diff --git a/test/interface/ad_tests.jl b/test/interface/ad_tests.jl
index 3230ff4920..847228388f 100644
--- a/test/interface/ad_tests.jl
+++ b/test/interface/ad_tests.jl
@@ -6,33 +6,100 @@ function f(du,u,p,t)
   du[2] = p[2]
 end
 
-cb = ContinuousCallback((u,t,i) -> u[1], (integrator)->(println("Stopped.");integrator.p[2]=zero(integrator.p[2])))
-function test_f(p)
-  prob = ODEProblem(f,eltype(p).([1.0,0.0]),eltype(p).((0.0,1.0)),copy(p))
-  integrator = init(prob,Tsit5(),abstol=1e-14,reltol=1e-14,callback=cb)
-  step!(integrator)
-  solve!(integrator).u[end]
+for x in 0:0.001:5
+  called = false
+  function test_f(p)
+    cb = ContinuousCallback((u,t,i) -> u[1], (integrator)->(called=true;integrator.p[2]=zero(integrator.p[2])))
+    prob = ODEProblem(f,eltype(p).([1.0,0.0]),eltype(p).((0.0,1.0)),copy(p))
+    integrator = init(prob,Tsit5(),abstol=1e-14,reltol=1e-14,callback=cb)
+    step!(integrator)
+    solve!(integrator).u[end]
+  end
+  p = [2.0, x]
+  called = false
+  findiff = Calculus.finite_difference_jacobian(test_f,p)
+  @test called
+  called = false
+  fordiff = ForwardDiff.jacobian(test_f,p)
+  @test called
+  @test findiff ≈ fordiff
 end
-p = [2.0, 1.0]
-findiff = Calculus.finite_difference_jacobian(test_f,p)
-fordiff = ForwardDiff.jacobian(test_f,p)
-@test findiff ≈ fordiff
 
 function f2(du,u,p,t)
-  du[1] = -u[1]
+  du[1] = -u[2]
   du[2] = p[2]
 end
 
+for x in 2.1:0.001:5
+  called = false
+  function test_f2(p)
+    cb = ContinuousCallback((u,t,i) -> u[1], (integrator)->(called=true;integrator.p[2]=zero(integrator.p[2])))
+    prob = ODEProblem(f2,eltype(p).([1.0,0.0]),eltype(p).((0.0,1.0)),copy(p))
+    integrator = init(prob,Tsit5(),abstol=1e-12,reltol=1e-12,callback=cb)
+    step!(integrator)
+    solve!(integrator).u[end]
+  end
+  p = [2.0, x]
+  findiff = Calculus.finite_difference_jacobian(test_f2,p)
+  @test called
+  called = false
+  fordiff = ForwardDiff.jacobian(test_f2,p)
+  @test called
+  @test findiff ≈ fordiff
+end
+
+#=
+#x = 2.0 is an interesting case
+
+x = 2.0
+
 function test_f2(p)
+  cb = ContinuousCallback((u,t,i) -> u[1], (integrator)->(@show(x,integrator.t);called=true;integrator.p[2]=zero(integrator.p[2])))
   prob = ODEProblem(f2,eltype(p).([1.0,0.0]),eltype(p).((0.0,1.0)),copy(p))
-  integrator = init(prob,Tsit5(),abstol=1e-14,reltol=1e-14,callback=cb)
+  integrator = init(prob,Tsit5(),abstol=1e-12,reltol=1e-12,callback=cb)
   step!(integrator)
   solve!(integrator).u[end]
 end
-p = [2.0, 1.0]
+
+p = [2.0, x]
 findiff = Calculus.finite_difference_jacobian(test_f2,p)
+@test called
+called = false
 fordiff = ForwardDiff.jacobian(test_f2,p)
-@test findiff ≈ fordiff
+@test called
+
+# At that value, it shouldn't be called, but a small perturbation will make it called, so finite difference is wrong!
+=#
+
+for x in 1.0:0.001:2.5
+  function lotka_volterra(du,u,p,t)
+    x, y = u
+    α, β, δ, γ = p
+    du[1] = dx = α*x - β*x*y
+    du[2] = dy = -δ*y + γ*x*y
+  end
+  u0 = [1.0,1.0]
+  tspan = (0.0,10.0)
+  p = [x,1.0,3.0,1.0]
+  prob = ODEProblem(lotka_volterra,u0,tspan,p)
+  sol = solve(prob,Tsit5())
+
+  called=false
+  function test_lotka(p)
+    cb = ContinuousCallback((u,t,i) -> u[1]-2.5, (integrator)->(called=true;integrator.p[4]=1.5))
+    prob = ODEProblem(lotka_volterra,eltype(p).([1.0,1.0]),eltype(p).((0.0,10.0)),copy(p))
+    integrator = init(prob,Tsit5(),abstol=1e-12,reltol=1e-12,callback=cb)
+    step!(integrator)
+    solve!(integrator).u[end]
+  end
+
+  findiff = Calculus.finite_difference_jacobian(test_lotka,p)
+  @test called
+  called = false
+  fordiff = ForwardDiff.jacobian(test_lotka,p)
+  @test called
+  @test findiff ≈ fordiff
+end
 
 # Gradients and Hessians