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. Applied simplify0.5

   \[\leadsto \color{blue}{\left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(0.5 + \left(\left(7 + 1\right) - \left(1 + z\right)\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right) \cdot e^{-\left(0.5 + \left(\left(7 + 1\right) - \left(1 + z\right)\right)\right)}\right)\right) \cdot \left(\left(\left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{\left(1 - z\right) - 0} + \frac{-1259.1392167224028}{\left(2 + 1\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)} + \frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)}\right) + \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(8 + 1\right) - \left(1 + z\right)}\right)}\]
3. Using strategy rm

4. Applied flip3-+0.5

   \[\leadsto \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(0.5 + \left(\left(7 + 1\right) - \left(1 + z\right)\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right) \cdot e^{-\left(0.5 + \left(\left(7 + 1\right) - \left(1 + z\right)\right)\right)}\right)\right) \cdot \left(\left(\left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{\left(1 - z\right) - 0} + \frac{-1259.1392167224028}{\left(2 + 1\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)} + \frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)}\right) + \color{blue}{\frac{{\left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)}\right)}^{3} + {\left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)}^{3}}{\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} - \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)}}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(8 + 1\right) - \left(1 + z\right)}\right)\]

5. Applied frac-add0.5

   \[\leadsto \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(0.5 + \left(\left(7 + 1\right) - \left(1 + z\right)\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right) \cdot e^{-\left(0.5 + \left(\left(7 + 1\right) - \left(1 + z\right)\right)\right)}\right)\right) \cdot \left(\left(\left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{\left(1 - z\right) - 0} + \frac{-1259.1392167224028}{\left(2 + 1\right) - \left(1 + z\right)}\right)\right) + \left(\color{blue}{\frac{12.507343278686905 \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right) + \left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot -176.6150291621406}{\left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right)}} + \frac{{\left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)}\right)}^{3} + {\left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)}^{3}}{\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} - \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(8 + 1\right) - \left(1 + z\right)}\right)\]

6. Applied frac-add0.5

   \[\leadsto \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(0.5 + \left(\left(7 + 1\right) - \left(1 + z\right)\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right) \cdot e^{-\left(0.5 + \left(\left(7 + 1\right) - \left(1 + z\right)\right)\right)}\right)\right) \cdot \left(\left(\left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + 0.9999999999998099\right) + \left(\frac{676.5203681218851}{\left(1 - z\right) - 0} + \frac{-1259.1392167224028}{\left(2 + 1\right) - \left(1 + z\right)}\right)\right) + \color{blue}{\frac{\left(12.507343278686905 \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right) + \left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot -176.6150291621406\right) \cdot \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} - \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)\right) + \left(\left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right)\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)}\right)}^{3} + {\left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)}^{3}\right)}{\left(\left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} - \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)\right)}}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(8 + 1\right) - \left(1 + z\right)}\right)\]

7. Applied frac-add0.5

   \[\leadsto \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(0.5 + \left(\left(7 + 1\right) - \left(1 + z\right)\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right) \cdot e^{-\left(0.5 + \left(\left(7 + 1\right) - \left(1 + z\right)\right)\right)}\right)\right) \cdot \left(\left(\left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + 0.9999999999998099\right) + \color{blue}{\frac{676.5203681218851 \cdot \left(\left(2 + 1\right) - \left(1 + z\right)\right) + \left(\left(1 - z\right) - 0\right) \cdot -1259.1392167224028}{\left(\left(1 - z\right) - 0\right) \cdot \left(\left(2 + 1\right) - \left(1 + z\right)\right)}}\right) + \frac{\left(12.507343278686905 \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right) + \left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot -176.6150291621406\right) \cdot \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} - \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)\right) + \left(\left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right)\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)}\right)}^{3} + {\left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)}^{3}\right)}{\left(\left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} - \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)\right)}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(8 + 1\right) - \left(1 + z\right)}\right)\]

8. Applied flip3-+0.5

   \[\leadsto \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(0.5 + \left(\left(7 + 1\right) - \left(1 + z\right)\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right) \cdot e^{-\left(0.5 + \left(\left(7 + 1\right) - \left(1 + z\right)\right)\right)}\right)\right) \cdot \left(\left(\left(\color{blue}{\frac{{\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)}\right)}^{3} + {0.9999999999998099}^{3}}{\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} \cdot \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} \cdot 0.9999999999998099\right)}} + \frac{676.5203681218851 \cdot \left(\left(2 + 1\right) - \left(1 + z\right)\right) + \left(\left(1 - z\right) - 0\right) \cdot -1259.1392167224028}{\left(\left(1 - z\right) - 0\right) \cdot \left(\left(2 + 1\right) - \left(1 + z\right)\right)}\right) + \frac{\left(12.507343278686905 \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right) + \left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot -176.6150291621406\right) \cdot \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} - \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)\right) + \left(\left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right)\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)}\right)}^{3} + {\left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)}^{3}\right)}{\left(\left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} - \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)\right)}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(8 + 1\right) - \left(1 + z\right)}\right)\]

9. Applied frac-add0.5

   \[\leadsto \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(0.5 + \left(\left(7 + 1\right) - \left(1 + z\right)\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right) \cdot e^{-\left(0.5 + \left(\left(7 + 1\right) - \left(1 + z\right)\right)\right)}\right)\right) \cdot \left(\left(\color{blue}{\frac{\left({\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)}\right)}^{3} + {0.9999999999998099}^{3}\right) \cdot \left(\left(\left(1 - z\right) - 0\right) \cdot \left(\left(2 + 1\right) - \left(1 + z\right)\right)\right) + \left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} \cdot \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} \cdot 0.9999999999998099\right)\right) \cdot \left(676.5203681218851 \cdot \left(\left(2 + 1\right) - \left(1 + z\right)\right) + \left(\left(1 - z\right) - 0\right) \cdot -1259.1392167224028\right)}{\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} \cdot \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} \cdot 0.9999999999998099\right)\right) \cdot \left(\left(\left(1 - z\right) - 0\right) \cdot \left(\left(2 + 1\right) - \left(1 + z\right)\right)\right)}} + \frac{\left(12.507343278686905 \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right) + \left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot -176.6150291621406\right) \cdot \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} - \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)\right) + \left(\left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right)\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)}\right)}^{3} + {\left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)}^{3}\right)}{\left(\left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} - \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)\right)}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(8 + 1\right) - \left(1 + z\right)}\right)\]

10. Applied frac-add0.5

    \[\leadsto \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(0.5 + \left(\left(7 + 1\right) - \left(1 + z\right)\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right) \cdot e^{-\left(0.5 + \left(\left(7 + 1\right) - \left(1 + z\right)\right)\right)}\right)\right) \cdot \left(\color{blue}{\frac{\left(\left({\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)}\right)}^{3} + {0.9999999999998099}^{3}\right) \cdot \left(\left(\left(1 - z\right) - 0\right) \cdot \left(\left(2 + 1\right) - \left(1 + z\right)\right)\right) + \left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} \cdot \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} \cdot 0.9999999999998099\right)\right) \cdot \left(676.5203681218851 \cdot \left(\left(2 + 1\right) - \left(1 + z\right)\right) + \left(\left(1 - z\right) - 0\right) \cdot -1259.1392167224028\right)\right) \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} - \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} \cdot \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} \cdot 0.9999999999998099\right)\right) \cdot \left(\left(\left(1 - z\right) - 0\right) \cdot \left(\left(2 + 1\right) - \left(1 + z\right)\right)\right)\right) \cdot \left(\left(12.507343278686905 \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right) + \left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot -176.6150291621406\right) \cdot \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} - \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)\right) + \left(\left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right)\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)}\right)}^{3} + {\left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)}^{3}\right)\right)}{\left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} \cdot \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} \cdot 0.9999999999998099\right)\right) \cdot \left(\left(\left(1 - z\right) - 0\right) \cdot \left(\left(2 + 1\right) - \left(1 + z\right)\right)\right)\right) \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} - \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)\right)\right)}} + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(8 + 1\right) - \left(1 + z\right)}\right)\]

11. Applied simplify0.5

    \[\leadsto \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(0.5 + \left(\left(7 + 1\right) - \left(1 + z\right)\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right) \cdot e^{-\left(0.5 + \left(\left(7 + 1\right) - \left(1 + z\right)\right)\right)}\right)\right) \cdot \left(\frac{\left(\left({\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)}\right)}^{3} + {0.9999999999998099}^{3}\right) \cdot \left(\left(\left(1 - z\right) - 0\right) \cdot \left(\left(2 + 1\right) - \left(1 + z\right)\right)\right) + \left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} \cdot \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} \cdot 0.9999999999998099\right)\right) \cdot \left(676.5203681218851 \cdot \left(\left(2 + 1\right) - \left(1 + z\right)\right) + \left(\left(1 - z\right) - 0\right) \cdot -1259.1392167224028\right)\right) \cdot \left(\left(\left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} - \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} \cdot \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} \cdot 0.9999999999998099\right)\right) \cdot \left(\left(\left(1 - z\right) - 0\right) \cdot \left(\left(2 + 1\right) - \left(1 + z\right)\right)\right)\right) \cdot \left(\left(12.507343278686905 \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right) + \left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot -176.6150291621406\right) \cdot \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)} - \frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)\right) + \left(\left(\left(1 - z\right) - \left(1 - 5\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 4\right)\right)\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)}\right)}^{3} + {\left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(7 + 1\right) - \left(1 + z\right)}\right)}^{3}\right)\right)}{\color{blue}{\left(\frac{-0.13857109526572012}{\left(1 + 6\right) - \left(1 + z\right)} \cdot \frac{-0.13857109526572012}{\left(1 + 6\right) - \left(1 + z\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(1 + 7\right) - \left(1 + z\right)} - \frac{-0.13857109526572012}{\left(1 + 6\right) - \left(1 + z\right)}\right) \cdot \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 + 7\right) - \left(1 + z\right)}\right) \cdot \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} \cdot \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{0.9999999999998099 \cdot 771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)}\right)\right) \cdot \left(\left(\left(1 - z\right) \cdot \left(\left(1 + 2\right) - \left(1 + z\right)\right)\right) \cdot \left(\left(\left(1 - z\right) - \left(1 - 4\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 5\right)\right)\right)\right)\right)}} + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(8 + 1\right) - \left(1 + z\right)}\right)\]

Runtime

Time bar (total: 10.0m)Debug logProfile

herbie shell --seed '#(1072840222 1305617769 1692503039 1353360431 4178980589 1488672652)' 
(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))))))