Initial program 0.0
\[e^{-\left(1 - x \cdot x\right)}\]
- Using strategy
rm Applied add-sqr-sqrt0.0
\[\leadsto e^{-\left(1 - \color{blue}{\sqrt{x \cdot x} \cdot \sqrt{x \cdot x}}\right)}\]
Applied *-un-lft-identity0.0
\[\leadsto e^{-\left(\color{blue}{1 \cdot 1} - \sqrt{x \cdot x} \cdot \sqrt{x \cdot x}\right)}\]
Applied difference-of-squares0.0
\[\leadsto e^{-\color{blue}{\left(1 + \sqrt{x \cdot x}\right) \cdot \left(1 - \sqrt{x \cdot x}\right)}}\]
Applied distribute-lft-neg-in0.0
\[\leadsto e^{\color{blue}{\left(-\left(1 + \sqrt{x \cdot x}\right)\right) \cdot \left(1 - \sqrt{x \cdot x}\right)}}\]
Applied exp-prod0.0
\[\leadsto \color{blue}{{\left(e^{-\left(1 + \sqrt{x \cdot x}\right)}\right)}^{\left(1 - \sqrt{x \cdot x}\right)}}\]
Final simplification0.0
\[\leadsto {\left(e^{-\left(\sqrt{x \cdot x} + 1\right)}\right)}^{\left(1 - \sqrt{x \cdot x}\right)}\]
