\((\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left((\left(\frac{\frac{\frac{3}{4}}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3}\right))_* + \frac{1}{\left|x\right|}\right) + \left(\frac{\frac{\frac{15}{8}}{\left|x\right|} \cdot \sqrt{\frac{1}{\pi}}}{{\left({\left(\left|x\right|\right)}^3\right)}^2} \cdot e^{\left|x\right| \cdot \left|x\right|}\right))_*\)
- Started with
\[\left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\left(\frac{1}{\left|x\right|} + \frac{1}{2} \cdot \left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{3}{4} \cdot \left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{15}{8} \cdot \left(\left(\left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right)\]
1.5
- Applied simplify to get
\[\color{red}{\left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\left(\frac{1}{\left|x\right|} + \frac{1}{2} \cdot \left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{3}{4} \cdot \left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{15}{8} \cdot \left(\left(\left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right)} \leadsto \color{blue}{(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\frac{15}{8} \cdot e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3}{\left|x\right|}\right))_*}\]
1.4
- Using strategy
rm 1.4
- Applied cube-div to get
\[(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\frac{15}{8} \cdot e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \color{red}{{\left(\frac{1}{\left|x\right|}\right)}^3}}{\left|x\right|}\right))_* \leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\frac{15}{8} \cdot e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \color{blue}{\frac{{1}^3}{{\left(\left|x\right|\right)}^3}}}{\left|x\right|}\right))_*\]
1.1
- Using strategy
rm 1.1
- Applied add-sqr-sqrt to get
\[(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\frac{15}{8} \cdot e^{\left|x\right| \cdot \left|x\right|}}{\color{red}{\sqrt{\pi}}} \cdot \frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \frac{{1}^3}{{\left(\left|x\right|\right)}^3}}{\left|x\right|}\right))_* \leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\frac{15}{8} \cdot e^{\left|x\right| \cdot \left|x\right|}}{\color{blue}{{\left(\sqrt{\sqrt{\pi}}\right)}^2}} \cdot \frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \frac{{1}^3}{{\left(\left|x\right|\right)}^3}}{\left|x\right|}\right))_*\]
1.0
- Applied taylor to get
\[(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\frac{15}{8} \cdot e^{\left|x\right| \cdot \left|x\right|}}{{\left(\sqrt{\sqrt{\pi}}\right)}^2} \cdot \frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \frac{{1}^3}{{\left(\left|x\right|\right)}^3}}{\left|x\right|}\right))_* \leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\frac{15}{8} \cdot e^{\left|x\right| \cdot \left|x\right|}}{{\left(\sqrt{\sqrt{\pi}}\right)}^2} \cdot \frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \frac{{1}^3}{{\left(\left|x\right|\right)}^3}}{\left|x\right|}\right))_*\]
1.0
- Taylor expanded around 0 to get
\[(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\frac{15}{8} \cdot e^{\left|x\right| \cdot \left|x\right|}}{{\left(\sqrt{\color{red}{\sqrt{\pi}}}\right)}^2} \cdot \frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \frac{{1}^3}{{\left(\left|x\right|\right)}^3}}{\left|x\right|}\right))_* \leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\frac{15}{8} \cdot e^{\left|x\right| \cdot \left|x\right|}}{{\left(\sqrt{\color{blue}{\sqrt{\pi}}}\right)}^2} \cdot \frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \frac{{1}^3}{{\left(\left|x\right|\right)}^3}}{\left|x\right|}\right))_*\]
1.0
- Applied simplify to get
\[\color{red}{(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\frac{15}{8} \cdot e^{\left|x\right| \cdot \left|x\right|}}{{\left(\sqrt{\sqrt{\pi}}\right)}^2} \cdot \frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \frac{{1}^3}{{\left(\left|x\right|\right)}^3}}{\left|x\right|}\right))_*} \leadsto \color{blue}{(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left((\left(\frac{3}{4} \cdot \frac{\frac{1}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3}\right))_* + \frac{1}{\left|x\right|}\right) + \left(\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \frac{\frac{1}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right) \cdot \left(\frac{\frac{15}{8}}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right)\right))_*}\]
1.2
- Applied taylor to get
\[(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left((\left(\frac{3}{4} \cdot \frac{\frac{1}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3}\right))_* + \frac{1}{\left|x\right|}\right) + \left(\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \frac{\frac{1}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right) \cdot \left(\frac{\frac{15}{8}}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right)\right))_* \leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left((\left(\frac{3}{4} \cdot \frac{\frac{1}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3}\right))_* + \frac{1}{\left|x\right|}\right) + \left(\frac{15}{8} \cdot \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot e^{{\left(\left|x\right|\right)}^2}}{{\left(\left|x\right|\right)}^3 \cdot \left|x\right|} \cdot \sqrt{\frac{1}{\pi}}\right)\right))_*\]
1.0
- Taylor expanded around 0 to get
\[(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left((\left(\frac{3}{4} \cdot \frac{\frac{1}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3}\right))_* + \frac{1}{\left|x\right|}\right) + \color{red}{\left(\frac{15}{8} \cdot \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot e^{{\left(\left|x\right|\right)}^2}}{{\left(\left|x\right|\right)}^3 \cdot \left|x\right|} \cdot \sqrt{\frac{1}{\pi}}\right)\right)})_* \leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left((\left(\frac{3}{4} \cdot \frac{\frac{1}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3}\right))_* + \frac{1}{\left|x\right|}\right) + \color{blue}{\left(\frac{15}{8} \cdot \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot e^{{\left(\left|x\right|\right)}^2}}{{\left(\left|x\right|\right)}^3 \cdot \left|x\right|} \cdot \sqrt{\frac{1}{\pi}}\right)\right)})_*\]
1.0
- Applied simplify to get
\[(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left((\left(\frac{3}{4} \cdot \frac{\frac{1}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3}\right))_* + \frac{1}{\left|x\right|}\right) + \left(\frac{15}{8} \cdot \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot e^{{\left(\left|x\right|\right)}^2}}{{\left(\left|x\right|\right)}^3 \cdot \left|x\right|} \cdot \sqrt{\frac{1}{\pi}}\right)\right))_* \leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left(\frac{\frac{\frac{3}{4}}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3}\right))_*\right) + \left(\left(\frac{\frac{\frac{1}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}}{{\left(\left|x\right|\right)}^3} \cdot \left(e^{\left|x\right| \cdot \left|x\right|} \cdot \sqrt{\frac{1}{\pi}}\right)\right) \cdot \frac{15}{8}\right))_*\]
0.8
- Applied final simplification
- Applied simplify to get
\[\color{red}{(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left(\frac{\frac{\frac{3}{4}}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3}\right))_*\right) + \left(\left(\frac{\frac{\frac{1}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}}{{\left(\left|x\right|\right)}^3} \cdot \left(e^{\left|x\right| \cdot \left|x\right|} \cdot \sqrt{\frac{1}{\pi}}\right)\right) \cdot \frac{15}{8}\right))_*} \leadsto \color{blue}{(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left((\left(\frac{\frac{\frac{3}{4}}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3}\right))_* + \frac{1}{\left|x\right|}\right) + \left(\frac{\frac{\frac{15}{8}}{\left|x\right|} \cdot \sqrt{\frac{1}{\pi}}}{{\left({\left(\left|x\right|\right)}^3\right)}^2} \cdot e^{\left|x\right| \cdot \left|x\right|}\right))_*}\]
0.8
