\(\frac{{1}^{3} - {\left(\sqrt{{\left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\left(1.061405429 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^2}\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}^2}{\left(\frac{\frac{\frac{\left(\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911} - 0.284496736\right) - \frac{1.453152027}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^2}}{1 + \left|x\right| \cdot 0.3275911} + \left(0.254829592 + \frac{\frac{1.061405429}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^3}}{1 + \left|x\right| \cdot 0.3275911}\right)}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}} + 1\right) + \frac{{\left(\frac{\frac{\left(\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911} - 0.284496736\right) - \frac{1.453152027}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^2}}{1 + \left|x\right| \cdot 0.3275911} + \left(0.254829592 + \frac{\frac{1.061405429}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^3}}{1 + \left|x\right| \cdot 0.3275911}\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^2}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^2}}\)
- Started with
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
13.8
- Applied taylor to get
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\left(1.061405429 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^2}\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
13.9
- Taylor expanded around 0 to get
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \color{red}{\left(\left(1.061405429 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^2}\right)\right)}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \color{blue}{\left(\left(1.061405429 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^2}\right)\right)}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
13.9
- Using strategy
rm 13.9
- Applied flip3-- to get
\[\color{red}{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(\left(1.061405429 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^2}\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}} \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(\left(1.061405429 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^2}\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}{{1}^2 + \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(\left(1.061405429 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^2}\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^2 + 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(\left(1.061405429 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^2}\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)\right)}}\]
13.8
- Applied simplify to get
\[\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(\left(1.061405429 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^2}\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}{\color{red}{{1}^2 + \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(\left(1.061405429 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^2}\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^2 + 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(\left(1.061405429 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^2}\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)\right)}} \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(\left(1.061405429 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^2}\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}{\color{blue}{\left(\frac{\frac{\frac{\left(\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911} - 0.284496736\right) - \frac{1.453152027}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^2}}{1 + \left|x\right| \cdot 0.3275911} + \left(0.254829592 + \frac{\frac{1.061405429}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^3}}{1 + \left|x\right| \cdot 0.3275911}\right)}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}} + 1\right) + \frac{{\left(\frac{\frac{\left(\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911} - 0.284496736\right) - \frac{1.453152027}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^2}}{1 + \left|x\right| \cdot 0.3275911} + \left(0.254829592 + \frac{\frac{1.061405429}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^3}}{1 + \left|x\right| \cdot 0.3275911}\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^2}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^2}}}\]
13.8
- Using strategy
rm 13.8
- Applied add-sqr-sqrt to get
\[\frac{{1}^{3} - \color{red}{{\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(\left(1.061405429 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^2}\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}}{\left(\frac{\frac{\frac{\left(\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911} - 0.284496736\right) - \frac{1.453152027}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^2}}{1 + \left|x\right| \cdot 0.3275911} + \left(0.254829592 + \frac{\frac{1.061405429}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^3}}{1 + \left|x\right| \cdot 0.3275911}\right)}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}} + 1\right) + \frac{{\left(\frac{\frac{\left(\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911} - 0.284496736\right) - \frac{1.453152027}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^2}}{1 + \left|x\right| \cdot 0.3275911} + \left(0.254829592 + \frac{\frac{1.061405429}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^3}}{1 + \left|x\right| \cdot 0.3275911}\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^2}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^2}} \leadsto \frac{{1}^{3} - \color{blue}{{\left(\sqrt{{\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(\left(1.061405429 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^2}\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}^2}}{\left(\frac{\frac{\frac{\left(\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911} - 0.284496736\right) - \frac{1.453152027}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^2}}{1 + \left|x\right| \cdot 0.3275911} + \left(0.254829592 + \frac{\frac{1.061405429}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^3}}{1 + \left|x\right| \cdot 0.3275911}\right)}{1 + \left|x\right| \cdot 0.3275911}}{e^{\left|x\right| \cdot \left|x\right|}} + 1\right) + \frac{{\left(\frac{\frac{\left(\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911} - 0.284496736\right) - \frac{1.453152027}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^2}}{1 + \left|x\right| \cdot 0.3275911} + \left(0.254829592 + \frac{\frac{1.061405429}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^3}}{1 + \left|x\right| \cdot 0.3275911}\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^2}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^2}}\]
13.1
