There's even a further optimization that could be had: use (and adapt) a [1/2] Padé on the inside of the if body. This is because small_x will always be less than the square root of 0.075 (which is ~0.27). The [1/2] Padé approximant for asin() can compute much faster, but only for smaller values of x. It can even be inlined into our function for further optimization. See below:
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