Initial program 1.5
\[\left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\left(\frac{1}{\left|x\right|} + \frac{1}{2} \cdot \left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{3}{4} \cdot \left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{15}{8} \cdot \left(\left(\left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right)\]
Initial simplification1.1
\[\leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) \cdot \left((\left(\left(\frac{3}{4} \cdot \frac{1}{\left|x\right|}\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right)\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) + \left((\left(\frac{1}{2} \cdot \frac{1}{\left|x\right|}\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) + \left(\frac{1}{\left|x\right|}\right))_*\right))_*\right) + \left(\left(\frac{1}{{\left(\left|x\right|\right)}^{3}} \cdot {\left(\frac{1}{\left|x\right|}\right)}^{4}\right) \cdot \left(e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\frac{1}{\sqrt{\pi}} \cdot \frac{15}{8}\right)\right)\right))_*\]
Taylor expanded around inf 0.5
\[\leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) \cdot \left((\left(\left(\frac{3}{4} \cdot \frac{1}{\left|x\right|}\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right)\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) + \left((\left(\frac{1}{2} \cdot \frac{1}{\left|x\right|}\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) + \left(\frac{1}{\left|x\right|}\right))_*\right))_*\right) + \color{blue}{\left(\frac{15}{8} \cdot \left(\frac{e^{{\left(\left|x\right|\right)}^{2}}}{{\left(\left|x\right|\right)}^{7}} \cdot \sqrt{\frac{1}{\pi}}\right)\right)})_*\]
- Using strategy
rm Applied pow10.5
\[\leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) \cdot \left((\left(\left(\frac{3}{4} \cdot \frac{1}{\left|x\right|}\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right)\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\color{blue}{{\left(\left|x\right|\right)}^{1}}}\right) + \left((\left(\frac{1}{2} \cdot \frac{1}{\left|x\right|}\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) + \left(\frac{1}{\left|x\right|}\right))_*\right))_*\right) + \left(\frac{15}{8} \cdot \left(\frac{e^{{\left(\left|x\right|\right)}^{2}}}{{\left(\left|x\right|\right)}^{7}} \cdot \sqrt{\frac{1}{\pi}}\right)\right))_*\]
Applied pow-flip0.5
\[\leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) \cdot \left((\left(\left(\frac{3}{4} \cdot \frac{1}{\left|x\right|}\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right)\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \color{blue}{{\left(\left|x\right|\right)}^{\left(-1\right)}}\right) + \left((\left(\frac{1}{2} \cdot \frac{1}{\left|x\right|}\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) + \left(\frac{1}{\left|x\right|}\right))_*\right))_*\right) + \left(\frac{15}{8} \cdot \left(\frac{e^{{\left(\left|x\right|\right)}^{2}}}{{\left(\left|x\right|\right)}^{7}} \cdot \sqrt{\frac{1}{\pi}}\right)\right))_*\]
Applied pow10.5
\[\leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) \cdot \left((\left(\left(\frac{3}{4} \cdot \frac{1}{\left|x\right|}\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right)\right) \cdot \left(\frac{1}{\color{blue}{{\left(\left|x\right|\right)}^{1}}} \cdot {\left(\left|x\right|\right)}^{\left(-1\right)}\right) + \left((\left(\frac{1}{2} \cdot \frac{1}{\left|x\right|}\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) + \left(\frac{1}{\left|x\right|}\right))_*\right))_*\right) + \left(\frac{15}{8} \cdot \left(\frac{e^{{\left(\left|x\right|\right)}^{2}}}{{\left(\left|x\right|\right)}^{7}} \cdot \sqrt{\frac{1}{\pi}}\right)\right))_*\]
Applied pow-flip0.5
\[\leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) \cdot \left((\left(\left(\frac{3}{4} \cdot \frac{1}{\left|x\right|}\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right)\right) \cdot \left(\color{blue}{{\left(\left|x\right|\right)}^{\left(-1\right)}} \cdot {\left(\left|x\right|\right)}^{\left(-1\right)}\right) + \left((\left(\frac{1}{2} \cdot \frac{1}{\left|x\right|}\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) + \left(\frac{1}{\left|x\right|}\right))_*\right))_*\right) + \left(\frac{15}{8} \cdot \left(\frac{e^{{\left(\left|x\right|\right)}^{2}}}{{\left(\left|x\right|\right)}^{7}} \cdot \sqrt{\frac{1}{\pi}}\right)\right))_*\]
Applied pow-prod-up0.5
\[\leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) \cdot \left((\left(\left(\frac{3}{4} \cdot \frac{1}{\left|x\right|}\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right)\right) \cdot \color{blue}{\left({\left(\left|x\right|\right)}^{\left(\left(-1\right) + \left(-1\right)\right)}\right)} + \left((\left(\frac{1}{2} \cdot \frac{1}{\left|x\right|}\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) + \left(\frac{1}{\left|x\right|}\right))_*\right))_*\right) + \left(\frac{15}{8} \cdot \left(\frac{e^{{\left(\left|x\right|\right)}^{2}}}{{\left(\left|x\right|\right)}^{7}} \cdot \sqrt{\frac{1}{\pi}}\right)\right))_*\]
Simplified0.5
\[\leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right) \cdot \left((\left(\left(\frac{3}{4} \cdot \frac{1}{\left|x\right|}\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right)\right) \cdot \left({\left(\left|x\right|\right)}^{\color{blue}{-2}}\right) + \left((\left(\frac{1}{2} \cdot \frac{1}{\left|x\right|}\right) \cdot \left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) + \left(\frac{1}{\left|x\right|}\right))_*\right))_*\right) + \left(\frac{15}{8} \cdot \left(\frac{e^{{\left(\left|x\right|\right)}^{2}}}{{\left(\left|x\right|\right)}^{7}} \cdot \sqrt{\frac{1}{\pi}}\right)\right))_*\]
Simplified0.5
\[\leadsto \color{blue}{(\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\frac{{\left(\left|x\right|\right)}^{7}}{\sqrt{\frac{1}{\pi}}}}\right) \cdot \frac{15}{8} + \left((\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \left((\left({\left(\left|x\right|\right)}^{-2}\right) \cdot \left(\frac{\frac{3}{4}}{\left|x\right|}\right) + \left(\frac{\frac{1}{2}}{\left|x\right|}\right))_*\right) + \left(\frac{1}{\left|x\right|}\right))_* \cdot \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right))_*}\]
- Using strategy
rm Applied div-inv0.6
\[\leadsto (\left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\color{blue}{{\left(\left|x\right|\right)}^{7} \cdot \frac{1}{\sqrt{\frac{1}{\pi}}}}}\right) \cdot \frac{15}{8} + \left((\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \left((\left({\left(\left|x\right|\right)}^{-2}\right) \cdot \left(\frac{\frac{3}{4}}{\left|x\right|}\right) + \left(\frac{\frac{1}{2}}{\left|x\right|}\right))_*\right) + \left(\frac{1}{\left|x\right|}\right))_* \cdot \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right))_*\]
Applied associate-/r*0.6
\[\leadsto (\color{blue}{\left(\frac{\frac{e^{\left|x\right| \cdot \left|x\right|}}{{\left(\left|x\right|\right)}^{7}}}{\frac{1}{\sqrt{\frac{1}{\pi}}}}\right)} \cdot \frac{15}{8} + \left((\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \left((\left({\left(\left|x\right|\right)}^{-2}\right) \cdot \left(\frac{\frac{3}{4}}{\left|x\right|}\right) + \left(\frac{\frac{1}{2}}{\left|x\right|}\right))_*\right) + \left(\frac{1}{\left|x\right|}\right))_* \cdot \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\right))_*\]
Final simplification0.6
\[\leadsto (\left(\frac{\frac{e^{\left|x\right| \cdot \left|x\right|}}{{\left(\left|x\right|\right)}^{7}}}{\frac{1}{\sqrt{\frac{1}{\pi}}}}\right) \cdot \frac{15}{8} + \left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}} \cdot (\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \left((\left({\left(\left|x\right|\right)}^{-2}\right) \cdot \left(\frac{\frac{3}{4}}{\left|x\right|}\right) + \left(\frac{\frac{1}{2}}{\left|x\right|}\right))_*\right) + \left(\frac{1}{\left|x\right|}\right))_*\right))_*\]
