Average Error: 16.1 → 7.6
Time: 2.5m
Precision: 64
\[\alpha \gt -1 \land \beta \gt -1\]
\[\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}\]
↓
\[\begin{array}{l} \mathbf{if}\;\alpha \le 6.203807759670183 \cdot 10^{+18}:\\ \;\;\;\;\frac{\beta \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) - \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)} - 1.0 \cdot 1.0\right) \cdot \left(2.0 + \left(\beta + \alpha\right)\right)}{\left(\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) \cdot \left(2.0 + \left(\beta + \alpha\right)\right)\right) \cdot 2.0}\\ \mathbf{elif}\;\alpha \le 3.102091968712784 \cdot 10^{+51}:\\ \;\;\;\;\frac{\frac{\beta}{2.0 + \left(\beta + \alpha\right)} - \left(\left(\frac{4.0}{\alpha \cdot \alpha} - \frac{2.0}{\alpha}\right) - \frac{\frac{8.0}{\alpha}}{\alpha \cdot \alpha}\right)}{2.0}\\ \mathbf{elif}\;\alpha \le 7.950393235852575 \cdot 10^{+108}:\\ \;\;\;\;\frac{\beta \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) - \frac{\frac{{\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right)}^{3} \cdot {\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right)}^{3} - {\left(1.0 \cdot 1.0\right)}^{3} \cdot {\left(1.0 \cdot 1.0\right)}^{3}}{{\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right)}^{3} + {\left(1.0 \cdot 1.0\right)}^{3}}}{\left(\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right) \cdot \left(1.0 \cdot 1.0\right) + \left(1.0 \cdot 1.0\right) \cdot \left(1.0 \cdot 1.0\right)\right) + \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right) \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right)} \cdot \left(2.0 + \left(\beta + \alpha\right)\right)}{\left(\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) \cdot \left(2.0 + \left(\beta + \alpha\right)\right)\right) \cdot 2.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\beta}{2.0 + \left(\beta + \alpha\right)} - \left(\left(\frac{4.0}{\alpha \cdot \alpha} - \frac{2.0}{\alpha}\right) - \frac{\frac{8.0}{\alpha}}{\alpha \cdot \alpha}\right)}{2.0}\\ \end{array}\]
\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}
↓
\begin{array}{l}
\mathbf{if}\;\alpha \le 6.203807759670183 \cdot 10^{+18}:\\
\;\;\;\;\frac{\beta \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) - \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)} - 1.0 \cdot 1.0\right) \cdot \left(2.0 + \left(\beta + \alpha\right)\right)}{\left(\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) \cdot \left(2.0 + \left(\beta + \alpha\right)\right)\right) \cdot 2.0}\\

\mathbf{elif}\;\alpha \le 3.102091968712784 \cdot 10^{+51}:\\
\;\;\;\;\frac{\frac{\beta}{2.0 + \left(\beta + \alpha\right)} - \left(\left(\frac{4.0}{\alpha \cdot \alpha} - \frac{2.0}{\alpha}\right) - \frac{\frac{8.0}{\alpha}}{\alpha \cdot \alpha}\right)}{2.0}\\

\mathbf{elif}\;\alpha \le 7.950393235852575 \cdot 10^{+108}:\\
\;\;\;\;\frac{\beta \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) - \frac{\frac{{\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right)}^{3} \cdot {\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right)}^{3} - {\left(1.0 \cdot 1.0\right)}^{3} \cdot {\left(1.0 \cdot 1.0\right)}^{3}}{{\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right)}^{3} + {\left(1.0 \cdot 1.0\right)}^{3}}}{\left(\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right) \cdot \left(1.0 \cdot 1.0\right) + \left(1.0 \cdot 1.0\right) \cdot \left(1.0 \cdot 1.0\right)\right) + \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right) \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right)} \cdot \left(2.0 + \left(\beta + \alpha\right)\right)}{\left(\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) \cdot \left(2.0 + \left(\beta + \alpha\right)\right)\right) \cdot 2.0}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{\beta}{2.0 + \left(\beta + \alpha\right)} - \left(\left(\frac{4.0}{\alpha \cdot \alpha} - \frac{2.0}{\alpha}\right) - \frac{\frac{8.0}{\alpha}}{\alpha \cdot \alpha}\right)}{2.0}\\

\end{array}
double f(double alpha, double beta) {
        double r18146285 = beta;
        double r18146286 = alpha;
        double r18146287 = r18146285 - r18146286;
        double r18146288 = r18146286 + r18146285;
        double r18146289 = 2.0;
        double r18146290 = r18146288 + r18146289;
        double r18146291 = r18146287 / r18146290;
        double r18146292 = 1.0;
        double r18146293 = r18146291 + r18146292;
        double r18146294 = r18146293 / r18146289;
        return r18146294;
}
↓
double f(double alpha, double beta) {
        double r18146295 = alpha;
        double r18146296 = 6.203807759670183e+18;
        bool r18146297 = r18146295 <= r18146296;
        double r18146298 = beta;
        double r18146299 = 2.0;
        double r18146300 = r18146298 + r18146295;
        double r18146301 = r18146299 + r18146300;
        double r18146302 = r18146295 / r18146301;
        double r18146303 = 1.0;
        double r18146304 = r18146302 + r18146303;
        double r18146305 = r18146298 * r18146304;
        double r18146306 = r18146302 * r18146302;
        double r18146307 = r18146303 * r18146303;
        double r18146308 = r18146306 - r18146307;
        double r18146309 = r18146308 * r18146301;
        double r18146310 = r18146305 - r18146309;
        double r18146311 = r18146304 * r18146301;
        double r18146312 = r18146311 * r18146299;
        double r18146313 = r18146310 / r18146312;
        double r18146314 = 3.102091968712784e+51;
        bool r18146315 = r18146295 <= r18146314;
        double r18146316 = r18146298 / r18146301;
        double r18146317 = 4.0;
        double r18146318 = r18146295 * r18146295;
        double r18146319 = r18146317 / r18146318;
        double r18146320 = r18146299 / r18146295;
        double r18146321 = r18146319 - r18146320;
        double r18146322 = 8.0;
        double r18146323 = r18146322 / r18146295;
        double r18146324 = r18146323 / r18146318;
        double r18146325 = r18146321 - r18146324;
        double r18146326 = r18146316 - r18146325;
        double r18146327 = r18146326 / r18146299;
        double r18146328 = 7.950393235852575e+108;
        bool r18146329 = r18146295 <= r18146328;
        double r18146330 = 3.0;
        double r18146331 = pow(r18146306, r18146330);
        double r18146332 = r18146331 * r18146331;
        double r18146333 = pow(r18146307, r18146330);
        double r18146334 = r18146333 * r18146333;
        double r18146335 = r18146332 - r18146334;
        double r18146336 = r18146331 + r18146333;
        double r18146337 = r18146335 / r18146336;
        double r18146338 = r18146306 * r18146307;
        double r18146339 = r18146307 * r18146307;
        double r18146340 = r18146338 + r18146339;
        double r18146341 = r18146306 * r18146306;
        double r18146342 = r18146340 + r18146341;
        double r18146343 = r18146337 / r18146342;
        double r18146344 = r18146343 * r18146301;
        double r18146345 = r18146305 - r18146344;
        double r18146346 = r18146345 / r18146312;
        double r18146347 = r18146329 ? r18146346 : r18146327;
        double r18146348 = r18146315 ? r18146327 : r18146347;
        double r18146349 = r18146297 ? r18146313 : r18146348;
        return r18146349;
}

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 3 regimes

  2. if alpha < 6.203807759670183e+18

    1. Initial program 0.6

      \[\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}\]
    2. Using strategy rm

    3. Applied div-sub0.6

      \[\leadsto \frac{\color{blue}{\left(\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)} + 1.0}{2.0}\]

    4. Applied associate-+l-0.6

      \[\leadsto \frac{\color{blue}{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0\right)}}{2.0}\]
    5. Using strategy rm

    6. Applied flip--0.6

      \[\leadsto \frac{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \color{blue}{\frac{\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0 \cdot 1.0}{\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}}}{2.0}\]

    7. Applied frac-sub0.6

      \[\leadsto \frac{\color{blue}{\frac{\beta \cdot \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0 \cdot 1.0\right)}{\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0\right)}}}{2.0}\]

    8. Applied associate-/l/0.6

      \[\leadsto \color{blue}{\frac{\beta \cdot \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0 \cdot 1.0\right)}{2.0 \cdot \left(\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0\right)\right)}}\]

    if 6.203807759670183e+18 < alpha < 3.102091968712784e+51 or 7.950393235852575e+108 < alpha

    1. Initial program 51.7

      \[\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}\]
    2. Using strategy rm

    3. Applied div-sub51.7

      \[\leadsto \frac{\color{blue}{\left(\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)} + 1.0}{2.0}\]

    4. Applied associate-+l-49.9

      \[\leadsto \frac{\color{blue}{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0\right)}}{2.0}\]

    5. Taylor expanded around inf 18.0

      \[\leadsto \frac{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \color{blue}{\left(4.0 \cdot \frac{1}{{\alpha}^{2}} - \left(2.0 \cdot \frac{1}{\alpha} + 8.0 \cdot \frac{1}{{\alpha}^{3}}\right)\right)}}{2.0}\]

    6. Simplified18.0

      \[\leadsto \frac{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \color{blue}{\left(\left(\frac{4.0}{\alpha \cdot \alpha} - \frac{2.0}{\alpha}\right) - \frac{\frac{8.0}{\alpha}}{\alpha \cdot \alpha}\right)}}{2.0}\]

    if 3.102091968712784e+51 < alpha < 7.950393235852575e+108

    1. Initial program 42.6

      \[\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}\]
    2. Using strategy rm

    3. Applied div-sub42.5

      \[\leadsto \frac{\color{blue}{\left(\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)} + 1.0}{2.0}\]

    4. Applied associate-+l-41.5

      \[\leadsto \frac{\color{blue}{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0\right)}}{2.0}\]
    5. Using strategy rm

    6. Applied flip--41.5

      \[\leadsto \frac{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \color{blue}{\frac{\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0 \cdot 1.0}{\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}}}{2.0}\]

    7. Applied frac-sub41.5

      \[\leadsto \frac{\color{blue}{\frac{\beta \cdot \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0 \cdot 1.0\right)}{\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0\right)}}}{2.0}\]

    8. Applied associate-/l/41.5

      \[\leadsto \color{blue}{\frac{\beta \cdot \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot \frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0 \cdot 1.0\right)}{2.0 \cdot \left(\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0\right)\right)}}\]
    9. Using strategy rm

    10. Applied flip3--41.5

      \[\leadsto \frac{\beta \cdot \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \color{blue}{\frac{{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^{3} - {\left(1.0 \cdot 1.0\right)}^{3}}{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right) \cdot \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right) + \left(\left(1.0 \cdot 1.0\right) \cdot \left(1.0 \cdot 1.0\right) + \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right) \cdot \left(1.0 \cdot 1.0\right)\right)}}}{2.0 \cdot \left(\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0\right)\right)}\]
    11. Using strategy rm

    12. Applied flip--41.5

      \[\leadsto \frac{\beta \cdot \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0\right) - \left(\left(\alpha + \beta\right) + 2.0\right) \cdot \frac{\color{blue}{\frac{{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^{3} \cdot {\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^{3} - {\left(1.0 \cdot 1.0\right)}^{3} \cdot {\left(1.0 \cdot 1.0\right)}^{3}}{{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)}^{3} + {\left(1.0 \cdot 1.0\right)}^{3}}}}{\left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right) \cdot \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right) + \left(\left(1.0 \cdot 1.0\right) \cdot \left(1.0 \cdot 1.0\right) + \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} \cdot \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right) \cdot \left(1.0 \cdot 1.0\right)\right)}}{2.0 \cdot \left(\left(\left(\alpha + \beta\right) + 2.0\right) \cdot \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0\right)\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification7.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\alpha \le 6.203807759670183 \cdot 10^{+18}:\\ \;\;\;\;\frac{\beta \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) - \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)} - 1.0 \cdot 1.0\right) \cdot \left(2.0 + \left(\beta + \alpha\right)\right)}{\left(\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) \cdot \left(2.0 + \left(\beta + \alpha\right)\right)\right) \cdot 2.0}\\ \mathbf{elif}\;\alpha \le 3.102091968712784 \cdot 10^{+51}:\\ \;\;\;\;\frac{\frac{\beta}{2.0 + \left(\beta + \alpha\right)} - \left(\left(\frac{4.0}{\alpha \cdot \alpha} - \frac{2.0}{\alpha}\right) - \frac{\frac{8.0}{\alpha}}{\alpha \cdot \alpha}\right)}{2.0}\\ \mathbf{elif}\;\alpha \le 7.950393235852575 \cdot 10^{+108}:\\ \;\;\;\;\frac{\beta \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) - \frac{\frac{{\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right)}^{3} \cdot {\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right)}^{3} - {\left(1.0 \cdot 1.0\right)}^{3} \cdot {\left(1.0 \cdot 1.0\right)}^{3}}{{\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right)}^{3} + {\left(1.0 \cdot 1.0\right)}^{3}}}{\left(\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right) \cdot \left(1.0 \cdot 1.0\right) + \left(1.0 \cdot 1.0\right) \cdot \left(1.0 \cdot 1.0\right)\right) + \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right) \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right)} \cdot \left(2.0 + \left(\beta + \alpha\right)\right)}{\left(\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) \cdot \left(2.0 + \left(\beta + \alpha\right)\right)\right) \cdot 2.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\beta}{2.0 + \left(\beta + \alpha\right)} - \left(\left(\frac{4.0}{\alpha \cdot \alpha} - \frac{2.0}{\alpha}\right) - \frac{\frac{8.0}{\alpha}}{\alpha \cdot \alpha}\right)}{2.0}\\ \end{array}\]

Reproduce

herbie shell --seed 2019120 
(FPCore (alpha beta)
  :name "Octave 3.8, jcobi/1"
  :pre (and (> alpha -1) (> beta -1))
  (/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0))