The term sub-exponential time is used to express that the running time of some algorithm may grow faster than any polynomial but is still significantly smaller than an exponential. In this sense, problems that have sub-exponential time algorithms are somewhat more tractable than those that only have exponential algorithms. The precise definition of "sub-exponential" is not generally agreed upon, and we list the two most widely used ones below.
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“They do not live in the world,
Are not in time and space.
From birth to death hurled
No word do they have, not one
To plant a foot upon,
Were never in any place.”
—Edwin Muir (1887–1959)