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\[\frac{1}{2} \cdot \log \left(\frac{1 + x}{1 - x}\right)\]

\frac{1}{2} \cdot \log \left(\frac{1 + x}{1 - x}\right)

double code(double x) {
	return ((double) (((double) (1.0 / 2.0)) * ((double) log(((double) (((double) (1.0 + x)) / ((double) (1.0 - x))))))));
}

Reproduce

herbie shell --seed 2020122 
(FPCore (x)
  :name "Hyperbolic arc-(co)tangent"
  :precision binary64
  (* (/ 1 2) (log (/ (+ 1 x) (- 1 x)))))