Initial program 0.0
\[e^{-\left(1 - x \cdot x\right)}\]
Initial simplification0.0
\[\leadsto e^{(x \cdot x + -1)_*}\]
- Using strategy
rm Applied fma-udef0.0
\[\leadsto e^{\color{blue}{x \cdot x + -1}}\]
Applied exp-sum0.0
\[\leadsto \color{blue}{e^{x \cdot x} \cdot e^{-1}}\]
- Using strategy
rm Applied exp-prod0.0
\[\leadsto \color{blue}{{\left(e^{x}\right)}^{x}} \cdot e^{-1}\]
- Using strategy
rm Applied add-sqr-sqrt0.0
\[\leadsto {\color{blue}{\left(\sqrt{e^{x}} \cdot \sqrt{e^{x}}\right)}}^{x} \cdot e^{-1}\]
Applied unpow-prod-down0.0
\[\leadsto \color{blue}{\left({\left(\sqrt{e^{x}}\right)}^{x} \cdot {\left(\sqrt{e^{x}}\right)}^{x}\right)} \cdot e^{-1}\]
- Using strategy
rm Applied add-sqr-sqrt0.0
\[\leadsto \color{blue}{\sqrt{\left({\left(\sqrt{e^{x}}\right)}^{x} \cdot {\left(\sqrt{e^{x}}\right)}^{x}\right) \cdot e^{-1}} \cdot \sqrt{\left({\left(\sqrt{e^{x}}\right)}^{x} \cdot {\left(\sqrt{e^{x}}\right)}^{x}\right) \cdot e^{-1}}}\]
Final simplification0.0
\[\leadsto \sqrt{e^{-1} \cdot \left({\left(\sqrt{e^{x}}\right)}^{x} \cdot {\left(\sqrt{e^{x}}\right)}^{x}\right)} \cdot \sqrt{e^{-1} \cdot \left({\left(\sqrt{e^{x}}\right)}^{x} \cdot {\left(\sqrt{e^{x}}\right)}^{x}\right)}\]
