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Which one is correct in American English:

This computer program is error-free.

This computer program is error free.

... and why? Are, perhaps, both correct? If so, is there any difference in the meaning? (Aside: we do not speak about "an error{ |-}free program" or "a program free of errors" here. The post-position of "whatever{ |-}free" is intentional.)

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According to the Chicago Manual of Style § 7.89(3), "[c]ompounds formed with free as second element are hyphenated both before and after a noun." The examples given are "toll-free number" and "accident-free driver."

Specifically, in the construction you listed, the examples are:

"The number is toll-free." and "The driver is accident-free."

Therefore, "The program is error-free." would be the proper construction under the Chicago Manual though other style-guides may say otherwise.

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According to this ngram both possibilities are correct, although it might be better to use the hyphen. In British English it is often the case that both forms of a compound are used. Nevertheless, as a trend started more than twenty years ago people tend to use more hyphens in this type of English.

Complement

ngram showing usage in the case of predicative use.

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    @Just_A_Man "error-free", "error free" and "free of error" are synonymous although their place in the noun phrase differs and this is, almost without doubt, true in American English too.
    – LPH
    Mar 23 '20 at 21:43

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