\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
Test:
Jmat.Real.gamma, branch z less than 0.5
Bits:
128 bits
Bits error versus z
Time: 53.1 s
Input Error: 1.7
Output Error: 0.7
Log: ⚲
Profile: 🕒
\(\left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + -1 \cdot z}}\right) \cdot \left(\frac{(\left(8 - z\right) * \left({\left(\frac{-0.13857109526572012}{\left(-z\right) + 6}\right)}^3 - {\left(\frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}^3\right) + \left((\left( 1.5056327351493116 \cdot 10^{-07} \right) * \left({\left(\frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}^2 - \frac{\frac{9.984369578019572 \cdot 10^{-06} \cdot -0.13857109526572012}{(z * -1 + 7)_*}}{\left(-z\right) + 6}\right) + \left(\frac{-0.13857109526572012}{\left(-z\right) + 6} \cdot \frac{-0.13857109526572012 \cdot 1.5056327351493116 \cdot 10^{-07}}{\left(-z\right) + 6}\right))_*\right))_*}{\left(\left(1 + 8\right) - \left(1 + z\right)\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 + \left({\left(\frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}^2 - \frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right)} + \left(\left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) + \left(\frac{771.3234287776531}{\left(1 + 3\right) - \left(1 + z\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right)\right)\)
  1. Started with
    \[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
    1.7
  2. Applied taylor to get
    \[\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) \leadsto \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}}{-1 \cdot z + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
    1.7
  3. Taylor expanded around 0 to get
    \[\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}}{\color{red}{-1 \cdot z} + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right) \leadsto \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}}{\color{blue}{-1 \cdot z} + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
    1.7
  4. Applied simplify to get
    \[\color{red}{\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}}{-1 \cdot z + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)} \leadsto \color{blue}{\left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \left(\left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) + \left(\frac{771.3234287776531}{\left(1 + 3\right) - \left(1 + z\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right)\right)}\]
    0.7
  5. Applied taylor to get
    \[\left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \left(\left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) + \left(\frac{771.3234287776531}{\left(1 + 3\right) - \left(1 + z\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right)\right) \leadsto \left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + -1 \cdot z}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \left(\left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) + \left(\frac{771.3234287776531}{\left(1 + 3\right) - \left(1 + z\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right)\right)\]
    0.7
  6. Taylor expanded around 0 to get
    \[\left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \color{red}{-1 \cdot z}}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \left(\left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) + \left(\frac{771.3234287776531}{\left(1 + 3\right) - \left(1 + z\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right)\right) \leadsto \left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \color{blue}{-1 \cdot z}}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \left(\left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) + \left(\frac{771.3234287776531}{\left(1 + 3\right) - \left(1 + z\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right)\right)\]
    0.7
  7. Using strategy rm
    0.7
  8. Applied flip3-+ to get
    \[\left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + -1 \cdot z}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \color{red}{\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}\right) + \left(\left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) + \left(\frac{771.3234287776531}{\left(1 + 3\right) - \left(1 + z\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right)\right) \leadsto \left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + -1 \cdot z}}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \color{blue}{\frac{{\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^{3} - {\left(\frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}^{3}}{{\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 + \left({\left(\frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}^2 - \frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}}\right) + \left(\left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) + \left(\frac{771.3234287776531}{\left(1 + 3\right) - \left(1 + z\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right)\right)\]
    0.7
  9. Applied frac-add to get
    \[\left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + -1 \cdot z}}\right) \cdot \left(\color{red}{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)} + \frac{{\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^{3} - {\left(\frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}^{3}}{{\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 + \left({\left(\frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}^2 - \frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}\right)} + \left(\left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) + \left(\frac{771.3234287776531}{\left(1 + 3\right) - \left(1 + z\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right)\right) \leadsto \left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + -1 \cdot z}}\right) \cdot \left(\color{blue}{\frac{1.5056327351493116 \cdot 10^{-07} \cdot \left({\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 + \left({\left(\frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}^2 - \frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \left(\left(1 + 8\right) - \left(1 + z\right)\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^{3} - {\left(\frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}^{3}\right)}{\left(\left(1 + 8\right) - \left(1 + z\right)\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 + \left({\left(\frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}^2 - \frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right)}} + \left(\left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) + \left(\frac{771.3234287776531}{\left(1 + 3\right) - \left(1 + z\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right)\right)\]
    0.7
  10. Applied simplify to get
    \[\left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + -1 \cdot z}}\right) \cdot \left(\frac{\color{red}{1.5056327351493116 \cdot 10^{-07} \cdot \left({\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 + \left({\left(\frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}^2 - \frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right) + \left(\left(1 + 8\right) - \left(1 + z\right)\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^{3} - {\left(\frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}^{3}\right)}}{\left(\left(1 + 8\right) - \left(1 + z\right)\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 + \left({\left(\frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}^2 - \frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right)} + \left(\left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) + \left(\frac{771.3234287776531}{\left(1 + 3\right) - \left(1 + z\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right)\right) \leadsto \left(\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \frac{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + -1 \cdot z}}\right) \cdot \left(\frac{\color{blue}{(\left(8 - z\right) * \left({\left(\frac{-0.13857109526572012}{\left(-z\right) + 6}\right)}^3 - {\left(\frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}^3\right) + \left((\left( 1.5056327351493116 \cdot 10^{-07} \right) * \left({\left(\frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}^2 - \frac{\frac{9.984369578019572 \cdot 10^{-06} \cdot -0.13857109526572012}{(z * -1 + 7)_*}}{\left(-z\right) + 6}\right) + \left(\frac{-0.13857109526572012}{\left(-z\right) + 6} \cdot \frac{-0.13857109526572012 \cdot 1.5056327351493116 \cdot 10^{-07}}{\left(-z\right) + 6}\right))_*\right))_*}}{\left(\left(1 + 8\right) - \left(1 + z\right)\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 + \left({\left(\frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)}^2 - \frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{(z * -1 + 7)_*}\right)\right)} + \left(\left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right) + \left(\frac{771.3234287776531}{\left(1 + 3\right) - \left(1 + z\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right)\right)\]
    0.7
  11. Removed slow pow expressions

Original test:


(lambda ((z default))
  #: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))))))