Error

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. Simplified1.2

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

4. Applied flip3-+0.6

   \[\leadsto \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(\left(1 - z\right) - -6\right) + 0.5\right)}^{\left(1 - \left(\left(z + 1\right) - 0.5\right)\right)}\right)\right) \cdot \left(\frac{1}{e^{\left(\left(1 - z\right) - -6\right) + 0.5}} \cdot \left(\left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + \left(\color{blue}{\frac{{\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}}{\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right)}} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]
5. Using strategy rm

6. Applied flip-+0.6

   \[\leadsto \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(\left(1 - z\right) - -6\right) + 0.5\right)}^{\left(1 - \left(\left(z + 1\right) - 0.5\right)\right)}\right)\right) \cdot \left(\frac{1}{e^{\left(\left(1 - z\right) - -6\right) + 0.5}} \cdot \left(\left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + \left(\frac{{\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}}{\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - \color{blue}{\frac{\frac{-1259.1392167224028}{\left(1 - z\right) + 1} \cdot \frac{-1259.1392167224028}{\left(1 - z\right) + 1} - 0.9999999999998099 \cdot 0.9999999999998099}{\frac{-1259.1392167224028}{\left(1 - z\right) + 1} - 0.9999999999998099}} \cdot \frac{676.5203681218851}{1 - z}\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]

7. Applied associate-*l/0.6

   \[\leadsto \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(\left(1 - z\right) - -6\right) + 0.5\right)}^{\left(1 - \left(\left(z + 1\right) - 0.5\right)\right)}\right)\right) \cdot \left(\frac{1}{e^{\left(\left(1 - z\right) - -6\right) + 0.5}} \cdot \left(\left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + \left(\frac{{\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}}{\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - \color{blue}{\frac{\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} \cdot \frac{-1259.1392167224028}{\left(1 - z\right) + 1} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}}{\frac{-1259.1392167224028}{\left(1 - z\right) + 1} - 0.9999999999998099}}\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]

8. Applied frac-times0.6

   \[\leadsto \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(\left(1 - z\right) - -6\right) + 0.5\right)}^{\left(1 - \left(\left(z + 1\right) - 0.5\right)\right)}\right)\right) \cdot \left(\frac{1}{e^{\left(\left(1 - z\right) - -6\right) + 0.5}} \cdot \left(\left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + \left(\frac{{\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}}{\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) + \left(\color{blue}{\frac{676.5203681218851 \cdot 676.5203681218851}{\left(1 - z\right) \cdot \left(1 - z\right)}} - \frac{\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} \cdot \frac{-1259.1392167224028}{\left(1 - z\right) + 1} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}}{\frac{-1259.1392167224028}{\left(1 - z\right) + 1} - 0.9999999999998099}\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]

9. Applied frac-sub0.6

   \[\leadsto \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(\left(1 - z\right) - -6\right) + 0.5\right)}^{\left(1 - \left(\left(z + 1\right) - 0.5\right)\right)}\right)\right) \cdot \left(\frac{1}{e^{\left(\left(1 - z\right) - -6\right) + 0.5}} \cdot \left(\left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + \left(\frac{{\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}}{\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) + \color{blue}{\frac{\left(676.5203681218851 \cdot 676.5203681218851\right) \cdot \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} - 0.9999999999998099\right) - \left(\left(1 - z\right) \cdot \left(1 - z\right)\right) \cdot \left(\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} \cdot \frac{-1259.1392167224028}{\left(1 - z\right) + 1} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right)}{\left(\left(1 - z\right) \cdot \left(1 - z\right)\right) \cdot \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} - 0.9999999999998099\right)}}} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]

10. Applied flip3-+0.6

    \[\leadsto \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(\left(1 - z\right) - -6\right) + 0.5\right)}^{\left(1 - \left(\left(z + 1\right) - 0.5\right)\right)}\right)\right) \cdot \left(\frac{1}{e^{\left(\left(1 - z\right) - -6\right) + 0.5}} \cdot \left(\left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + \left(\frac{{\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}}{\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} + 0.9999999999998099\right) \cdot \color{blue}{\frac{{\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)}^{3} + {0.9999999999998099}^{3}}{\frac{-1259.1392167224028}{\left(1 - z\right) + 1} \cdot \frac{-1259.1392167224028}{\left(1 - z\right) + 1} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-1259.1392167224028}{\left(1 - z\right) + 1} \cdot 0.9999999999998099\right)}} + \frac{\left(676.5203681218851 \cdot 676.5203681218851\right) \cdot \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} - 0.9999999999998099\right) - \left(\left(1 - z\right) \cdot \left(1 - z\right)\right) \cdot \left(\left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} \cdot \frac{-1259.1392167224028}{\left(1 - z\right) + 1} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \frac{676.5203681218851}{1 - z}\right)}{\left(\left(1 - z\right) \cdot \left(1 - z\right)\right) \cdot \left(\frac{-1259.1392167224028}{\left(1 - z\right) + 1} - 0.9999999999998099\right)}} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{9 - \left(z + 1\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - -6}\right)\right)\right)\right)\]

11. Applied flip3-+0.6

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

12. Applied frac-times0.6

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

13. Applied frac-add0.6

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

14. Applied associate-/r/0.6

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

15. Applied fma-def0.6

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

16. Simplified0.6

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

18. Applied distribute-rgt-in0.6

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

19. Applied distribute-rgt-in0.6

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

20. Final simplification0.6

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

Reproduce

herbie shell --seed 2019094 +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))))))