Average Error: 13.9 → 13.2
Time: 1.0m
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]{\sqrt[3]{1 - \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}} \cdot \log \left(e^{\sqrt[3]{1 - \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}} \cdot \sqrt[3]{1 - \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}}}\right)} \cdot \left(\sqrt[3]{\log \left(e^{\left(\frac{0.284496736}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + \frac{1.453152027}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^{4}}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|} + \left(\left(1 - e^{\left(-\left|x\right|\right) \cdot \left|x\right|} \cdot \left(\frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + \frac{0.254829592}{1 + \left|x\right| \cdot 0.3275911}\right)\right) - \frac{1.061405429 \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^{5}}\right)}\right)} \cdot \sqrt[3]{\log \left(e^{1 - \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}}\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

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

  4. Applied add-log-exp13.9

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

  6. Applied add-cube-cbrt13.9

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

  8. Applied add-cube-cbrt13.9

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

  9. Applied exp-prod13.9

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

  10. Applied log-pow13.2

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

  11. Taylor expanded around 0 14.5

    \[\leadsto \left(\sqrt[3]{\log \left(e^{1 - \frac{\frac{\frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + 0.254829592}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}}\right)} \cdot \sqrt[3]{\log \left(e^{\color{blue}{\left(0.284496736 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2} \cdot e^{{\left(\left|x\right|\right)}^{2}}} + \left(1.453152027 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4} \cdot e^{{\left(\left|x\right|\right)}^{2}}} + 1\right)\right) - \left(0.254829592 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(1.421413741 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot e^{{\left(\left|x\right|\right)}^{2}}} + 1.061405429 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot e^{{\left(\left|x\right|\right)}^{2}}}\right)\right)}}\right)}\right) \cdot \sqrt[3]{\sqrt[3]{1 - \frac{\frac{\frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + 0.254829592}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}} \cdot \log \left(e^{\sqrt[3]{1 - \frac{\frac{\frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + 0.254829592}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}} \cdot \sqrt[3]{1 - \frac{\frac{\frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + 0.254829592}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}}}\right)}\]

  12. Simplified13.2

    \[\leadsto \left(\sqrt[3]{\log \left(e^{1 - \frac{\frac{\frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + 0.254829592}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}}\right)} \cdot \sqrt[3]{\log \left(e^{\color{blue}{e^{-\left|x\right| \cdot \left|x\right|} \cdot \left(\frac{1.453152027}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^{4}} + \frac{0.284496736}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)}\right) + \left(\left(1 - e^{-\left|x\right| \cdot \left|x\right|} \cdot \left(\frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + \frac{0.254829592}{1 + \left|x\right| \cdot 0.3275911}\right)\right) - \frac{1.061405429 \cdot e^{-\left|x\right| \cdot \left|x\right|}}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^{5}}\right)}}\right)}\right) \cdot \sqrt[3]{\sqrt[3]{1 - \frac{\frac{\frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + 0.254829592}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}} \cdot \log \left(e^{\sqrt[3]{1 - \frac{\frac{\frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + 0.254829592}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}} \cdot \sqrt[3]{1 - \frac{\frac{\frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911} + 1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911} + 0.254829592}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}}}\right)}\]

  13. Final simplification13.2

    \[\leadsto \sqrt[3]{\sqrt[3]{1 - \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}} \cdot \log \left(e^{\sqrt[3]{1 - \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}} \cdot \sqrt[3]{1 - \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}}}\right)} \cdot \left(\sqrt[3]{\log \left(e^{\left(\frac{0.284496736}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + \frac{1.453152027}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^{4}}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|} + \left(\left(1 - e^{\left(-\left|x\right|\right) \cdot \left|x\right|} \cdot \left(\frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} + \frac{0.254829592}{1 + \left|x\right| \cdot 0.3275911}\right)\right) - \frac{1.061405429 \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^{5}}\right)}\right)} \cdot \sqrt[3]{\log \left(e^{1 - \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911} + -1.453152027}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}}\right)}\right)\]

Reproduce

herbie shell --seed 2019068 
(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)))))))