diff --git a/src/chainrules.jl b/src/chainrules.jl
index 0c7269d1..68ebcce3 100644
--- a/src/chainrules.jl
+++ b/src/chainrules.jl
@@ -31,10 +31,12 @@ function rrule(::typeof(extract_derivative), t::TaylorScalar{T, N},
 end
 
 function rrule(::typeof(*), A::AbstractMatrix{S},
-    t::Vector{TaylorScalar{T, N}}) where {N, S <: Number, T}
+    t::AbstractVector{TaylorScalar{T, N}}) where {N, S <: Number, T}
     project_A = ProjectTo(A)
     function gemv_pullback(x̄)
-        NoTangent(), @thunk(project_A(contract.(x̄, transpose(t)))), @thunk(transpose(A)*x̄)
+        x̂ = reinterpret(reshape, T, x̄)
+        t̂ = reinterpret(reshape, T, t)
+        NoTangent(), @thunk(project_A(transpose(x̂) * t̂)), @thunk(transpose(A)*x̄)
     end
     return A * t, gemv_pullback
 end
diff --git a/src/derivative.jl b/src/derivative.jl
index 00cbcc05..81b66da7 100644
--- a/src/derivative.jl
+++ b/src/derivative.jl
@@ -18,8 +18,8 @@ function derivative end
     derivative(f, x, Val{order + 1}())
 end
 
-@inline function derivative(f, x::V, l::V,
-    order::Int64) where {V <: AbstractArray{<:Number, 1}}
+@inline function derivative(f, x::AbstractVector{T}, l::AbstractVector{S},
+    order::Int64) where {T <: Number, S <: Number}
     derivative(f, x, l, Val{order + 1}())
 end
 
@@ -29,10 +29,10 @@ end
 end
 
 # Need to rewrite like this to help Zygote infer types
-make_taylor(t0::T, t1::T, ::Val{N}) where {T, N} = TaylorScalar{T, N}(t0, t1)
+make_taylor(t0::T, t1::S, ::Val{N}) where {T, S, N} = TaylorScalar{T, N}(t0, T(t1))
 
-@inline function derivative(f, x::V, l::V,
-    vN::Val{N}) where {V <: AbstractArray{<:Number, 1}, N}
+@inline function derivative(f, x::AbstractVector{T}, l::AbstractVector{S},
+    vN::Val{N}) where {T <: Number, S <: Number, N}
     t = map((t0, t1) -> make_taylor(t0, t1, vN), x, l) # i.e. map(TaylorScalar{T, N}, x, l)
     return extract_derivative(f(t), N)
 end