\((\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left((\left(\frac{3}{4} \cdot \frac{\frac{1}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{1}{2 \cdot {\left(\left|x\right|\right)}^3}\right))_* + \frac{1}{\left|x\right|}\right) + \left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\left|x\right|} \cdot {\left(\left({\left(\frac{1}{\pi}\right)}^{\frac{1}{4}} \cdot \sqrt{\frac{15}{8}}\right) \cdot \frac{1}{{\left(\left|x\right|\right)}^3}\right)}^2\right))_*\)
- Started with
\[\left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\left(\frac{1}{\left|x\right|} + \frac{1}{2} \cdot \left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{3}{4} \cdot \left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{15}{8} \cdot \left(\left(\left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right)\]
0.7
- Applied simplify to get
\[\color{red}{\left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\left(\frac{1}{\left|x\right|} + \frac{1}{2} \cdot \left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{3}{4} \cdot \left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{15}{8} \cdot \left(\left(\left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right)} \leadsto \color{blue}{(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\frac{15}{8} \cdot e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3}{\left|x\right|}\right))_*}\]
0.7
- Using strategy
rm 0.7
- Applied add-sqr-sqrt to get
\[(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\frac{15}{8} \cdot e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \color{red}{\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3}{\left|x\right|}}\right))_* \leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\frac{15}{8} \cdot e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \color{blue}{{\left(\sqrt{\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3}{\left|x\right|}}\right)}^2}\right))_*\]
0.9
- Applied add-sqr-sqrt to get
\[(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\frac{15}{8} \cdot e^{\left|x\right| \cdot \left|x\right|}}{\color{red}{\sqrt{\pi}}} \cdot {\left(\sqrt{\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3}{\left|x\right|}}\right)}^2\right))_* \leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\frac{15}{8} \cdot e^{\left|x\right| \cdot \left|x\right|}}{\color{blue}{{\left(\sqrt{\sqrt{\pi}}\right)}^2}} \cdot {\left(\sqrt{\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3}{\left|x\right|}}\right)}^2\right))_*\]
1.2
- Applied add-sqr-sqrt to get
\[(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\frac{15}{8} \cdot \color{red}{e^{\left|x\right| \cdot \left|x\right|}}}{{\left(\sqrt{\sqrt{\pi}}\right)}^2} \cdot {\left(\sqrt{\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3}{\left|x\right|}}\right)}^2\right))_* \leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\frac{15}{8} \cdot \color{blue}{{\left(\sqrt{e^{\left|x\right| \cdot \left|x\right|}}\right)}^2}}{{\left(\sqrt{\sqrt{\pi}}\right)}^2} \cdot {\left(\sqrt{\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3}{\left|x\right|}}\right)}^2\right))_*\]
1.3
- Applied add-sqr-sqrt to get
\[(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\color{red}{\frac{15}{8}} \cdot {\left(\sqrt{e^{\left|x\right| \cdot \left|x\right|}}\right)}^2}{{\left(\sqrt{\sqrt{\pi}}\right)}^2} \cdot {\left(\sqrt{\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3}{\left|x\right|}}\right)}^2\right))_* \leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\color{blue}{{\left(\sqrt{\frac{15}{8}}\right)}^2} \cdot {\left(\sqrt{e^{\left|x\right| \cdot \left|x\right|}}\right)}^2}{{\left(\sqrt{\sqrt{\pi}}\right)}^2} \cdot {\left(\sqrt{\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3}{\left|x\right|}}\right)}^2\right))_*\]
1.0
- Applied square-unprod to get
\[(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\color{red}{{\left(\sqrt{\frac{15}{8}}\right)}^2 \cdot {\left(\sqrt{e^{\left|x\right| \cdot \left|x\right|}}\right)}^2}}{{\left(\sqrt{\sqrt{\pi}}\right)}^2} \cdot {\left(\sqrt{\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3}{\left|x\right|}}\right)}^2\right))_* \leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\frac{\color{blue}{{\left(\sqrt{\frac{15}{8}} \cdot \sqrt{e^{\left|x\right| \cdot \left|x\right|}}\right)}^2}}{{\left(\sqrt{\sqrt{\pi}}\right)}^2} \cdot {\left(\sqrt{\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3}{\left|x\right|}}\right)}^2\right))_*\]
1.0
- Applied square-undiv to get
\[(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\color{red}{\frac{{\left(\sqrt{\frac{15}{8}} \cdot \sqrt{e^{\left|x\right| \cdot \left|x\right|}}\right)}^2}{{\left(\sqrt{\sqrt{\pi}}\right)}^2}} \cdot {\left(\sqrt{\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3}{\left|x\right|}}\right)}^2\right))_* \leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left(\color{blue}{{\left(\frac{\sqrt{\frac{15}{8}} \cdot \sqrt{e^{\left|x\right| \cdot \left|x\right|}}}{\sqrt{\sqrt{\pi}}}\right)}^2} \cdot {\left(\sqrt{\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3}{\left|x\right|}}\right)}^2\right))_*\]
1.0
- Applied square-unprod to get
\[(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \color{red}{\left({\left(\frac{\sqrt{\frac{15}{8}} \cdot \sqrt{e^{\left|x\right| \cdot \left|x\right|}}}{\sqrt{\sqrt{\pi}}}\right)}^2 \cdot {\left(\sqrt{\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3}{\left|x\right|}}\right)}^2\right)})_* \leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \color{blue}{\left({\left(\frac{\sqrt{\frac{15}{8}} \cdot \sqrt{e^{\left|x\right| \cdot \left|x\right|}}}{\sqrt{\sqrt{\pi}}} \cdot \sqrt{\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3}{\left|x\right|}}\right)}^2\right)})_*\]
1.0
- Applied taylor to get
\[(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left({\left(\frac{\sqrt{\frac{15}{8}} \cdot \sqrt{e^{\left|x\right| \cdot \left|x\right|}}}{\sqrt{\sqrt{\pi}}} \cdot \sqrt{\frac{{\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3}{\left|x\right|}}\right)}^2\right))_* \leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left({\left(\left(\sqrt{\frac{15}{8}} \cdot {\left(\frac{1}{\left|x\right|}\right)}^3\right) \cdot \left({\left(\frac{1}{\pi}\right)}^{\frac{1}{4}} \cdot \sqrt{\frac{e^{{\left(\left|x\right|\right)}^2}}{\left|x\right|}}\right)\right)}^2\right))_*\]
0.8
- Taylor expanded around 0 to get
\[(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left({\color{red}{\left(\left(\sqrt{\frac{15}{8}} \cdot {\left(\frac{1}{\left|x\right|}\right)}^3\right) \cdot \left({\left(\frac{1}{\pi}\right)}^{\frac{1}{4}} \cdot \sqrt{\frac{e^{{\left(\left|x\right|\right)}^2}}{\left|x\right|}}\right)\right)}}^2\right))_* \leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left({\color{blue}{\left(\left(\sqrt{\frac{15}{8}} \cdot {\left(\frac{1}{\left|x\right|}\right)}^3\right) \cdot \left({\left(\frac{1}{\pi}\right)}^{\frac{1}{4}} \cdot \sqrt{\frac{e^{{\left(\left|x\right|\right)}^2}}{\left|x\right|}}\right)\right)}}^2\right))_*\]
0.8
- Applied simplify to get
\[(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left(\frac{1}{\left|x\right|} + (\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right))_*\right) + \left({\left(\left(\sqrt{\frac{15}{8}} \cdot {\left(\frac{1}{\left|x\right|}\right)}^3\right) \cdot \left({\left(\frac{1}{\pi}\right)}^{\frac{1}{4}} \cdot \sqrt{\frac{e^{{\left(\left|x\right|\right)}^2}}{\left|x\right|}}\right)\right)}^2\right))_* \leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) * \left((\left(\frac{3}{4} \cdot \frac{\frac{1}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right) * \left(\frac{1}{\left|x\right|}\right) + \left(\frac{1}{2 \cdot {\left(\left|x\right|\right)}^3}\right))_* + \frac{1}{\left|x\right|}\right) + \left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\left|x\right|} \cdot {\left(\left({\left(\frac{1}{\pi}\right)}^{\frac{1}{4}} \cdot \sqrt{\frac{15}{8}}\right) \cdot \frac{1}{{\left(\left|x\right|\right)}^3}\right)}^2\right))_*\]
0.6
- Applied final simplification
- Removed slow pow expressions