\(\frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{\frac{1}{{\left({\left(\left|x\right|\right)}^3\right)}^2}}{\left|x\right|}}{\frac{{\left(\sqrt{\sqrt{\pi}}\right)}^2}{e^{\left|x\right| \cdot \left|x\right|}}}\)
- 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 square-div to get
\[\frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{\color{red}{{\left(\frac{{1}^3}{{\left(\left|x\right|\right)}^3}\right)}^2}}{\left|x\right|}}{\frac{{\left(\sqrt{\sqrt{\pi}}\right)}^2}{e^{\left|x\right| \cdot \left|x\right|}}} \leadsto \frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{\color{blue}{\frac{{\left({1}^3\right)}^2}{{\left({\left(\left|x\right|\right)}^3\right)}^2}}}{\left|x\right|}}{\frac{{\left(\sqrt{\sqrt{\pi}}\right)}^2}{e^{\left|x\right| \cdot \left|x\right|}}}\]
0.9
- Applied simplify to get
\[\frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{\frac{\color{red}{{\left({1}^3\right)}^2}}{{\left({\left(\left|x\right|\right)}^3\right)}^2}}{\left|x\right|}}{\frac{{\left(\sqrt{\sqrt{\pi}}\right)}^2}{e^{\left|x\right| \cdot \left|x\right|}}} \leadsto \frac{\left(\left(\frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2} + \frac{1}{\left|x\right|}\right) + \left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{3}{4}\right)\right) \cdot \frac{1}{\left|x\right|}\right) + \frac{15}{8} \cdot \frac{\frac{\color{blue}{1}}{{\left({\left(\left|x\right|\right)}^3\right)}^2}}{\left|x\right|}}{\frac{{\left(\sqrt{\sqrt{\pi}}\right)}^2}{e^{\left|x\right| \cdot \left|x\right|}}}\]
0.9
- Removed slow pow expressions