\(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\left(\frac{1}{\left|x\right|} + \frac{\frac{\frac{1}{\left|x\right|}}{\left|x\right| \cdot \left|x\right|}}{2}\right) + \left(\frac{\frac{\frac{\frac{15}{8}}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}}{{\left(\left|x\right|\right)}^3} + \frac{\frac{\frac{3}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}}{4 \cdot \left|x\right|}\right)\right)\)
- 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
\[\color{red}{\left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\left(\frac{1}{\left|x\right|} + \frac{1}{2} \cdot \left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{3}{4} \cdot \left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{15}{8} \cdot \left(\left(\left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right)} \leadsto \color{blue}{\frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left({\left(\frac{1}{\left|x\right|}\right)}^3\right)}^2}{\left|x\right|}}{\frac{\sqrt{\pi}}{e^{\left|x\right| \cdot \left|x\right|}}}}\]
1.5
- Using strategy
rm 1.5
- Applied cube-div to get
\[\frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\color{red}{\left({\left(\frac{1}{\left|x\right|}\right)}^3\right)}}^2}{\left|x\right|}}{\frac{\sqrt{\pi}}{e^{\left|x\right| \cdot \left|x\right|}}} \leadsto \frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\color{blue}{\left(\frac{{1}^3}{{\left(\left|x\right|\right)}^3}\right)}}^2}{\left|x\right|}}{\frac{\sqrt{\pi}}{e^{\left|x\right| \cdot \left|x\right|}}}\]
1.0
- Using strategy
rm 1.0
- Applied add-sqr-sqrt to get
\[\frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left(\frac{{1}^3}{{\left(\left|x\right|\right)}^3}\right)}^2}{\left|x\right|}}{\frac{\color{red}{\sqrt{\pi}}}{e^{\left|x\right| \cdot \left|x\right|}}} \leadsto \frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left(\frac{{1}^3}{{\left(\left|x\right|\right)}^3}\right)}^2}{\left|x\right|}}{\frac{\color{blue}{{\left(\sqrt{\sqrt{\pi}}\right)}^2}}{e^{\left|x\right| \cdot \left|x\right|}}}\]
1.0
- Using strategy
rm 1.0
- Applied cube-mult to get
\[\frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left(\frac{{1}^3}{\color{red}{{\left(\left|x\right|\right)}^3}}\right)}^2}{\left|x\right|}}{\frac{{\left(\sqrt{\sqrt{\pi}}\right)}^2}{e^{\left|x\right| \cdot \left|x\right|}}} \leadsto \frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left(\frac{{1}^3}{\color{blue}{\left|x\right| \cdot \left(\left|x\right| \cdot \left|x\right|\right)}}\right)}^2}{\left|x\right|}}{\frac{{\left(\sqrt{\sqrt{\pi}}\right)}^2}{e^{\left|x\right| \cdot \left|x\right|}}}\]
1.0
- Applied cube-mult to get
\[\frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left(\frac{\color{red}{{1}^3}}{\left|x\right| \cdot \left(\left|x\right| \cdot \left|x\right|\right)}\right)}^2}{\left|x\right|}}{\frac{{\left(\sqrt{\sqrt{\pi}}\right)}^2}{e^{\left|x\right| \cdot \left|x\right|}}} \leadsto \frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left(\frac{\color{blue}{1 \cdot \left(1 \cdot 1\right)}}{\left|x\right| \cdot \left(\left|x\right| \cdot \left|x\right|\right)}\right)}^2}{\left|x\right|}}{\frac{{\left(\sqrt{\sqrt{\pi}}\right)}^2}{e^{\left|x\right| \cdot \left|x\right|}}}\]
1.0
- Applied times-frac to get
\[\frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\color{red}{\left(\frac{1 \cdot \left(1 \cdot 1\right)}{\left|x\right| \cdot \left(\left|x\right| \cdot \left|x\right|\right)}\right)}}^2}{\left|x\right|}}{\frac{{\left(\sqrt{\sqrt{\pi}}\right)}^2}{e^{\left|x\right| \cdot \left|x\right|}}} \leadsto \frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\color{blue}{\left(\frac{1}{\left|x\right|} \cdot \frac{1 \cdot 1}{\left|x\right| \cdot \left|x\right|}\right)}}^2}{\left|x\right|}}{\frac{{\left(\sqrt{\sqrt{\pi}}\right)}^2}{e^{\left|x\right| \cdot \left|x\right|}}}\]
1.1
- Applied simplify to get
\[\frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left(\frac{1}{\left|x\right|} \cdot \color{red}{\frac{1 \cdot 1}{\left|x\right| \cdot \left|x\right|}}\right)}^2}{\left|x\right|}}{\frac{{\left(\sqrt{\sqrt{\pi}}\right)}^2}{e^{\left|x\right| \cdot \left|x\right|}}} \leadsto \frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left(\frac{1}{\left|x\right|} \cdot \color{blue}{\frac{\frac{1}{\left|x\right|}}{\left|x\right|}}\right)}^2}{\left|x\right|}}{\frac{{\left(\sqrt{\sqrt{\pi}}\right)}^2}{e^{\left|x\right| \cdot \left|x\right|}}}\]
1.2
- Applied taylor to get
\[\frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left(\frac{1}{\left|x\right|} \cdot \frac{\frac{1}{\left|x\right|}}{\left|x\right|}\right)}^2}{\left|x\right|}}{\frac{{\left(\sqrt{\sqrt{\pi}}\right)}^2}{e^{\left|x\right| \cdot \left|x\right|}}} \leadsto \frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left(\frac{1}{\left|x\right|} \cdot \frac{\frac{1}{\left|x\right|}}{\left|x\right|}\right)}^2}{\left|x\right|}}{\frac{{\left(\sqrt{\sqrt{\pi}}\right)}^2}{e^{\left|x\right| \cdot \left|x\right|}}}\]
1.2
- Taylor expanded around 0 to get
\[\frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left(\frac{1}{\left|x\right|} \cdot \frac{\frac{1}{\left|x\right|}}{\left|x\right|}\right)}^2}{\left|x\right|}}{\frac{{\left(\sqrt{\color{red}{\sqrt{\pi}}}\right)}^2}{e^{\left|x\right| \cdot \left|x\right|}}} \leadsto \frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left(\frac{1}{\left|x\right|} \cdot \frac{\frac{1}{\left|x\right|}}{\left|x\right|}\right)}^2}{\left|x\right|}}{\frac{{\left(\sqrt{\color{blue}{\sqrt{\pi}}}\right)}^2}{e^{\left|x\right| \cdot \left|x\right|}}}\]
1.2
- Applied simplify to get
\[\frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{{\left(\frac{1}{\left|x\right|} \cdot \frac{\frac{1}{\left|x\right|}}{\left|x\right|}\right)}^2}{\left|x\right|}}{\frac{{\left(\sqrt{\sqrt{\pi}}\right)}^2}{e^{\left|x\right| \cdot \left|x\right|}}} \leadsto \frac{\left(\left(\frac{\frac{\frac{1}{\left|x\right|}}{\left|x\right| \cdot \left|x\right|}}{2} + \frac{1}{\left|x\right|}\right) + \frac{\frac{\frac{1}{\left|x\right|}}{\left|x\right| \cdot \left|x\right|}}{\frac{\left|x\right|}{\frac{\frac{3}{4}}{\left|x\right|}}}\right) + \frac{\left(\frac{15}{8} \cdot \frac{\frac{1}{\left|x\right|}}{\left|x\right| \cdot \left|x\right|}\right) \cdot \frac{\frac{1}{\left|x\right|}}{\left|x\right| \cdot \left|x\right|}}{\left|x\right|}}{\frac{\sqrt{\pi}}{e^{\left|x\right| \cdot \left|x\right|}}}\]
1.0
- Applied final simplification
- Applied simplify to get
\[\color{red}{\frac{\left(\left(\frac{\frac{\frac{1}{\left|x\right|}}{\left|x\right| \cdot \left|x\right|}}{2} + \frac{1}{\left|x\right|}\right) + \frac{\frac{\frac{1}{\left|x\right|}}{\left|x\right| \cdot \left|x\right|}}{\frac{\left|x\right|}{\frac{\frac{3}{4}}{\left|x\right|}}}\right) + \frac{\left(\frac{15}{8} \cdot \frac{\frac{1}{\left|x\right|}}{\left|x\right| \cdot \left|x\right|}\right) \cdot \frac{\frac{1}{\left|x\right|}}{\left|x\right| \cdot \left|x\right|}}{\left|x\right|}}{\frac{\sqrt{\pi}}{e^{\left|x\right| \cdot \left|x\right|}}}} \leadsto \color{blue}{\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot \left(\left(\frac{1}{\left|x\right|} + \frac{\frac{\frac{1}{\left|x\right|}}{\left|x\right| \cdot \left|x\right|}}{2}\right) + \left(\frac{\frac{\frac{\frac{15}{8}}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}}{{\left(\left|x\right|\right)}^3} + \frac{\frac{\frac{3}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}}{4 \cdot \left|x\right|}\right)\right)}\]
0.9