The affix vati (vat) comes after a word in the Instrumental -3rd case in construction, in the sense of 'like that' when the meaning is 'similarity of action'.,
As ब्राह्मणेन तुल्यं वर्तते = ब्राह्मणवत्, राजवत् ॥
Why do we say \action\? The affix will not be joined when the similarity is in 'quality'. As पुत्रेणसह स्थूलः \as big as the son\, पुत्रेण तुल्यः पिङ्गलः ॥,