Average Error: 14.1 → 13.1
Time: 3.3m
Precision: 64
Internal Precision: 384
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
\[\frac{\frac{{\left({1}^{3}\right)}^{3} - {\left(\frac{{\left(0.254829592 \cdot 0.254829592 - \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\left(\frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1} + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + 1.421413741\right) + -0.284496736\right)\right) \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\left(\frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1} + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + 1.421413741\right) + -0.284496736\right)\right)\right)}^{3}}{{\left(e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\left(0.254829592 - \frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\left(\frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1} + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + 1.421413741\right) + -0.284496736\right)\right) \cdot \left(\left|x\right| \cdot 0.3275911 + 1\right)\right)\right)}^{3}}\right)}^{3}}{{1}^{3} \cdot {1}^{3} + \left(\frac{{\left(0.254829592 \cdot 0.254829592 - \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\left(\frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1} + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + 1.421413741\right) + -0.284496736\right)\right) \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\left(\frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1} + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + 1.421413741\right) + -0.284496736\right)\right)\right)}^{3}}{{\left(e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\left(0.254829592 - \frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\left(\frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1} + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + 1.421413741\right) + -0.284496736\right)\right) \cdot \left(\left|x\right| \cdot 0.3275911 + 1\right)\right)\right)}^{3}} \cdot {1}^{3} + \frac{{\left(0.254829592 \cdot 0.254829592 - \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\left(\frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1} + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + 1.421413741\right) + -0.284496736\right)\right) \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\left(\frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1} + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + 1.421413741\right) + -0.284496736\right)\right)\right)}^{3}}{{\left(e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\left(0.254829592 - \frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\left(\frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1} + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + 1.421413741\right) + -0.284496736\right)\right) \cdot \left(\left|x\right| \cdot 0.3275911 + 1\right)\right)\right)}^{3}} \cdot \frac{{\left(0.254829592 \cdot 0.254829592 - \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\left(\frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1} + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + 1.421413741\right) + -0.284496736\right)\right) \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\left(\frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1} + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + 1.421413741\right) + -0.284496736\right)\right)\right)}^{3}}{{\left(e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\left(0.254829592 - \frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\left(\frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1} + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + 1.421413741\right) + -0.284496736\right)\right) \cdot \left(\left|x\right| \cdot 0.3275911 + 1\right)\right)\right)}^{3}}\right)}}{\left(\frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + 1\right) + \frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} \cdot \frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\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. Using strategy rm
  3. Applied distribute-lft-in14.1

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \color{blue}{\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot -1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)}\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  4. Applied simplify14.1

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \left(\color{blue}{\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}} + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  5. Applied simplify14.1

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \color{blue}{\frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  6. Using strategy rm
  7. Applied flip3--14.1

    \[\leadsto \color{blue}{\frac{{1}^{3} - {\left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}{1 \cdot 1 + \left(\left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) + 1 \cdot \left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)\right)}}\]
  8. Applied simplify14.1

    \[\leadsto \frac{{1}^{3} - {\left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}{\color{blue}{\left(\frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + 1\right) + \frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} \cdot \frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}}\]
  9. Using strategy rm
  10. Applied exp-neg14.1

    \[\leadsto \frac{{1}^{3} - {\left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right) \cdot \color{blue}{\frac{1}{e^{\left|x\right| \cdot \left|x\right|}}}\right)}^{3}}{\left(\frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + 1\right) + \frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} \cdot \frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}\]
  11. Applied flip-+14.1

    \[\leadsto \frac{{1}^{3} - {\left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \color{blue}{\frac{0.254829592 \cdot 0.254829592 - \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right) \cdot \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)}{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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)}}\right) \cdot \frac{1}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3}}{\left(\frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + 1\right) + \frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} \cdot \frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}\]
  12. Applied frac-times14.1

    \[\leadsto \frac{{1}^{3} - {\left(\color{blue}{\frac{1 \cdot \left(0.254829592 \cdot 0.254829592 - \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right) \cdot \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right)}{\left(1 + 0.3275911 \cdot \left|x\right|\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)}} \cdot \frac{1}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3}}{\left(\frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + 1\right) + \frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} \cdot \frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}\]
  13. Applied frac-times14.1

    \[\leadsto \frac{{1}^{3} - {\color{blue}{\left(\frac{\left(1 \cdot \left(0.254829592 \cdot 0.254829592 - \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right) \cdot \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right)\right) \cdot 1}{\left(\left(1 + 0.3275911 \cdot \left|x\right|\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)}}^{3}}{\left(\frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + 1\right) + \frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} \cdot \frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}\]
  14. Applied cube-div13.3

    \[\leadsto \frac{{1}^{3} - \color{blue}{\frac{{\left(\left(1 \cdot \left(0.254829592 \cdot 0.254829592 - \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right) \cdot \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right)\right) \cdot 1\right)}^{3}}{{\left(\left(\left(1 + 0.3275911 \cdot \left|x\right|\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right) \cdot e^{\left|x\right| \cdot \left|x\right|}\right)}^{3}}}}{\left(\frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + 1\right) + \frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} \cdot \frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}\]
  15. Using strategy rm
  16. Applied flip3--13.1

    \[\leadsto \frac{\color{blue}{\frac{{\left({1}^{3}\right)}^{3} - {\left(\frac{{\left(\left(1 \cdot \left(0.254829592 \cdot 0.254829592 - \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right) \cdot \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right)\right) \cdot 1\right)}^{3}}{{\left(\left(\left(1 + 0.3275911 \cdot \left|x\right|\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right) \cdot e^{\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}^{3}}{{1}^{3} \cdot {1}^{3} + \left(\frac{{\left(\left(1 \cdot \left(0.254829592 \cdot 0.254829592 - \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right) \cdot \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right)\right) \cdot 1\right)}^{3}}{{\left(\left(\left(1 + 0.3275911 \cdot \left|x\right|\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right) \cdot e^{\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \frac{{\left(\left(1 \cdot \left(0.254829592 \cdot 0.254829592 - \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right) \cdot \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right)\right) \cdot 1\right)}^{3}}{{\left(\left(\left(1 + 0.3275911 \cdot \left|x\right|\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right) \cdot e^{\left|x\right| \cdot \left|x\right|}\right)}^{3}} + {1}^{3} \cdot \frac{{\left(\left(1 \cdot \left(0.254829592 \cdot 0.254829592 - \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right) \cdot \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right)\right) \cdot 1\right)}^{3}}{{\left(\left(\left(1 + 0.3275911 \cdot \left|x\right|\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right) \cdot e^{\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}}}{\left(\frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + 1\right) + \frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} \cdot \frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}\]
  17. Applied simplify13.1

    \[\leadsto \frac{\frac{\color{blue}{{\left({1}^{3}\right)}^{3} - {\left(\frac{{\left(0.254829592 \cdot 0.254829592 - \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\left(\frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1} + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + 1.421413741\right) + -0.284496736\right)\right) \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\left(\frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1} + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + 1.421413741\right) + -0.284496736\right)\right)\right)}^{3}}{{\left(e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\left(0.254829592 - \frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \left(\left(\frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1} + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + 1.421413741\right) + -0.284496736\right)\right) \cdot \left(\left|x\right| \cdot 0.3275911 + 1\right)\right)\right)}^{3}}\right)}^{3}}}{{1}^{3} \cdot {1}^{3} + \left(\frac{{\left(\left(1 \cdot \left(0.254829592 \cdot 0.254829592 - \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right) \cdot \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right)\right) \cdot 1\right)}^{3}}{{\left(\left(\left(1 + 0.3275911 \cdot \left|x\right|\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right) \cdot e^{\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \frac{{\left(\left(1 \cdot \left(0.254829592 \cdot 0.254829592 - \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right) \cdot \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right)\right) \cdot 1\right)}^{3}}{{\left(\left(\left(1 + 0.3275911 \cdot \left|x\right|\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right) \cdot e^{\left|x\right| \cdot \left|x\right|}\right)}^{3}} + {1}^{3} \cdot \frac{{\left(\left(1 \cdot \left(0.254829592 \cdot 0.254829592 - \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right) \cdot \left(\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right)\right) \cdot 1\right)}^{3}}{{\left(\left(\left(1 + 0.3275911 \cdot \left|x\right|\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 + \left(\frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)\right)\right)\right)\right) \cdot e^{\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}}{\left(\frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + 1\right) + \frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} \cdot \frac{\left(0.254829592 + \frac{-0.284496736}{0.3275911 \cdot \left|x\right| + 1}\right) + \frac{\frac{1.061405429}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)} + \left(\frac{-1.453152027}{0.3275911 \cdot \left|x\right| + 1} + 1.421413741\right)}{\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}\]
  18. Applied simplify13.1

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

Runtime

Time bar (total: 3.3m)Debug logProfile

herbie shell --seed '#(1070227846 1561819246 480764335 4016816270 2602869839 2117310382)' 
(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)))))))