\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
Test:
Jmat.Real.gamma, branch z less than 0.5
Bits:
128 bits
Bits error versus z
Time: 1.7 m
Input Error: 1.8
Output Error: 0.7
Log: ⚲
Profile: 🕒
\(\frac{\frac{\pi}{\frac{\sin \left(\pi \cdot z\right)}{\sqrt{2} \cdot \sqrt{\pi}}}}{\frac{e^{7 + \left(0.5 - z\right)}}{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}} \cdot \frac{\left(\left(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\right) \cdot \left({\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^2 + \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^2 - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right) + \left(\left(\left(1 - z\right) - \left(1 - 3\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) \cdot \left({\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^{3} - {\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^{3}\right)\right) \cdot \left(\left(7 - z\right) \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right)\right) + \left(\left(\left(\left(1 - z\right) - \left(1 - 3\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) \cdot \left({\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^2 + \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^2 - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)\right) \cdot \left(9.984369578019572 \cdot 10^{-06} \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right) + \left(7 - z\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 - {\left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)}^2\right)\right)}{\left(\left(\left(\left(1 - z\right) - \left(1 - 3\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) \cdot \left({\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^2 + \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^2 - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)\right) \cdot \left(\left(7 - z\right) \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right)\right)}\)
  1. Started with
    \[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
    1.8
  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)}}}\]
    1.3
  3. Using strategy rm
    1.3
  4. Applied sqrt-prod to get
    \[\left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\frac{\pi \cdot \color{red}{\sqrt{\pi \cdot 2}}}{\sin \left(z \cdot \pi\right)} \cdot {\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}} \leadsto \left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\frac{\pi \cdot \color{blue}{\left(\sqrt{\pi} \cdot \sqrt{2}\right)}}{\sin \left(z \cdot \pi\right)} \cdot {\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}}\]
    0.6
  5. Applied taylor to get
    \[\left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\frac{\pi \cdot \left(\sqrt{\pi} \cdot \sqrt{2}\right)}{\sin \left(z \cdot \pi\right)} \cdot {\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)}} \leadsto \left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\frac{\pi \cdot \left(\sqrt{\pi} \cdot \sqrt{2}\right)}{\sin \left(z \cdot \pi\right)} \cdot {\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + -1 \cdot z}}\]
    0.6
  6. Taylor expanded around 0 to get
    \[\left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\frac{\pi \cdot \left(\sqrt{\pi} \cdot \sqrt{2}\right)}{\sin \left(z \cdot \pi\right)} \cdot {\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \color{red}{-1 \cdot z}}} \leadsto \left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\frac{\pi \cdot \left(\sqrt{\pi} \cdot \sqrt{2}\right)}{\sin \left(z \cdot \pi\right)} \cdot {\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \color{blue}{-1 \cdot z}}}\]
    0.6
  7. Applied simplify to get
    \[\color{red}{\left(\left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 + 5\right) - \left(1 + z\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(1 + 8\right) - \left(1 + z\right)}\right) \cdot \frac{\frac{\pi \cdot \left(\sqrt{\pi} \cdot \sqrt{2}\right)}{\sin \left(z \cdot \pi\right)} \cdot {\left(\left(0.5 + 7\right) + \left(1 - \left(1 + z\right)\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + -1 \cdot z}}} \leadsto \color{blue}{\frac{\frac{\pi}{\frac{\sin \left(\pi \cdot z\right)}{\sqrt{2} \cdot \sqrt{\pi}}}}{\frac{e^{7 + \left(0.5 - z\right)}}{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}} \cdot \left(\left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right)\right)\right)}\]
    0.8
  8. Using strategy rm
    0.8
  9. Applied flip-+ to get
    \[\frac{\frac{\pi}{\frac{\sin \left(\pi \cdot z\right)}{\sqrt{2} \cdot \sqrt{\pi}}}}{\frac{e^{7 + \left(0.5 - z\right)}}{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}} \cdot \left(\left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \color{red}{\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right)}\right)\right) \leadsto \frac{\frac{\pi}{\frac{\sin \left(\pi \cdot z\right)}{\sqrt{2} \cdot \sqrt{\pi}}}}{\frac{e^{7 + \left(0.5 - z\right)}}{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}} \cdot \left(\left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \color{blue}{\frac{{\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 - {\left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)}^2}{\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)}}\right)\right)\]
    0.8
  10. Applied frac-add to get
    \[\frac{\frac{\pi}{\frac{\sin \left(\pi \cdot z\right)}{\sqrt{2} \cdot \sqrt{\pi}}}}{\frac{e^{7 + \left(0.5 - z\right)}}{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}} \cdot \left(\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(\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right) + \color{red}{\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{{\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 - {\left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)}^2}{\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)}\right)}\right) \leadsto \frac{\frac{\pi}{\frac{\sin \left(\pi \cdot z\right)}{\sqrt{2} \cdot \sqrt{\pi}}}}{\frac{e^{7 + \left(0.5 - z\right)}}{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}} \cdot \left(\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(\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right) + \color{blue}{\frac{9.984369578019572 \cdot 10^{-06} \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right) + \left(7 - z\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 - {\left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)}^2\right)}{\left(7 - z\right) \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right)}}\right)\]
    0.8
  11. Applied flip3-+ to get
    \[\frac{\frac{\pi}{\frac{\sin \left(\pi \cdot z\right)}{\sqrt{2} \cdot \sqrt{\pi}}}}{\frac{e^{7 + \left(0.5 - z\right)}}{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}} \cdot \left(\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) + \color{red}{\left(\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}\right) + \frac{9.984369578019572 \cdot 10^{-06} \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right) + \left(7 - z\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 - {\left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)}^2\right)}{\left(7 - z\right) \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right)}\right) \leadsto \frac{\frac{\pi}{\frac{\sin \left(\pi \cdot z\right)}{\sqrt{2} \cdot \sqrt{\pi}}}}{\frac{e^{7 + \left(0.5 - z\right)}}{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}} \cdot \left(\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) + \color{blue}{\frac{{\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^{3} - {\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^{3}}{{\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^2 + \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^2 - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}}\right) + \frac{9.984369578019572 \cdot 10^{-06} \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right) + \left(7 - z\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 - {\left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)}^2\right)}{\left(7 - z\right) \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right)}\right)\]
    0.8
  12. Applied frac-add to get
    \[\frac{\frac{\pi}{\frac{\sin \left(\pi \cdot z\right)}{\sqrt{2} \cdot \sqrt{\pi}}}}{\frac{e^{7 + \left(0.5 - z\right)}}{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}} \cdot \left(\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)} + \frac{{\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^{3} - {\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^{3}}{{\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^2 + \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^2 - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}\right) + \frac{9.984369578019572 \cdot 10^{-06} \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right) + \left(7 - z\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 - {\left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)}^2\right)}{\left(7 - z\right) \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right)}\right) \leadsto \frac{\frac{\pi}{\frac{\sin \left(\pi \cdot z\right)}{\sqrt{2} \cdot \sqrt{\pi}}}}{\frac{e^{7 + \left(0.5 - z\right)}}{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}} \cdot \left(\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)}} + \frac{{\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^{3} - {\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^{3}}{{\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^2 + \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^2 - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}\right) + \frac{9.984369578019572 \cdot 10^{-06} \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right) + \left(7 - z\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 - {\left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)}^2\right)}{\left(7 - z\right) \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right)}\right)\]
    0.8
  13. Applied frac-add to get
    \[\frac{\frac{\pi}{\frac{\sin \left(\pi \cdot z\right)}{\sqrt{2} \cdot \sqrt{\pi}}}}{\frac{e^{7 + \left(0.5 - z\right)}}{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}} \cdot \left(\color{red}{\left(\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)} + \frac{{\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^{3} - {\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^{3}}{{\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^2 + \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^2 - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}\right)} + \frac{9.984369578019572 \cdot 10^{-06} \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right) + \left(7 - z\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 - {\left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)}^2\right)}{\left(7 - z\right) \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right)}\right) \leadsto \frac{\frac{\pi}{\frac{\sin \left(\pi \cdot z\right)}{\sqrt{2} \cdot \sqrt{\pi}}}}{\frac{e^{7 + \left(0.5 - z\right)}}{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}} \cdot \left(\color{blue}{\frac{\left(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\right) \cdot \left({\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^2 + \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^2 - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right) + \left(\left(\left(1 - z\right) - \left(1 - 3\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) \cdot \left({\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^{3} - {\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^{3}\right)}{\left(\left(\left(1 - z\right) - \left(1 - 3\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) \cdot \left({\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^2 + \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^2 - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)}} + \frac{9.984369578019572 \cdot 10^{-06} \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right) + \left(7 - z\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 - {\left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)}^2\right)}{\left(7 - z\right) \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right)}\right)\]
    0.8
  14. Applied frac-add to get
    \[\frac{\frac{\pi}{\frac{\sin \left(\pi \cdot z\right)}{\sqrt{2} \cdot \sqrt{\pi}}}}{\frac{e^{7 + \left(0.5 - z\right)}}{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}} \cdot \color{red}{\left(\frac{\left(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\right) \cdot \left({\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^2 + \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^2 - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right) + \left(\left(\left(1 - z\right) - \left(1 - 3\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) \cdot \left({\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^{3} - {\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^{3}\right)}{\left(\left(\left(1 - z\right) - \left(1 - 3\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) \cdot \left({\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^2 + \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^2 - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)} + \frac{9.984369578019572 \cdot 10^{-06} \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right) + \left(7 - z\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 - {\left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)}^2\right)}{\left(7 - z\right) \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right)}\right)} \leadsto \frac{\frac{\pi}{\frac{\sin \left(\pi \cdot z\right)}{\sqrt{2} \cdot \sqrt{\pi}}}}{\frac{e^{7 + \left(0.5 - z\right)}}{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}} \cdot \color{blue}{\frac{\left(\left(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\right) \cdot \left({\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^2 + \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^2 - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right) + \left(\left(\left(1 - z\right) - \left(1 - 3\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) \cdot \left({\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^{3} - {\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^{3}\right)\right) \cdot \left(\left(7 - z\right) \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right)\right) + \left(\left(\left(\left(1 - z\right) - \left(1 - 3\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) \cdot \left({\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^2 + \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^2 - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)\right) \cdot \left(9.984369578019572 \cdot 10^{-06} \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right) + \left(7 - z\right) \cdot \left({\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)}^2 - {\left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)}^2\right)\right)}{\left(\left(\left(\left(1 - z\right) - \left(1 - 3\right)\right) \cdot \left(\left(1 - z\right) - \left(1 - 2\right)\right)\right) \cdot \left({\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right)}^2 + \left({\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)}^2 - \left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)\right) \cdot \left(\left(7 - z\right) \cdot \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} - \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right)\right)}}\]
    0.7

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))))))