Logistic sigmoid

Implement the logistic sigmoid function applied elementwise to a list of real numbers. Sigmoid(x) = 1 / (1 + exp(-x)). To avoid math range overflow for very negative inputs, use the equivalent stable form exp(x) / (1 + exp(x)) when x is negative. Return the list of outputs, each rounded to 6 decimal places. The input list may be empty (return an empty list).