Average Error: 14.0 → 2.0
Time: 2.6m
Precision: 64
Internal Precision: 384
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\sqrt{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left(\sqrt{(\left((\left((\left(\frac{1.061405429}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -1.453152027\right) \cdot \left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) + 1.421413741)_*\right) \cdot \left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) + -0.284496736)_*\right) \cdot \left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} \cdot \frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) + \left(\frac{0.254829592}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right))_*} \cdot \sqrt{(\left((\left((\left(\frac{1.061405429}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -1.453152027\right) \cdot \left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) + 1.421413741)_*\right) \cdot \left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) + -0.284496736)_*\right) \cdot \left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} \cdot \frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) + \left(\frac{0.254829592}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right))_*}\right) + 1)_*} \cdot \sqrt{e^{\log_* (1 + (\left(\frac{\frac{\frac{-1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}}{e^{\left|x\right| \cdot \left|x\right|}}}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) \cdot \left((\left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) \cdot \left((\left(\frac{1.061405429}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -1.453152027\right) \cdot \left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) + 1.421413741)_*\right) + -0.284496736)_*\right) + \left(\frac{\frac{-0.254829592}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}}{e^{\left|x\right| \cdot \left|x\right|}}\right))_*)}}\]

Error

Bits error versus x

Derivation

  1. Initial program 14.0

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

  2. Applied simplify13.9

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

  4. Applied add-log-exp13.9

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

  6. Applied add-sqr-sqrt13.9

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

  8. Applied add-sqr-sqrt13.9

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

  9. Applied exp-prod13.9

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

  10. Applied log-pow13.9

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

  11. Applied simplify2.3

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

  13. Applied add-exp-log2.0

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

  14. Applied simplify2.0

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

Runtime

Time bar (total: 2.6m)Debug logProfile

herbie shell --seed '#(1070991898 1055468627 4280279443 640792587 928206309 3646738750)' +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)))))))