Initial program 0.0
\[e^{-\left(1 - x \cdot x\right)}\]
- Using strategy
rm Applied *-un-lft-identity0.0
\[\leadsto e^{-\color{blue}{1 \cdot \left(1 - x \cdot x\right)}}\]
Applied distribute-lft-neg-in0.0
\[\leadsto e^{\color{blue}{\left(-1\right) \cdot \left(1 - x \cdot x\right)}}\]
Applied exp-prod0.0
\[\leadsto \color{blue}{{\left(e^{-1}\right)}^{\left(1 - x \cdot x\right)}}\]
Simplified0.0
\[\leadsto {\color{blue}{\left(\frac{1}{e}\right)}}^{\left(1 - x \cdot x\right)}\]
- Using strategy
rm Applied sub-neg0.0
\[\leadsto {\left(\frac{1}{e}\right)}^{\color{blue}{\left(1 + \left(-x \cdot x\right)\right)}}\]
Applied unpow-prod-up0.0
\[\leadsto \color{blue}{{\left(\frac{1}{e}\right)}^{1} \cdot {\left(\frac{1}{e}\right)}^{\left(-x \cdot x\right)}}\]
- Using strategy
rm Applied distribute-rgt-neg-in0.0
\[\leadsto {\left(\frac{1}{e}\right)}^{1} \cdot {\left(\frac{1}{e}\right)}^{\color{blue}{\left(x \cdot \left(-x\right)\right)}}\]
Applied pow-unpow0.0
\[\leadsto {\left(\frac{1}{e}\right)}^{1} \cdot \color{blue}{{\left({\left(\frac{1}{e}\right)}^{x}\right)}^{\left(-x\right)}}\]
- Using strategy
rm Applied add-exp-log0.0
\[\leadsto {\left(\frac{1}{e}\right)}^{1} \cdot {\left({\color{blue}{\left(e^{\log \left(\frac{1}{e}\right)}\right)}}^{x}\right)}^{\left(-x\right)}\]
Applied pow-exp0.0
\[\leadsto {\left(\frac{1}{e}\right)}^{1} \cdot {\color{blue}{\left(e^{\log \left(\frac{1}{e}\right) \cdot x}\right)}}^{\left(-x\right)}\]
Simplified0.0
\[\leadsto {\left(\frac{1}{e}\right)}^{1} \cdot {\left(e^{\color{blue}{-x}}\right)}^{\left(-x\right)}\]
Final simplification0.0
\[\leadsto \frac{1}{e} \cdot {\left(e^{-x}\right)}^{\left(-x\right)}\]
