Average Error: 13.8 → 13.0
Time: 3.9m
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]{\log \left(e^{(1 \cdot 1 + \left(\frac{(\left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(1.421413741 + \frac{\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) + -0.284496736)_*\right) \cdot \left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) + 0.254829592)_* \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{\sqrt{e^{\left|x\right| \cdot \left|x\right|}}} \cdot \frac{-1}{\sqrt{e^{\left|x\right| \cdot \left|x\right|}}}\right))_*}\right)} \cdot \left(\sqrt[3]{(1 \cdot 1 + \left(\frac{(\left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(1.421413741 + \frac{\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) + -0.284496736)_*\right) \cdot \left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) + 0.254829592)_* \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{\sqrt{e^{\left|x\right| \cdot \left|x\right|}}} \cdot \frac{-1}{\sqrt{e^{\left|x\right| \cdot \left|x\right|}}}\right))_*} \cdot \sqrt[3]{\log \left(e^{(1 \cdot 1 + \left(\frac{(\left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(1.421413741 + \frac{\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) + -0.284496736)_*\right) \cdot \left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) + 0.254829592)_* \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{\sqrt{e^{\left|x\right| \cdot \left|x\right|}}} \cdot \frac{-1}{\sqrt{e^{\left|x\right| \cdot \left|x\right|}}}\right))_*}\right)}\right) + (\left(-\frac{(\left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(1.421413741 + \frac{\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) + -0.284496736)_*\right) \cdot \left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) + 0.254829592)_* \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{\sqrt{e^{\left|x\right| \cdot \left|x\right|}}}\right) \cdot \left(\frac{1}{\sqrt{e^{\left|x\right| \cdot \left|x\right|}}}\right) + \left(\frac{(\left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(1.421413741 + \frac{\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) + -0.284496736)_*\right) \cdot \left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) + 0.254829592)_* \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{\sqrt{e^{\left|x\right| \cdot \left|x\right|}}} \cdot \frac{1}{\sqrt{e^{\left|x\right| \cdot \left|x\right|}}}\right))_*\]

Error

Bits error versus x

Derivation

  1. Initial program 13.8

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

  2. Simplified13.8

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

  4. Applied add-sqr-sqrt13.8

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

  5. Applied *-un-lft-identity13.8

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

  6. Applied times-frac13.8

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

  7. Applied *-un-lft-identity13.8

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

  8. Applied prod-diff13.8

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

  10. Applied add-cube-cbrt13.8

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

  12. Applied add-log-exp13.0

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

  14. Applied add-log-exp13.0

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

  15. Final simplification13.0

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

Reproduce

herbie shell --seed 2019072 +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)))))))