\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
Test:
Jmat.Real.gamma, branch z less than 0.5
Bits:
128 bits
Bits error versus z
Time: 8.5 m
Input Error: 2.0
Output Error: 1.2
Log:
Profile: 🕒
\(\left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\frac{771.3234287776531 \cdot \left(2 - z\right) + -1259.1392167224028 \cdot \left(3 - z\right)}{\left(2 - z\right) \cdot \left(3 - z\right)} + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot {\left(\frac{\sqrt[3]{{\left(\left(0.5 - z\right) + 7\right)}^{\left(0.5 - z\right)}} \cdot \sqrt[3]{\pi \cdot \sqrt{2 \cdot \pi}}}{\sqrt[3]{\sin \left(\pi \cdot z\right)} \cdot \sqrt[3]{e^{\left(0.5 - z\right) + 7}}}\right)}^3\)
  1. Started with
    \[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
    2.0
  2. 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}}{\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 \color{blue}{\left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot {\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)}}}\]
    2.1
  3. Using strategy rm
    2.1
  4. Applied add-cube-cbrt to get
    \[\left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot {\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)}}{\color{red}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}} \leadsto \left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot {\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)}}{\color{blue}{{\left(\sqrt[3]{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right)}^3}}\]
    1.8
  5. Applied add-cube-cbrt to get
    \[\left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \color{red}{{\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)}}}{{\left(\sqrt[3]{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right)}^3} \leadsto \left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)} \cdot \color{blue}{{\left(\sqrt[3]{{\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)}}\right)}^3}}{{\left(\sqrt[3]{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right)}^3}\]
    0.8
  6. Applied add-cube-cbrt to get
    \[\left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\color{red}{\sin \left(z \cdot \pi\right)}} \cdot {\left(\sqrt[3]{{\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)}}\right)}^3}{{\left(\sqrt[3]{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right)}^3} \leadsto \left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\frac{\pi \cdot \sqrt{\pi \cdot 2}}{\color{blue}{{\left(\sqrt[3]{\sin \left(z \cdot \pi\right)}\right)}^3}} \cdot {\left(\sqrt[3]{{\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)}}\right)}^3}{{\left(\sqrt[3]{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right)}^3}\]
    1.2
  7. Applied add-cube-cbrt to get
    \[\left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\frac{\color{red}{\pi \cdot \sqrt{\pi \cdot 2}}}{{\left(\sqrt[3]{\sin \left(z \cdot \pi\right)}\right)}^3} \cdot {\left(\sqrt[3]{{\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)}}\right)}^3}{{\left(\sqrt[3]{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right)}^3} \leadsto \left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\frac{\color{blue}{{\left(\sqrt[3]{\pi \cdot \sqrt{\pi \cdot 2}}\right)}^3}}{{\left(\sqrt[3]{\sin \left(z \cdot \pi\right)}\right)}^3} \cdot {\left(\sqrt[3]{{\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)}}\right)}^3}{{\left(\sqrt[3]{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right)}^3}\]
    1.2
  8. Applied cube-undiv to get
    \[\left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\color{red}{\frac{{\left(\sqrt[3]{\pi \cdot \sqrt{\pi \cdot 2}}\right)}^3}{{\left(\sqrt[3]{\sin \left(z \cdot \pi\right)}\right)}^3}} \cdot {\left(\sqrt[3]{{\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)}}\right)}^3}{{\left(\sqrt[3]{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right)}^3} \leadsto \left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\color{blue}{{\left(\frac{\sqrt[3]{\pi \cdot \sqrt{\pi \cdot 2}}}{\sqrt[3]{\sin \left(z \cdot \pi\right)}}\right)}^3} \cdot {\left(\sqrt[3]{{\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)}}\right)}^3}{{\left(\sqrt[3]{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right)}^3}\]
    1.2
  9. Applied cube-unprod to get
    \[\left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\color{red}{{\left(\frac{\sqrt[3]{\pi \cdot \sqrt{\pi \cdot 2}}}{\sqrt[3]{\sin \left(z \cdot \pi\right)}}\right)}^3 \cdot {\left(\sqrt[3]{{\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)}}\right)}^3}}{{\left(\sqrt[3]{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right)}^3} \leadsto \left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\color{blue}{{\left(\frac{\sqrt[3]{\pi \cdot \sqrt{\pi \cdot 2}}}{\sqrt[3]{\sin \left(z \cdot \pi\right)}} \cdot \sqrt[3]{{\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)}}\right)}^3}}{{\left(\sqrt[3]{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right)}^3}\]
    1.2
  10. Applied cube-undiv to get
    \[\left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \color{red}{\frac{{\left(\frac{\sqrt[3]{\pi \cdot \sqrt{\pi \cdot 2}}}{\sqrt[3]{\sin \left(z \cdot \pi\right)}} \cdot \sqrt[3]{{\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)}}\right)}^3}{{\left(\sqrt[3]{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\right)}^3}} \leadsto \left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \color{blue}{{\left(\frac{\frac{\sqrt[3]{\pi \cdot \sqrt{\pi \cdot 2}}}{\sqrt[3]{\sin \left(z \cdot \pi\right)}} \cdot \sqrt[3]{{\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)}}}{\sqrt[3]{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}}\right)}^3}\]
    1.2
  11. Applied simplify to get
    \[\left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot {\color{red}{\left(\frac{\frac{\sqrt[3]{\pi \cdot \sqrt{\pi \cdot 2}}}{\sqrt[3]{\sin \left(z \cdot \pi\right)}} \cdot \sqrt[3]{{\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}}{\sqrt[3]{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}}\right)}}^3 \leadsto \left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot {\color{blue}{\left(\frac{\sqrt[3]{{\left(\left(0.5 - z\right) + 7\right)}^{\left(0.5 - z\right)}} \cdot \sqrt[3]{\pi \cdot \sqrt{2 \cdot \pi}}}{\sqrt[3]{\sin \left(\pi \cdot z\right)} \cdot \sqrt[3]{e^{\left(0.5 - z\right) + 7}}}\right)}}^3\]
    1.2
  12. Using strategy rm
    1.2
  13. Applied frac-add to get
    \[\left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\color{red}{\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)} + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot {\left(\frac{\sqrt[3]{{\left(\left(0.5 - z\right) + 7\right)}^{\left(0.5 - z\right)}} \cdot \sqrt[3]{\pi \cdot \sqrt{2 \cdot \pi}}}{\sqrt[3]{\sin \left(\pi \cdot z\right)} \cdot \sqrt[3]{e^{\left(0.5 - z\right) + 7}}}\right)}^3 \leadsto \left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\color{blue}{\frac{771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right) + \left(\left(1 - z\right) - \left(1 - 3\right)\right) \cdot -1259.1392167224028}{\left(\left(1 - z\right) - \left(1 - 3\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)}} + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot {\left(\frac{\sqrt[3]{{\left(\left(0.5 - z\right) + 7\right)}^{\left(0.5 - z\right)}} \cdot \sqrt[3]{\pi \cdot \sqrt{2 \cdot \pi}}}{\sqrt[3]{\sin \left(\pi \cdot z\right)} \cdot \sqrt[3]{e^{\left(0.5 - z\right) + 7}}}\right)}^3\]
    1.2
  14. Applied simplify to get
    \[\left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\frac{\color{red}{771.3234287776531 \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right) + \left(\left(1 - z\right) - \left(1 - 3\right)\right) \cdot -1259.1392167224028}}{\left(\left(1 - z\right) - \left(1 - 3\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)} + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot {\left(\frac{\sqrt[3]{{\left(\left(0.5 - z\right) + 7\right)}^{\left(0.5 - z\right)}} \cdot \sqrt[3]{\pi \cdot \sqrt{2 \cdot \pi}}}{\sqrt[3]{\sin \left(\pi \cdot z\right)} \cdot \sqrt[3]{e^{\left(0.5 - z\right) + 7}}}\right)}^3 \leadsto \left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\frac{\color{blue}{771.3234287776531 \cdot \left(2 - z\right) + -1259.1392167224028 \cdot \left(3 - z\right)}}{\left(\left(1 - z\right) - \left(1 - 3\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)} + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot {\left(\frac{\sqrt[3]{{\left(\left(0.5 - z\right) + 7\right)}^{\left(0.5 - z\right)}} \cdot \sqrt[3]{\pi \cdot \sqrt{2 \cdot \pi}}}{\sqrt[3]{\sin \left(\pi \cdot z\right)} \cdot \sqrt[3]{e^{\left(0.5 - z\right) + 7}}}\right)}^3\]
    1.2
  15. Applied simplify to get
    \[\left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\frac{771.3234287776531 \cdot \left(2 - z\right) + -1259.1392167224028 \cdot \left(3 - z\right)}{\color{red}{\left(\left(1 - z\right) - \left(1 - 3\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)}} + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot {\left(\frac{\sqrt[3]{{\left(\left(0.5 - z\right) + 7\right)}^{\left(0.5 - z\right)}} \cdot \sqrt[3]{\pi \cdot \sqrt{2 \cdot \pi}}}{\sqrt[3]{\sin \left(\pi \cdot z\right)} \cdot \sqrt[3]{e^{\left(0.5 - z\right) + 7}}}\right)}^3 \leadsto \left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\frac{771.3234287776531 \cdot \left(2 - z\right) + -1259.1392167224028 \cdot \left(3 - z\right)}{\color{blue}{\left(2 - z\right) \cdot \left(3 - z\right)}} + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot {\left(\frac{\sqrt[3]{{\left(\left(0.5 - z\right) + 7\right)}^{\left(0.5 - z\right)}} \cdot \sqrt[3]{\pi \cdot \sqrt{2 \cdot \pi}}}{\sqrt[3]{\sin \left(\pi \cdot z\right)} \cdot \sqrt[3]{e^{\left(0.5 - z\right) + 7}}}\right)}^3\]
    1.2

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))))))