Mr Stenzel, CEO of Waldorf Music GmbH, decided to disclose his excellent pseudo sinusoidal formula: .

Here is a plot of the function:

As you can see, this really looks like a sine wave! The following error plot reveals a maximum error of 0.056:

In terms of distortion, Mr. Stenzel is right. This function is 2.85 times better than the previous pseudo sine.

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If you can afford a division try: 4*y/(1.25 – y) where y = x*(1-x). This is much better than using 4*y on its own. For some background see: https://en.wikipedia.org/wiki/Bhaskara_I's_sine_approximation_formula