diff --git a/Library/Homebrew/cask/cask_loader.rb b/Library/Homebrew/cask/cask_loader.rb
index a3a288f620..d9e8fd452a 100644
--- a/Library/Homebrew/cask/cask_loader.rb
+++ b/Library/Homebrew/cask/cask_loader.rb
@@ -207,9 +207,9 @@ module Cask
       def self.try_new(ref, warn: false)
         ref = ref.to_s
 
-        return unless ref.match?(HOMEBREW_TAP_CASK_REGEX)
+        return unless (token_tap_type = CaskLoader.tap_cask_token_type(ref, warn: warn))
 
-        token, tap, = CaskLoader.tap_cask_token_type(ref, warn: warn)
+        token, tap, = token_tap_type
         new("#{tap}/#{token}")
       end
 
@@ -529,9 +529,12 @@ module Cask
       self.for(ref, warn: warn).load(config: config)
     end
 
+    sig { params(tapped_token: String, warn: T::Boolean).returns(T.nilable([String, Tap, T.nilable(Symbol)])) }
     def self.tap_cask_token_type(tapped_token, warn:)
-      user, repo, token = tapped_token.split("/", 3).map(&:downcase)
-      tap = Tap.fetch(user, repo)
+      return unless (tap_with_token = Tap.with_cask_token(tapped_token))
+
+      tap, token = tap_with_token
+
       type = nil
 
       if (new_token = tap.cask_renames[token].presence)
@@ -550,7 +553,9 @@ module Cask
           opoo "Tap migration for #{tapped_token} points to itself, stopping recursion."
         else
           old_token = tap.core_cask_tap? ? token : tapped_token
-          token, tap, = tap_cask_token_type(new_tapped_token, warn: false)
+          return unless (token_tap_type = tap_cask_token_type(new_tapped_token, warn: false))
+
+          token, tap, = token_tap_type
           new_token = new_tap.core_cask_tap? ? token : "#{tap}/#{token}"
           type = :migration
         end
diff --git a/Library/Homebrew/cask/installer.rb b/Library/Homebrew/cask/installer.rb
index f7a2ce0ed7..8786d187b0 100644
--- a/Library/Homebrew/cask/installer.rb
+++ b/Library/Homebrew/cask/installer.rb
@@ -142,8 +142,8 @@ on_request: true)
       return unless @cask.conflicts_with
 
       @cask.conflicts_with[:cask].each do |conflicting_cask|
-        if (match = conflicting_cask.match(HOMEBREW_TAP_CASK_REGEX))
-          conflicting_cask_tap = Tap.fetch(match[1], match[2])
+        if (conflicting_cask_tap_with_token = Tap.with_cask_token(conflicting_cask))
+          conflicting_cask_tap, = conflicting_cask_tap_with_token
           next unless conflicting_cask_tap.installed?
         end
 
diff --git a/Library/Homebrew/cmd/install.rb b/Library/Homebrew/cmd/install.rb
index 16b5d80034..ca9293f15f 100644
--- a/Library/Homebrew/cmd/install.rb
+++ b/Library/Homebrew/cmd/install.rb
@@ -175,11 +175,13 @@ module Homebrew
     end
 
     args.named.each do |name|
-      next if File.exist?(name)
-      next unless name =~ HOMEBREW_TAP_FORMULA_REGEX
+      if (tap_with_name = Tap.with_formula_name(name))
+        tap, = tap_with_name
+      elsif (tap_with_token = Tap.with_cask_token(name))
+        tap, = tap_with_token
+      end
 
-      tap = Tap.fetch(Regexp.last_match(1), Regexp.last_match(2))
-      tap.ensure_installed!
+      tap&.ensure_installed!
     end
 
     if args.ignore_dependencies?
diff --git a/Library/Homebrew/dependency.rb b/Library/Homebrew/dependency.rb
index 8896435b67..d4ea978768 100644
--- a/Library/Homebrew/dependency.rb
+++ b/Library/Homebrew/dependency.rb
@@ -19,7 +19,9 @@ class Dependency
     @name = name
     @tags = tags
 
-    @tap = Tap.fetch(Regexp.last_match(1), Regexp.last_match(2)) if name =~ HOMEBREW_TAP_FORMULA_REGEX
+    return unless (tap_with_name = Tap.with_formula_name(name))
+
+    @tap, = tap_with_name
   end
 
   def to_s
diff --git a/Library/Homebrew/dev-cmd/extract.rb b/Library/Homebrew/dev-cmd/extract.rb
index 257cd30450..1f8ed18374 100644
--- a/Library/Homebrew/dev-cmd/extract.rb
+++ b/Library/Homebrew/dev-cmd/extract.rb
@@ -34,9 +34,8 @@ module Homebrew
   def self.extract
     args = extract_args.parse
 
-    if (match = args.named.first.match(HOMEBREW_TAP_FORMULA_REGEX))
-      name = match[3].downcase
-      source_tap = Tap.fetch(match[1], match[2])
+    if (tap_with_name = args.named.first&.then { Tap.with_formula_name(_1) })
+      source_tap, name = tap_with_name
     else
       name = args.named.first.downcase
       source_tap = CoreTap.instance
diff --git a/Library/Homebrew/formulary.rb b/Library/Homebrew/formulary.rb
index 90fb41557b..9a43cef169 100644
--- a/Library/Homebrew/formulary.rb
+++ b/Library/Homebrew/formulary.rb
@@ -721,15 +721,15 @@ module Formulary
     }
     def self.try_new(ref, from: T.unsafe(nil), warn: false)
       ref = ref.to_s
-      return unless (name = ref[HOMEBREW_TAP_FORMULA_REGEX, :name])
 
-      alias_name = name
+      return unless (name_tap_type = Formulary.tap_formula_name_type(ref, warn: warn))
 
-      name, tap, type = Formulary.tap_formula_name_type(ref, warn: warn)
+      name, tap, type = name_tap_type
       path = Formulary.find_formula_in_tap(name, tap)
 
       options = if type == :alias
-        { alias_name: alias_name.downcase }
+        # TODO: Simplify this by making `tap_formula_name_type` return the alias name.
+        { alias_name: T.must(ref[HOMEBREW_TAP_FORMULA_REGEX, :name]).downcase }
       else
         {}
       end
@@ -893,7 +893,9 @@ module Formulary
 
       ref = "#{CoreTap.instance}/#{name}"
 
-      name, tap, type = Formulary.tap_formula_name_type(ref, warn: warn)
+      return unless (name_tap_type = Formulary.tap_formula_name_type(ref, warn: warn))
+
+      name, tap, type = name_tap_type
 
       options =  if type == :alias
         { alias_name: alias_name.downcase }
@@ -1127,9 +1129,12 @@ module Formulary
     loader_for(ref).path
   end
 
+  sig { params(tapped_name: String, warn: T::Boolean).returns(T.nilable([String, Tap, T.nilable(Symbol)])) }
   def self.tap_formula_name_type(tapped_name, warn:)
-    user, repo, name = tapped_name.split("/", 3).map(&:downcase)
-    tap = Tap.fetch(user, repo)
+    return unless (tap_with_name = Tap.with_formula_name(tapped_name))
+
+    tap, name = tap_with_name
+
     type = nil
 
     # FIXME: Remove the need to do this here.
@@ -1138,7 +1143,7 @@ module Formulary
     if (possible_alias = tap.alias_table[alias_table_key].presence)
       # FIXME: Remove the need to split the name and instead make
       #        the alias table only contain short names.
-      name = possible_alias.split("/").last
+      name = T.must(possible_alias.split("/").last)
       type = :alias
     elsif (new_name = tap.formula_renames[name].presence)
       old_name = tap.core_tap? ? name : tapped_name
@@ -1156,7 +1161,10 @@ module Formulary
         opoo "Tap migration for #{tapped_name} points to itself, stopping recursion."
       else
         old_name = tap.core_tap? ? name : tapped_name
-        name, tap, = tap_formula_name_type(new_tapped_name, warn: false)
+        return unless (name_tap_type = tap_formula_name_type(new_tapped_name, warn: false))
+
+        name, tap, = name_tap_type
+
         new_name = new_tap.core_tap? ? name : "#{tap}/#{name}"
         type = :migration
       end
diff --git a/Library/Homebrew/tap.rb b/Library/Homebrew/tap.rb
index 256816d647..5bad532b3b 100644
--- a/Library/Homebrew/tap.rb
+++ b/Library/Homebrew/tap.rb
@@ -65,6 +65,38 @@ class Tap
     fetch(match[:user], match[:repo])
   end
 
+  # @private
+  sig { params(name: String).returns(T.nilable([T.attached_class, String])) }
+  def self.with_formula_name(name)
+    return unless (match = name.match(HOMEBREW_TAP_FORMULA_REGEX))
+
+    user = T.must(match[:user])
+    repo = T.must(match[:repo])
+    name = T.must(match[:name])
+
+    # Relative paths are not taps.
+    return if [user, repo].intersect?([".", ".."])
+
+    tap = fetch(user, repo)
+    [tap, name.downcase]
+  end
+
+  # @private
+  sig { params(token: String).returns(T.nilable([T.attached_class, String])) }
+  def self.with_cask_token(token)
+    return unless (match = token.match(HOMEBREW_TAP_CASK_REGEX))
+
+    user = T.must(match[:user])
+    repo = T.must(match[:repo])
+    token = T.must(match[:token])
+
+    # Relative paths are not taps.
+    return if [user, repo].intersect?([".", ".."])
+
+    tap = fetch(user, repo)
+    [tap, token.downcase]
+  end
+
   sig { returns(CoreCaskTap) }
   def self.default_cask_tap
     odisabled "`Tap.default_cask_tap`", "`CoreCaskTap.instance`"
diff --git a/Library/Homebrew/test/formulary_spec.rb b/Library/Homebrew/test/formulary_spec.rb
index cd4dec18c3..92e1343225 100644
--- a/Library/Homebrew/test/formulary_spec.rb
+++ b/Library/Homebrew/test/formulary_spec.rb
@@ -535,6 +535,22 @@ RSpec.describe Formulary do
   end
 
   describe "::loader_for" do
+    context "when given a relative path with two slashes" do
+      it "returns a `FromPathLoader`" do
+        mktmpdir.cd do
+          FileUtils.mkdir "Formula"
+          FileUtils.touch "Formula/gcc.rb"
+          expect(described_class.loader_for("./Formula/gcc.rb")).to be_a Formulary::FromPathLoader
+        end
+      end
+    end
+
+    context "when given a tapped name" do
+      it "returns a `FromTapLoader`" do
+        expect(described_class.loader_for("homebrew/core/gcc")).to be_a Formulary::FromTapLoader
+      end
+    end
+
     context "when not using the API" do
       before do
         ENV["HOMEBREW_NO_INSTALL_FROM_API"] = "1"
diff --git a/Library/Homebrew/test/tap_spec.rb b/Library/Homebrew/test/tap_spec.rb
index 2b735c9d44..0fd9fb11d9 100644
--- a/Library/Homebrew/test/tap_spec.rb
+++ b/Library/Homebrew/test/tap_spec.rb
@@ -599,4 +599,24 @@ RSpec.describe Tap do
       expect(described_class.fetch("my", "tap-with-@-symbol").repo_var_suffix).to eq "_MY_HOMEBREW_TAP_WITH___SYMBOL"
     end
   end
+
+  describe "::with_formula_name" do
+    it "returns the tap and formula name when given a full name" do
+      expect(described_class.with_formula_name("homebrew/core/gcc")).to eq [CoreTap.instance, "gcc"]
+    end
+
+    it "returns nil when given a relative path" do
+      expect(described_class.with_formula_name("./Formula/gcc.rb")).to be_nil
+    end
+  end
+
+  describe "::with_cask_token" do
+    it "returns the tap and cask token when given a full token" do
+      expect(described_class.with_cask_token("homebrew/cask/alfred")).to eq [CoreCaskTap.instance, "alfred"]
+    end
+
+    it "returns nil when given a relative path" do
+      expect(described_class.with_cask_token("./Casks/alfred.rb")).to be_nil
+    end
+  end
 end