Sigmoid neurons: http://neuralnetworksanddeeplearning.com/chap1.html#sigmoid_neurons

Fast sigmoid algorithm: http://stackoverflow.com/questions/10732027/fast-sigmoid-algorithm

**(*fun)(xs[i]);
**
atan(pi*x/2)*2/pi 24.1 ns
atan(x) 23.0 ns
1/(1+exp(-x)) 20.4 ns
1/sqrt(1+x^2) 13.4 ns
erf(sqrt(pi)*x/2) 6.7 ns
tanh(x) 5.5 ns
x/(1+|x|) 5.5 ns

**xs[i] = (*fun)(xs[i]);
**
atan(pi*x/2)*2/pi 9.2 ns
atan(x) 7.9 ns
1/(1+exp(-x)) 19.3 ns
1/sqrt(1+x^2) 10.8 ns
erf(sqrt(pi)*x/2) 6.5 ns
tanh(x) 15.4 ns
x/(1+|x|) 4.4 ns

**xs[i] = (*fun)(xs[i]) + 0.5;
**
atan(pi*x/2)*2/pi 20.5 ns
atan(x) 19.4 ns
1/(1+exp(-x)) 19.3 ns
1/sqrt(1+x^2) 10.8 ns
erf(sqrt(pi)*x/2) 49.9 ns
tanh(x) 28.1 ns
x/(1+|x|) 2.5 ns

Source: https://gist.github.com/astanin/5270668 (‘Benchmark various sigmoid functions’ by https://github.com/astanin)

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