Average Error: 14.2 → 10.9
Time: 2.9m
Precision: 64
Internal Precision: 128
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\frac{e^{\log \left(1 - \frac{\frac{\left(0.254829592 + \frac{1.061405429}{\left(\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)\right) \cdot \left(\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)\right)}\right) + \left(\left(\frac{1.421413741}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} - \frac{0.284496736}{1 + \left|x\right| \cdot 0.3275911}\right) - \frac{1.453152027}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)\right)}\right)}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\frac{\log \left(\frac{e^{\frac{1.421413741}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} - \frac{0.284496736}{1 + \left|x\right| \cdot 0.3275911}}}{e^{\frac{1.453152027}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)\right)}}}\right) + \left(0.254829592 + \frac{1.061405429}{\left(\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)\right) \cdot \left(\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)\right)}\right)}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}\right)}}{1 + \frac{\frac{\left(0.254829592 + \frac{1.061405429}{\left(\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)\right) \cdot \left(\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)\right)}\right) + \left(\left(\frac{1.421413741}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)} - \frac{0.284496736}{1 + \left|x\right| \cdot 0.3275911}\right) - \frac{1.453152027}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot \left(1 + \left|x\right| \cdot 0.3275911\right)\right)}\right)}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}}}\]

Error

Bits error versus x

Derivation

  1. Initial program 14.2

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

  2. Simplified14.2

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

  3. Taylor expanded around inf 15.0

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

  4. Simplified14.2

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

  6. Applied flip--14.2

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

  8. Applied add-log-exp14.2

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

  9. Applied add-log-exp14.2

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

  10. Applied diff-log10.9

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

  12. Applied add-exp-log10.9

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

  13. Final simplification10.9

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

Reproduce

herbie shell --seed 2019094 
(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)))))))