Is it OK to say that something reaches 1/5th of its original size? Like in the following sentence:
"Not only that, but the output images are also highly compressed, sometimes reaching (up?) to 1/5th of their original size..."
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According to the Oxford Online English Dictionary, definition 2.1:
Attain or extend to (a specified point, level, or condition):
unemployment reached a peak in 1933
[NO OBJECT]: in its native habitat it will reach to about 6 m in height
Attain certainly can mean both directions, so I think it can technically be used in that fashion.
As far as should? Given that smaller is better in this case, I think it's reasonable. Certainly it is common to say:
I reached my goal weight of 140 lbs
which certainly wasn't reached from a lower weight in the majority of instances. For your particular usage, "shrinking" is probably more common (emphasizing the reduction in size), but I think "reach" is perfectly fine.
I would not use "reached" to mean regressed (ie, got worse).
Though the underlying word picture of reach is extending or stretching out, it has embraced metaphoric applications for a long time:
Old English ræcan, reccan "reach out, stretch out, extend, hold forth,"
also "succeed in touching, succeed in striking; address, speak to,"
also "offer, present, give, grant,"
from West Germanic *raikjan "stretch out the hand"
(cognates: Old Frisian reka, Middle Dutch reiken, Dutch reiken, Old High German and German reichen),
from Proto-Germanic *raikijanau,
perhaps from PIE root *reig- "to stretch out"
(cognates: Sanskrit rjyati "he stretches himself," riag "torture" (by racking);
Greek oregein "to reach, extend;" Lithuanian raižius "to stretch oneself;" Old Irish rigim "I stretch").
As other answers have indicated, the current definition seems to be quite consistent with attaining a goal or hitting a target--even if the target implies the restriction to a fractional proportion.
I'd go along with Joe's suggestion and use "sometimes shrinking to...". It follows naturally from "highly compressed", I'd say.
I definitely wouldn't say "up to".
If you're making something smaller, you don't say "up".
I'd have put something like "down to as little as 1/5", rather than "up to", unless you rephrase to something more like "with compression ratios up to 5:1" (since the compression ratio is higher when the end result is smaller).