Average Error: 13.9 → 13.1
Time: 49.9s
Precision: 64
Internal Precision: 128
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\sqrt[3]{e^{\log \left(\log \left(e^{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)\right)} \cdot \left(e^{\log \left(\log \left(e^{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)\right)} \cdot e^{\log \left(\log \left(e^{\sqrt[3]{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*} \cdot \sqrt[3]{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}}\right) \cdot \sqrt[3]{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)}\right)}\]

Error

Bits error versus x

Derivation

  1. Initial program 13.9

    \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  2. Simplified13.9

    \[\leadsto \color{blue}{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\]
  3. Using strategy rm

  4. Applied add-log-exp13.9

    \[\leadsto \color{blue}{\log \left(e^{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)}\]
  5. Using strategy rm

  6. Applied add-exp-log13.9

    \[\leadsto \color{blue}{e^{\log \left(\log \left(e^{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)\right)}}\]
  7. Using strategy rm

  8. Applied add-cbrt-cube13.9

    \[\leadsto \color{blue}{\sqrt[3]{\left(e^{\log \left(\log \left(e^{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)\right)} \cdot e^{\log \left(\log \left(e^{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)\right)}\right) \cdot e^{\log \left(\log \left(e^{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)\right)}}}\]
  9. Using strategy rm

  10. Applied add-cube-cbrt13.9

    \[\leadsto \sqrt[3]{\left(e^{\log \left(\log \left(e^{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)\right)} \cdot e^{\log \left(\log \left(e^{\color{blue}{\left(\sqrt[3]{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*} \cdot \sqrt[3]{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right) \cdot \sqrt[3]{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}}}\right)\right)}\right) \cdot e^{\log \left(\log \left(e^{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)\right)}}\]

  11. Applied exp-prod13.9

    \[\leadsto \sqrt[3]{\left(e^{\log \left(\log \left(e^{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)\right)} \cdot e^{\log \left(\log \color{blue}{\left({\left(e^{\sqrt[3]{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*} \cdot \sqrt[3]{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}}\right)}^{\left(\sqrt[3]{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)}\right)}\right)}\right) \cdot e^{\log \left(\log \left(e^{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)\right)}}\]

  12. Applied log-pow13.1

    \[\leadsto \sqrt[3]{\left(e^{\log \left(\log \left(e^{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)\right)} \cdot e^{\log \color{blue}{\left(\sqrt[3]{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*} \cdot \log \left(e^{\sqrt[3]{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*} \cdot \sqrt[3]{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}}\right)\right)}}\right) \cdot e^{\log \left(\log \left(e^{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)\right)}}\]

  13. Final simplification13.1

    \[\leadsto \sqrt[3]{e^{\log \left(\log \left(e^{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)\right)} \cdot \left(e^{\log \left(\log \left(e^{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)\right)} \cdot e^{\log \left(\log \left(e^{\sqrt[3]{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*} \cdot \sqrt[3]{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}}\right) \cdot \sqrt[3]{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)}\right)}\]

Reproduce

herbie shell --seed 2019002 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.erf"
  (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))

Details

Time bar (total: 47.9s)Debug log

sample142.0ms

Algorithm
intervals

simplify324.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

323.0ms
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.3b

localize87.0ms

Local error

Found 4 expressions with local error:

15.3b
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)
0.5b
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))
0.2b
(* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1)))
0.2b
(/ 1 (fma 0.3275911 (fabs x) 1))

rewrite22.0ms

Algorithm
rewrite-expression-head
Counts
4 → 75
Calls

4 calls. Slowest were:

18.0ms
(* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1)))
2.0ms
(/ 1 (fma 0.3275911 (fabs x) 1))
0.0ms
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)

series672.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

428.0ms
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)
196.0ms
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))
29.0ms
(* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1)))
19.0ms
(/ 1 (fma 0.3275911 (fabs x) 1))

simplify3.2s

Counts
47 → 87
Calls

47 calls. Slowest were:

407.0ms
(- (+ (* 0.254829592 (/ 1 (+ (* 0.3275911 (fabs x)) 1))) (+ (* 1.061405429 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 5))) (* 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 3))))) (+ (* 0.284496736 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 2))) (* 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 4)))))
357.0ms
(- (+ (* 0.254829592 (/ 1 (+ (* 0.3275911 (fabs x)) 1))) (+ (* 1.061405429 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 5))) (* 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 3))))) (+ (* 0.284496736 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 2))) (* 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 4)))))
336.0ms
(- (+ (* 0.254829592 (/ 1 (+ (* 0.3275911 (fabs x)) 1))) (+ (* 1.061405429 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 5))) (* 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 3))))) (+ (* 0.284496736 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 2))) (* 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 4)))))

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.3b

localize10.0ms

Local error

Found 4 expressions with local error:

15.3b
(log (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))
15.3b
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)
0.5b
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))
0.2b
(* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
4 → 75
Calls

4 calls. Slowest were:

4.0ms
(* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1)))
2.0ms
(log (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))
0.0ms
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)

series1.1s

Counts
4 → 12
Calls

4 calls. Slowest were:

407.0ms
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)
374.0ms
(log (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))
233.0ms
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))
50.0ms
(* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1)))

simplify6.4s

Counts
51 → 87
Calls

51 calls. Slowest were:

589.0ms
(log (* (cbrt (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1))) (cbrt (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))))
509.0ms
(log (exp (* (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))))))
439.0ms
(cbrt (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1))

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.3b

localize18.0ms

Local error

Found 4 expressions with local error:

15.3b
(log (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))
15.3b
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)
1.4b
(exp (log (log (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))))
0.5b
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
4 → 59
Calls

4 calls. Slowest were:

5.0ms
(exp (log (log (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))))
4.0ms
(log (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))
0.0ms
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)

series1.3s

Counts
4 → 12
Calls

4 calls. Slowest were:

416.0ms
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)
379.0ms
(log (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))
326.0ms
(exp (log (log (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))))
186.0ms
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))

simplify10.3s

Counts
32 → 71
Calls

32 calls. Slowest were:

779.0ms
(sqrt (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1))
688.0ms
(log (exp (* (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))))))
552.0ms
(cbrt (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1))

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.3b

localize33.0ms

Local error

Found 4 expressions with local error:

15.3b
(log (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))
15.3b
(log (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))
15.3b
(log (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))
15.3b
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
4 → 64
Calls

4 calls. Slowest were:

4.0ms
(log (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))
4.0ms
(log (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))
4.0ms
(log (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))

series1.5s

Counts
4 → 12
Calls

4 calls. Slowest were:

432.0ms
(log (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))
386.0ms
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)
332.0ms
(log (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))
329.0ms
(log (exp (fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)))

simplify11.2s

Counts
36 → 76
Calls

36 calls. Slowest were:

647.0ms
(log (exp (* (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))))))
622.0ms
(log (exp (* (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))))))
544.0ms
(log (exp (* (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))))))

prune2.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.4b

regimes167.0ms

Accuracy

0% (0.0b remaining)

Error of 13.1b against oracle of 13.1b and baseline of 13.1b

bsearch12.0ms

end0.0ms

sample3.8s

Algorithm
intervals