Approximate square root or logarithm with addition, subtraction, multiplication and division

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In some data science applications, one would like to normalize a count number with the square root, the logarithm, log(x+1) or a related subadditive function.

In the SPARQL 1.1 language, only addition, subtraction, multiplication and division exist. I would like to construct a subadditive or logarithm-like function SPARQL.

Is it possible to construct a finite non-iterative (x>a)-subadditive function, e.g., an approximate square root function, with only addition, subtraction, multiplication and division that works across a "reasonable" range of non-negative integers?

My current best bet is some form of finite continued fraction on log(x+1). However, the test that I made on one form showed it to be "insufficiently" subadditive, i.e., just a linear asymptote.