Average Error: 14.1 → 13.3
Time: 9.4m
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{1 - \frac{\frac{\frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + 0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot \left((0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*\right)} \cdot \sqrt{\frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + 0.254829592}}{{\left(e^{\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \left(\left(\frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + 0.254829592\right) \cdot \sqrt{\frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + 0.254829592}\right)}{1 + \left(\frac{\frac{\sqrt{\frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + 0.254829592} \cdot \sqrt{\frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + 0.254829592}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{\frac{\sqrt{\frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + 0.254829592} \cdot \sqrt{\frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + 0.254829592}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{e^{\left|x\right| \cdot \left|x\right|}} + \frac{\frac{\sqrt{\frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + 0.254829592} \cdot \sqrt{\frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + 0.254829592}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{e^{\left|x\right| \cdot \left|x\right|}}\right)}\]

Error

Bits error versus x

Derivation

  1. Initial program 14.1

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

  2. Simplified14.1

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

  4. Applied add-sqr-sqrt14.0

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

  6. Applied flip3--14.1

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

  8. Applied *-un-lft-identity14.1

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

  9. Applied *-un-lft-identity14.1

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

  10. Applied times-frac14.1

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

  11. Applied times-frac14.1

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

  12. Applied unpow-prod-down14.1

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

  13. Simplified13.3

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

  15. Applied cube-div13.3

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

  16. Simplified13.3

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

  17. Final simplification13.3

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

Reproduce

herbie shell --seed 2019093 +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)))))))