Softsign Function Calculator

Compute the softsign function softsign(x)=x/(1+|x|) and its derivative, compared with tanh as an ML activation.

Input

Enter x to compute softsign(x) = x / (1 + |x|), its derivative, and a comparison with tanh.

Input x

Enter any real number.

softsign(1)

0.5

Derivative softsign'(1)

0.25

Comparison tanh(1)

0.761594156

Input x

Graph of softsign(x)

The softsign function is defined as softsign(x) = x / (1 + |x|) and its output is bounded to the open interval (-1, 1).
The first derivative is softsign'(x) = 1 / (1 + |x|)^2. It reaches its maximum value of 1 at x = 0 and approaches 0 as |x| grows.
Like tanh, softsign is an S-shaped (sigmoidal) activation, but its tails saturate more gently (polynomial approach to 1), which can help reduce vanishing gradients.
The input x is any real number and the dimensionless output is used as an activation function in neural networks.

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