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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 simplification0.6

   \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left({\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right)\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\]
3. Using strategy rm

4. Applied exp-diff0.6

   \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left({\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \frac{1}{\color{blue}{\frac{e^{1 - z}}{e^{-6 - 0.5}}}}\right)\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\]

5. Applied associate-/r/0.6

   \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left({\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \color{blue}{\left(\frac{1}{e^{1 - z}} \cdot e^{-6 - 0.5}\right)}\right)\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\]

6. Applied associate-*r*0.6

   \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \color{blue}{\left(\left({\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \frac{1}{e^{1 - z}}\right) \cdot e^{-6 - 0.5}\right)}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\]
7. Using strategy rm

8. Applied associate-+l+0.6

   \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\left({\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \frac{1}{e^{1 - z}}\right) \cdot e^{-6 - 0.5}\right)\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \color{blue}{\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)}\right)\]

9. Simplified0.6

   \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\left({\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \frac{1}{e^{1 - z}}\right) \cdot e^{-6 - 0.5}\right)\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\color{blue}{\frac{-0.13857109526572012}{6 - z}} + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]
10. Using strategy rm

11. Applied exp-diff0.6

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\left({\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)} \cdot \frac{1}{e^{1 - z}}\right) \cdot \color{blue}{\frac{e^{-6}}{e^{0.5}}}\right)\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]

12. Applied pow-sub0.6

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\left(\color{blue}{\frac{{\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(1 - z\right)}}{{\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(1 - 0.5\right)}}} \cdot \frac{1}{e^{1 - z}}\right) \cdot \frac{e^{-6}}{e^{0.5}}\right)\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]

13. Applied frac-times0.6

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\color{blue}{\frac{{\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(1 - z\right)} \cdot 1}{{\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(1 - 0.5\right)} \cdot e^{1 - z}}} \cdot \frac{e^{-6}}{e^{0.5}}\right)\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]

14. Applied frac-times0.6

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \color{blue}{\frac{\left({\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(1 - z\right)} \cdot 1\right) \cdot e^{-6}}{\left({\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(1 - 0.5\right)} \cdot e^{1 - z}\right) \cdot e^{0.5}}}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]

15. Simplified0.6

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \frac{\color{blue}{{\left(\left(0.5 + 7\right) - z\right)}^{\left(1 - z\right)} \cdot e^{-6}}}{\left({\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(1 - 0.5\right)} \cdot e^{1 - z}\right) \cdot e^{0.5}}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]

16. Simplified0.6

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \frac{{\left(\left(0.5 + 7\right) - z\right)}^{\left(1 - z\right)} \cdot e^{-6}}{\color{blue}{\frac{{\left(0.5 - \left(z + -7\right)\right)}^{\left(1 - 0.5\right)}}{e^{z - \left(1 + 0.5\right)}}}}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]
17. Using strategy rm

18. Applied sub-neg0.6

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \frac{{\left(\left(0.5 + 7\right) - z\right)}^{\left(1 - z\right)} \cdot e^{-6}}{\frac{{\left(0.5 - \left(z + -7\right)\right)}^{\left(1 - 0.5\right)}}{e^{\color{blue}{z + \left(-\left(1 + 0.5\right)\right)}}}}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]

19. Applied exp-sum0.6

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \frac{{\left(\left(0.5 + 7\right) - z\right)}^{\left(1 - z\right)} \cdot e^{-6}}{\frac{{\left(0.5 - \left(z + -7\right)\right)}^{\left(1 - 0.5\right)}}{\color{blue}{e^{z} \cdot e^{-\left(1 + 0.5\right)}}}}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]

20. Applied add-sqr-sqrt0.6

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \frac{{\left(\left(0.5 + 7\right) - z\right)}^{\left(1 - z\right)} \cdot e^{-6}}{\frac{{\color{blue}{\left(\sqrt{0.5 - \left(z + -7\right)} \cdot \sqrt{0.5 - \left(z + -7\right)}\right)}}^{\left(1 - 0.5\right)}}{e^{z} \cdot e^{-\left(1 + 0.5\right)}}}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]

21. Applied unpow-prod-down0.6

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \frac{{\left(\left(0.5 + 7\right) - z\right)}^{\left(1 - z\right)} \cdot e^{-6}}{\frac{\color{blue}{{\left(\sqrt{0.5 - \left(z + -7\right)}\right)}^{\left(1 - 0.5\right)} \cdot {\left(\sqrt{0.5 - \left(z + -7\right)}\right)}^{\left(1 - 0.5\right)}}}{e^{z} \cdot e^{-\left(1 + 0.5\right)}}}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]

22. Applied times-frac0.6

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \frac{{\left(\left(0.5 + 7\right) - z\right)}^{\left(1 - z\right)} \cdot e^{-6}}{\color{blue}{\frac{{\left(\sqrt{0.5 - \left(z + -7\right)}\right)}^{\left(1 - 0.5\right)}}{e^{z}} \cdot \frac{{\left(\sqrt{0.5 - \left(z + -7\right)}\right)}^{\left(1 - 0.5\right)}}{e^{-\left(1 + 0.5\right)}}}}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]

23. Applied times-frac0.6

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \color{blue}{\left(\frac{{\left(\left(0.5 + 7\right) - z\right)}^{\left(1 - z\right)}}{\frac{{\left(\sqrt{0.5 - \left(z + -7\right)}\right)}^{\left(1 - 0.5\right)}}{e^{z}}} \cdot \frac{e^{-6}}{\frac{{\left(\sqrt{0.5 - \left(z + -7\right)}\right)}^{\left(1 - 0.5\right)}}{e^{-\left(1 + 0.5\right)}}}\right)}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]

24. Simplified0.6

    \[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\frac{{\left(\left(0.5 + 7\right) - z\right)}^{\left(1 - z\right)}}{\frac{{\left(\sqrt{0.5 - \left(z + -7\right)}\right)}^{\left(1 - 0.5\right)}}{e^{z}}} \cdot \color{blue}{\frac{e^{-7 - 0.5}}{{\left(\sqrt{0.5 - \left(z + -7\right)}\right)}^{\left(1 - 0.5\right)}}}\right)\right) \cdot \left(\left(\left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]

25. Final simplification0.6

    \[\leadsto \left(\left(\frac{{\left(\left(7 + 0.5\right) - z\right)}^{\left(1 - z\right)}}{\frac{{\left(\sqrt{0.5 - \left(z + -7\right)}\right)}^{\left(1 - 0.5\right)}}{e^{z}}} \cdot \frac{e^{-7 - 0.5}}{{\left(\sqrt{0.5 - \left(z + -7\right)}\right)}^{\left(1 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{1 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)\right) + \left(\frac{771.3234287776531}{1 - \left(-2 + z\right)} + \frac{-176.6150291621406}{5 - \left(1 + z\right)}\right)\right) + \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(1 + z\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right) + \frac{12.507343278686905}{6 - \left(1 + z\right)}\right) + \frac{-0.13857109526572012}{6 - z}\right)\right)\]

Runtime

Time bar (total: 2.6m)Debug logProfile

herbie shell --seed 2018339 +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))))))