There are no equivalent senses in the verb fast (which covers many of the same senses as fasten). Similarly, the verb slow is frequently found either simply (for example in the car slowed as it reached us) or in the phrasal verb to slow down. Fast, by contrast, is nowhere near as common as a noun referring to speed. The noun slow has various senses referring to speed including ‘a sluggish person’, ‘a slowly-bowled cricket bowl’, and (in the phrase the slows) ‘a tendency to move or act slowly’. We can see similar divergences with regards to the related nouns and verbs. While here’s the equivalent for quickly and slowly:

This frequency chart from the Google Ngram Viewer shows just how rare fastly is, compared to slowly: When slow is used in expressions such as to drive slow and to walk slow it is usually regional or nonstandard by contrast, the adverb fastly meaning ‘quickly, rapidly’ is rare, with fast being the standard adverb in all contexts. Slow and slowly are both used as adverbs corresponding to the adjective slow, with slow being particularly common with participles, as in slow-cooked, slow-growing, slow-moving, etc. One striking example is the adverbs which are used to correspond to the adjectives. Given fast’s origin and development as compared to slow, it is perhaps not surprising that the two words exhibit different patterns of behaviour. The same semantic development is found slightly earlier in the adverb fastly. This sense probably arose as a specific use of sense 5c of the adverb where it is used as an intensifier with the meaning ‘vigorously, hard thoroughly, greatly’ examples include ‘Wepe fast and be sory’ (a1450) and ‘Fast sheo knokyd, till at the last the ussher opynd the dure’ (a1475). Whereas the ‘firm’ sense of fast is found in Old English, the sense to do with speed emerged in the Middle English period, and originally in the adverb rather than the adjective. It seems somewhat counterintuitive that a word meaning ‘firmly fixed’ should have developed the sense ‘quick, rapid’.

Although the sense of fast referring to speed is now much more common, we can still see this first strand of meaning in words and phrases such as fast asleep, fast friends, fast and loose, steadfast, and the verb fasten. By contrast fast (the adjective and the adverb) in its earliest use refers to firmness and fixity, before developing a strand of meaning relating to speediness. Senses referring to speed or rate of progress emerge in the Middle English period. The earliest senses of the adjective slow refer to negative qualities such as sluggishness (mental and physical) and lack of liveliness. Although fast and slow are antonyms the entries, and those for derived words, do not exactly mirror each other, instead showing quite different semantic development and coverage of senses. Published this quarter are the revised entries for fastand slow. Speed read: the revision of fast and slow

Speediness meaning