Average Error: 3.5 → 2.1
Time: 26.6s
Precision: 64
\[\alpha \gt -1 \land \beta \gt -1\]
\[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;\alpha \le 6.365999385200841945719823444498939725586 \cdot 10^{194}:\\ \;\;\;\;\frac{\frac{\frac{1 + \left(\beta \cdot \alpha + \left(\beta + \alpha\right)\right)}{2 \cdot 1 + \left(\beta + \alpha\right)}}{2 \cdot 1 + \left(\beta + \alpha\right)}}{\left(2 \cdot 1 + \left(\beta + \alpha\right)\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1}
↓
\begin{array}{l}
\mathbf{if}\;\alpha \le 6.365999385200841945719823444498939725586 \cdot 10^{194}:\\
\;\;\;\;\frac{\frac{\frac{1 + \left(\beta \cdot \alpha + \left(\beta + \alpha\right)\right)}{2 \cdot 1 + \left(\beta + \alpha\right)}}{2 \cdot 1 + \left(\beta + \alpha\right)}}{\left(2 \cdot 1 + \left(\beta + \alpha\right)\right) + 1}\\

\mathbf{else}:\\
\;\;\;\;0\\

\end{array}
double f(double alpha, double beta) {
        double r4482833 = alpha;
        double r4482834 = beta;
        double r4482835 = r4482833 + r4482834;
        double r4482836 = r4482834 * r4482833;
        double r4482837 = r4482835 + r4482836;
        double r4482838 = 1.0;
        double r4482839 = r4482837 + r4482838;
        double r4482840 = 2.0;
        double r4482841 = r4482840 * r4482838;
        double r4482842 = r4482835 + r4482841;
        double r4482843 = r4482839 / r4482842;
        double r4482844 = r4482843 / r4482842;
        double r4482845 = r4482842 + r4482838;
        double r4482846 = r4482844 / r4482845;
        return r4482846;
}
↓
double f(double alpha, double beta) {
        double r4482847 = alpha;
        double r4482848 = 6.365999385200842e+194;
        bool r4482849 = r4482847 <= r4482848;
        double r4482850 = 1.0;
        double r4482851 = beta;
        double r4482852 = r4482851 * r4482847;
        double r4482853 = r4482851 + r4482847;
        double r4482854 = r4482852 + r4482853;
        double r4482855 = r4482850 + r4482854;
        double r4482856 = 2.0;
        double r4482857 = r4482856 * r4482850;
        double r4482858 = r4482857 + r4482853;
        double r4482859 = r4482855 / r4482858;
        double r4482860 = r4482859 / r4482858;
        double r4482861 = r4482858 + r4482850;
        double r4482862 = r4482860 / r4482861;
        double r4482863 = 0.0;
        double r4482864 = r4482849 ? r4482862 : r4482863;
        return r4482864;
}

Error

Bits error versus alpha

Bits error versus beta

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if alpha < 6.365999385200842e+194

    1. Initial program 1.6

      \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1}\]
    2. Using strategy rm

    3. Applied +-commutative1.6

      \[\leadsto \frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\color{blue}{1 + \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)}}\]

    if 6.365999385200842e+194 < alpha

    1. Initial program 16.8

      \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1}\]

    2. Taylor expanded around inf 5.7

      \[\leadsto \color{blue}{0}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\alpha \le 6.365999385200841945719823444498939725586 \cdot 10^{194}:\\ \;\;\;\;\frac{\frac{\frac{1 + \left(\beta \cdot \alpha + \left(\beta + \alpha\right)\right)}{2 \cdot 1 + \left(\beta + \alpha\right)}}{2 \cdot 1 + \left(\beta + \alpha\right)}}{\left(2 \cdot 1 + \left(\beta + \alpha\right)\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (alpha beta)
  :name "Octave 3.8, jcobi/3"
  :pre (and (> alpha -1.0) (> beta -1.0))
  (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))