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 without using the built-in `sqrt()` function in Python, you can use the Newton-Raphson method. This method iteratively approximates the square root of a number using a mathematical formula. Here's a Python function that implements the Newton-Raphson method to calculate the square root: 

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def my_sqrt(x, precision=1e-10, max_iterations=100):
    if x < 0:
        raise ValueError("Cannot compute square root of negative numbers.")
    
    if x == 0:
        return 0
    
    guess = x / 2  # Initial guess
    
    for _ in range(max_iterations):
        new_guess = (guess + x / guess) / 2
        if abs(new_guess - guess) < precision:
            return new_guess
        guess = new_guess
    
    return guess
Explanation: 1. The function takes three parameters: - `x`: The number for which we want to compute the square root. - `precision` (optional): The desired precision of the result. Default value is 1e-10. - `max_iterations` (optional): The maximum number of iterations allowed. Default value is 100. 2. The function first checks if `x` is negative. If it is, it raises a `ValueError` since the square root of negative numbers is not defined in the real number system. 3. If `x` is zero, the function immediately returns zero since the square root of zero is zero. 4. The initial guess for the square root is set to `x / 2`. This is a reasonable starting point for the Newton-Raphson method. 5. The function then enters a loop that iterates up to `max_iterations` times: - It calculates a new guess using the Newton-Raphson formula: `new_guess = (guess + x / guess) / 2`. - It checks the absolute difference between the new guess and the previous guess. If the difference is less than the specified `precision`, the function returns the new guess as the square root. - If the difference is greater than or equal to the `precision`, the function updates the `guess` variable with the new guess and continues to the next iteration. 6. If the loop completes without finding a satisfactory approximation within the specified precision, the function returns the final guess as the square root. Note: The Newton-Raphson method converges quickly for most numbers, but it may require more iterations for certain inputs to achieve the desired precision. Increasing the `max_iterations` parameter can help in such cases, but it may also increase the computation time. You can use this `my_sqrt()` function to compute the square root of a number with high precision without relying on the built-in `sqrt()` function.

Extract Code

I extracted the following code from that output: 

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def my_sqrt(x, precision=1e-10, max_iterations=100):
    if x < 0:
        raise ValueError("Cannot compute square root of negative numbers.")
    
    if x == 0:
        return 0
    
    guess = x / 2  # Initial guess
    
    for _ in range(max_iterations):
        new_guess = (guess + x / guess) / 2
        if abs(new_guess - guess) < precision:
            return new_guess
        guess = new_guess
    
    return 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, precision=1e-10, max_iterations=100):
    if x < 0:
        raise ValueError("Cannot compute square root of negative numbers.")
    
    if x == 0:
        return 0
    
    guess = x / 2  # Initial guess
    
    for _ in range(max_iterations):
        new_guess = (guess + x / guess) / 2
        if abs(new_guess - guess) < precision:
            return new_guess
        guess = new_guess
    
    return 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, precision=1e-10, max_iterations=100): if x < 0: raise ValueError("Cannot compute square root of negative numbers.") if x == 0: return 0 guess = x / 2 # Initial guess for _ in range(max_iterations): new_guess = (guess + x / guess) / 2 if abs(new_guess - guess) < precision: return new_guess guess = new_guess return guess

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 Check for Negative Input:** 

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   if x < 0:
       raise ValueError("Cannot compute square root of negative numbers.")
This part of the code checks if the input `x` is negative and raises an error if it is. This is a standard check for square root functions since the square root of a negative number is not defined in the set of real numbers. 2. **Check for Zero Input:** 
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   if x == 0:
       return 0
This part handles the special case where the input is zero. The square root of zero is zero, so it returns 0 directly. 3. **Initial Guess:** 
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   guess = x / 2  # Initial guess
The code initializes the guess for the square root as half of the input value `x`. This is a common starting point for iterative methods like the Newton-Raphson method. 4. **Iterative Improvement:** 
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   for _ in range(max_iterations):
       new_guess = (guess + x / guess) / 2
       if abs(new_guess - guess) < precision:
           return new_guess
       guess = new_guess
This loop iteratively improves the guess using the Newton-Raphson method (also known as the Heron's method for square roots). The formula `(guess + x / guess) / 2` is used to update the guess. The loop continues until the difference between the new guess and the old guess is smaller than the specified precision or until the maximum number of iterations is reached. 5. **Return Final Guess:** 
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   return guess
If the loop completes without meeting the precision requirement, the function returns the last computed guess. **Conclusion:** The student implemented the square root calculation using the Newton-Raphson method. They did not call the `sqrt` function from any library directly. The code shows a clear iterative approach to approximate the square root, which is a valid method for this purpose. **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

To compute the square root of a number without using the built-in `sqrt()` function in Python, you can use the Newton-Raphson method. This iterative algorithm approximates the square root of a number by repeatedly improving the estimate. Here's a function that implements the Newton-Raphson method to calculate the square root: 

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def my_sqrt(x, precision=1e-10, max_iterations=100):
    if x < 0:
        raise ValueError("Cannot compute square root of negative number.")
    
    if x == 0:
        return 0
    
    # Initial guess for the square root
    guess = x / 2
    
    # Iterate until the desired precision is achieved or maximum iterations are reached
    for _ in range(max_iterations):
        new_guess = (guess + x / guess) / 2
        if abs(new_guess - guess) < precision:
            return new_guess
        guess = new_guess
    
    # If maximum iterations are reached without achieving the desired precision
    return guess
Explanation: 1. The function `my_sqrt` takes three parameters: - `x`: The number for which we want to compute the square root. - `precision` (optional): The desired precision of the result. It defaults to 1e-10. - `max_iterations` (optional): The maximum number of iterations allowed. It defaults to 100. 2. If `x` is negative, the function raises a `ValueError` since square roots of negative numbers are undefined in the real domain. 3. If `x` is zero, the function returns zero since the square root of zero is zero. 4. The initial guess for the square root is set to `x / 2`. This is a reasonable starting point for the Newton-Raphson method. 5. The function enters a loop that iterates until either the desired precision is achieved or the maximum number of iterations is reached. 6. Inside the loop, a new guess is calculated using the formula: `new_guess = (guess + x / guess) / 2`. This formula is derived from the Newton-Raphson method. 7. If the absolute difference between the new guess and the previous guess is less than the specified precision, the function returns the new guess as the square root. 8. If the maximum number of iterations is reached without achieving the desired precision, the function returns the latest guess as the square root. This implementation provides a precise approximation of the square root using the Newton-Raphson method. The precision can be adjusted by modifying the `precision` parameter, and the maximum number of iterations can be controlled by the `max_iterations` parameter. Note: The Newton-Raphson method converges quickly for most cases, but it may require more iterations for certain inputs to achieve the desired precision.

Extract Code

I extracted the following code from that output: 

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def my_sqrt(x, precision=1e-10, max_iterations=100):
    if x < 0:
        raise ValueError("Cannot compute square root of negative number.")
    
    if x == 0:
        return 0
    
    # Initial guess for the square root
    guess = x / 2
    
    # Iterate until the desired precision is achieved or maximum iterations are reached
    for _ in range(max_iterations):
        new_guess = (guess + x / guess) / 2
        if abs(new_guess - guess) < precision:
            return new_guess
        guess = new_guess
    
    # If maximum iterations are reached without achieving the desired precision
    return 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, precision=1e-10, max_iterations=100):
    if x < 0:
        raise ValueError("Cannot compute square root of negative number.")
    
    if x == 0:
        return 0
    
    # Initial guess for the square root
    guess = x / 2
    
    # Iterate until the desired precision is achieved or maximum iterations are reached
    for _ in range(max_iterations):
        new_guess = (guess + x / guess) / 2
        if abs(new_guess - guess) < precision:
            return new_guess
        guess = new_guess
    
    # If maximum iterations are reached without achieving the desired precision
    return 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, precision=1e-10, max_iterations=100): if x < 0: raise ValueError("Cannot compute square root of negative number.") if x == 0: return 0 # Initial guess for the square root guess = x / 2 # Iterate until the desired precision is achieved or maximum iterations are reached for _ in range(max_iterations): new_guess = (guess + x / guess) / 2 if abs(new_guess - guess) < precision: return new_guess guess = new_guess # If maximum iterations are reached without achieving the desired precision return guess

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`. This is a common starting point for iterative methods like the Newton-Raphson method. 3. **Iterative Method**: - The function uses a `for` loop to iterate up to `max_iterations` times. - In each iteration, it calculates a new guess using the formula `(guess + x / guess) / 2`. This is the core of the Newton-Raphson method for finding square roots. - The function checks if the absolute difference between the new guess and the old guess is less than the specified precision. If it is, the function returns the new guess as the result. - If the precision condition is not met, the guess is updated to the new guess, and the loop continues. 4. **Return Statement**: - If the loop completes without finding a sufficiently precise result, the function returns the last guess. **Conclusion**: The student implemented the square root calculation using the Newton-Raphson iterative method. They did not call the `sqrt` function from any library directly. The method they used is a well-known algorithm for computing square roots and is implemented correctly in the provided code. **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

To compute the square root of a number in Python without using the built-in `sqrt()` function, you can use the Newton's method. Newton's method is an iterative algorithm that approximates the square root of a number by iteratively improving an initial guess. Here's a Python function that implements Newton's method to calculate the square root: 

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def my_sqrt(num, precision=1e-10, max_iterations=100):
    if num < 0:
        raise ValueError("Cannot calculate square root of negative numbers.")
    
    if num == 0:
        return 0
    
    guess = num / 2  # Initial guess
    
    for _ in range(max_iterations):
        new_guess = (guess + num / guess) / 2
        if abs(new_guess - guess) < precision:
            return new_guess
        guess = new_guess
    
    return guess
Explanation of the `my_sqrt()` function: 1. The function takes three parameters: - `num`: The number for which we want to calculate the square root. - `precision` (optional): The desired precision of the result. It defaults to 1e-10, which means the function will stop iterating when the difference between consecutive guesses is less than 1e-10. - `max_iterations` (optional): The maximum number of iterations to perform. It defaults to 100 to prevent infinite loops. 2. The function first checks if the input number is negative. If it is, it raises a `ValueError` since square roots of negative numbers are not defined in the real number system. 3. If the input number is zero, the function returns zero since the square root of zero is zero. 4. An initial guess is made by dividing the input number by 2. This is a reasonable starting point for the iterative process. 5. The function enters a loop that iterates up to `max_iterations` times: - It calculates a new guess using the formula: `new_guess = (guess + num / guess) / 2`. This formula is derived from Newton's method for finding the square root. - If the absolute difference between the new guess and the previous guess is less than the specified `precision`, the function returns the new guess as the square root. - Otherwise, the current guess is updated with the new guess, and the loop continues. 6. If the loop completes without reaching the desired precision, the function returns the final guess as the approximate square root. You can call the `my_sqrt()` function like this: 
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result = my_sqrt(25)
print(result)  # Output: 5.0

result = my_sqrt(2)
print(result)  # Output: 1.4142135623730951
The `my_sqrt()` function provides a precise approximation of the square root. You can adjust the `precision` parameter to control the desired level of accuracy. Increasing the `precision` will result in more iterations and a more precise result, but it may also increase the computation time.

Extract Code

I extracted the following code from that output: 

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def my_sqrt(num, precision=1e-10, max_iterations=100):
    if num < 0:
        raise ValueError("Cannot calculate square root of negative numbers.")
    
    if num == 0:
        return 0
    
    guess = num / 2  # Initial guess
    
    for _ in range(max_iterations):
        new_guess = (guess + num / guess) / 2
        if abs(new_guess - guess) < precision:
            return new_guess
        guess = new_guess
    
    return guess

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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def my_sqrt(num, precision=1e-10, max_iterations=100):
    if num < 0:
        raise ValueError("Cannot calculate square root of negative numbers.")
    
    if num == 0:
        return 0
    
    guess = num / 2  # Initial guess
    
    for _ in range(max_iterations):
        new_guess = (guess + num / guess) / 2
        if abs(new_guess - guess) < precision:
            return new_guess
        guess = new_guess
    
    return 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(num, precision=1e-10, max_iterations=100): if num < 0: raise ValueError("Cannot calculate square root of negative numbers.") if num == 0: return 0 guess = num / 2 # Initial guess for _ in range(max_iterations): new_guess = (guess + num / guess) / 2 if abs(new_guess - guess) < precision: return new_guess guess = new_guess return 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. **Function Definition and Parameters**: - The function `my_sqrt` takes three parameters: `num`, `precision`, and `max_iterations`. - The default precision is set to `1e-10`, and the maximum number of iterations is set to 100. 2. **Handling Negative Numbers**: - The function raises a `ValueError` if the input number is negative, which is a reasonable check for square root calculations. 3. **Handling Zero**: - The function returns 0 if the input number is zero, which is correct since the square root of zero is zero. 4. **Initial Guess**: - The initial guess for the square root is set to `num / 2`. This is a common starting point for iterative methods like the Newton-Raphson method. 5. **Iterative Calculation**: - The function uses a `for` loop to iterate up to `max_iterations` times. - Inside the loop, it calculates a new guess using the formula `(guess + num / guess) / 2`. This is the core of the Newton-Raphson method for finding square roots. - It checks if the absolute difference between the new guess and the old guess is less than the specified precision. If so, it returns the new guess as the result. - If the precision condition is not met, it updates the guess and continues iterating. 6. **Return Statement**: - If the loop completes without meeting the precision condition, the function returns the last guess. **Conclusion**: The student implemented the square root calculation using the Newton-Raphson method, which is a well-known iterative approach. There is no direct call to the `sqrt` function from any library. The logic and steps are consistent with an implementation from scratch. **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

To compute the square root of a number without using the built-in `sqrt()` function in Python, you can use the Newton-Raphson method. This method iteratively approximates the square root of a number using the following formula: 

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x_next = (x + n / x) / 2
Where `x` is the current approximation of the square root, and `n` is the number for which we want to find the square root. We start with an initial guess for `x` and iteratively refine it until the difference between consecutive approximations is within a small tolerance. Here's an implementation of the `my_sqrt()` function using the Newton-Raphson method: 
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def my_sqrt(n, tolerance=1e-10, max_iterations=100):
    if n < 0:
        raise ValueError("Cannot compute square root of a negative number.")
    
    if n == 0:
        return 0
    
    x = n / 2  # Initial guess
    
    for i in range(max_iterations):
        x_next = (x + n / x) / 2
        if abs(x_next - x) < tolerance:
            return x_next
        x = x_next
    
    return x
Explanation: 1. We first check if the input number `n` is negative. If it is, we raise a `ValueError` since the square root of a negative number is undefined in the real number system. 2. If `n` is zero, we directly return zero as the square root. 3. We start with an initial guess for `x`, which is half of `n`. This is a reasonable starting point for the approximation. 4. We enter a loop that iterates up to `max_iterations` times (default is 100). In each iteration: - We calculate the next approximation `x_next` using the Newton-Raphson formula. - We check if the absolute difference between `x_next` and `x` is less than the specified `tolerance` (default is 1e-10). If it is, we have converged to a sufficiently accurate approximation and return `x_next`. - If the difference is still greater than the tolerance, we update `x` with `x_next` and continue to the next iteration. 5. If the loop completes without reaching the desired tolerance, we return the final approximation `x`. You can call this function by providing the number for which you want to find the square root, and optionally, the tolerance and maximum number of iterations: 
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print(my_sqrt(16))  # Output: 4.0
print(my_sqrt(2))   # Output: 1.4142135623730951
print(my_sqrt(1e-8))  # Output: 0.0001
The function returns a highly precise approximation of the square root, limited only by the specified tolerance and the maximum number of iterations. Note: The Newton-Raphson method converges quickly for most numbers, but it may not always converge for certain edge cases or very large numbers. In such cases, you might need to adjust the tolerance or increase the maximum number of iterations.

Extract Code

I extracted the following code from that output: 

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def my_sqrt(n, tolerance=1e-10, max_iterations=100):
    if n < 0:
        raise ValueError("Cannot compute square root of a negative number.")
    
    if n == 0:
        return 0
    
    x = n / 2  # Initial guess
    
    for i in range(max_iterations):
        x_next = (x + n / x) / 2
        if abs(x_next - x) < tolerance:
            return x_next
        x = x_next
    
    return x

Check if all of the following conditions are true:

Run Code Interpreter

Running the following program: 

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def my_sqrt(n, tolerance=1e-10, max_iterations=100):
    if n < 0:
        raise ValueError("Cannot compute square root of a negative number.")
    
    if n == 0:
        return 0
    
    x = n / 2  # Initial guess
    
    for i in range(max_iterations):
        x_next = (x + n / x) / 2
        if abs(x_next - x) < tolerance:
            return x_next
        x = x_next
    
    return x





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(n, tolerance=1e-10, max_iterations=100): if n < 0: raise ValueError("Cannot compute square root of a negative number.") if n == 0: return 0 x = n / 2 # Initial guess for i in range(max_iterations): x_next = (x + n / x) / 2 if abs(x_next - x) < tolerance: return x_next x = x_next return x

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 the input `n` is negative and raises a `ValueError` if it is. This is a good practice to handle invalid input. - If `n` is zero, the function returns zero immediately. This is correct because the square root of zero is zero. 2. **Initial Guess**: - The initial guess for the square root is set to `n / 2`. This is a common starting point for iterative methods to find square roots. 3. **Iterative Method**: - The function uses a `for` loop to iterate up to `max_iterations` times. - In each iteration, it calculates `x_next` using the formula `(x + n / x) / 2`. This is the formula for the Newton-Raphson method (also known as the Heron's method) for finding square roots. - The function checks if the difference between `x_next` and `x` is less than the specified `tolerance`. If it is, the function returns `x_next` as the result. - If the difference is not less than the tolerance, the function updates `x` to `x_next` and continues to the next iteration. 4. **Return Statement**: - If the loop completes without finding a sufficiently accurate result, the function returns the last computed value of `x`. The Newton-Raphson method is a well-known algorithm for finding square roots, and the student has implemented it correctly. There is no direct call to the `sqrt` function from any library. **Conclusion**: The student did not cheat. They implemented the square root calculation from scratch using the Newton-Raphson method. **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

To compute the square root of a number without using the built-in `sqrt()` function in Python, you can use the Newton-Raphson method. This method iteratively approximates the square root of a number by refining an initial guess. Here's a function that implements the Newton-Raphson method to calculate the square root: 

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def my_sqrt(x, precision=1e-10, max_iterations=100):
    if x < 0:
        raise ValueError("Cannot compute square root of negative numbers.")
    
    if x == 0:
        return 0
    
    guess = x / 2  # Initial guess
    
    for _ in range(max_iterations):
        new_guess = (guess + x / guess) / 2
        if abs(new_guess - guess) < precision:
            break
        guess = new_guess
    
    return new_guess
Explanation: 1. The function takes three parameters: - `x`: The number for which we want to compute the square root. - `precision` (optional): The desired precision of the result. It defaults to 1e-10, which means the function will continue iterating until the difference between consecutive guesses is less than this value. - `max_iterations` (optional): The maximum number of iterations allowed. It defaults to 100 to prevent infinite loops if the desired precision is not reached. 2. The function first checks if `x` is negative. If it is, it raises a `ValueError` since the square root of negative numbers is not defined in the real number system. 3. If `x` is zero, the function immediately returns zero since the square root of zero is zero. 4. The function initializes the `guess` variable with `x / 2` as an initial guess for the square root. 5. It then enters a loop that iteratively refines the guess using the Newton-Raphson method. The new guess is calculated using the formula: `new_guess = (guess + x / guess) / 2`. 6. The loop continues until either the difference between the new guess and the previous guess is less than the specified `precision` or the maximum number of iterations (`max_iterations`) is reached. 7. Finally, the function returns the approximate square root of `x`. You can use this function to compute the square root of a number with high precision. Here are a few examples: 
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print(my_sqrt(4))  # Output: 2.0
print(my_sqrt(2))  # Output: 1.414213562373095
print(my_sqrt(1000000))  # Output: 1000.0
Note that the precision of the result depends on the specified `precision` parameter and the number of iterations. Increasing the precision or the maximum number of iterations can improve the accuracy of the result, but it may also increase the computation time.

Extract Code

I extracted the following code from that output: 

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def my_sqrt(x, precision=1e-10, max_iterations=100):
    if x < 0:
        raise ValueError("Cannot compute square root of negative numbers.")
    
    if x == 0:
        return 0
    
    guess = x / 2  # Initial guess
    
    for _ in range(max_iterations):
        new_guess = (guess + x / guess) / 2
        if abs(new_guess - guess) < precision:
            break
        guess = new_guess
    
    return 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, precision=1e-10, max_iterations=100):
    if x < 0:
        raise ValueError("Cannot compute square root of negative numbers.")
    
    if x == 0:
        return 0
    
    guess = x / 2  # Initial guess
    
    for _ in range(max_iterations):
        new_guess = (guess + x / guess) / 2
        if abs(new_guess - guess) < precision:
            break
        guess = new_guess
    
    return 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, precision=1e-10, max_iterations=100): if x < 0: raise ValueError("Cannot compute square root of negative numbers.") if x == 0: return 0 guess = x / 2 # Initial guess for _ in range(max_iterations): new_guess = (guess + x / guess) / 2 if abs(new_guess - guess) < precision: break guess = new_guess return new_guess

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 Parameters**: - The function `my_sqrt` takes two parameters: `x` (the number to find the square root of) and `precision` (the desired precision of the result), with a default value of `1e-10`. It also has a `max_iterations` parameter with a default value of 100. 2. **Handling Negative Input**: - The function raises a `ValueError` if `x` is negative, which is appropriate since the square root of a negative number is not a real number. 3. **Handling Zero Input**: - If `x` is zero, the function returns 0 immediately, which is correct since the square root of 0 is 0. 4. **Initial Guess**: - The initial guess for the square root is set to `x / 2`. This is a common starting point for iterative methods. 5. **Iterative Method**: - The function uses a loop to iteratively improve the guess. The new guess is calculated using the formula `(guess + x / guess) / 2`, which is the core of the Newton-Raphson method for finding square roots. - The loop continues until the difference between the new guess and the old guess is less than the specified precision or until the maximum number of iterations is reached. 6. **Return Statement**: - The function returns the final guess after the loop terminates. **Conclusion**: - The student implemented the Newton-Raphson method (also known as the Heron's method) to compute the square root. This method is a well-known iterative approach to finding square roots and does not involve directly calling 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