diff --git a/Project.toml b/Project.toml
index 69bd3e23b..1c45dde83 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "ProbNumDiffEq"
 uuid = "bf3e78b0-7d74-48a5-b855-9609533b56a5"
 authors = ["Nathanael Bosch"]
-version = "0.3.2"
+version = "0.4.0"
 
 [deps]
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
diff --git a/src/alg_utils.jl b/src/alg_utils.jl
index d036553c0..57e57bb16 100644
--- a/src/alg_utils.jl
+++ b/src/alg_utils.jl
@@ -4,6 +4,9 @@
 ############################################################################################
 
 OrdinaryDiffEq.alg_autodiff(alg::AbstractEK) = true
+OrdinaryDiffEq.alg_autodiff(alg::EK1{CS,AD}) where {CS,AD} = AD
+OrdinaryDiffEq.alg_difftype(alg::EK1{CS,AD,DiffType}) where {CS,AD,DiffType} = DiffType
+@inline DiffEqBase.get_tmp_cache(integ, alg::EK1, cache) = (cache.tmp, cache.atmp)
 OrdinaryDiffEq.get_chunksize(alg::AbstractEK) = Val(0)
 OrdinaryDiffEq.isfsal(alg::AbstractEK) = false
 
diff --git a/src/algorithms.jl b/src/algorithms.jl
index 05f4777be..af379b4d7 100644
--- a/src/algorithms.jl
+++ b/src/algorithms.jl
@@ -43,13 +43,29 @@ See also: [`EK0`](@ref)
 - N. Bosch, P. Hennig, F. Tronarp: **Calibrated Adaptive Probabilistic ODE Solvers** (2021)
 - F. Tronarp, H. Kersting, S. Särkkä, and P. Hennig: **Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective** (2019)
 """
-Base.@kwdef struct EK1{IT} <: AbstractEK
-    prior::Symbol = :ibm
-    order::Int = 3
-    diffusionmodel::Symbol = :dynamic
-    smooth::Bool = true
-    initialization::IT = TaylorModeInit()
+struct EK1{CS,AD,DiffType,IT} <: AbstractEK
+    prior::Symbol
+    order::Int
+    diffusionmodel::Symbol
+    smooth::Bool
+    initialization::IT
 end
+EK1(;
+    prior=:ibm,
+    order=3,
+    diffusionmodel=:dynamic,
+    smooth=true,
+    initialization=TaylorModeInit(),
+    chunk_size=0,
+    autodiff=true,
+    diff_type=Val{:forward},
+) = EK1{chunk_size,autodiff,diff_type,typeof(initialization)}(
+    prior,
+    order,
+    diffusionmodel,
+    smooth,
+    initialization,
+)
 
 Base.@kwdef struct EK1FDB{IT} <: AbstractEK
     prior::Symbol = :ibm
diff --git a/src/caches.jl b/src/caches.jl
index 64977e91c..31410defe 100644
--- a/src/caches.jl
+++ b/src/caches.jl
@@ -21,6 +21,10 @@ mutable struct GaussianODEFilterCache{
     puType,
     llType,
     CType,
+    rateType,
+    UF,
+    JC,
+    uNoUnitsType,
 } <: ODEFiltersCache
     # Constants
     d::Int                  # Dimension of the problem
@@ -44,6 +48,7 @@ mutable struct GaussianODEFilterCache{
     u_pred::uType
     u_filt::uType
     tmp::uType
+    atmp::uNoUnitsType
     x::xType
     x_pred::xType
     x_filt::xType
@@ -66,6 +71,9 @@ mutable struct GaussianODEFilterCache{
     log_likelihood::llType
     C1::CType
     C2::CType
+    du1::rateType
+    uf::UF
+    jac_config::JC
 end
 
 function OrdinaryDiffEq.alg_cache(
@@ -83,8 +91,8 @@ function OrdinaryDiffEq.alg_cache(
     reltol,
     p,
     calck,
-    IIP,
-)
+    ::Val{IIP},
+) where {IIP}
     initialize_derivatives = true
 
     if u isa Number
@@ -174,6 +182,16 @@ function OrdinaryDiffEq.alg_cache(
     K2 = similar(K)
     G2 = similar(G)
     err_tmp = similar(du)
+
+    # Things for calc_J
+    uf =
+        IIP == true ? OrdinaryDiffEq.UJacobianWrapper(f, t, p) :
+        OrdinaryDiffEq.UDerivativeWrapper(f, t, p)
+    du1 = similar(rate_prototype)
+    dw1 = zero(u)
+    jac_config = OrdinaryDiffEq.build_jac_config(alg, f, uf, du1, uprev, u, tmp, dw1)
+    atmp = similar(u, uEltypeNoUnits)
+
     return GaussianODEFilterCache{
         typeof(R),
         typeof(Proj),
@@ -193,6 +211,10 @@ function OrdinaryDiffEq.alg_cache(
         typeof(pu_tmp),
         uEltypeNoUnits,
         typeof(C1),
+        typeof(du1),
+        typeof(uf),
+        typeof(jac_config),
+        typeof(atmp),
     }(
         # Constants
         d,
@@ -215,6 +237,7 @@ function OrdinaryDiffEq.alg_cache(
         u_pred,
         u_filt,
         tmp,
+        atmp,
         x0,
         x_pred,
         x_filt,
@@ -237,5 +260,8 @@ function OrdinaryDiffEq.alg_cache(
         zero(uEltypeNoUnits),
         C1,
         C2,
+        du1,
+        uf,
+        jac_config,
     )
 end
diff --git a/src/perform_step.jl b/src/perform_step.jl
index 921dacd2d..b83082591 100644
--- a/src/perform_step.jl
+++ b/src/perform_step.jl
@@ -174,12 +174,17 @@ function evaluate_ode!(
         # Jacobian is computed either with the given jac, or ForwardDiff
         if !isnothing(f.jac)
             _eval_f_jac!(ddu, u_lin, p, t, f)
-        elseif isinplace(f)
-            ForwardDiff.jacobian!(ddu, (du, u) -> f(du, u, p, t), du, u_lin)
-            integ.destats.nf += 1
         else
-            ddu .= ForwardDiff.jacobian(u -> f(u, p, t), u_lin)
-            integ.destats.nf += 1
+            !isnothing(f.jac)
+            @unpack du1, uf, jac_config = integ.cache
+            uf.f = OrdinaryDiffEq.nlsolve_f(f, alg)
+            uf.t = t
+            uf.p = p
+            if isinplace(f)
+                OrdinaryDiffEq.jacobian!(ddu, uf, u_lin, du1, integ, jac_config)
+            else
+                ddu .= OrdinaryDiffEq.jacobian(uf, u_lin, integ)
+            end
         end
         integ.destats.njacs += 1
 
diff --git a/test/specific_problems.jl b/test/specific_problems.jl
index 61e171dc9..efd325cd8 100644
--- a/test/specific_problems.jl
+++ b/test/specific_problems.jl
@@ -92,7 +92,7 @@ end
 end
 
 @testset "OOP problem" begin
-    f(u, p, t) = ([p[1] * u[1] .* (1 .- u[1])])
+    f(u, p, t) = p .* u .* (1 .- u)
     prob = ODEProblem(f, [1e-1], (0.0, 5), [3.0])
     @testset "without jacobian" begin
         # first without defined jac
@@ -211,3 +211,19 @@ end
     sol2 = solve(prob, RadauIIA5())
     @test sol1[end] ≈ sol2[end] rtol = 1e-5
 end
+
+@testset "EK1 Jacobian computation" begin
+    prob = prob_ode_fitzhughnagumo
+    @assert isnothing(prob.f.jac)
+
+    # make sure that the kwarg works
+    sol1 = solve(prob, EK1())
+    sol2 = solve(prob, EK1(autodiff=false))
+    @test sol2 isa ProbNumDiffEq.ProbODESolution
+
+    # check that forwarddiff leads to a smaller nf than finite diff
+    @test sol1.destats.nf < sol2.destats.nf
+
+    # use the EK1 on a non-forwarddiffable function
+    # TODO
+end