Initial program 13.9
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
- Using strategy
rm Applied add-sqr-sqrt13.9
\[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{\color{blue}{\sqrt{1 + 0.3275911 \cdot \left|x\right|} \cdot \sqrt{1 + 0.3275911 \cdot \left|x\right|}}} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
Applied associate-/r*13.9
\[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \color{blue}{\frac{\frac{1}{\sqrt{1 + 0.3275911 \cdot \left|x\right|}}}{\sqrt{1 + 0.3275911 \cdot \left|x\right|}}} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
Taylor expanded around 0 13.9
\[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \color{blue}{\frac{1}{0.3275911 \cdot \left|x\right| + 1}} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{\frac{1}{\sqrt{1 + 0.3275911 \cdot \left|x\right|}}}{\sqrt{1 + 0.3275911 \cdot \left|x\right|}} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
Applied simplify13.9
\[\leadsto \color{blue}{1 - \frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \frac{\frac{\left(1.421413741 + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}}{\frac{\left|x\right| \cdot 0.3275911 + 1}{\frac{1}{\left|x\right| \cdot 0.3275911 + 1}}} + \left(0.254829592 + \frac{-0.284496736}{\left|x\right| \cdot 0.3275911 + 1}\right)}{e^{\left|x\right| \cdot \left|x\right|}}}\]
- Using strategy
rm Applied add-exp-log13.9
\[\leadsto 1 - \frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \frac{\frac{\left(1.421413741 + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}}{\frac{\left|x\right| \cdot 0.3275911 + 1}{\frac{1}{\color{blue}{e^{\log \left(\left|x\right| \cdot 0.3275911 + 1\right)}}}}} + \left(0.254829592 + \frac{-0.284496736}{\left|x\right| \cdot 0.3275911 + 1}\right)}{e^{\left|x\right| \cdot \left|x\right|}}\]
Applied rec-exp13.9
\[\leadsto 1 - \frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \frac{\frac{\left(1.421413741 + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}}{\frac{\left|x\right| \cdot 0.3275911 + 1}{\color{blue}{e^{-\log \left(\left|x\right| \cdot 0.3275911 + 1\right)}}}} + \left(0.254829592 + \frac{-0.284496736}{\left|x\right| \cdot 0.3275911 + 1}\right)}{e^{\left|x\right| \cdot \left|x\right|}}\]
Applied add-exp-log13.9
\[\leadsto 1 - \frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \frac{\frac{\left(1.421413741 + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}}{\frac{\color{blue}{e^{\log \left(\left|x\right| \cdot 0.3275911 + 1\right)}}}{e^{-\log \left(\left|x\right| \cdot 0.3275911 + 1\right)}}} + \left(0.254829592 + \frac{-0.284496736}{\left|x\right| \cdot 0.3275911 + 1}\right)}{e^{\left|x\right| \cdot \left|x\right|}}\]
Applied div-exp13.9
\[\leadsto 1 - \frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \frac{\frac{\left(1.421413741 + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}}{\color{blue}{e^{\log \left(\left|x\right| \cdot 0.3275911 + 1\right) - \left(-\log \left(\left|x\right| \cdot 0.3275911 + 1\right)\right)}}} + \left(0.254829592 + \frac{-0.284496736}{\left|x\right| \cdot 0.3275911 + 1}\right)}{e^{\left|x\right| \cdot \left|x\right|}}\]
Applied add-exp-log13.9
\[\leadsto 1 - \frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \frac{\frac{\color{blue}{e^{\log \left(\left(1.421413741 + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right)}}}{e^{\log \left(\left|x\right| \cdot 0.3275911 + 1\right) - \left(-\log \left(\left|x\right| \cdot 0.3275911 + 1\right)\right)}} + \left(0.254829592 + \frac{-0.284496736}{\left|x\right| \cdot 0.3275911 + 1}\right)}{e^{\left|x\right| \cdot \left|x\right|}}\]
Applied div-exp13.9
\[\leadsto 1 - \frac{1}{\left|x\right| \cdot 0.3275911 + 1} \cdot \frac{\color{blue}{e^{\log \left(\left(1.421413741 + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + \frac{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right) - \left(\log \left(\left|x\right| \cdot 0.3275911 + 1\right) - \left(-\log \left(\left|x\right| \cdot 0.3275911 + 1\right)\right)\right)}} + \left(0.254829592 + \frac{-0.284496736}{\left|x\right| \cdot 0.3275911 + 1}\right)}{e^{\left|x\right| \cdot \left|x\right|}}\]
