Phrase and symbol for "geometric absolute value"$ e^{|\ln(x)|}?$

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I'm calculate the median fractional difference between two vectors (to characterise the error in a quantity with a high dynamic range). If $a/b = 0.1$, the fractional difference is $10$, and if $a/b = 10$, the fractional difference is also 10. My quantity, which is only defined if $x>0$, is defined as

$$ \begin{cases} x, & \mbox{if } x \ge 1 \\ \frac{1}{x}, & \mbox{if } x < 1\end{cases} $$

which is equal to (as $x>0$),

$$ e^{|\ln(x)|}. $$

Do mathematicians have a usual word and symbol for this quantity?