Average Error: 23.3 → 11.5
Time: 34.3s
Precision: 64
\[\alpha \gt -1 \land \beta \gt -1 \land i \gt 0\]
\[\frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}\]
↓
\[\begin{array}{l} \mathbf{if}\;\alpha \le 3.5798925943844464 \cdot 10^{+172}:\\ \;\;\;\;\frac{\sqrt[3]{\left(\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right) + 1.0\right) \cdot e^{\log \left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right) + 1.0\right)}\right) \cdot \left(\left(\frac{\sqrt[3]{\beta - \alpha} \cdot \sqrt[3]{\beta - \alpha}}{\sqrt[3]{\left(\beta + \alpha\right) + 2 \cdot i} \cdot \sqrt[3]{\left(\beta + \alpha\right) + 2 \cdot i}} \cdot \left(\beta + \alpha\right)\right) \cdot \frac{\frac{\sqrt[3]{\beta - \alpha}}{\sqrt[3]{\left(\beta + \alpha\right) + 2 \cdot i}}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} + 1.0\right)}}{2.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{8.0}{\left(\alpha \cdot \alpha\right) \cdot \alpha} + \left(\frac{2.0}{\alpha} - \frac{4.0}{\alpha \cdot \alpha}\right)}{2.0}\\ \end{array}\]
\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 3.5798925943844464 \cdot 10^{+172}:\\
\;\;\;\;\frac{\sqrt[3]{\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 e^{\log \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) \cdot \left(\left(\frac{\sqrt[3]{\beta - \alpha} \cdot \sqrt[3]{\beta - \alpha}}{\sqrt[3]{\left(\beta + \alpha\right) + 2 \cdot i} \cdot \sqrt[3]{\left(\beta + \alpha\right) + 2 \cdot i}} \cdot \left(\beta + \alpha\right)\right) \cdot \frac{\frac{\sqrt[3]{\beta - \alpha}}{\sqrt[3]{\left(\beta + \alpha\right) + 2 \cdot i}}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} + 1.0\right)}}{2.0}\\

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

\end{array}
double f(double alpha, double beta, double i) {
        double r3867149 = alpha;
        double r3867150 = beta;
        double r3867151 = r3867149 + r3867150;
        double r3867152 = r3867150 - r3867149;
        double r3867153 = r3867151 * r3867152;
        double r3867154 = 2.0;
        double r3867155 = i;
        double r3867156 = r3867154 * r3867155;
        double r3867157 = r3867151 + r3867156;
        double r3867158 = r3867153 / r3867157;
        double r3867159 = 2.0;
        double r3867160 = r3867157 + r3867159;
        double r3867161 = r3867158 / r3867160;
        double r3867162 = 1.0;
        double r3867163 = r3867161 + r3867162;
        double r3867164 = r3867163 / r3867159;
        return r3867164;
}
↓
double f(double alpha, double beta, double i) {
        double r3867165 = alpha;
        double r3867166 = 3.5798925943844464e+172;
        bool r3867167 = r3867165 <= r3867166;
        double r3867168 = beta;
        double r3867169 = r3867168 - r3867165;
        double r3867170 = r3867168 + r3867165;
        double r3867171 = 2.0;
        double r3867172 = i;
        double r3867173 = r3867171 * r3867172;
        double r3867174 = r3867170 + r3867173;
        double r3867175 = r3867169 / r3867174;
        double r3867176 = 2.0;
        double r3867177 = r3867176 + r3867174;
        double r3867178 = r3867175 / r3867177;
        double r3867179 = r3867178 * r3867170;
        double r3867180 = 1.0;
        double r3867181 = r3867179 + r3867180;
        double r3867182 = log(r3867181);
        double r3867183 = exp(r3867182);
        double r3867184 = r3867181 * r3867183;
        double r3867185 = cbrt(r3867169);
        double r3867186 = r3867185 * r3867185;
        double r3867187 = cbrt(r3867174);
        double r3867188 = r3867187 * r3867187;
        double r3867189 = r3867186 / r3867188;
        double r3867190 = r3867189 * r3867170;
        double r3867191 = r3867185 / r3867187;
        double r3867192 = r3867191 / r3867177;
        double r3867193 = r3867190 * r3867192;
        double r3867194 = r3867193 + r3867180;
        double r3867195 = r3867184 * r3867194;
        double r3867196 = cbrt(r3867195);
        double r3867197 = r3867196 / r3867176;
        double r3867198 = 8.0;
        double r3867199 = r3867165 * r3867165;
        double r3867200 = r3867199 * r3867165;
        double r3867201 = r3867198 / r3867200;
        double r3867202 = r3867176 / r3867165;
        double r3867203 = 4.0;
        double r3867204 = r3867203 / r3867199;
        double r3867205 = r3867202 - r3867204;
        double r3867206 = r3867201 + r3867205;
        double r3867207 = r3867206 / r3867176;
        double r3867208 = r3867167 ? r3867197 : r3867207;
        return r3867208;
}

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 < 3.5798925943844464e+172

    1. Initial program 16.3

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

    3. Applied *-un-lft-identity16.3

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

    4. Applied *-un-lft-identity16.3

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

    5. Applied distribute-lft-out16.3

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

    6. Applied *-un-lft-identity16.3

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

    7. Applied times-frac6.1

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

    8. Applied times-frac6.1

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

    9. Simplified6.1

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

    11. Applied add-cbrt-cube6.1

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

    13. Applied *-un-lft-identity6.1

      \[\leadsto \frac{\sqrt[3]{\left(\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right)\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + \color{blue}{1 \cdot 2.0}} + 1.0\right)}}{2.0}\]

    14. Applied *-un-lft-identity6.1

      \[\leadsto \frac{\sqrt[3]{\left(\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right)\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\color{blue}{1 \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)} + 1 \cdot 2.0} + 1.0\right)}}{2.0}\]

    15. Applied distribute-lft-out6.1

      \[\leadsto \frac{\sqrt[3]{\left(\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right)\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\color{blue}{1 \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0\right)}} + 1.0\right)}}{2.0}\]

    16. Applied add-cube-cbrt6.2

      \[\leadsto \frac{\sqrt[3]{\left(\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right)\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\color{blue}{\left(\sqrt[3]{\left(\alpha + \beta\right) + 2 \cdot i} \cdot \sqrt[3]{\left(\alpha + \beta\right) + 2 \cdot i}\right) \cdot \sqrt[3]{\left(\alpha + \beta\right) + 2 \cdot i}}}}{1 \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0\right)} + 1.0\right)}}{2.0}\]

    17. Applied add-cube-cbrt6.1

      \[\leadsto \frac{\sqrt[3]{\left(\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right)\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\color{blue}{\left(\sqrt[3]{\beta - \alpha} \cdot \sqrt[3]{\beta - \alpha}\right) \cdot \sqrt[3]{\beta - \alpha}}}{\left(\sqrt[3]{\left(\alpha + \beta\right) + 2 \cdot i} \cdot \sqrt[3]{\left(\alpha + \beta\right) + 2 \cdot i}\right) \cdot \sqrt[3]{\left(\alpha + \beta\right) + 2 \cdot i}}}{1 \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0\right)} + 1.0\right)}}{2.0}\]

    18. Applied times-frac6.1

      \[\leadsto \frac{\sqrt[3]{\left(\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right)\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\color{blue}{\frac{\sqrt[3]{\beta - \alpha} \cdot \sqrt[3]{\beta - \alpha}}{\sqrt[3]{\left(\alpha + \beta\right) + 2 \cdot i} \cdot \sqrt[3]{\left(\alpha + \beta\right) + 2 \cdot i}} \cdot \frac{\sqrt[3]{\beta - \alpha}}{\sqrt[3]{\left(\alpha + \beta\right) + 2 \cdot i}}}}{1 \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0\right)} + 1.0\right)}}{2.0}\]

    19. Applied times-frac6.1

      \[\leadsto \frac{\sqrt[3]{\left(\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right)\right) \cdot \left(\left(\beta + \alpha\right) \cdot \color{blue}{\left(\frac{\frac{\sqrt[3]{\beta - \alpha} \cdot \sqrt[3]{\beta - \alpha}}{\sqrt[3]{\left(\alpha + \beta\right) + 2 \cdot i} \cdot \sqrt[3]{\left(\alpha + \beta\right) + 2 \cdot i}}}{1} \cdot \frac{\frac{\sqrt[3]{\beta - \alpha}}{\sqrt[3]{\left(\alpha + \beta\right) + 2 \cdot i}}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right)} + 1.0\right)}}{2.0}\]

    20. Applied associate-*r*6.1

      \[\leadsto \frac{\sqrt[3]{\left(\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right)\right) \cdot \left(\color{blue}{\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\sqrt[3]{\beta - \alpha} \cdot \sqrt[3]{\beta - \alpha}}{\sqrt[3]{\left(\alpha + \beta\right) + 2 \cdot i} \cdot \sqrt[3]{\left(\alpha + \beta\right) + 2 \cdot i}}}{1}\right) \cdot \frac{\frac{\sqrt[3]{\beta - \alpha}}{\sqrt[3]{\left(\alpha + \beta\right) + 2 \cdot i}}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}} + 1.0\right)}}{2.0}\]
    21. Using strategy rm

    22. Applied add-exp-log6.1

      \[\leadsto \frac{\sqrt[3]{\left(\color{blue}{e^{\log \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right)}} \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right)\right) \cdot \left(\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\sqrt[3]{\beta - \alpha} \cdot \sqrt[3]{\beta - \alpha}}{\sqrt[3]{\left(\alpha + \beta\right) + 2 \cdot i} \cdot \sqrt[3]{\left(\alpha + \beta\right) + 2 \cdot i}}}{1}\right) \cdot \frac{\frac{\sqrt[3]{\beta - \alpha}}{\sqrt[3]{\left(\alpha + \beta\right) + 2 \cdot i}}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0\right)}}{2.0}\]

    if 3.5798925943844464e+172 < alpha

    1. Initial program 63.2

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

    2. Taylor expanded around -inf 42.2

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

    3. Simplified42.2

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

  4. Final simplification11.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\alpha \le 3.5798925943844464 \cdot 10^{+172}:\\ \;\;\;\;\frac{\sqrt[3]{\left(\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right) + 1.0\right) \cdot e^{\log \left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right) + 1.0\right)}\right) \cdot \left(\left(\frac{\sqrt[3]{\beta - \alpha} \cdot \sqrt[3]{\beta - \alpha}}{\sqrt[3]{\left(\beta + \alpha\right) + 2 \cdot i} \cdot \sqrt[3]{\left(\beta + \alpha\right) + 2 \cdot i}} \cdot \left(\beta + \alpha\right)\right) \cdot \frac{\frac{\sqrt[3]{\beta - \alpha}}{\sqrt[3]{\left(\beta + \alpha\right) + 2 \cdot i}}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} + 1.0\right)}}{2.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{8.0}{\left(\alpha \cdot \alpha\right) \cdot \alpha} + \left(\frac{2.0}{\alpha} - \frac{4.0}{\alpha \cdot \alpha}\right)}{2.0}\\ \end{array}\]

Reproduce

herbie shell --seed 2019135 
(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))