For $x \in \mathbb { R }$, let $\tan ^ { - 1 } ( x ) \in \left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$. Then the minimum value of the function $f : \mathbb { R } \rightarrow \mathbb { R }$ defined by $f ( x ) = \int _ { 0 } ^ { x \tan ^ { - 1 } x } \frac { e ^ { ( t - \cos t ) } } { 1 + t ^ { 2023 } } d t$ is