\(\left(\left(\frac{1}{\left|x\right|} + \frac{1 \cdot \frac{\frac{3}{4}}{\left|x\right|}}{\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right)}\right) + \left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3} + \frac{\frac{\frac{\frac{15}{8}}{\left|x\right|}}{\left|x\right| \cdot \left|x\right|}}{\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right)}\right)\right) \cdot \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\)
- 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
\[\color{red}{\left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\left(\frac{1}{\left|x\right|} + \frac{1}{2} \cdot \left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{3}{4} \cdot \left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{15}{8} \cdot \left(\left(\left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right)} \leadsto \color{blue}{\frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left({\left(\frac{1}{\left|x\right|}\right)}^3\right)}^2}{\left|x\right|}}{\frac{\sqrt{\pi}}{e^{\left|x\right| \cdot \left|x\right|}}}}\]
1.4
- Applied taylor to get
\[\frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left({\left(\frac{1}{\left|x\right|}\right)}^3\right)}^2}{\left|x\right|}}{\frac{\sqrt{\pi}}{e^{\left|x\right| \cdot \left|x\right|}}} \leadsto \frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left({\left(\frac{1}{\left|x\right|}\right)}^3\right)}^2}{\left|x\right|}}{\frac{\sqrt{\pi}}{e^{\left|x\right| \cdot \left|x\right|}}}\]
1.4
- Taylor expanded around 0 to get
\[\frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left({\left(\frac{1}{\left|x\right|}\right)}^3\right)}^2}{\left|x\right|}}{\frac{\color{red}{\sqrt{\pi}}}{e^{\left|x\right| \cdot \left|x\right|}}} \leadsto \frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left({\left(\frac{1}{\left|x\right|}\right)}^3\right)}^2}{\left|x\right|}}{\frac{\color{blue}{\sqrt{\pi}}}{e^{\left|x\right| \cdot \left|x\right|}}}\]
1.4
- Applied simplify to get
\[\color{red}{\frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left({\left(\frac{1}{\left|x\right|}\right)}^3\right)}^2}{\left|x\right|}}{\frac{\sqrt{\pi}}{e^{\left|x\right| \cdot \left|x\right|}}}} \leadsto \color{blue}{\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3} + \frac{\frac{15}{\frac{8}{1} \cdot \left|x\right|}}{{\left(\left|x\right| \cdot \left|x\right|\right)}^3}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{\frac{\left|x\right|}{\frac{\frac{3}{4}}{\left|x\right|}}} + \frac{1}{\left|x\right|}\right)\right)}\]
0.9
- Using strategy
rm 0.9
- Applied add-sqr-sqrt to get
\[\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3} + \frac{\color{red}{\frac{15}{\frac{8}{1} \cdot \left|x\right|}}}{{\left(\left|x\right| \cdot \left|x\right|\right)}^3}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{\frac{\left|x\right|}{\frac{\frac{3}{4}}{\left|x\right|}}} + \frac{1}{\left|x\right|}\right)\right) \leadsto \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3} + \frac{\color{blue}{{\left(\sqrt{\frac{15}{\frac{8}{1} \cdot \left|x\right|}}\right)}^2}}{{\left(\left|x\right| \cdot \left|x\right|\right)}^3}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{\frac{\left|x\right|}{\frac{\frac{3}{4}}{\left|x\right|}}} + \frac{1}{\left|x\right|}\right)\right)\]
1.0
- Applied simplify to get
\[\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3} + \frac{{\color{red}{\left(\sqrt{\frac{15}{\frac{8}{1} \cdot \left|x\right|}}\right)}}^2}{{\left(\left|x\right| \cdot \left|x\right|\right)}^3}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{\frac{\left|x\right|}{\frac{\frac{3}{4}}{\left|x\right|}}} + \frac{1}{\left|x\right|}\right)\right) \leadsto \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3} + \frac{{\color{blue}{\left(\sqrt{\frac{\frac{15}{8}}{\left|x\right|}}\right)}}^2}{{\left(\left|x\right| \cdot \left|x\right|\right)}^3}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{\frac{\left|x\right|}{\frac{\frac{3}{4}}{\left|x\right|}}} + \frac{1}{\left|x\right|}\right)\right)\]
1.0
- Applied taylor to get
\[\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3} + \frac{{\left(\sqrt{\frac{\frac{15}{8}}{\left|x\right|}}\right)}^2}{{\left(\left|x\right| \cdot \left|x\right|\right)}^3}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{\frac{\left|x\right|}{\frac{\frac{3}{4}}{\left|x\right|}}} + \frac{1}{\left|x\right|}\right)\right) \leadsto \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3} + \frac{{\left(\sqrt{\frac{\frac{15}{8}}{\left|x\right|}}\right)}^2}{{\left(\left|x\right| \cdot \left|x\right|\right)}^3}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{\frac{\left|x\right|}{\frac{\frac{3}{4}}{\left|x\right|}}} + \frac{1}{\left|x\right|}\right)\right)\]
1.0
- Taylor expanded around 0 to get
\[\frac{e^{\left|x\right| \cdot \left|x\right|}}{\color{red}{\sqrt{\pi}}} \cdot \left(\left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3} + \frac{{\left(\sqrt{\frac{\frac{15}{8}}{\left|x\right|}}\right)}^2}{{\left(\left|x\right| \cdot \left|x\right|\right)}^3}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{\frac{\left|x\right|}{\frac{\frac{3}{4}}{\left|x\right|}}} + \frac{1}{\left|x\right|}\right)\right) \leadsto \frac{e^{\left|x\right| \cdot \left|x\right|}}{\color{blue}{\sqrt{\pi}}} \cdot \left(\left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3} + \frac{{\left(\sqrt{\frac{\frac{15}{8}}{\left|x\right|}}\right)}^2}{{\left(\left|x\right| \cdot \left|x\right|\right)}^3}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{\frac{\left|x\right|}{\frac{\frac{3}{4}}{\left|x\right|}}} + \frac{1}{\left|x\right|}\right)\right)\]
1.0
- Applied simplify to get
\[\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3} + \frac{{\left(\sqrt{\frac{\frac{15}{8}}{\left|x\right|}}\right)}^2}{{\left(\left|x\right| \cdot \left|x\right|\right)}^3}\right) + \left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{\frac{\left|x\right|}{\frac{\frac{3}{4}}{\left|x\right|}}} + \frac{1}{\left|x\right|}\right)\right) \leadsto \left(\left(\frac{1}{\left|x\right|} + \frac{1 \cdot \frac{\frac{3}{4}}{\left|x\right|}}{\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right)}\right) + \left(\frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3} + \frac{\frac{\frac{\frac{15}{8}}{\left|x\right|}}{\left|x\right| \cdot \left|x\right|}}{\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right)}\right)\right) \cdot \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\]
0.9
- Applied final simplification
- Removed slow pow expressions