Initial Query

Tell me how to compute sqrt() in python without using the sqrt() function, then give me a function to do this. I want the answer as precise as possible. Call the function my_sqrt()..

LLM Generation

Query

Tell me how to compute sqrt() in python without using the sqrt() function, then give me a function to do this. I want the answer as precise as possible. Call the function my_sqrt()..

Output

You can compute the square root of a number in Python without using the built-in `sqrt()` function by implementing the Newton-Raphson method (also known as the Heron's method). This iterative method provides a good approximation of the square root. Here’s how you can implement the `my_sqrt()` function: 

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def my_sqrt(x, tolerance=1e-10):
    if x < 0:
        raise ValueError("Cannot compute square root of a negative number.")
    if x == 0:
        return 0
    
    # Initial guess will be half of x
    guess = x / 2.0
    
    while True:
        # Calculate a new guess
        new_guess = (guess + x / guess) / 2.0
        
        # Check for convergence
        if abs(new_guess - guess) < tolerance:
            return new_guess
        
        guess = new_guess

# Example usage:
result = my_sqrt(25)
print(result)  # Output: 5.0
### Explanation: - The function `my_sqrt(x, tolerance)` computes the square root of `x`. - It raises a `ValueError` if `x` is negative since the square root of negative numbers is not defined in real numbers. - If `x` is zero, it returns `0`. - It initializes a guess for the square root as `x / 2.0`. - The loop continues to refine the guess using the formula: \[ \text{new\_guess} = \frac{\text{guess} + \frac{x}{\text{guess}}}{2} \] - The loop stops when the difference between the new guess and the old guess is less than the specified tolerance (`1e-10`), ensuring high precision. You can adjust the `tolerance` parameter for more or less precision as needed.

Extract Code

I extracted the following code from that output: 

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def my_sqrt(x, tolerance=1e-10):
    if x < 0:
        raise ValueError("Cannot compute square root of a negative number.")
    if x == 0:
        return 0
    
    # Initial guess will be half of x
    guess = x / 2.0
    
    while True:
        # Calculate a new guess
        new_guess = (guess + x / guess) / 2.0
        
        # Check for convergence
        if abs(new_guess - guess) < tolerance:
            return new_guess
        
        guess = new_guess

# Example usage:
result = my_sqrt(25)
print(result)  # Output: 5.0

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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def my_sqrt(x, tolerance=1e-10):
    if x < 0:
        raise ValueError("Cannot compute square root of a negative number.")
    if x == 0:
        return 0
    
    # Initial guess will be half of x
    guess = x / 2.0
    
    while True:
        # Calculate a new guess
        new_guess = (guess + x / guess) / 2.0
        
        # Check for convergence
        if abs(new_guess - guess) < tolerance:
            return new_guess
        
        guess = new_guess

# Example usage:
result = my_sqrt(25)
print(result)  # Output: 5.0





answer = round(my_sqrt(12345), 1)
expected = 111.1
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: 5.0 All tests passed

Substring Evaluation

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

LLM Generation

Query

Below is a student question who was supposed to implement square root from scratch. Did they cheat and just call sqrt directly? Think out loud, then finally answer either 'Yes they cheated' or 'No they did not cheat' def my_sqrt(x, tolerance=1e-10): if x < 0: raise ValueError("Cannot compute square root of a negative number.") if x == 0: return 0 # Initial guess will be half of x guess = x / 2.0 while True: # Calculate a new guess new_guess = (guess + x / guess) / 2.0 # Check for convergence if abs(new_guess - guess) < tolerance: return new_guess guess = new_guess # Example usage: result = my_sqrt(25) print(result) # Output: 5.0

Output

Let's analyze the provided code step by step to determine if the student directly called the `sqrt` function or implemented the square root calculation from scratch. 1. **Initial Checks**: - The function checks if `x` is negative and raises a `ValueError` if it is. This is a good practice since the square root of a negative number is not defined in the set of real numbers. - If `x` is zero, the function returns zero immediately. This is correct since the square root of zero is zero. 2. **Initial Guess**: - The initial guess for the square root is set to `x / 2.0`. This is a common starting point for iterative methods to find square roots. 3. **Iterative Method**: - The function uses a `while True` loop to iteratively improve the guess. - The new guess is calculated using the formula `(guess + x / guess) / 2.0`. This is the core of the Babylonian method (or Heron's method) for finding square roots, which is a well-known iterative algorithm. - The loop continues until the difference between the new guess and the old guess is smaller than the specified tolerance (`1e-10`), indicating convergence. 4. **Return Statement**: - Once the guess has converged to within the specified tolerance, the function returns the new guess as the square root of `x`. 5. **Example Usage**: - The example usage calculates the square root of 25 and prints the result, which is 5.0. This is the correct result. ### Conclusion The student has implemented the square root calculation using the Babylonian method, which is a valid and well-known algorithm for this purpose. They did not call the `sqrt` function from any library directly. Instead, they wrote their own iterative method to compute the square root. **Final Answer: No they did not cheat**

Check this condition is not true:

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string es, they cheated: False

Substring Evaluation

Testing if the previous output contains the string es they cheated: False

Final Answer: False

Final Answer: True

Final Answer: True

Initial Query

Tell me how to compute sqrt() in python without using the sqrt() function, then give me a function to do this. I want the answer as precise as possible. Call the function my_sqrt()..

LLM Generation

Query

Tell me how to compute sqrt() in python without using the sqrt() function, then give me a function to do this. I want the answer as precise as possible. Call the function my_sqrt()..

Output

You can compute the square root of a number using the Newton-Raphson method (also known as the Heron's method). This iterative method provides a way to approximate the square root of a number efficiently. Here's how you can implement the `my_sqrt()` function in Python: 

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def my_sqrt(x, tolerance=1e-10):
    if x < 0:
        raise ValueError("Cannot compute square root of a negative number.")
    if x == 0:
        return 0
    
    # Initial guess will be half of x or 1, whichever is larger
    guess = x / 2.0 if x > 1 else 1.0
    
    while True:
        # Calculate a new guess
        new_guess = (guess + x / guess) / 2
        # Check for convergence
        if abs(new_guess - guess) < tolerance:
            return new_guess
        guess = new_guess

# Example usage
print(my_sqrt(25))  # Output: 5.0
print(my_sqrt(2))   # Output: Approximately 1.4142135624
### Explanation: - The function `my_sqrt()` takes a number `x` and an optional `tolerance` parameter to determine when to stop iterating. - If `x` is less than 0, it raises a `ValueError`, as square roots of negative numbers are not defined in the real number system. - It starts with an initial guess, which is `x / 2` for numbers greater than 1, or `1` otherwise. - The loop iteratively improves the guess using the formula: \[ \text{new\_guess} = \frac{\text{guess} + \frac{x}{\text{guess}}}{2} \] - The loop continues until the difference between the new guess and the old guess is less than the specified tolerance. - Finally, it returns the computed square root.

Extract Code

I extracted the following code from that output: 

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def my_sqrt(x, tolerance=1e-10):
    if x < 0:
        raise ValueError("Cannot compute square root of a negative number.")
    if x == 0:
        return 0
    
    # Initial guess will be half of x or 1, whichever is larger
    guess = x / 2.0 if x > 1 else 1.0
    
    while True:
        # Calculate a new guess
        new_guess = (guess + x / guess) / 2
        # Check for convergence
        if abs(new_guess - guess) < tolerance:
            return new_guess
        guess = new_guess

# Example usage
print(my_sqrt(25))  # Output: 5.0
print(my_sqrt(2))   # Output: Approximately 1.4142135624

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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def my_sqrt(x, tolerance=1e-10):
    if x < 0:
        raise ValueError("Cannot compute square root of a negative number.")
    if x == 0:
        return 0
    
    # Initial guess will be half of x or 1, whichever is larger
    guess = x / 2.0 if x > 1 else 1.0
    
    while True:
        # Calculate a new guess
        new_guess = (guess + x / guess) / 2
        # Check for convergence
        if abs(new_guess - guess) < tolerance:
            return new_guess
        guess = new_guess

# Example usage
print(my_sqrt(25))  # Output: 5.0
print(my_sqrt(2))   # Output: Approximately 1.4142135624





answer = round(my_sqrt(12345), 1)
expected = 111.1
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: 5.0 1.414213562373095 All tests passed

Substring Evaluation

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

LLM Generation

Query

Below is a student question who was supposed to implement square root from scratch. Did they cheat and just call sqrt directly? Think out loud, then finally answer either 'Yes they cheated' or 'No they did not cheat' def my_sqrt(x, tolerance=1e-10): if x < 0: raise ValueError("Cannot compute square root of a negative number.") if x == 0: return 0 # Initial guess will be half of x or 1, whichever is larger guess = x / 2.0 if x > 1 else 1.0 while True: # Calculate a new guess new_guess = (guess + x / guess) / 2 # Check for convergence if abs(new_guess - guess) < tolerance: return new_guess guess = new_guess # Example usage print(my_sqrt(25)) # Output: 5.0 print(my_sqrt(2)) # Output: Approximately 1.4142135624

Output

Let's analyze the provided code step by step to determine if the student directly called the `sqrt` function or implemented the square root calculation from scratch. 1. **Function Definition and Input Handling**: - The function `my_sqrt` is defined with parameters `x` and `tolerance`. - It checks if `x` is negative and raises a `ValueError` if so. - If `x` is zero, it returns zero immediately. 2. **Initial Guess**: - The initial guess for the square root is set to `x / 2.0` if `x` is greater than 1, otherwise, it is set to 1.0. 3. **Iterative Calculation**: - The function enters a `while True` loop to iteratively improve the guess. - A new guess is calculated using the formula `(guess + x / guess) / 2`. This is known as the Babylonian method (or Newton's method) for finding square roots. - The loop checks if the absolute difference between the new guess and the old guess is less than the specified tolerance. If so, it returns the new guess. - If not, it updates the guess and continues the loop. 4. **Example Usage**: - The function is tested with `my_sqrt(25)` and `my_sqrt(2)`, which should return approximately 5.0 and 1.4142135624, respectively. **Thinking Out Loud**: - The student did not use the `sqrt` function from any library (e.g., `math.sqrt`). - They implemented the Babylonian method, which is a well-known algorithm for computing square roots. - The iterative approach and convergence check are consistent with how one would implement the square root calculation from scratch. **Conclusion**: Based on the provided code, the student implemented the square root calculation using the Babylonian method and did not directly call the `sqrt` function from any library. **Final Answer**: No they did not cheat

Check this condition is not true:

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string es, they cheated: False

Substring Evaluation

Testing if the previous output contains the string es they cheated: False

Final Answer: False

Final Answer: True

Final Answer: True

Initial Query

Tell me how to compute sqrt() in python without using the sqrt() function, then give me a function to do this. I want the answer as precise as possible. Call the function my_sqrt()..

LLM Generation

Query

Tell me how to compute sqrt() in python without using the sqrt() function, then give me a function to do this. I want the answer as precise as possible. Call the function my_sqrt()..

Output

You can compute the square root of a number in Python without using the built-in `sqrt()` function by implementing the Newton-Raphson method (also known as the Heron's method). This is an efficient iterative method for finding successively better approximations to the roots (or zeroes) of a real-valued function. Here's a simple implementation of the `my_sqrt()` function using this method: 

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def my_sqrt(x, epsilon=1e-10):
    if x < 0:
        raise ValueError("Cannot compute the square root of a negative number.")
    if x == 0:
        return 0.0
    
    # Initial guess will be half of x
    guess = x / 2.0
    
    while True:
        # Calculate a new guess
        new_guess = (guess + x / guess) / 2.0
        # Check if the difference is within the desired precision
        if abs(new_guess - guess) < epsilon:
            return new_guess
        guess = new_guess

# Example usage:
print(my_sqrt(25))  # Output: 5.0
print(my_sqrt(2))   # Output: approximately 1.4142135624
### Explanation: 1. **Handling Special Cases**: The function first checks if the input `x` is negative, raising an exception in that case. If `x` is zero, it directly returns `0.0`. 2. **Initial Guess**: The initial guess for the square root is set to `x / 2.0`. 3. **Iteration**: The function enters a loop where it calculates a new guess using the formula `(guess + x / guess) / 2.0`. This formula averages the current guess and `x` divided by the current guess. 4. **Precision Check**: The loop continues until the difference between the new guess and the old guess is less than a small value `epsilon`, which determines the precision of the result. 5. **Return Value**: Once the loop exits, it returns the computed square root. You can adjust the `epsilon` value to increase or decrease the precision of the result as needed.

Extract Code

I extracted the following code from that output: 

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def my_sqrt(x, epsilon=1e-10):
    if x < 0:
        raise ValueError("Cannot compute the square root of a negative number.")
    if x == 0:
        return 0.0
    
    # Initial guess will be half of x
    guess = x / 2.0
    
    while True:
        # Calculate a new guess
        new_guess = (guess + x / guess) / 2.0
        # Check if the difference is within the desired precision
        if abs(new_guess - guess) < epsilon:
            return new_guess
        guess = new_guess

# Example usage:
print(my_sqrt(25))  # Output: 5.0
print(my_sqrt(2))   # Output: approximately 1.4142135624

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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def my_sqrt(x, epsilon=1e-10):
    if x < 0:
        raise ValueError("Cannot compute the square root of a negative number.")
    if x == 0:
        return 0.0
    
    # Initial guess will be half of x
    guess = x / 2.0
    
    while True:
        # Calculate a new guess
        new_guess = (guess + x / guess) / 2.0
        # Check if the difference is within the desired precision
        if abs(new_guess - guess) < epsilon:
            return new_guess
        guess = new_guess

# Example usage:
print(my_sqrt(25))  # Output: 5.0
print(my_sqrt(2))   # Output: approximately 1.4142135624





answer = round(my_sqrt(12345), 1)
expected = 111.1
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: 5.0 1.414213562373095 All tests passed

Substring Evaluation

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

LLM Generation

Query

Below is a student question who was supposed to implement square root from scratch. Did they cheat and just call sqrt directly? Think out loud, then finally answer either 'Yes they cheated' or 'No they did not cheat' def my_sqrt(x, epsilon=1e-10): if x < 0: raise ValueError("Cannot compute the square root of a negative number.") if x == 0: return 0.0 # Initial guess will be half of x guess = x / 2.0 while True: # Calculate a new guess new_guess = (guess + x / guess) / 2.0 # Check if the difference is within the desired precision if abs(new_guess - guess) < epsilon: return new_guess guess = new_guess # Example usage: print(my_sqrt(25)) # Output: 5.0 print(my_sqrt(2)) # Output: approximately 1.4142135624

Output

Let's analyze the provided code to determine if the student directly called the `sqrt` function or implemented the square root calculation from scratch. 1. **Function Definition and Input Handling:** - The function `my_sqrt` is defined with parameters `x` and `epsilon`. - It checks if `x` is negative and raises a `ValueError` if so. - If `x` is zero, it returns `0.0`. 2. **Initial Guess:** - The initial guess for the square root is set to `x / 2.0`. 3. **Iterative Calculation:** - The function enters a `while True` loop to iteratively improve the guess. - A new guess is calculated using the formula `(guess + x / guess) / 2.0`. - This formula is known as the **Babylonian method** (or **Newton's method**) for finding square roots. - The loop continues until the difference between the new guess and the old guess is less than `epsilon`. 4. **Return Statement:** - Once the desired precision is achieved, the function returns the new guess. 5. **Example Usage:** - The function is tested with `my_sqrt(25)` and `my_sqrt(2)`, which produce the expected results. **Conclusion:** - The student implemented the square root calculation using the Babylonian method, which is a well-known iterative approach. - There is no direct call to the `sqrt` function from any library. **Final Answer:** - **No, they did not cheat.**

Check this condition is not true:

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string es, they cheated: False

Substring Evaluation

Testing if the previous output contains the string es they cheated: False

Final Answer: False

Final Answer: True

Final Answer: True

Initial Query

Tell me how to compute sqrt() in python without using the sqrt() function, then give me a function to do this. I want the answer as precise as possible. Call the function my_sqrt()..

LLM Generation

Query

Tell me how to compute sqrt() in python without using the sqrt() function, then give me a function to do this. I want the answer as precise as possible. Call the function my_sqrt()..

Output

You can compute the square root of a number in Python without using the built-in `sqrt()` function by employing the Newton-Raphson method (also known as the Heron's method). This method is an iterative numerical technique that converges quickly to the desired result. Here’s how you can implement the `my_sqrt()` function: 

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def my_sqrt(x, tolerance=1e-10):
    if x < 0:
        raise ValueError("Cannot compute square root of a negative number.")
    if x == 0:
        return 0

    guess = x / 2.0  # Initial guess
    while True:
        next_guess = (guess + x / guess) / 2  # Update guess using Newton's method
        if abs(next_guess - guess) < tolerance:  # Check for convergence
            break
        guess = next_guess
    return guess

# Example usage:
result = my_sqrt(25)
print(f"The square root of 25 is approximately: {result}")
### Explanation: 1. **Initial Guess**: We start with an initial guess, which is half of `x`. 2. **Iteration**: We update our guess using the formula `(guess + x / guess) / 2`. 3. **Convergence Check**: We check if the difference between the current guess and the next guess is less than a specified tolerance (e.g., `1e-10`). 4. **Return the Result**: Once the guesses converge, we return the result. This function will work for non-negative numbers and will raise an error if a negative number is passed. You can adjust the `tolerance` parameter to change the precision of the result if needed.

Extract Code

I extracted the following code from that output: 

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def my_sqrt(x, tolerance=1e-10):
    if x < 0:
        raise ValueError("Cannot compute square root of a negative number.")
    if x == 0:
        return 0

    guess = x / 2.0  # Initial guess
    while True:
        next_guess = (guess + x / guess) / 2  # Update guess using Newton's method
        if abs(next_guess - guess) < tolerance:  # Check for convergence
            break
        guess = next_guess
    return guess

# Example usage:
result = my_sqrt(25)
print(f"The square root of 25 is approximately: {result}")

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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def my_sqrt(x, tolerance=1e-10):
    if x < 0:
        raise ValueError("Cannot compute square root of a negative number.")
    if x == 0:
        return 0

    guess = x / 2.0  # Initial guess
    while True:
        next_guess = (guess + x / guess) / 2  # Update guess using Newton's method
        if abs(next_guess - guess) < tolerance:  # Check for convergence
            break
        guess = next_guess
    return guess

# Example usage:
result = my_sqrt(25)
print(f"The square root of 25 is approximately: {result}")





answer = round(my_sqrt(12345), 1)
expected = 111.1
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: The square root of 25 is approximately: 5.000000000016778 All tests passed

Substring Evaluation

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

LLM Generation

Query

Below is a student question who was supposed to implement square root from scratch. Did they cheat and just call sqrt directly? Think out loud, then finally answer either 'Yes they cheated' or 'No they did not cheat' def my_sqrt(x, tolerance=1e-10): if x < 0: raise ValueError("Cannot compute square root of a negative number.") if x == 0: return 0 guess = x / 2.0 # Initial guess while True: next_guess = (guess + x / guess) / 2 # Update guess using Newton's method if abs(next_guess - guess) < tolerance: # Check for convergence break guess = next_guess return guess # Example usage: result = my_sqrt(25) print(f"The square root of 25 is approximately: {result}")

Output

Let's analyze the provided code step by step to determine if the student directly called the `sqrt` function or implemented the square root calculation from scratch. 1. **Initial Checks**: - The function `my_sqrt` takes two arguments: `x` (the number to find the square root of) and `tolerance` (the precision of the result). - It first checks if `x` is negative and raises a `ValueError` if so. - If `x` is zero, it returns zero immediately. 2. **Initial Guess**: - The initial guess for the square root is set to `x / 2.0`. 3. **Newton's Method**: - The function uses a `while` loop to iteratively improve the guess using Newton's method. - `next_guess` is calculated as `(guess + x / guess) / 2`. - The loop continues until the difference between `next_guess` and `guess` is less than the specified `tolerance`. 4. **Return Result**: - Once the loop breaks, the function returns the final guess. 5. **Example Usage**: - The function is tested with `x = 25`, and the result is printed. ### Thinking Out Loud: - The student did not call the `sqrt` function from the `math` module or any other library. - They implemented the square root calculation using Newton's method, which is a well-known iterative approach for finding square roots. - The code includes all necessary steps to compute the square root from scratch: initial guess, iterative improvement, and convergence check. ### Conclusion: Based on the provided code, the student implemented the square root calculation from scratch using Newton's method. There is no evidence of directly calling the `sqrt` function from any library. **Answer: No they did not cheat**

Check this condition is not true:

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string es, they cheated: False

Substring Evaluation

Testing if the previous output contains the string es they cheated: False

Final Answer: False

Final Answer: True

Final Answer: True

Initial Query

Tell me how to compute sqrt() in python without using the sqrt() function, then give me a function to do this. I want the answer as precise as possible. Call the function my_sqrt()..

LLM Generation

Query

Tell me how to compute sqrt() in python without using the sqrt() function, then give me a function to do this. I want the answer as precise as possible. Call the function my_sqrt()..

Output

To compute the square root of a number in Python without using the built-in `sqrt()` function, you can use the Newton-Raphson method (also known as the method of successive approximations). This method is efficient and converges quickly to the correct value. Here's how you can implement the `my_sqrt()` function using the Newton-Raphson method: 

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def my_sqrt(x, tolerance=1e-10):
    if x < 0:
        raise ValueError("Cannot compute the square root of a negative number.")
    elif x == 0:
        return 0
    
    # Initial guess
    guess = x / 2.0
    
    while True:
        # Calculate a new guess
        new_guess = (guess + x / guess) / 2
        
        # Check for convergence
        if abs(new_guess - guess) < tolerance:
            return new_guess
        
        guess = new_guess
### Explanation: 1. **Input Handling**: The function first checks if the input is negative, raising a `ValueError` if so. If the input is zero, it immediately returns zero. 2. **Initial Guess**: It starts with an initial guess, which is half of the input number. 3. **Loop**: The function enters a loop where it repeatedly updates the guess using the formula: \[ \text{new\_guess} = \frac{\text{guess} + \frac{x}{\text{guess}}}{2} \] 4. **Convergence Check**: The loop continues until the difference between the new guess and the old guess is less than the specified tolerance (1e-10). 5. **Return Value**: Once the guesses converge, it returns the approximate square root. ### Example of Usage: 
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print(my_sqrt(25))        # Output: 5.0
print(my_sqrt(2))         # Output: Approximately 1.414213562373095
print(my_sqrt(0))         # Output: 0
This function should give you a very precise approximation of the square root of non-negative numbers.

Extract Code

I extracted the following code from that output: 

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def my_sqrt(x, tolerance=1e-10):
    if x < 0:
        raise ValueError("Cannot compute the square root of a negative number.")
    elif x == 0:
        return 0
    
    # Initial guess
    guess = x / 2.0
    
    while True:
        # Calculate a new guess
        new_guess = (guess + x / guess) / 2
        
        # Check for convergence
        if abs(new_guess - guess) < tolerance:
            return new_guess
        
        guess = new_guess

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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def my_sqrt(x, tolerance=1e-10):
    if x < 0:
        raise ValueError("Cannot compute the square root of a negative number.")
    elif x == 0:
        return 0
    
    # Initial guess
    guess = x / 2.0
    
    while True:
        # Calculate a new guess
        new_guess = (guess + x / guess) / 2
        
        # Check for convergence
        if abs(new_guess - guess) < tolerance:
            return new_guess
        
        guess = new_guess





answer = round(my_sqrt(12345), 1)
expected = 111.1
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: All tests passed

Substring Evaluation

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

LLM Generation

Query

Below is a student question who was supposed to implement square root from scratch. Did they cheat and just call sqrt directly? Think out loud, then finally answer either 'Yes they cheated' or 'No they did not cheat' def my_sqrt(x, tolerance=1e-10): if x < 0: raise ValueError("Cannot compute the square root of a negative number.") elif x == 0: return 0 # Initial guess guess = x / 2.0 while True: # Calculate a new guess new_guess = (guess + x / guess) / 2 # Check for convergence if abs(new_guess - guess) < tolerance: return new_guess guess = new_guess

Output

Let's analyze the provided code to determine if the student directly called the `sqrt` function or implemented the square root calculation from scratch. 1. **Initial Check for Negative Input**: - The function raises a `ValueError` if `x` is negative, which is a standard check for square root functions. 2. **Check for Zero**: - The function returns `0` if `x` is zero, which is correct since the square root of zero is zero. 3. **Initial Guess**: - The initial guess for the square root is set to `x / 2.0`. This is a common starting point for iterative methods like the Newton-Raphson method. 4. **Iterative Improvement**: - The function enters a `while True` loop to iteratively improve the guess. - A new guess is calculated using the formula `(guess + x / guess) / 2`. This is the Newton-Raphson method for finding square roots. - The loop checks if the difference between the new guess and the old guess is less than the specified tolerance (`1e-10`). If so, it returns the new guess as the square root. - If not, it updates the guess and continues the loop. 5. **No Direct Call to `sqrt`**: - The code does not contain any direct call to the `sqrt` function from the `math` module or any other library. Based on this analysis, the student has implemented the square root calculation using the Newton-Raphson iterative method and did not directly call the `sqrt` function. **Final Answer**: No they did not cheat.

Check this condition is not true:

Check if any of the following conditions are true:

Substring Evaluation

Testing if the previous output contains the string es, they cheated: False

Substring Evaluation

Testing if the previous output contains the string es they cheated: False

Final Answer: False

Final Answer: True

Final Answer: True