\(1 - \frac{\left(\left(\frac{-1.453152027}{1 + 0.3275911 \cdot \left|x\right|} + 1.421413741\right) + \frac{\frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}\right) \cdot \frac{\frac{1 - 0.3275911 \cdot \left|x\right|}{1 + 0.3275911 \cdot \left|x\right|}}{1 - \left(\left|x\right| \cdot \left|x\right|\right) \cdot 0.10731592879921002} + \left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right)}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + 0.3275911 \cdot \left|x\right|\right)}\)
- Started with
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
13.9
- Using strategy
rm 13.9
- Applied add-sqr-sqrt to get
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \color{red}{\frac{1}{1 + 0.3275911 \cdot \left|x\right|}} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \color{blue}{{\left(\sqrt{\frac{1}{1 + 0.3275911 \cdot \left|x\right|}}\right)}^2} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
13.9
- Using strategy
rm 13.9
- Applied flip-+ to get
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + {\left(\sqrt{\frac{1}{\color{red}{1 + 0.3275911 \cdot \left|x\right|}}}\right)}^2 \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + {\left(\sqrt{\frac{1}{\color{blue}{\frac{{1}^2 - {\left(0.3275911 \cdot \left|x\right|\right)}^2}{1 - 0.3275911 \cdot \left|x\right|}}}}\right)}^2 \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
13.9
- Applied associate-/r/ to get
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + {\left(\sqrt{\color{red}{\frac{1}{\frac{{1}^2 - {\left(0.3275911 \cdot \left|x\right|\right)}^2}{1 - 0.3275911 \cdot \left|x\right|}}}}\right)}^2 \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + {\left(\sqrt{\color{blue}{\frac{1}{{1}^2 - {\left(0.3275911 \cdot \left|x\right|\right)}^2} \cdot \left(1 - 0.3275911 \cdot \left|x\right|\right)}}\right)}^2 \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
13.9
- Applied sqrt-prod to get
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + {\color{red}{\left(\sqrt{\frac{1}{{1}^2 - {\left(0.3275911 \cdot \left|x\right|\right)}^2} \cdot \left(1 - 0.3275911 \cdot \left|x\right|\right)}\right)}}^2 \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + {\color{blue}{\left(\sqrt{\frac{1}{{1}^2 - {\left(0.3275911 \cdot \left|x\right|\right)}^2}} \cdot \sqrt{1 - 0.3275911 \cdot \left|x\right|}\right)}}^2 \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
44.7
- Applied square-prod to get
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \color{red}{{\left(\sqrt{\frac{1}{{1}^2 - {\left(0.3275911 \cdot \left|x\right|\right)}^2}} \cdot \sqrt{1 - 0.3275911 \cdot \left|x\right|}\right)}^2} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \color{blue}{\left({\left(\sqrt{\frac{1}{{1}^2 - {\left(0.3275911 \cdot \left|x\right|\right)}^2}}\right)}^2 \cdot {\left(\sqrt{1 - 0.3275911 \cdot \left|x\right|}\right)}^2\right)} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
44.7
- Applied simplify to get
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \left({\left(\sqrt{\frac{1}{{1}^2 - {\left(0.3275911 \cdot \left|x\right|\right)}^2}}\right)}^2 \cdot \color{red}{{\left(\sqrt{1 - 0.3275911 \cdot \left|x\right|}\right)}^2}\right) \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \left({\left(\sqrt{\frac{1}{{1}^2 - {\left(0.3275911 \cdot \left|x\right|\right)}^2}}\right)}^2 \cdot \color{blue}{\left(1 - \left|x\right| \cdot 0.3275911\right)}\right) \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
29.0
- Applied taylor to get
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \left({\left(\sqrt{\frac{1}{{1}^2 - {\left(0.3275911 \cdot \left|x\right|\right)}^2}}\right)}^2 \cdot \left(1 - \left|x\right| \cdot 0.3275911\right)\right) \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \left({\left(\sqrt{\frac{1}{1 - 0.10731592879921002 \cdot {\left(\left|x\right|\right)}^2}}\right)}^2 \cdot \left(1 - \left|x\right| \cdot 0.3275911\right)\right) \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
28.9
- Taylor expanded around 0 to get
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \left({\color{red}{\left(\sqrt{\frac{1}{1 - 0.10731592879921002 \cdot {\left(\left|x\right|\right)}^2}}\right)}}^2 \cdot \left(1 - \left|x\right| \cdot 0.3275911\right)\right) \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \left({\color{blue}{\left(\sqrt{\frac{1}{1 - 0.10731592879921002 \cdot {\left(\left|x\right|\right)}^2}}\right)}}^2 \cdot \left(1 - \left|x\right| \cdot 0.3275911\right)\right) \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
28.9
- Applied simplify to get
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \left({\left(\sqrt{\frac{1}{1 - 0.10731592879921002 \cdot {\left(\left|x\right|\right)}^2}}\right)}^2 \cdot \left(1 - \left|x\right| \cdot 0.3275911\right)\right) \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \leadsto 1 - \frac{\frac{\left(\frac{-0.284496736}{\left|x\right| \cdot 0.3275911 + 1} + 0.254829592\right) + \left(\frac{1 - \left|x\right| \cdot 0.3275911}{1 - \left(\left|x\right| \cdot \left|x\right|\right) \cdot 0.10731592879921002} \cdot \frac{1}{\left|x\right| \cdot 0.3275911 + 1}\right) \cdot \left(\left(1.421413741 + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + \frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1} \cdot \frac{1}{\left|x\right| \cdot 0.3275911 + 1}\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\left|x\right| \cdot 0.3275911 + 1}\]
13.9
- Applied final simplification
- Applied simplify to get
\[\color{red}{1 - \frac{\frac{\left(\frac{-0.284496736}{\left|x\right| \cdot 0.3275911 + 1} + 0.254829592\right) + \left(\frac{1 - \left|x\right| \cdot 0.3275911}{1 - \left(\left|x\right| \cdot \left|x\right|\right) \cdot 0.10731592879921002} \cdot \frac{1}{\left|x\right| \cdot 0.3275911 + 1}\right) \cdot \left(\left(1.421413741 + \frac{-1.453152027}{\left|x\right| \cdot 0.3275911 + 1}\right) + \frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1} \cdot \frac{1}{\left|x\right| \cdot 0.3275911 + 1}\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\left|x\right| \cdot 0.3275911 + 1}} \leadsto \color{blue}{1 - \frac{\left(\left(\frac{-1.453152027}{1 + 0.3275911 \cdot \left|x\right|} + 1.421413741\right) + \frac{\frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}\right) \cdot \frac{\frac{1 - 0.3275911 \cdot \left|x\right|}{1 + 0.3275911 \cdot \left|x\right|}}{1 - \left(\left|x\right| \cdot \left|x\right|\right) \cdot 0.10731592879921002} + \left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right)}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(1 + 0.3275911 \cdot \left|x\right|\right)}}\]
13.9