[froogie]

The first routine is about 3 rands per point minus rate of discarded, about half? So 6 rands per point. Now, since the second one has three rands in it, and plenty of trig, it really becomes a question if you can make the trigonometry faster than three rands. But as you saw, straightforward attempt will pretty much certainly end up having worse performance.

But what if one used optimizations like lookup tables and trigonometric approximations instead? Could they end up costing less cycles than three rands? Maybe not LUTs, maybe other trickery someone knows of?

And what about the cost of those three rands? Could one use a fast xorshift with good enough results here? Does one even need thee random vectors? Maybe two + modulo trickery will do?

[acqq]

Typically the generation of the uniform random numbers can be made quite cheaply, especially if the resolution is not critical (e.g. if uniform floats are enough and not uniform doubles etc) or if the quality of the randomness is not critical, and in these cases discarding half of these will win versus other costly operations.