Are they grammatically correct? Perhaps. Are they sensible? Not really.
Expense and length are directly measurable attributes. Cheapness and shortness only make sense in contrast to some other expense or length. Allow me to offer two examples:
First, let's assume we find something that costs $10. A ten dollar pack of chewing gum is fairly expensive, while a ten dollar three-piece suit is quite cheap. Regardless, if another item is twice as expensive, we immediately know that it costs (around) twenty dollars. Also, an item that's exactly half as expensive costs $5. Only one number is needed to express expense, and it's easy to do the math to that number.
Second, let's assume we find another store selling the same item for $8. Compared to the $10 price, sure, that's cheap. If we're looking for an item that's twice as cheap, what price do we want? Do we want a $6 item because that's twice the two-dollar discount from $10? Do we want a $4 item because that's half the $8 price? Cheapness can't be represented by only one number, and I have no idea what math that phrasing is meant to indicate.
In my dialect, I am aware of one obvious exception to this pattern. In the absolute sense, heat is a directly measurable attribute, but cold only makes sense in comparison to some other amount of heat. However, if the current weather happens to include a sub-zero temperature (which, locally, implies the Fahrenheit scale), I might say "tomorrow will be twice as cold" as shorthand for "tomorrow will be twice as far below zero."
Other exceptions also exist, but those exceptions involve an easily-reached absolute zero. For instance, I understand that "twice as dark" and "half as bright" are directly equivalent. As far as my naked eye can tell, zero brightness is as easy to find as a windowless room or an artist-quality charcoal pencil.
Above all else, please remember that "grammatically correct" and "sensible" are two completely different ideas.
This colorless green idea sleeps successfully.
The grammar of the above sentence is impeccable and beyond reproach. However, it was designed (within the constraints of good grammar) to make no sense. There exists an entire class of sentences like it, all designed to be examples of "when good English goes bad".
The questions "Is it good English grammar?" and "Is it good English?" can have completely different answers. Phrases like "twice as cheap" or "twice as short" are grammatically sound and easy to produce, but they are difficult to parse and practically impossible to understand.