For a "happy enough" approximation to the Weierstrass function, you can cut off the series once a^n/(1 - a) < epsilon and get a function that's differentiable e

For a "happy enough" approximation to the Weierstrass function, you can cut off the series once a^n/(1 - a) < epsilon and get a function that's differentiable everywhere. But it'll have an extremely large number of local optima, which is still bad for gradient descent.