Average Error: 1.8 → 0.6
Time: 3.0m
Precision: 64
Internal Precision: 128
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(\left(\frac{-176.6150291621406}{5 - \left(z + 1\right)} + \frac{771.3234287776531}{1 - \left(z + -2\right)}\right) + \frac{\left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right) \cdot \frac{\frac{\left(\left(\left(2 - z\right) \cdot 0.9999999999998099 - -1259.1392167224028\right) \cdot \left(676.5203681218851 \cdot \left(2 - z\right)\right)\right) \cdot \left(\left(\left(2 - z\right) \cdot 0.9999999999998099 - -1259.1392167224028\right) \cdot \left(676.5203681218851 \cdot \left(2 - z\right)\right)\right) - \left(\left(\left(-1259.1392167224028 + \left(2 - z\right) \cdot 0.9999999999998099\right) \cdot \left(1 - z\right)\right) \cdot \left(\left(2 - z\right) \cdot 0.9999999999998099 - -1259.1392167224028\right)\right) \cdot \left(\left(\left(-1259.1392167224028 + \left(2 - z\right) \cdot 0.9999999999998099\right) \cdot \left(1 - z\right)\right) \cdot \left(\left(2 - z\right) \cdot 0.9999999999998099 - -1259.1392167224028\right)\right)}{e^{\log \left(\left(\left(\left(2 - z\right) \cdot 0.9999999999998099 - -1259.1392167224028\right) \cdot \left(\left(2 - z\right) \cdot 0.9999999999998099 - -1259.1392167224028\right)\right) \cdot \left(\left(1 - z\right) \cdot \left(1 - z\right)\right)\right)}}}{\frac{676.5203681218851 \cdot \left(2 - z\right)}{1 - z} - \left(-1259.1392167224028 + \left(2 - z\right) \cdot 0.9999999999998099\right)}}{\left(0.9999999999998099 - \frac{676.5203681218851}{1 - z}\right) \cdot \left(1 + \left(1 - z\right)\right)}\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{9.984369578019572 \cdot 10^{-06}}{6 + \left(1 - z\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)}\right)\right)\right) \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right)\]

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Initial simplification0.6

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

  4. Applied flip-+0.6

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

  5. Applied frac-add1.0

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

  6. Simplified0.6

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

  8. Applied flip-+0.6

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

  10. Applied add-exp-log0.8

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

  12. Applied flip-+0.8

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

  13. Applied flip-+0.8

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

  14. Applied frac-times0.8

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

  15. Applied frac-times0.8

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

  16. Applied frac-sub0.8

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

  17. Applied log-div0.8

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

  18. Applied exp-diff0.8

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

  19. Simplified0.6

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

  20. Final simplification0.6

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

Reproduce

herbie shell --seed 2018365 
(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))))))

Details

Time bar (total: 1.6m)Debug log

start2.6s

Algorithm
intervals

setup237.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize188.0ms

Local error

Found 4 expressions with local error:

2.6b
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
1.0b
(sqrt (* 2 PI))
1.0b
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
1.0b
(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
4 → 50
Calls

4 calls. Slowest were:

6.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
5.0ms
(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))
4.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

series67.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

23.0ms
(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))
23.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
21.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms
(sqrt (* 2 PI))

simplify4.6s

Counts
25 → 60
Calls

25 calls. Slowest were:

575.0ms
(+ (* (- (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z)))) (+ (- 1 z) 1)) (* (- 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) -1259.1392167224028))
529.0ms
(* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) (+ (- 1 z) 1))
382.0ms
(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1 z)) 3)) (+ (- 1 z) 1)) (* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 (/ 676.5203681218851 (- 1 z))))) -1259.1392167224028))

prune5.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize86.0ms

Local error

Found 4 expressions with local error:

2.6b
(+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
1.0b
(sqrt (* 2 PI))
1.0b
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
1.0b
(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Counts
4 → 50
Calls

4 calls. Slowest were:

22.0ms
(+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
5.0ms
(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))
4.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

series71.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

25.0ms
(+ (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
23.0ms
(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))
23.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
0.0ms
(sqrt (* 2 PI))

simplify3.9s

Counts
25 → 60
Calls

25 calls. Slowest were:

419.0ms
(* (- 1 z) (- (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
343.0ms
(+ (* -0.13857109526572012 (- 6 (+ z 1))) (* (- 7 (+ z 1)) 12.507343278686905))
334.0ms
(- (+ (* 4116.070392404628 (/ 1 (pow z 3))) (+ (* 1607.5101696843972 (/ 1 (pow z 2))) (* 594.7083996155126 (/ 1 z)))))

prune5.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize82.0ms

Local error

Found 4 expressions with local error:

2.5b
(- (* (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (/ (* 676.5203681218851 (- 2 z)) (- 1 z))) (* (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))
1.0b
(sqrt (* 2 PI))
1.0b
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
1.0b
(* (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))

rewrite50.0ms

Algorithm
rewrite-expression-head
Counts
4 → 91
Calls

4 calls. Slowest were:

30.0ms
(- (* (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (/ (* 676.5203681218851 (- 2 z)) (- 1 z))) (* (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))
14.0ms
(* (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
4.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

series115.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

58.0ms
(- (* (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (/ (* 676.5203681218851 (- 2 z)) (- 1 z))) (* (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))
40.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
17.0ms
(* (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
0.0ms
(sqrt (* 2 PI))

simplify22.6s

Counts
92 → 101
Calls

92 calls. Slowest were:

1.1s
(* (+ (pow (* (- 2 z) 0.9999999999998099) 3) (pow -1259.1392167224028 3)) (+ (pow (* (- 2 z) 0.9999999999998099) 3) (pow -1259.1392167224028 3)))
852.0ms
(* (+ (pow (* (- 2 z) 0.9999999999998099) 3) (pow -1259.1392167224028 3)) (- (* (* (- 2 z) 0.9999999999998099) (* (- 2 z) 0.9999999999998099)) (* -1259.1392167224028 -1259.1392167224028)))
756.0ms
(* (+ (pow (* (- 2 z) 0.9999999999998099) 3) (pow -1259.1392167224028 3)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))

prune10.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize65.0ms

Local error

Found 4 expressions with local error:

2.5b
(- (* (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (/ (* 676.5203681218851 (- 2 z)) (- 1 z))) (* (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))
2.3b
(exp (log (- (* (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (/ (* 676.5203681218851 (- 2 z)) (- 1 z))) (* (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))))
1.0b
(sqrt (* 2 PI))
1.0b
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Counts
4 → 103
Calls

4 calls. Slowest were:

34.0ms
(exp (log (- (* (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (/ (* 676.5203681218851 (- 2 z)) (- 1 z))) (* (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))))
23.0ms
(- (* (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (/ (* 676.5203681218851 (- 2 z)) (- 1 z))) (* (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))
9.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

series108.0ms

Counts
4 → 10
Calls

4 calls. Slowest were:

45.0ms
(- (* (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (/ (* 676.5203681218851 (- 2 z)) (- 1 z))) (* (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))
39.0ms
(exp (log (- (* (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (/ (* 676.5203681218851 (- 2 z)) (- 1 z))) (* (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))))
25.0ms
(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
0.0ms
(sqrt (* 2 PI))

simplify27.3s

Counts
102 → 113
Calls

102 calls. Slowest were:

693.0ms
(exp (log (- (* (* (* 676.5203681218851 (- 2 z)) (* 676.5203681218851 (- 2 z))) (+ (* (* (- 2 z) 0.9999999999998099) (* (- 2 z) 0.9999999999998099)) (- (* -1259.1392167224028 -1259.1392167224028) (* (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))) (* (* (- 1 z) (- 1 z)) (* (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028) (+ (pow (* (- 2 z) 0.9999999999998099) 3) (pow -1259.1392167224028 3)))))))
657.0ms
(- (* (* (* 676.5203681218851 (- 2 z)) (* 676.5203681218851 (- 2 z))) (* (+ (* (* (- 2 z) 0.9999999999998099) (* (- 2 z) 0.9999999999998099)) (- (* -1259.1392167224028 -1259.1392167224028) (* (* (- 2 z) 0.9999999999998099) -1259.1392167224028))) (- (* (- 2 z) 0.9999999999998099) -1259.1392167224028))) (* (* (- 1 z) (- 1 z)) (* (+ (pow (* (- 2 z) 0.9999999999998099) 3) (pow -1259.1392167224028 3)) (- (* (* (- 2 z) 0.9999999999998099) (* (- 2 z) 0.9999999999998099)) (* -1259.1392167224028 -1259.1392167224028)))))
591.0ms
(- (* (* (/ (* 676.5203681218851 (- 2 z)) (- 1 z)) (* 676.5203681218851 (- 2 z))) (* (- (* (- 2 z) 0.9999999999998099) -1259.1392167224028) (+ (* (* (- 2 z) 0.9999999999998099) (* (- 2 z) 0.9999999999998099)) (- (* -1259.1392167224028 -1259.1392167224028) (* (* (- 2 z) 0.9999999999998099) -1259.1392167224028))))) (* (- 1 z) (* (- (* (* (- 2 z) 0.9999999999998099) (* (- 2 z) 0.9999999999998099)) (* -1259.1392167224028 -1259.1392167224028)) (+ (pow (* (- 2 z) 0.9999999999998099) 3) (pow -1259.1392167224028 3)))))

prune12.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

regimes1.1s

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 0.6b

bsearch15.0ms