Average Error: 1.8 → 0.5
Time: 3.4m
Precision: 64
Internal Precision: 576
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\frac{\left(\pi \cdot \left(\left(\frac{\frac{(\left((\left(3 - z\right) \cdot \left((\left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z}\right) + \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right))_*\right) + \left(\left((\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right))_* - \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right) \cdot 771.3234287776531\right))_*\right) \cdot \left(4 - z\right) + \left(\left((\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right))_* - \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right) \cdot \left(\left(3 - z\right) \cdot -176.6150291621406\right)\right))_*}{\left(4 - z\right) \cdot \left(3 - z\right)}}{(\left(\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) - \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z}\right) + \left(e^{\log \left(\sqrt[3]{\left(\left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right)}\right)}\right))_*} + \left(\frac{-0.13857109526572012}{6 - z} + \frac{12.507343278686905}{5 - z}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)\right) \cdot \frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \sqrt{\pi \cdot 2}}{e^{0.5 + \left(7 - z\right)}}}{\sin \left(z \cdot \pi\right)}\]

Error

Bits error versus z

Derivation

  1. Initial program 1.8

    \[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]

  2. Initial simplification1.3

    \[\leadsto \left({\left(\left(1 - \left(z + -6\right)\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \left(\sqrt{2 \cdot \pi} \cdot \frac{1}{e^{\left(1 - \left(z + -6\right)\right) + 0.5}}\right)\right) \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{1 - \left(z + -6\right)}\right) + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\left(\frac{-176.6150291621406}{5 - \left(z + 1\right)} + \left(\frac{771.3234287776531}{\left(1 - z\right) - -2} + \left(\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) + \frac{676.5203681218851}{1 - z}\right)\right)\right) + \frac{-0.13857109526572012}{7 - \left(z + 1\right)}\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]
  3. Using strategy rm

  4. Applied flip3-+1.3

    \[\leadsto \left({\left(\left(1 - \left(z + -6\right)\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \left(\sqrt{2 \cdot \pi} \cdot \frac{1}{e^{\left(1 - \left(z + -6\right)\right) + 0.5}}\right)\right) \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{1 - \left(z + -6\right)}\right) + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\left(\frac{-176.6150291621406}{5 - \left(z + 1\right)} + \left(\frac{771.3234287776531}{\left(1 - z\right) - -2} + \color{blue}{\frac{{\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}}{\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right)}}\right)\right) + \frac{-0.13857109526572012}{7 - \left(z + 1\right)}\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  5. Applied frac-add1.3

    \[\leadsto \left({\left(\left(1 - \left(z + -6\right)\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \left(\sqrt{2 \cdot \pi} \cdot \frac{1}{e^{\left(1 - \left(z + -6\right)\right) + 0.5}}\right)\right) \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{1 - \left(z + -6\right)}\right) + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\left(\frac{-176.6150291621406}{5 - \left(z + 1\right)} + \color{blue}{\frac{771.3234287776531 \cdot \left(\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right)\right) + \left(\left(1 - z\right) - -2\right) \cdot \left({\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}\right)}{\left(\left(1 - z\right) - -2\right) \cdot \left(\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right)\right)}}\right) + \frac{-0.13857109526572012}{7 - \left(z + 1\right)}\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  6. Applied frac-add0.9

    \[\leadsto \left({\left(\left(1 - \left(z + -6\right)\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \left(\sqrt{2 \cdot \pi} \cdot \frac{1}{e^{\left(1 - \left(z + -6\right)\right) + 0.5}}\right)\right) \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{1 - \left(z + -6\right)}\right) + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\color{blue}{\frac{-176.6150291621406 \cdot \left(\left(\left(1 - z\right) - -2\right) \cdot \left(\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right)\right)\right) + \left(5 - \left(z + 1\right)\right) \cdot \left(771.3234287776531 \cdot \left(\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right)\right) + \left(\left(1 - z\right) - -2\right) \cdot \left({\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}\right)\right)}{\left(5 - \left(z + 1\right)\right) \cdot \left(\left(\left(1 - z\right) - -2\right) \cdot \left(\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right)\right)\right)}} + \frac{-0.13857109526572012}{7 - \left(z + 1\right)}\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  7. Simplified0.9

    \[\leadsto \left({\left(\left(1 - \left(z + -6\right)\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \left(\sqrt{2 \cdot \pi} \cdot \frac{1}{e^{\left(1 - \left(z + -6\right)\right) + 0.5}}\right)\right) \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{1 - \left(z + -6\right)}\right) + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\frac{\color{blue}{(\left((\left(3 - z\right) \cdot \left((\left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z}\right) + \left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right)\right))_*\right) + \left(\left((\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right))_* - \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right) \cdot 771.3234287776531\right))_*\right) \cdot \left(4 - z\right) + \left(\left(\left(3 - z\right) \cdot -176.6150291621406\right) \cdot \left((\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right))_* - \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right)\right))_*}}{\left(5 - \left(z + 1\right)\right) \cdot \left(\left(\left(1 - z\right) - -2\right) \cdot \left(\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right)\right)\right)} + \frac{-0.13857109526572012}{7 - \left(z + 1\right)}\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  8. Simplified0.9

    \[\leadsto \left({\left(\left(1 - \left(z + -6\right)\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \left(\sqrt{2 \cdot \pi} \cdot \frac{1}{e^{\left(1 - \left(z + -6\right)\right) + 0.5}}\right)\right) \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{1 - \left(z + -6\right)}\right) + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\frac{(\left((\left(3 - z\right) \cdot \left((\left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z}\right) + \left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right)\right))_*\right) + \left(\left((\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right))_* - \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right) \cdot 771.3234287776531\right))_*\right) \cdot \left(4 - z\right) + \left(\left(\left(3 - z\right) \cdot -176.6150291621406\right) \cdot \left((\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right))_* - \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right)\right))_*}{\color{blue}{\left(\left(3 - z\right) \cdot \left(4 - z\right)\right) \cdot (\left(\frac{676.5203681218851}{1 - z} - \left(0.9999999999998099 + \frac{-1259.1392167224028}{2 - z}\right)\right) \cdot \left(\frac{676.5203681218851}{1 - z}\right) + \left(\left(0.9999999999998099 + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(0.9999999999998099 + \frac{-1259.1392167224028}{2 - z}\right)\right))_*}} + \frac{-0.13857109526572012}{7 - \left(z + 1\right)}\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\]

  9. Simplified0.5

    \[\leadsto \color{blue}{\frac{\left(\left(\left(\left(\frac{12.507343278686905}{5 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \frac{\frac{(\left((\left(3 - z\right) \cdot \left((\left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z}\right) + \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right))_*\right) + \left(771.3234287776531 \cdot \left((\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right))_* - \frac{676.5203681218851}{1 - z} \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right)\right))_*\right) \cdot \left(4 - z\right) + \left(\left(-176.6150291621406 \cdot \left(3 - z\right)\right) \cdot \left((\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right))_* - \frac{676.5203681218851}{1 - z} \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right)\right))_*}{\left(4 - z\right) \cdot \left(3 - z\right)}}{(\left(\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) - \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z}\right) + \left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right))_*}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right) \cdot \pi\right) \cdot \frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{0.5 + \left(7 - z\right)}}}{\sin \left(z \cdot \pi\right)}}\]
  10. Using strategy rm

  11. Applied add-exp-log0.5

    \[\leadsto \frac{\left(\left(\left(\left(\frac{12.507343278686905}{5 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \frac{\frac{(\left((\left(3 - z\right) \cdot \left((\left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z}\right) + \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right))_*\right) + \left(771.3234287776531 \cdot \left((\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right))_* - \frac{676.5203681218851}{1 - z} \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right)\right))_*\right) \cdot \left(4 - z\right) + \left(\left(-176.6150291621406 \cdot \left(3 - z\right)\right) \cdot \left((\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right))_* - \frac{676.5203681218851}{1 - z} \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right)\right))_*}{\left(4 - z\right) \cdot \left(3 - z\right)}}{(\left(\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) - \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z}\right) + \color{blue}{\left(e^{\log \left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right)}\right)})_*}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right) \cdot \pi\right) \cdot \frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{0.5 + \left(7 - z\right)}}}{\sin \left(z \cdot \pi\right)}\]
  12. Using strategy rm

  13. Applied add-cbrt-cube0.5

    \[\leadsto \frac{\left(\left(\left(\left(\frac{12.507343278686905}{5 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \frac{\frac{(\left((\left(3 - z\right) \cdot \left((\left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z}\right) + \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right))_*\right) + \left(771.3234287776531 \cdot \left((\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right))_* - \frac{676.5203681218851}{1 - z} \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right)\right))_*\right) \cdot \left(4 - z\right) + \left(\left(-176.6150291621406 \cdot \left(3 - z\right)\right) \cdot \left((\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right))_* - \frac{676.5203681218851}{1 - z} \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right)\right))_*}{\left(4 - z\right) \cdot \left(3 - z\right)}}{(\left(\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) - \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z}\right) + \left(e^{\log \left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \color{blue}{\sqrt[3]{\left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)}}\right)}\right))_*}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right) \cdot \pi\right) \cdot \frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{0.5 + \left(7 - z\right)}}}{\sin \left(z \cdot \pi\right)}\]

  14. Applied add-cbrt-cube0.5

    \[\leadsto \frac{\left(\left(\left(\left(\frac{12.507343278686905}{5 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \frac{\frac{(\left((\left(3 - z\right) \cdot \left((\left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z}\right) + \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right))_*\right) + \left(771.3234287776531 \cdot \left((\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right))_* - \frac{676.5203681218851}{1 - z} \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right)\right))_*\right) \cdot \left(4 - z\right) + \left(\left(-176.6150291621406 \cdot \left(3 - z\right)\right) \cdot \left((\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right))_* - \frac{676.5203681218851}{1 - z} \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right)\right))_*}{\left(4 - z\right) \cdot \left(3 - z\right)}}{(\left(\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) - \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z}\right) + \left(e^{\log \left(\color{blue}{\sqrt[3]{\left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)}} \cdot \sqrt[3]{\left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)}\right)}\right))_*}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right) \cdot \pi\right) \cdot \frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{0.5 + \left(7 - z\right)}}}{\sin \left(z \cdot \pi\right)}\]

  15. Applied cbrt-unprod0.5

    \[\leadsto \frac{\left(\left(\left(\left(\frac{12.507343278686905}{5 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \frac{\frac{(\left((\left(3 - z\right) \cdot \left((\left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z}\right) + \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right))_*\right) + \left(771.3234287776531 \cdot \left((\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right))_* - \frac{676.5203681218851}{1 - z} \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right)\right))_*\right) \cdot \left(4 - z\right) + \left(\left(-176.6150291621406 \cdot \left(3 - z\right)\right) \cdot \left((\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right))_* - \frac{676.5203681218851}{1 - z} \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right)\right))_*}{\left(4 - z\right) \cdot \left(3 - z\right)}}{(\left(\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) - \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z}\right) + \left(e^{\log \color{blue}{\left(\sqrt[3]{\left(\left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right)}\right)}}\right))_*}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right) \cdot \pi\right) \cdot \frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \sqrt{2 \cdot \pi}}{e^{0.5 + \left(7 - z\right)}}}{\sin \left(z \cdot \pi\right)}\]

  16. Final simplification0.5

    \[\leadsto \frac{\left(\pi \cdot \left(\left(\frac{\frac{(\left((\left(3 - z\right) \cdot \left((\left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z}\right) + \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right))_*\right) + \left(\left((\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right))_* - \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right) \cdot 771.3234287776531\right))_*\right) \cdot \left(4 - z\right) + \left(\left((\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z}\right))_* - \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right) \cdot \left(\left(3 - z\right) \cdot -176.6150291621406\right)\right))_*}{\left(4 - z\right) \cdot \left(3 - z\right)}}{(\left(\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) - \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z}\right) + \left(e^{\log \left(\sqrt[3]{\left(\left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right) \cdot \left(\frac{-1259.1392167224028}{2 - z} + 0.9999999999998099\right)\right)}\right)}\right))_*} + \left(\frac{-0.13857109526572012}{6 - z} + \frac{12.507343278686905}{5 - z}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)\right) \cdot \frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \sqrt{\pi \cdot 2}}{e^{0.5 + \left(7 - z\right)}}}{\sin \left(z \cdot \pi\right)}\]

Runtime

Time bar (total: 3.4m)Debug logProfile

herbie shell --seed 2018234 +o rules:numerics
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- (- 1 z) 1) 7) 0.5) (+ (- (- 1 z) 1) 0.5))) (exp (- (+ (+ (- (- 1 z) 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1 z) 1) 1))) (/ -1259.1392167224028 (+ (- (- 1 z) 1) 2))) (/ 771.3234287776531 (+ (- (- 1 z) 1) 3))) (/ -176.6150291621406 (+ (- (- 1 z) 1) 4))) (/ 12.507343278686905 (+ (- (- 1 z) 1) 5))) (/ -0.13857109526572012 (+ (- (- 1 z) 1) 6))) (/ 9.984369578019572e-06 (+ (- (- 1 z) 1) 7))) (/ 1.5056327351493116e-07 (+ (- (- 1 z) 1) 8))))))