#saturation

A logistic-regression model outputs $p = \sigma(z)$, and an example with label $y = 1$ has $z = -5$, a confident wrong prediction. With cross-entropy loss, $\partial L / \partial z = p - y$; with squared error $L = (p - y)^2$, $\partial L / \partial z = 2(p - y)\,p(1 - p)$. How many times larger in magnitude is the cross-entropy gradient? Round to the nearest whole number.