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\[\alpha \gt -1 \land \beta \gt -1\]
\[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}
double f(double alpha, double beta) {
        double r55163057 = alpha;
        double r55163058 = beta;
        double r55163059 = r55163057 + r55163058;
        double r55163060 = r55163058 * r55163057;
        double r55163061 = r55163059 + r55163060;
        double r55163062 = 1.0;
        double r55163063 = r55163061 + r55163062;
        double r55163064 = 2.0;
        double r55163065 = 1.0;
        double r55163066 = r55163064 * r55163065;
        double r55163067 = r55163059 + r55163066;
        double r55163068 = r55163063 / r55163067;
        double r55163069 = r55163068 / r55163067;
        double r55163070 = r55163067 + r55163062;
        double r55163071 = r55163069 / r55163070;
        return r55163071;
}

Reproduce

herbie shell --seed 2019121 +o rules:numerics
(FPCore (alpha beta)
  :name "Octave 3.8, jcobi/3"
  :pre (and (> alpha -1) (> beta -1))
  (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))