Optimization

  The following expressions are especially optimized with a map to an internal function:

• a = -a, where $a\in\textsf{Integer}$ or $a\in\textsf{Rational}$.
• c += a*b, c -= a*b, where ($a,c\in\textsf{Natural}$ or $a,c\in\textsf{Integer}$) and $b\in\textsf{Digit}$.
• c += a*b, c -= a*b, where $a\in\textsf{Digit}$ and ($b,c\in\textsf{Natural}$ or $b,c\in\textsf{Integer}$).
• a = a+b, a = b+a, where $a,b\in\textsf{Natural}$ or $a,b\in\textsf{Integer}$.
• b = a*a, b *= b, where $a,b\in\textsf{Natural}$, $a,b\in\textsf{Integer}$ or $a,b\in\textsf{Rational}$.
• c = a $\langle$op$\rangle$ b, where $a,b,c\in\{\textsf{Natural}, \textsf{Integer}\}, \langle$op$\rangle\in\{\texttt{+,-,*,/,\%,\&,\vert,\^{}}\}$.
• c = a $\langle$op$\rangle$ b, where $a,b,c\in\textsf{Rational}, \langle$op$\rangle\in\{\texttt{+,-,*,/}\}$.
• c = a $\langle$op$\rangle$ b, where $a,c\in\{\textsf{Natural}, \textsf{Integer}, \textsf{Rational}\}, b\in\texttt{size\_t}, \langle$op$\rangle\in\{\texttt{<<,\gt\gt}\}$.
• b = ~a, b = -a, where $a,b\in\textsf{Natural}$ or $a,b\in\textsf{Integer}$.
• b = sqrt(a), where $a,b\in\textsf{Natural}$ or $a,b\in\textsf{Integer}$.
• $\langle$ct$\rangle$ c = a $\langle$op$\rangle$ b, where $\langle$ct$\rangle\in\{\textsf{Natural}, \textsf{Integer}\}, a,b,c\in\langle$ct$\rangle, \langle$op$\rangle\in\{\texttt{+,-,*,/,\%,\&,\vert,\^{}}\}$.
• $\langle$ct$\rangle$ c = a $\langle$op$\rangle$ b, where $\langle$ct$\rangle\in\textsf{Rational}, a,b,c\in\langle$ct$\rangle, \langle$op$\rangle\in\{\texttt{+,-,*,/}\}$.
• $\langle$ct$\rangle$ c = a $\langle$op$\rangle$ b, where $\langle$ct$\rangle\in\{\textsf{Natural}, \textsf{Integer}, \textsf{Rational}\}, a,c\in\langle$ct$\rangle, b\in\texttt{size\_t}, \langle$op$\rangle\in\{\texttt{<<,\gt\gt}\}$.
• $\langle$ct$\rangle$ b = ~a, where $\langle$ct$\rangle\in\{\textsf{Natural}, \textsf{Integer}\}, a,b\in\langle$ct$\rangle$.