Average Error: 23.8 → 11.4
Time: 30.7s
Precision: 64
\[\alpha \gt -1 \land \beta \gt -1 \land i \gt 0\]
\[\frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}\]
↓
\[\begin{array}{l} \mathbf{if}\;\alpha \le 6.412191516043432 \cdot 10^{+136}:\\ \;\;\;\;\frac{\sqrt[3]{\sqrt[3]{\left(\left(1.0 + \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}}{\sqrt{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}} \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}} \cdot \sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}}{\sqrt{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}}\right)\right) \cdot \left(1.0 + \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}}{\sqrt{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}} \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}} \cdot \sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}}{\sqrt{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}}\right)\right)\right) \cdot \left(1.0 + \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}}{\sqrt{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}} \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}} \cdot \sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}}{\sqrt{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}}\right)\right)} \cdot \left(\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right) + 1.0\right) \cdot \left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right) + 1.0\right)\right)}}{2.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\frac{2.0}{\alpha} - \frac{4.0}{\alpha \cdot \alpha}\right) + \frac{8.0}{\alpha \cdot \left(\alpha \cdot \alpha\right)}}{2.0}\\ \end{array}\]
\frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}
↓
\begin{array}{l}
\mathbf{if}\;\alpha \le 6.412191516043432 \cdot 10^{+136}:\\
\;\;\;\;\frac{\sqrt[3]{\sqrt[3]{\left(\left(1.0 + \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}}{\sqrt{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}} \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}} \cdot \sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}}{\sqrt{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}}\right)\right) \cdot \left(1.0 + \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}}{\sqrt{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}} \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}} \cdot \sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}}{\sqrt{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}}\right)\right)\right) \cdot \left(1.0 + \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}}{\sqrt{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}} \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}} \cdot \sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}}{\sqrt{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}}\right)\right)} \cdot \left(\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right) + 1.0\right) \cdot \left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right) + 1.0\right)\right)}}{2.0}\\

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

\end{array}
double f(double alpha, double beta, double i) {
        double r3841543 = alpha;
        double r3841544 = beta;
        double r3841545 = r3841543 + r3841544;
        double r3841546 = r3841544 - r3841543;
        double r3841547 = r3841545 * r3841546;
        double r3841548 = 2.0;
        double r3841549 = i;
        double r3841550 = r3841548 * r3841549;
        double r3841551 = r3841545 + r3841550;
        double r3841552 = r3841547 / r3841551;
        double r3841553 = 2.0;
        double r3841554 = r3841551 + r3841553;
        double r3841555 = r3841552 / r3841554;
        double r3841556 = 1.0;
        double r3841557 = r3841555 + r3841556;
        double r3841558 = r3841557 / r3841553;
        return r3841558;
}
↓
double f(double alpha, double beta, double i) {
        double r3841559 = alpha;
        double r3841560 = 6.412191516043432e+136;
        bool r3841561 = r3841559 <= r3841560;
        double r3841562 = 1.0;
        double r3841563 = beta;
        double r3841564 = r3841563 - r3841559;
        double r3841565 = r3841563 + r3841559;
        double r3841566 = 2.0;
        double r3841567 = i;
        double r3841568 = r3841566 * r3841567;
        double r3841569 = r3841565 + r3841568;
        double r3841570 = r3841564 / r3841569;
        double r3841571 = cbrt(r3841570);
        double r3841572 = 2.0;
        double r3841573 = r3841572 + r3841569;
        double r3841574 = sqrt(r3841573);
        double r3841575 = r3841571 / r3841574;
        double r3841576 = r3841571 * r3841571;
        double r3841577 = r3841576 / r3841574;
        double r3841578 = r3841565 * r3841577;
        double r3841579 = r3841575 * r3841578;
        double r3841580 = r3841562 + r3841579;
        double r3841581 = r3841580 * r3841580;
        double r3841582 = r3841581 * r3841580;
        double r3841583 = cbrt(r3841582);
        double r3841584 = r3841570 / r3841573;
        double r3841585 = r3841584 * r3841565;
        double r3841586 = r3841585 + r3841562;
        double r3841587 = r3841586 * r3841586;
        double r3841588 = r3841583 * r3841587;
        double r3841589 = cbrt(r3841588);
        double r3841590 = r3841589 / r3841572;
        double r3841591 = r3841572 / r3841559;
        double r3841592 = 4.0;
        double r3841593 = r3841559 * r3841559;
        double r3841594 = r3841592 / r3841593;
        double r3841595 = r3841591 - r3841594;
        double r3841596 = 8.0;
        double r3841597 = r3841559 * r3841593;
        double r3841598 = r3841596 / r3841597;
        double r3841599 = r3841595 + r3841598;
        double r3841600 = r3841599 / r3841572;
        double r3841601 = r3841561 ? r3841590 : r3841600;
        return r3841601;
}

Error

Bits error versus alpha

Bits error versus beta

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if alpha < 6.412191516043432e+136

    1. Initial program 15.2

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

    3. Applied *-un-lft-identity15.2

      \[\leadsto \frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\color{blue}{1 \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0\right)}} + 1.0}{2.0}\]

    4. Applied *-un-lft-identity15.2

      \[\leadsto \frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\color{blue}{1 \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}}{1 \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0\right)} + 1.0}{2.0}\]

    5. Applied times-frac4.5

      \[\leadsto \frac{\frac{\color{blue}{\frac{\alpha + \beta}{1} \cdot \frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}}{1 \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0\right)} + 1.0}{2.0}\]

    6. Applied times-frac4.5

      \[\leadsto \frac{\color{blue}{\frac{\frac{\alpha + \beta}{1}}{1} \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}} + 1.0}{2.0}\]

    7. Simplified4.5

      \[\leadsto \frac{\color{blue}{\left(\beta + \alpha\right)} \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}\]
    8. Using strategy rm

    9. Applied add-cbrt-cube4.5

      \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right)\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right)}}}{2.0}\]
    10. Using strategy rm

    11. Applied add-sqr-sqrt4.5

      \[\leadsto \frac{\sqrt[3]{\left(\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right)\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\color{blue}{\sqrt{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} \cdot \sqrt{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}}} + 1.0\right)}}{2.0}\]

    12. Applied add-cube-cbrt4.5

      \[\leadsto \frac{\sqrt[3]{\left(\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right)\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\color{blue}{\left(\sqrt[3]{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}} \cdot \sqrt[3]{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}\right) \cdot \sqrt[3]{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}}}{\sqrt{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} \cdot \sqrt{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}} + 1.0\right)}}{2.0}\]

    13. Applied times-frac4.5

      \[\leadsto \frac{\sqrt[3]{\left(\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right)\right) \cdot \left(\left(\beta + \alpha\right) \cdot \color{blue}{\left(\frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}} \cdot \sqrt[3]{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}}{\sqrt{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}} \cdot \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}}{\sqrt{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}}\right)} + 1.0\right)}}{2.0}\]

    14. Applied associate-*r*4.5

      \[\leadsto \frac{\sqrt[3]{\left(\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right)\right) \cdot \left(\color{blue}{\left(\left(\beta + \alpha\right) \cdot \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}} \cdot \sqrt[3]{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}}{\sqrt{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}}\right) \cdot \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}}{\sqrt{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}}} + 1.0\right)}}{2.0}\]
    15. Using strategy rm

    16. Applied add-cbrt-cube4.5

      \[\leadsto \frac{\sqrt[3]{\left(\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right)\right) \cdot \color{blue}{\sqrt[3]{\left(\left(\left(\left(\beta + \alpha\right) \cdot \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}} \cdot \sqrt[3]{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}}{\sqrt{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}}\right) \cdot \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}}{\sqrt{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}} + 1.0\right) \cdot \left(\left(\left(\beta + \alpha\right) \cdot \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}} \cdot \sqrt[3]{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}}{\sqrt{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}}\right) \cdot \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}}{\sqrt{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}} + 1.0\right)\right) \cdot \left(\left(\left(\beta + \alpha\right) \cdot \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}} \cdot \sqrt[3]{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}}{\sqrt{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}}\right) \cdot \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}}{\sqrt{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}} + 1.0\right)}}}}{2.0}\]

    if 6.412191516043432e+136 < alpha

    1. Initial program 61.3

      \[\frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}\]

    2. Taylor expanded around inf 41.6

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

    3. Simplified41.6

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

  4. Final simplification11.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\alpha \le 6.412191516043432 \cdot 10^{+136}:\\ \;\;\;\;\frac{\sqrt[3]{\sqrt[3]{\left(\left(1.0 + \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}}{\sqrt{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}} \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}} \cdot \sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}}{\sqrt{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}}\right)\right) \cdot \left(1.0 + \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}}{\sqrt{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}} \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}} \cdot \sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}}{\sqrt{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}}\right)\right)\right) \cdot \left(1.0 + \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}}{\sqrt{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}} \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}} \cdot \sqrt[3]{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}}{\sqrt{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}}\right)\right)} \cdot \left(\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right) + 1.0\right) \cdot \left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right) + 1.0\right)\right)}}{2.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\frac{2.0}{\alpha} - \frac{4.0}{\alpha \cdot \alpha}\right) + \frac{8.0}{\alpha \cdot \left(\alpha \cdot \alpha\right)}}{2.0}\\ \end{array}\]

Reproduce

herbie shell --seed 2019130 
(FPCore (alpha beta i)
  :name "Octave 3.8, jcobi/2"
  :pre (and (> alpha -1) (> beta -1) (> i 0))
  (/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0))