Average Error: 16.4 → 6.1
Time: 30.8s
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 7.41319761099139 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{\beta \cdot \left(1.0 \cdot 1.0 + \left(\frac{\alpha}{2.0 + \left(\alpha + \beta\right)} + 1.0\right) \cdot \frac{\alpha}{2.0 + \left(\alpha + \beta\right)}\right) - \frac{\left(\left(\left(\frac{\alpha}{2.0 + \left(\alpha + \beta\right)} \cdot \frac{\sqrt[3]{\alpha} \cdot \sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\alpha + \beta\right)} \cdot \sqrt[3]{2.0 + \left(\alpha + \beta\right)}}\right) \cdot \frac{\sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\alpha + \beta\right)}}\right) \cdot \frac{\alpha}{2.0 + \left(\alpha + \beta\right)}\right) \cdot \left(\left(\left(\frac{\alpha}{2.0 + \left(\alpha + \beta\right)} \cdot \frac{\sqrt[3]{\alpha} \cdot \sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\alpha + \beta\right)} \cdot \sqrt[3]{2.0 + \left(\alpha + \beta\right)}}\right) \cdot \frac{\sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\alpha + \beta\right)}}\right) \cdot \frac{\alpha}{2.0 + \left(\alpha + \beta\right)}\right) - \left(\left(1.0 \cdot 1.0\right) \cdot 1.0\right) \cdot \left(\left(1.0 \cdot 1.0\right) \cdot 1.0\right)}{\left(1.0 \cdot 1.0\right) \cdot 1.0 + \left(\left(\frac{\alpha}{2.0 + \left(\alpha + \beta\right)} \cdot \frac{\sqrt[3]{\alpha} \cdot \sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\alpha + \beta\right)} \cdot \sqrt[3]{2.0 + \left(\alpha + \beta\right)}}\right) \cdot \frac{\sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\alpha + \beta\right)}}\right) \cdot \frac{\alpha}{2.0 + \left(\alpha + \beta\right)}} \cdot \left(2.0 + \left(\alpha + \beta\right)\right)}{\left(1.0 \cdot 1.0 + \left(\frac{\alpha}{2.0 + \left(\alpha + \beta\right)} + 1.0\right) \cdot \frac{\alpha}{2.0 + \left(\alpha + \beta\right)}\right) \cdot \left(2.0 + \left(\alpha + \beta\right)\right)}}{2.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\beta}{2.0 + \left(\alpha + \beta\right)} - \left(\left(\frac{4.0}{\alpha \cdot \alpha} - \frac{8.0}{\left(\alpha \cdot \alpha\right) \cdot \alpha}\right) - \frac{2.0}{\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 7.41319761099139 \cdot 10^{+16}:\\
\;\;\;\;\frac{\frac{\beta \cdot \left(1.0 \cdot 1.0 + \left(\frac{\alpha}{2.0 + \left(\alpha + \beta\right)} + 1.0\right) \cdot \frac{\alpha}{2.0 + \left(\alpha + \beta\right)}\right) - \frac{\left(\left(\left(\frac{\alpha}{2.0 + \left(\alpha + \beta\right)} \cdot \frac{\sqrt[3]{\alpha} \cdot \sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\alpha + \beta\right)} \cdot \sqrt[3]{2.0 + \left(\alpha + \beta\right)}}\right) \cdot \frac{\sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\alpha + \beta\right)}}\right) \cdot \frac{\alpha}{2.0 + \left(\alpha + \beta\right)}\right) \cdot \left(\left(\left(\frac{\alpha}{2.0 + \left(\alpha + \beta\right)} \cdot \frac{\sqrt[3]{\alpha} \cdot \sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\alpha + \beta\right)} \cdot \sqrt[3]{2.0 + \left(\alpha + \beta\right)}}\right) \cdot \frac{\sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\alpha + \beta\right)}}\right) \cdot \frac{\alpha}{2.0 + \left(\alpha + \beta\right)}\right) - \left(\left(1.0 \cdot 1.0\right) \cdot 1.0\right) \cdot \left(\left(1.0 \cdot 1.0\right) \cdot 1.0\right)}{\left(1.0 \cdot 1.0\right) \cdot 1.0 + \left(\left(\frac{\alpha}{2.0 + \left(\alpha + \beta\right)} \cdot \frac{\sqrt[3]{\alpha} \cdot \sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\alpha + \beta\right)} \cdot \sqrt[3]{2.0 + \left(\alpha + \beta\right)}}\right) \cdot \frac{\sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\alpha + \beta\right)}}\right) \cdot \frac{\alpha}{2.0 + \left(\alpha + \beta\right)}} \cdot \left(2.0 + \left(\alpha + \beta\right)\right)}{\left(1.0 \cdot 1.0 + \left(\frac{\alpha}{2.0 + \left(\alpha + \beta\right)} + 1.0\right) \cdot \frac{\alpha}{2.0 + \left(\alpha + \beta\right)}\right) \cdot \left(2.0 + \left(\alpha + \beta\right)\right)}}{2.0}\\

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

\end{array}
double f(double alpha, double beta) {
        double r4690381 = beta;
        double r4690382 = alpha;
        double r4690383 = r4690381 - r4690382;
        double r4690384 = r4690382 + r4690381;
        double r4690385 = 2.0;
        double r4690386 = r4690384 + r4690385;
        double r4690387 = r4690383 / r4690386;
        double r4690388 = 1.0;
        double r4690389 = r4690387 + r4690388;
        double r4690390 = r4690389 / r4690385;
        return r4690390;
}
↓
double f(double alpha, double beta) {
        double r4690391 = alpha;
        double r4690392 = 7.41319761099139e+16;
        bool r4690393 = r4690391 <= r4690392;
        double r4690394 = beta;
        double r4690395 = 1.0;
        double r4690396 = r4690395 * r4690395;
        double r4690397 = 2.0;
        double r4690398 = r4690391 + r4690394;
        double r4690399 = r4690397 + r4690398;
        double r4690400 = r4690391 / r4690399;
        double r4690401 = r4690400 + r4690395;
        double r4690402 = r4690401 * r4690400;
        double r4690403 = r4690396 + r4690402;
        double r4690404 = r4690394 * r4690403;
        double r4690405 = cbrt(r4690391);
        double r4690406 = r4690405 * r4690405;
        double r4690407 = cbrt(r4690399);
        double r4690408 = r4690407 * r4690407;
        double r4690409 = r4690406 / r4690408;
        double r4690410 = r4690400 * r4690409;
        double r4690411 = r4690405 / r4690407;
        double r4690412 = r4690410 * r4690411;
        double r4690413 = r4690412 * r4690400;
        double r4690414 = r4690413 * r4690413;
        double r4690415 = r4690396 * r4690395;
        double r4690416 = r4690415 * r4690415;
        double r4690417 = r4690414 - r4690416;
        double r4690418 = r4690415 + r4690413;
        double r4690419 = r4690417 / r4690418;
        double r4690420 = r4690419 * r4690399;
        double r4690421 = r4690404 - r4690420;
        double r4690422 = r4690403 * r4690399;
        double r4690423 = r4690421 / r4690422;
        double r4690424 = r4690423 / r4690397;
        double r4690425 = r4690394 / r4690399;
        double r4690426 = 4.0;
        double r4690427 = r4690391 * r4690391;
        double r4690428 = r4690426 / r4690427;
        double r4690429 = 8.0;
        double r4690430 = r4690427 * r4690391;
        double r4690431 = r4690429 / r4690430;
        double r4690432 = r4690428 - r4690431;
        double r4690433 = r4690397 / r4690391;
        double r4690434 = r4690432 - r4690433;
        double r4690435 = r4690425 - r4690434;
        double r4690436 = r4690435 / r4690397;
        double r4690437 = r4690393 ? r4690424 : r4690436;
        return r4690437;
}

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 < 7.41319761099139e+16

    1. Initial program 0.5

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

    3. Applied div-sub0.5

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

    4. Applied associate-+l-0.5

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

    6. Applied flip3--0.5

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

    7. Applied frac-sub0.5

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

    8. Simplified0.5

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

    9. Simplified0.5

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

    11. Applied add-cube-cbrt0.6

      \[\leadsto \frac{\frac{\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) + 1.0 \cdot 1.0\right) \cdot \beta - \left(\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\alpha}{\color{blue}{\left(\sqrt[3]{2.0 + \left(\beta + \alpha\right)} \cdot \sqrt[3]{2.0 + \left(\beta + \alpha\right)}\right) \cdot \sqrt[3]{2.0 + \left(\beta + \alpha\right)}}}\right) \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)} - \left(1.0 \cdot 1.0\right) \cdot 1.0\right) \cdot \left(2.0 + \left(\beta + \alpha\right)\right)}{\left(2.0 + \left(\beta + \alpha\right)\right) \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) + 1.0 \cdot 1.0\right)}}{2.0}\]

    12. Applied add-cube-cbrt0.6

      \[\leadsto \frac{\frac{\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) + 1.0 \cdot 1.0\right) \cdot \beta - \left(\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\color{blue}{\left(\sqrt[3]{\alpha} \cdot \sqrt[3]{\alpha}\right) \cdot \sqrt[3]{\alpha}}}{\left(\sqrt[3]{2.0 + \left(\beta + \alpha\right)} \cdot \sqrt[3]{2.0 + \left(\beta + \alpha\right)}\right) \cdot \sqrt[3]{2.0 + \left(\beta + \alpha\right)}}\right) \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)} - \left(1.0 \cdot 1.0\right) \cdot 1.0\right) \cdot \left(2.0 + \left(\beta + \alpha\right)\right)}{\left(2.0 + \left(\beta + \alpha\right)\right) \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) + 1.0 \cdot 1.0\right)}}{2.0}\]

    13. Applied times-frac0.6

      \[\leadsto \frac{\frac{\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) + 1.0 \cdot 1.0\right) \cdot \beta - \left(\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \color{blue}{\left(\frac{\sqrt[3]{\alpha} \cdot \sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\beta + \alpha\right)} \cdot \sqrt[3]{2.0 + \left(\beta + \alpha\right)}} \cdot \frac{\sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\beta + \alpha\right)}}\right)}\right) \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)} - \left(1.0 \cdot 1.0\right) \cdot 1.0\right) \cdot \left(2.0 + \left(\beta + \alpha\right)\right)}{\left(2.0 + \left(\beta + \alpha\right)\right) \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) + 1.0 \cdot 1.0\right)}}{2.0}\]

    14. Applied associate-*r*0.6

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

    16. Applied flip--0.6

      \[\leadsto \frac{\frac{\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) + 1.0 \cdot 1.0\right) \cdot \beta - \color{blue}{\frac{\left(\left(\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\sqrt[3]{\alpha} \cdot \sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\beta + \alpha\right)} \cdot \sqrt[3]{2.0 + \left(\beta + \alpha\right)}}\right) \cdot \frac{\sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\beta + \alpha\right)}}\right) \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right) \cdot \left(\left(\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\sqrt[3]{\alpha} \cdot \sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\beta + \alpha\right)} \cdot \sqrt[3]{2.0 + \left(\beta + \alpha\right)}}\right) \cdot \frac{\sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\beta + \alpha\right)}}\right) \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)}\right) - \left(\left(1.0 \cdot 1.0\right) \cdot 1.0\right) \cdot \left(\left(1.0 \cdot 1.0\right) \cdot 1.0\right)}{\left(\left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \frac{\sqrt[3]{\alpha} \cdot \sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\beta + \alpha\right)} \cdot \sqrt[3]{2.0 + \left(\beta + \alpha\right)}}\right) \cdot \frac{\sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\beta + \alpha\right)}}\right) \cdot \frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + \left(1.0 \cdot 1.0\right) \cdot 1.0}} \cdot \left(2.0 + \left(\beta + \alpha\right)\right)}{\left(2.0 + \left(\beta + \alpha\right)\right) \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} \cdot \left(\frac{\alpha}{2.0 + \left(\beta + \alpha\right)} + 1.0\right) + 1.0 \cdot 1.0\right)}}{2.0}\]

    if 7.41319761099139e+16 < alpha

    1. Initial program 49.8

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

    3. Applied div-sub49.8

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

    4. Applied associate-+l-48.4

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

    5. Taylor expanded around -inf 17.7

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

    6. Simplified17.7

      \[\leadsto \frac{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \color{blue}{\left(\left(\frac{4.0}{\alpha \cdot \alpha} - \frac{8.0}{\alpha \cdot \left(\alpha \cdot \alpha\right)}\right) - \frac{2.0}{\alpha}\right)}}{2.0}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification6.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\alpha \le 7.41319761099139 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{\beta \cdot \left(1.0 \cdot 1.0 + \left(\frac{\alpha}{2.0 + \left(\alpha + \beta\right)} + 1.0\right) \cdot \frac{\alpha}{2.0 + \left(\alpha + \beta\right)}\right) - \frac{\left(\left(\left(\frac{\alpha}{2.0 + \left(\alpha + \beta\right)} \cdot \frac{\sqrt[3]{\alpha} \cdot \sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\alpha + \beta\right)} \cdot \sqrt[3]{2.0 + \left(\alpha + \beta\right)}}\right) \cdot \frac{\sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\alpha + \beta\right)}}\right) \cdot \frac{\alpha}{2.0 + \left(\alpha + \beta\right)}\right) \cdot \left(\left(\left(\frac{\alpha}{2.0 + \left(\alpha + \beta\right)} \cdot \frac{\sqrt[3]{\alpha} \cdot \sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\alpha + \beta\right)} \cdot \sqrt[3]{2.0 + \left(\alpha + \beta\right)}}\right) \cdot \frac{\sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\alpha + \beta\right)}}\right) \cdot \frac{\alpha}{2.0 + \left(\alpha + \beta\right)}\right) - \left(\left(1.0 \cdot 1.0\right) \cdot 1.0\right) \cdot \left(\left(1.0 \cdot 1.0\right) \cdot 1.0\right)}{\left(1.0 \cdot 1.0\right) \cdot 1.0 + \left(\left(\frac{\alpha}{2.0 + \left(\alpha + \beta\right)} \cdot \frac{\sqrt[3]{\alpha} \cdot \sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\alpha + \beta\right)} \cdot \sqrt[3]{2.0 + \left(\alpha + \beta\right)}}\right) \cdot \frac{\sqrt[3]{\alpha}}{\sqrt[3]{2.0 + \left(\alpha + \beta\right)}}\right) \cdot \frac{\alpha}{2.0 + \left(\alpha + \beta\right)}} \cdot \left(2.0 + \left(\alpha + \beta\right)\right)}{\left(1.0 \cdot 1.0 + \left(\frac{\alpha}{2.0 + \left(\alpha + \beta\right)} + 1.0\right) \cdot \frac{\alpha}{2.0 + \left(\alpha + \beta\right)}\right) \cdot \left(2.0 + \left(\alpha + \beta\right)\right)}}{2.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\beta}{2.0 + \left(\alpha + \beta\right)} - \left(\left(\frac{4.0}{\alpha \cdot \alpha} - \frac{8.0}{\left(\alpha \cdot \alpha\right) \cdot \alpha}\right) - \frac{2.0}{\alpha}\right)}{2.0}\\ \end{array}\]

Reproduce

herbie shell --seed 2019149 
(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))