doc-comments-ai

```python
def calculate_discount(price: float, discount_rate: float) -> float:
    """
    Calculate the final price after applying a discount rate to the original price.

    Args:
        price (float): The original price of the item before discount. Must be a positive number.
        discount_rate (float): The discount rate to apply (e.g., 0.20 for 20%). Must be between 0 and 1.

    Returns:
        float: The final price after applying the discount. Returns 0 if inputs are invalid.

    Raises:
        ValueError: If `price` is negative or `discount_rate` is outside the range [0, 1].

    Examples:
        >>> calculate_discount(100.0, 0.20)
        80.0
        >>> calculate_discount(50.0, 0.50)
        25.0
        >>> calculate_discount(-10.0, 0.10)
        Traceback (most recent call last):
            ...
        ValueError: Price cannot be negative.
    """
    if price < 0:
        raise ValueError("Price cannot be negative.")
    if not (0 <= discount_rate <= 1):
        raise ValueError("Discount rate must be between 0 and 1.")
    return price * (1 - discount_rate)
```