diff --git a/Project.toml b/Project.toml
index 05a7ce8..0453009 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "FunctionProperties"
 uuid = "f62d2435-5019-4c03-9749-2d4c77af0cbc"
-version = "0.1.4"
+version = "0.1.5"
 authors = ["SciML"]
 
 [deps]
diff --git a/src/FunctionProperties.jl b/src/FunctionProperties.jl
index 761e7fa..bd17be9 100644
--- a/src/FunctionProperties.jl
+++ b/src/FunctionProperties.jl
@@ -2,11 +2,15 @@ module FunctionProperties
 
 using Core: GotoIfNot
 
+# Backstop against pathological recursion depth; real call trees that matter here are shallow.
+const RECURSION_LIMIT = 256
+
 """
     is_leaf(f, args...) -> Bool
 
 Override this to exempt a function from `hasbranching` analysis.
-Return `true` to treat `f` as branch-free regardless of its implementation.
+Return `true` to treat `f` as branch-free regardless of its implementation, which also
+stops [`hasbranching`](@ref) from recursing into its callees.
 
 ## Example
 
@@ -31,12 +35,19 @@ like ReverseDiff.jl.
 
 ## Outputs
 
-Boolean for whether the function's immediate IR contains a conditional branch (`GotoIfNot`).
+Boolean for whether the function contains a value-dependent conditional branch
+(`GotoIfNot`). The type-inferred IR (`code_typed(...; optimize = false)`) of `f` is scanned,
+and the scan recurses through statically resolved calls into other user-defined methods so
+that branches living behind a non-inlined call boundary are still detected. Calls into
+`Base`, `Core`, and the standard libraries are treated as leaves: their internal branches
+are structural/compile-time rather than value-dependent user logic, and recursing into them
+(e.g. matrix multiply, broadcasting, `getindex` bounds checks) produces false positives.
 
 ## Customizing and Removing Functions from the Checks
 
 Some functions may produce false positives because their internal branches are compile-time
-constants. Override `FunctionProperties.is_leaf` to opt them out:
+constants. Override [`is_leaf`](@ref) to opt them out (this also prevents recursion into
+them):
 
 ```julia
 FunctionProperties.is_leaf(::typeof(my_fn)) = true
@@ -44,17 +55,121 @@ FunctionProperties.is_leaf(::typeof(my_fn)) = true
 """
 function hasbranching(f, x...)
     is_leaf(f, x...) && return false
-    argtypes = Tuple{Core.Typeof.(x)...}
+    sig = Tuple{Core.Typeof(f), Core.Typeof.(x)...}
+    return _hasbranching(sig, Set{Any}(), 0)
+end
+
+function _hasbranching(@nospecialize(sig), seen, depth)
+    depth > RECURSION_LIMIT && return false
+    sig in seen && return false
+    push!(seen, sig)
+
     results = try
-        code_typed(f, argtypes; optimize = false)
+        Base.code_typed_by_type(sig; optimize = false)
+    catch
+        return false
+    end
+
+    for pair in results
+        ci = first(pair)
+        # Generated functions that were not expanded come back as `Method`, not `CodeInfo`;
+        # there is no body to scan, so treat them as leaves.
+        ci isa Core.CodeInfo || continue
+        any(stmt -> isa(stmt, GotoIfNot), ci.code) && return true
+        for stmt in ci.code
+            _recurse_call(stmt, ci, seen, depth) && return true
+        end
+    end
+    return false
+end
+
+# Inspect a single IR statement: if it is a statically resolvable call into a non-library
+# method, recurse into that method's IR. Returns `true` if a branch is found downstream.
+function _recurse_call(@nospecialize(stmt), ci, seen, depth)
+    call = Meta.isexpr(stmt, :(=)) ? stmt.args[2] : stmt
+
+    if Meta.isexpr(call, :invoke)
+        mi = call.args[1]
+        callsig = mi isa Core.MethodInstance ? mi.specTypes :
+            (
+                isdefined(mi, :def) && getfield(mi, :def) isa Core.MethodInstance ?
+                getfield(mi, :def).specTypes : nothing
+            )
+        callsig === nothing && return false
+        return _recurse_sig(callsig, nothing, seen, depth)
+    end
+
+    Meta.isexpr(call, :call) || return false
+    ftype, fval = _resolve_callee(call.args[1], ci)
+    ftype === nothing && return false
+    argtypes = Any[_value_type(a, ci) for a in @view call.args[2:end]]
+    return _recurse_sig(Tuple{ftype, argtypes...}, fval, seen, depth)
+end
+
+function _recurse_sig(@nospecialize(callsig), @nospecialize(fval), seen, depth)
+    # Honor user `is_leaf` overrides when the concrete function value is recoverable.
+    fval !== nothing && is_leaf(fval) && return false
+    m = try
+        Base.which(callsig)
     catch
         return false
     end
-    isempty(results) && return false
-    ci = first(results)[1]
-    return any(isa(s, GotoIfNot) for s in ci.code)
+    _is_library_method(m) && return false
+    return _hasbranching(callsig, seen, depth + 1)
+end
+
+# Library code (`Base`, `Core`, stdlibs) is treated as a leaf: its branches are structural or
+# compile-time, not the value-dependent user logic `hasbranching` is meant to surface.
+function _is_library_method(m::Method)
+    root = Base.moduleroot(m.module)
+    (root === Base || root === Core) && return true
+    pkgdir = Base.pkgdir(root)
+    pkgdir === nothing && return false
+    return startswith(pkgdir, Sys.STDLIB)
+end
+
+function _resolve_callee(@nospecialize(fexpr), ci)
+    if fexpr isa GlobalRef
+        if isdefined(fexpr.mod, fexpr.name) && isconst(fexpr.mod, fexpr.name)
+            v = getglobal(fexpr.mod, fexpr.name)
+            return (Core.Typeof(v), v)
+        end
+        return (nothing, nothing)
+    elseif fexpr isa QuoteNode
+        return (Core.Typeof(fexpr.value), fexpr.value)
+    elseif fexpr isa Core.SSAValue
+        t = ci.ssavaluetypes[fexpr.id]
+        t isa Core.Const && return (Core.Typeof(t.val), t.val)
+        return (_widen(t), nothing)
+    else
+        return (_value_type(fexpr, ci), nothing)
+    end
+end
+
+function _value_type(@nospecialize(a), ci)
+    if a isa Core.SSAValue
+        return _widen(ci.ssavaluetypes[a.id])
+    elseif a isa Core.Argument
+        st = ci.slottypes
+        return st === nothing ? Any : _widen(st[a.n])
+    elseif a isa Core.SlotNumber
+        st = ci.slottypes
+        return st === nothing ? Any : _widen(st[a.id])
+    elseif a isa GlobalRef
+        return (isdefined(a.mod, a.name) && isconst(a.mod, a.name)) ?
+            Core.Typeof(getglobal(a.mod, a.name)) : Any
+    elseif a isa QuoteNode
+        return Core.Typeof(a.value)
+    else
+        return Core.Typeof(a)
+    end
 end
 
+_widen(@nospecialize t) =
+    t isa Core.Const ? Core.Typeof(t.val) :
+    t isa Core.PartialStruct ? t.typ :
+    isa(t, Type) ? t : Any
+
 export hasbranching, is_leaf
 
 end
diff --git a/test/core_tests.jl b/test/core_tests.jl
index e46c81b..e166bd7 100644
--- a/test/core_tests.jl
+++ b/test/core_tests.jl
@@ -17,6 +17,23 @@ f_branch() = true ? 1 : 0
 FunctionProperties.is_leaf(::typeof(f_branch)) = true
 @test !FunctionProperties.hasbranching(f_branch)
 
+# Branches behind a non-inlined call boundary must still be detected: the value-dependent
+# `if` lives in `branchy_helper`, not in the immediate IR of the entry function.
+@noinline branchy_helper(x) = x < 0 ? -x : x
+nested_branch_rhs(u, p, t) = branchy_helper(u) + p
+@test FunctionProperties.hasbranching(nested_branch_rhs, 1.0, 2.0, 0.0)
+
+@noinline branchfree_helper(x) = x * x + one(x)
+nested_branchfree_rhs(u, p, t) = branchfree_helper(u) + p
+@test !FunctionProperties.hasbranching(nested_branchfree_rhs, 1.0, 2.0, 0.0)
+
+# An `is_leaf` override stops recursion into the marked callee.
+@noinline opted_out_helper(x) = x < 0 ? -x : x
+opted_out_rhs(u, p, t) = opted_out_helper(u) + p
+@test FunctionProperties.hasbranching(opted_out_rhs, 1.0, 2.0, 0.0)
+FunctionProperties.is_leaf(::typeof(opted_out_helper)) = true
+@test !FunctionProperties.hasbranching(opted_out_rhs, 1.0, 2.0, 0.0)
+
 # Test simple mutating functions
 function f(dx, x)
     return @inbounds dx[1] = x[1]