about Differentiable approximation to rounding

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⌊x⌉approx = ⌊x⌉ + (x −⌊x⌉)^3 , Why don't you use a larger power to approximate ⌊x⌉ ? for example , ⌊x⌉approx = ⌊x⌉ + (x −⌊x⌉)^7