Average Error: 1.8 → 0.6
Time: 3.3m
Precision: 64
Internal Precision: 384
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(\sqrt{\pi + \pi} \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right) \cdot \left(\frac{{\left(\sqrt[3]{\left(0.5 - z\right) + 7} \cdot \sqrt[3]{\left(0.5 - z\right) + 7}\right)}^{\left(0.5 - z\right)}}{e^{0.5 - z}} \cdot \frac{{\left(\sqrt[3]{\sqrt{\left(0.5 - z\right) + 7}}\right)}^{\left(0.5 - z\right)}}{\frac{e^{7}}{{\left(\sqrt[3]{\sqrt{\left(0.5 - z\right) + 7}}\right)}^{\left(0.5 - z\right)}}}\right)\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{\left(8 + 1\right) - \left(1 + z\right)} + \left(\left(\frac{676.5203681218851}{1 - \left(z + 0\right)} + \frac{-1259.1392167224028}{\left(2 + 1\right) - \left(1 + z\right)}\right) + \left(\frac{771.3234287776531}{\left(1 + 3\right) - \left(1 + z\right)} + 0.9999999999998099\right)\right)\right) + \left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right) + \left(\frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)} + \frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)}\right)\right)\right)\]

Error

Bits error versus z

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 simplify0.7

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

  4. Applied associate--r-0.7

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

  5. Applied exp-sum0.7

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

  6. Applied add-cube-cbrt0.7

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

  7. Applied unpow-prod-down0.7

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

  8. Applied times-frac0.6

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

  9. Applied simplify0.6

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

  10. Applied simplify0.6

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

  12. Applied add-sqr-sqrt0.6

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

  13. Applied cbrt-prod0.6

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

  14. Applied unpow-prod-down0.6

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

  15. Applied associate-/l*0.6

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

Runtime

Time bar (total: 3.3m)Debug logProfile

herbie shell --seed '#(1070355188 2193211668 3977393919 3454156579 3755371326 1656365382)' 
(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))))))