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\[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}
double f(double t) {
        double r32954475 = 1.0;
        double r32954476 = 2.0;
        double r32954477 = t;
        double r32954478 = r32954476 / r32954477;
        double r32954479 = r32954475 / r32954477;
        double r32954480 = r32954475 + r32954479;
        double r32954481 = r32954478 / r32954480;
        double r32954482 = r32954476 - r32954481;
        double r32954483 = r32954482 * r32954482;
        double r32954484 = r32954475 + r32954483;
        double r32954485 = r32954476 + r32954483;
        double r32954486 = r32954484 / r32954485;
        return r32954486;
}

Reproduce

herbie shell --seed 2019120 +o rules:numerics
(FPCore (t)
  :name "Kahan p13 Example 2"
  (/ (+ 1 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))) (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))))))