Given X (n, d), binary labels y (n,) and weights w (d,), return (loss, grad):

• loss is the mean logistic loss, grad its (d,) gradient
• no loops
• must not overflow when |X @ w| is around 800

Input

X =
[[ 1.  2.]
 [ 3.  4.]
 [-1.  0.]]
y = [1. 0. 1.]
w = [ 0.5  -0.25]

Output

(0.8804337163067194, array([0.66327911, 0.49661244]))