elif token[0] in ('SIN', 'COS'):
            func = token[0]
            self.consume(func)
            self.consume('LPAREN')
            result = self.parse_expression()
            self.consume('RPAREN')
            if func == 'SIN':
                return math.sin(result)
            elif func == 'COS':
                return math.cos(result)
        else:
            raise RuntimeError(f'Unexpected token: {token}')

def parse_expression(tokens):
    parser = Parser(tokens)
    return parser.parse_expression()

# Example usage
expr = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expr)
print(f"{expr} = {result:.6f}")

Run Code Interpreter

Running the following program: 

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import math
import re

def evaluate(expression: str) -> float:
    tokens = tokenize(expression)
    return parse_expression(tokens)

def tokenize(expression: str):
    token_specification = [
        ('NUMBER',   r'\d+(\.\d*)?'), # Integer or decimal number
        ('PLUS',     r'\+'),          # Addition operator
        ('MINUS',    r'-'),           # Subtraction operator
        ('TIMES',    r'\*'),          # Multiplication operator
        ('DIVIDE',   r'/'),           # Division operator
        ('LPAREN',   r'\('),          # Left parenthesis
        ('RPAREN',   r'\)'),          # Right parenthesis
        ('SIN',      r'sin'),         # Sine function
        ('COS',      r'cos'),         # Cosine function
        ('SKIP',     r'[ \t]+'),      # Skip over spaces and tabs
        ('MISMATCH', r'.'),           # Any other character
    ]
    token_regex = '|'.join('(?P<%s>%s)' % pair for pair in token_specification)
    get_token = re.compile(token_regex).match
    line = expression
    pos = 0
    tokens = []
    mo = get_token(line)
    while mo is not None:
        kind = mo.lastgroup
        value = mo.group(kind)
        if kind == 'NUMBER':
            value = float(value) if '.' in value else int(value)
            tokens.append((kind, value))
        elif kind in ('PLUS', 'MINUS', 'TIMES', 'DIVIDE', 'LPAREN', 'RPAREN', 'SIN', 'COS'):
            tokens.append((kind, value))
        elif kind == 'SKIP':
            pass
        else:
            raise RuntimeError(f'{value}: unexpected character')
        pos = mo.end()
        mo = get_token(line, pos)
    tokens.append(('EOF', None))
    return tokens

class Parser:
    def __init__(self, tokens):
        self.tokens = tokens
        self.pos = 0

    def consume(self, expected_type=None):
        token = self.tokens[self.pos]
        if expected_type and token[0] != expected_type:
            raise RuntimeError(f'Expected {expected_type} but got {token[0]}')
        self.pos += 1
        return token

    def parse_expression(self):
        result = self.parse_term()
        while self.tokens[self.pos][0] in ('PLUS', 'MINUS'):
            if self.tokens[self.pos][0] == 'PLUS':
                self.consume('PLUS')
                result += self.parse_term()
            elif self.tokens[self.pos][0] == 'MINUS':
                self.consume('MINUS')
                result -= self.parse_term()
        return result

    def parse_term(self):
        result = self.parse_factor()
        while self.tokens[self.pos][0] in ('TIMES', 'DIVIDE'):
            if self.tokens[self.pos][0] == 'TIMES':
                self.consume('TIMES')
                result *= self.parse_factor()
            elif self.tokens[self.pos][0] == 'DIVIDE':
                self.consume('DIVIDE')
                result /= self.parse_factor()
        return result

    def parse_factor(self):
        token = self.tokens[self.pos]
        if token[0] == 'NUMBER':
            self.consume('NUMBER')
            return token[1]
        elif token[0] == 'LPAREN':
            self.consume('LPAREN')
            result = self.parse_expression()
            self.consume('RPAREN')
            return result
        elif token[0] in ('SIN', 'COS'):
            func = token[0]
            self.consume(func)
            self.consume('LPAREN')
            result = self.parse_expression()
            self.consume('RPAREN')
            if func == 'SIN':
                return math.sin(result)
            elif func == 'COS':
                return math.cos(result)
        else:
            raise RuntimeError(f'Unexpected token: {token}')

def parse_expression(tokens):
    parser = Parser(tokens)
    return parser.parse_expression()

# Example usage
expr = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expr)
print(f"{expr} = {result:.6f}")





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: sin(3 + 2 * 4) - cos(15) = -0.240302 All tests passed

Substring Evaluation

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

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

To implement a parser and evaluator for the given BNF-style grammar, we can leverage Python's `re` module for regular expressions and the `math` module for trigonometric functions. The approach involves writing a recursive descent parser that processes the input string according to the grammar rules and then evaluates the parsed expression. Here is how you can implement this: 

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import re
import math

class Parser:
    def __init__(self, expression):
        self.tokens = re.findall(r'\d+|sin|cos|[-+*/()]', expression)
        self.pos = 0

    def consume(self):
        self.pos += 1

    def current_token(self):
        if self.pos < len(self.tokens):
            return self.tokens[self.pos]
        return None

    def parse_expression(self):
        term_value = self.parse_term()
        while self.current_token() in ('+', '-'):
            op = self.current_token()
            self.consume()
            next_term_value = self.parse_term()
            if op == '+':
                term_value += next_term_value
            elif op == '-':
                term_value -= next_term_value
        return term_value

    def parse_term(self):
        factor_value = self.parse_factor()
        while self.current_token() in ('*', '/'):
            op = self.current_token()
            self.consume()
            next_factor_value = self.parse_factor()
            if op == '*':
                factor_value *= next_factor_value
            elif op == '/':
                factor_value /= next_factor_value
        return factor_value

    def parse_factor(self):
        token = self.current_token()
        if re.match(r'\d+', token):
            self.consume()
            return float(token)
        elif token == '(':
            self.consume()
            expr_value = self.parse_expression()
            if self.current_token() == ')':
                self.consume()
            return expr_value
        elif token in ('sin', 'cos'):
            op = token
            self.consume()
            if self.current_token() == '(':
                self.consume()
                expr_value = self.parse_expression()
                if self.current_token() == ')':
                    self.consume()
                if op == 'sin':
                    return math.sin(expr_value)
                elif op == 'cos':
                    return math.cos(expr_value)
        raise ValueError(f"Unexpected token: {token}")

def evaluate(expression):
    parser = Parser(expression)
    return parser.parse_expression()

# Example usage
expr = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expr)
print(f"{expr} = {result:.6f}")
### Explanation: 1. **Tokenization**: The `Parser` class takes the input expression and tokenizes it using regular expressions. This simplifies the parsing process. 2. **Recursive Descent Parsing**: - `parse_expression` handles expressions with addition and subtraction. - `parse_term` handles terms with multiplication and division. - `parse_factor` handles numbers, parentheses, and prefix operators (`sin` and `cos`). 3. **Evaluation**: - Each parsing function returns the evaluated value of the parsed tokens. - Mathematical operations are performed according to the parsed tokens. ### Example: For the input `sin(3 + 2 * 4) - cos(15)`, the output will be approximately `-0.240302` as expected. You can run the code with different expressions to see the results.

Extract Code

I extracted the following code from that output: 

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import re
import math

class Parser:
    def __init__(self, expression):
        self.tokens = re.findall(r'\d+|sin|cos|[-+*/()]', expression)
        self.pos = 0

    def consume(self):
        self.pos += 1

    def current_token(self):
        if self.pos < len(self.tokens):
            return self.tokens[self.pos]
        return None

    def parse_expression(self):
        term_value = self.parse_term()
        while self.current_token() in ('+', '-'):
            op = self.current_token()
            self.consume()
            next_term_value = self.parse_term()
            if op == '+':
                term_value += next_term_value
            elif op == '-':
                term_value -= next_term_value
        return term_value

    def parse_term(self):
        factor_value = self.parse_factor()
        while self.current_token() in ('*', '/'):
            op = self.current_token()
            self.consume()
            next_factor_value = self.parse_factor()
            if op == '*':
                factor_value *= next_factor_value
            elif op == '/':
                factor_value /= next_factor_value
        return factor_value

    def parse_factor(self):
        token = self.current_token()
        if re.match(r'\d+', token):
            self.consume()
            return float(token)
        elif token == '(':
            self.consume()
            expr_value = self.parse_expression()
            if self.current_token() == ')':
                self.consume()
            return expr_value
        elif token in ('sin', 'cos'):
            op = token
            self.consume()
            if self.current_token() == '(':
                self.consume()
                expr_value = self.parse_expression()
                if self.current_token() == ')':
                    self.consume()
                if op == 'sin':
                    return math.sin(expr_value)
                elif op == 'cos':
                    return math.cos(expr_value)
        raise ValueError(f"Unexpected token: {token}")

def evaluate(expression):
    parser = Parser(expression)
    return parser.parse_expression()

# Example usage
expr = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expr)
print(f"{expr} = {result:.6f}")

Run Code Interpreter

Running the following program: 

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import re
import math

class Parser:
    def __init__(self, expression):
        self.tokens = re.findall(r'\d+|sin|cos|[-+*/()]', expression)
        self.pos = 0

    def consume(self):
        self.pos += 1

    def current_token(self):
        if self.pos < len(self.tokens):
            return self.tokens[self.pos]
        return None

    def parse_expression(self):
        term_value = self.parse_term()
        while self.current_token() in ('+', '-'):
            op = self.current_token()
            self.consume()
            next_term_value = self.parse_term()
            if op == '+':
                term_value += next_term_value
            elif op == '-':
                term_value -= next_term_value
        return term_value

    def parse_term(self):
        factor_value = self.parse_factor()
        while self.current_token() in ('*', '/'):
            op = self.current_token()
            self.consume()
            next_factor_value = self.parse_factor()
            if op == '*':
                factor_value *= next_factor_value
            elif op == '/':
                factor_value /= next_factor_value
        return factor_value

    def parse_factor(self):
        token = self.current_token()
        if re.match(r'\d+', token):
            self.consume()
            return float(token)
        elif token == '(':
            self.consume()
            expr_value = self.parse_expression()
            if self.current_token() == ')':
                self.consume()
            return expr_value
        elif token in ('sin', 'cos'):
            op = token
            self.consume()
            if self.current_token() == '(':
                self.consume()
                expr_value = self.parse_expression()
                if self.current_token() == ')':
                    self.consume()
                if op == 'sin':
                    return math.sin(expr_value)
                elif op == 'cos':
                    return math.cos(expr_value)
        raise ValueError(f"Unexpected token: {token}")

def evaluate(expression):
    parser = Parser(expression)
    return parser.parse_expression()

# Example usage
expr = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expr)
print(f"{expr} = {result:.6f}")





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: sin(3 + 2 * 4) - cos(15) = -0.240302 All tests passed

Substring Evaluation

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

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

To evaluate expressions based on the given BNF grammar, we can write a parser in Python. The parser will need to handle the different components of the grammar, such as expressions, terms, factors, and prefix operations. We will also use Python's `math` module to handle trigonometric functions like `sin` and `cos`. Here's the implementation of the `evaluate` function: 

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import math
import re

class ExpressionEvaluator:
    def __init__(self, expression):
        self.tokens = re.findall(r'\d+|sin|cos|\+|\-|\*|\/|\(|\)', expression)
        self.index = 0

    def parse_expression(self):
        term = self.parse_term()
        while self.index < len(self.tokens) and self.tokens[self.index] in ('+', '-'):
            op = self.tokens[self.index]
            self.index += 1
            next_term = self.parse_term()
            if op == '+':
                term += next_term
            elif op == '-':
                term -= next_term
        return term

    def parse_term(self):
        factor = self.parse_factor()
        while self.index < len(self.tokens) and self.tokens[self.index] in ('*', '/'):
            op = self.tokens[self.index]
            self.index += 1
            next_factor = self.parse_factor()
            if op == '*':
                factor *= next_factor
            elif op == '/':
                factor /= next_factor
        return factor

    def parse_factor(self):
        if self.index < len(self.tokens):
            token = self.tokens[self.index]
            if token.isdigit():
                self.index += 1
                return float(token)
            elif token == '(':
                self.index += 1
                expr = self.parse_expression()
                if self.tokens[self.index] == ')':
                    self.index += 1
                return expr
            elif token in ('sin', 'cos'):
                self.index += 1
                factor = self.parse_factor()
                if token == 'sin':
                    return math.sin(factor)
                elif token == 'cos':
                    return math.cos(factor)
        raise ValueError("Invalid expression")

def evaluate(expression):
    evaluator = ExpressionEvaluator(expression)
    return evaluator.parse_expression()

# Example usage
expression = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expression)
print(f"{expression} = {result:.6f}")
### Explanation: 1. **Tokenizer**: The `ExpressionEvaluator` class initializes by tokenizing the input string using a regular expression to split the input into meaningful tokens (numbers, operators, parentheses, and function names). 2. **Recursive Parsing**: The functions `parse_expression`, `parse_term`, and `parse_factor` implement the recursive descent parsing method: - `parse_expression` handles addition and subtraction. - `parse_term` handles multiplication and division. - `parse_factor` handles numbers, parenthesized expressions, and prefix operations (`sin`, `cos`). 3. **Evaluation**: - For numbers, it converts the token to a float. - For parentheses, it recursively evaluates the expression inside. - For `sin` and `cos`, it applies the trigonometric function to the evaluated factor. 4. **Error Handling**: The parser raises a `ValueError` if it encounters an invalid expression. ### Example: The provided example expression `sin(3 + 2 * 4) - cos(15)` will be parsed and evaluated to approximately `-0.240302`. This implementation should correctly handle the given grammar and evaluate the expressions as required.

Extract Code

I extracted the following code from that output: 

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import math
import re

class ExpressionEvaluator:
    def __init__(self, expression):
        self.tokens = re.findall(r'\d+|sin|cos|\+|\-|\*|\/|\(|\)', expression)
        self.index = 0

    def parse_expression(self):
        term = self.parse_term()
        while self.index < len(self.tokens) and self.tokens[self.index] in ('+', '-'):
            op = self.tokens[self.index]
            self.index += 1
            next_term = self.parse_term()
            if op == '+':
                term += next_term
            elif op == '-':
                term -= next_term
        return term

    def parse_term(self):
        factor = self.parse_factor()
        while self.index < len(self.tokens) and self.tokens[self.index] in ('*', '/'):
            op = self.tokens[self.index]
            self.index += 1
            next_factor = self.parse_factor()
            if op == '*':
                factor *= next_factor
            elif op == '/':
                factor /= next_factor
        return factor

    def parse_factor(self):
        if self.index < len(self.tokens):
            token = self.tokens[self.index]
            if token.isdigit():
                self.index += 1
                return float(token)
            elif token == '(':
                self.index += 1
                expr = self.parse_expression()
                if self.tokens[self.index] == ')':
                    self.index += 1
                return expr
            elif token in ('sin', 'cos'):
                self.index += 1
                factor = self.parse_factor()
                if token == 'sin':
                    return math.sin(factor)
                elif token == 'cos':
                    return math.cos(factor)
        raise ValueError("Invalid expression")

def evaluate(expression):
    evaluator = ExpressionEvaluator(expression)
    return evaluator.parse_expression()

# Example usage
expression = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expression)
print(f"{expression} = {result:.6f}")

Run Code Interpreter

Running the following program: 

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import math
import re

class ExpressionEvaluator:
    def __init__(self, expression):
        self.tokens = re.findall(r'\d+|sin|cos|\+|\-|\*|\/|\(|\)', expression)
        self.index = 0

    def parse_expression(self):
        term = self.parse_term()
        while self.index < len(self.tokens) and self.tokens[self.index] in ('+', '-'):
            op = self.tokens[self.index]
            self.index += 1
            next_term = self.parse_term()
            if op == '+':
                term += next_term
            elif op == '-':
                term -= next_term
        return term

    def parse_term(self):
        factor = self.parse_factor()
        while self.index < len(self.tokens) and self.tokens[self.index] in ('*', '/'):
            op = self.tokens[self.index]
            self.index += 1
            next_factor = self.parse_factor()
            if op == '*':
                factor *= next_factor
            elif op == '/':
                factor /= next_factor
        return factor

    def parse_factor(self):
        if self.index < len(self.tokens):
            token = self.tokens[self.index]
            if token.isdigit():
                self.index += 1
                return float(token)
            elif token == '(':
                self.index += 1
                expr = self.parse_expression()
                if self.tokens[self.index] == ')':
                    self.index += 1
                return expr
            elif token in ('sin', 'cos'):
                self.index += 1
                factor = self.parse_factor()
                if token == 'sin':
                    return math.sin(factor)
                elif token == 'cos':
                    return math.cos(factor)
        raise ValueError("Invalid expression")

def evaluate(expression):
    evaluator = ExpressionEvaluator(expression)
    return evaluator.parse_expression()

# Example usage
expression = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expression)
print(f"{expression} = {result:.6f}")





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: sin(3 + 2 * 4) - cos(15) = -0.240302 All tests passed

Substring Evaluation

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

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

To evaluate expressions based on the given BNF-style grammar, we'll need to implement a parser that can handle the specified grammar rules and evaluate the expressions accordingly. Here's a Python function `evaluate` that does this: 

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import math
import re

class Evaluator:
    def __init__(self, expression):
        self.tokens = re.findall(r'\d+|[()+\-*/]|sin|cos', expression)
        self.index = 0

    def parse_expression(self):
        result = self.parse_term()
        while self.index < len(self.tokens) and self.tokens[self.index] in ('+', '-'):
            op = self.tokens[self.index]
            self.index += 1
            if op == '+':
                result += self.parse_term()
            elif op == '-':
                result -= self.parse_term()
        return result

    def parse_term(self):
        result = self.parse_factor()
        while self.index < len(self.tokens) and self.tokens[self.index] in ('*', '/'):
            op = self.tokens[self.index]
            self.index += 1
            if op == '*':
                result *= self.parse_factor()
            elif op == '/':
                result /= self.parse_factor()
        return result

    def parse_factor(self):
        if self.tokens[self.index] == '(':
            self.index += 1
            result = self.parse_expression()
            self.index += 1  # Skipping ')'
            return result
        elif self.tokens[self.index] in ('sin', 'cos'):
            op = self.tokens[self.index]
            self.index += 1
            self.index += 1  # Skipping '('
            value = self.parse_expression()
            self.index += 1  # Skipping ')'
            if op == 'sin':
                return math.sin(value)
            elif op == 'cos':
                return math.cos(value)
        else:
            result = int(self.tokens[self.index])
            self.index += 1
            return result

def evaluate(expression):
    evaluator = Evaluator(expression)
    return evaluator.parse_expression()

# Example usage
expression = 'sin(3 + 2 * 4) - cos(15)'
result = evaluate(expression)
print(result)  # Output: -0.240302
Explanation: 1. **Tokenization**: We use regular expressions to tokenize the input string into numbers, operators, and functions. 2. **Parsing Functions**: We define recursive functions to parse expressions (`parse_expression`), terms (`parse_term`), and factors (`parse_factor`) according to the given BNF grammar. 3. **Evaluation**: Each parsing function computes and returns the evaluation of its corresponding part of the expression. The `evaluate` function creates an instance of the `Evaluator` class and starts the parsing process from the top-level expression. The example usage demonstrates how to evaluate the expression `sin(3 + 2 * 4) - cos(15)`. This implementation assumes valid input according to the grammar. For real-world usage, you'd want to add error handling for invalid inputs.

Extract Code

I extracted the following code from that output: 

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import math
import re

class Evaluator:
    def __init__(self, expression):
        self.tokens = re.findall(r'\d+|[()+\-*/]|sin|cos', expression)
        self.index = 0

    def parse_expression(self):
        result = self.parse_term()
        while self.index < len(self.tokens) and self.tokens[self.index] in ('+', '-'):
            op = self.tokens[self.index]
            self.index += 1
            if op == '+':
                result += self.parse_term()
            elif op == '-':
                result -= self.parse_term()
        return result

    def parse_term(self):
        result = self.parse_factor()
        while self.index < len(self.tokens) and self.tokens[self.index] in ('*', '/'):
            op = self.tokens[self.index]
            self.index += 1
            if op == '*':
                result *= self.parse_factor()
            elif op == '/':
                result /= self.parse_factor()
        return result

    def parse_factor(self):
        if self.tokens[self.index] == '(':
            self.index += 1
            result = self.parse_expression()
            self.index += 1  # Skipping ')'
            return result
        elif self.tokens[self.index] in ('sin', 'cos'):
            op = self.tokens[self.index]
            self.index += 1
            self.index += 1  # Skipping '('
            value = self.parse_expression()
            self.index += 1  # Skipping ')'
            if op == 'sin':
                return math.sin(value)
            elif op == 'cos':
                return math.cos(value)
        else:
            result = int(self.tokens[self.index])
            self.index += 1
            return result

def evaluate(expression):
    evaluator = Evaluator(expression)
    return evaluator.parse_expression()

# Example usage
expression = 'sin(3 + 2 * 4) - cos(15)'
result = evaluate(expression)
print(result)  # Output: -0.240302

Run Code Interpreter

Running the following program: 

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import math
import re

class Evaluator:
    def __init__(self, expression):
        self.tokens = re.findall(r'\d+|[()+\-*/]|sin|cos', expression)
        self.index = 0

    def parse_expression(self):
        result = self.parse_term()
        while self.index < len(self.tokens) and self.tokens[self.index] in ('+', '-'):
            op = self.tokens[self.index]
            self.index += 1
            if op == '+':
                result += self.parse_term()
            elif op == '-':
                result -= self.parse_term()
        return result

    def parse_term(self):
        result = self.parse_factor()
        while self.index < len(self.tokens) and self.tokens[self.index] in ('*', '/'):
            op = self.tokens[self.index]
            self.index += 1
            if op == '*':
                result *= self.parse_factor()
            elif op == '/':
                result /= self.parse_factor()
        return result

    def parse_factor(self):
        if self.tokens[self.index] == '(':
            self.index += 1
            result = self.parse_expression()
            self.index += 1  # Skipping ')'
            return result
        elif self.tokens[self.index] in ('sin', 'cos'):
            op = self.tokens[self.index]
            self.index += 1
            self.index += 1  # Skipping '('
            value = self.parse_expression()
            self.index += 1  # Skipping ')'
            if op == 'sin':
                return math.sin(value)
            elif op == 'cos':
                return math.cos(value)
        else:
            result = int(self.tokens[self.index])
            self.index += 1
            return result

def evaluate(expression):
    evaluator = Evaluator(expression)
    return evaluator.parse_expression()

# Example usage
expression = 'sin(3 + 2 * 4) - cos(15)'
result = evaluate(expression)
print(result)  # Output: -0.240302






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: -0.24030229369188216 All tests passed

Substring Evaluation

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