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\[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}\]

\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}

double code(double x) {
	return ((1.0 / sqrt(x)) - (1.0 / sqrt((x + 1.0))));
}

Reproduce

herbie shell --seed 2020106 +o rules:numerics
(FPCore (x)
  :name "2isqrt (example 3.6)"
  :precision binary64

  :herbie-target
  (/ 1 (+ (* (+ x 1) (sqrt x)) (* x (sqrt (+ x 1)))))

  (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))