Production Engineering: Fused, Numerically-Stable Loss

Implement:

def bce_with_logits_loss(z: np.ndarray, y: np.ndarray) -> float:
    """
    Numerically stable BCE computed directly from raw logits z,
    without ever computing a separate sigmoid(z) probability array.
    """

Your function should:

1. Never call sigmoid() or compute exp(z) for positive z anywhere in the implementation — only exp(-|z|).
2. Match plain bce_loss(sigmoid(z), y) on ordinary, non-extreme inputs.
3. Stay finite and correct for z values large enough that sigmoid(z) itself would already round to exactly 0.0 or 1.0.