# Allocations with nested Jacobians with StaticArrays and ForwardDiff

**URL:** <https://discourse.julialang.org/t/allocations-with-nested-jacobians-with-staticarrays-and-forwarddiff/136789>\
**Category:** General Usage\
**Created:** [April 20, 2026, 9:13am UTC](https://discourse.julialang.org/t/allocations-with-nested-jacobians-with-staticarrays-and-forwarddiff/136789 "2026-04-20T09:13:26Z")\
**Posts on this page:** 9\
**Page:** 1

<div class="post-metadata">

**Author:** ![Albert\_de\_montserrat](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/albert_de_montserrat/32/9135_2.png) [@Albert\_de\_montserrat](https://discourse.julialang.org/u/Albert_de_montserrat)\
**Post date:** [April 20, 2026, 9:13am UTC](https://discourse.julialang.org/t/allocations-with-nested-jacobians-with-staticarrays-and-forwarddiff/136789/1 "2026-04-20T09:13:26Z")

</div>

I am working a code where we do some nested Jacobians with StaticArrays, however I do not seem to manage to get it done without some allocations due to some internal type instability.

The MWE below shows the allocations, and a weird behavior I have also seen while debugging our larger code, where type stability and allocations disappear if, after benchmarking (or simply calling) my function, I redefine `J_flat`:

```julia
using ForwardDiff, StaticArrays, Chairmarks

@inline f(x) = SVector(x[1]^2 * x[2], sin(x[1]) + x[2]^3)

function J_flat(x) 
    y = ForwardDiff.jacobian(f, x)
    SA[y[1], y[2]]
end

function nested_jacobian(x0::SVector{2, T}) where T
    ForwardDiff.jacobian(J_flat, x0)
end

x0 = SVector(1.0, 2.0)
@code_warntype nested_jacobian(x0) # shows a type instability
@b nested_jacobian($x0) # 131.447 ns (4 allocs: 176 bytes)

function J_flat(x) 
    y = ForwardDiff.jacobian(f, x)
    SA[y[1], y[2]]
end

@code_warntype nested_jacobian(x0) # type instability is gone
@b nested_jacobian($x0) # 26.594 ns

```

Redefining `J_flat` without benchmarking or calling `nested_jacobian` does not result in allocation-free call

```julia
using ForwardDiff, StaticArrays, Chairmarks

@inline f(x) = SVector(x[1]^2 * x[2], sin(x[1]) + x[2]^3)

function J_flat(x) 
    y = ForwardDiff.jacobian(f, x)
    SA[y[1], y[2]]
end

function nested_jacobian(x0::SVector{2, T}) where T
    ForwardDiff.jacobian(J_flat, x0)
end

x0 = SVector(1.0, 2.0)

function J_flat(x) 
    y = ForwardDiff.jacobian(f, x)
    SA[y[1], y[2]]
end

@code_warntype nested_jacobian(x0) # shows a type instability
@b nested_jacobian($x0) # 129.829 ns (4 allocs: 176 bytes)

```

Is there any workaround to avoid these allocations?

---

<div class="post-metadata">

**Author:** ![JonasWickman](https://avatars.discourse-cdn.com/v4/letter/j/9de0a6/32.png) [@JonasWickman](https://discourse.julialang.org/u/JonasWickman)\
**Post date:** [April 20, 2026, 1:16pm UTC](https://discourse.julialang.org/t/allocations-with-nested-jacobians-with-staticarrays-and-forwarddiff/136789/2 "2026-04-20T13:16:35Z")

</div>

> [@Albert\_de\_montserrat](#):
>
> ```julia-auto
> f(x) = SVector(x[1]^2 * x[2], sin(x[1]) + x[2]^3)
> 
> function J_flat(x) 
> y = ForwardDiff.jacobian(f, x)
> SA[y[1], y[2]]
> end
> 
> function nested_jacobian(x0::SVector{2, T}) where T
> ForwardDiff.jacobian(J_flat, x0)
> end
> 
> x0 = SVector(1.0, 2.0)
> @code_warntype nested_jacobian(x0) # shows a type instability
> @b nested_jacobian($x0)
> 
> ```

I think there have been a few threads on this over the years, but the only one I can find at the moment is my own from quite a while ago now: [Type stability for higher derivatives in ForwardDiff](https://discourse.julialang.org/t/type-stability-for-higher-derivatives-in-forwarddiff/66686)

As best as I’m aware there is currently no easy workaround for this. However, if some manual intervention is feasible in your case, then you can do something like this:

```julia-auto
f(x) = SVector(x[1]^2 * x[2], sin(x[1]) + x[2]^3)

function J_flat(x)  
    y1 = ForwardDiff.derivative(x1 -> f(SA[x1, x[2]])[1], x[1])
    y2 = ForwardDiff.derivative(x1 -> f(SA[x1, x[2]])[2], x[1])

    SA[y1, y2]
end

function nested_jacobian(x0::SVector{2, T}) where T
    ForwardDiff.jacobian(J_flat, x0)
end

x0 = SVector(1.0, 2.0)
@code_warntype nested_jacobian(x0) # Is now type stable

```

Edit: Forgot to get first index of the output of `f`  
Edit 2: Got the wrong indices I think. I guess this showcase why doing this manually is less than ideal.

---

<div class="post-metadata">

**Author:** ![tremelow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tremelow/32/221943_2.png) [@tremelow](https://discourse.julialang.org/u/tremelow)\
**Post date:** [May 19, 2026, 10:49am UTC](https://discourse.julialang.org/t/allocations-with-nested-jacobians-with-staticarrays-and-forwarddiff/136789/3 "2026-05-19T10:49:33Z")

</div>

I’m having the same issue when computing Lie brackets (which means the issue also exists in OptimalControl.jl). In your case, I found that simply specifying the input/output of `J_flat` seems to fix the issue.

```julia
using ForwardDiff, StaticArrays, BenchmarkTools

@inline f(x) = SVector(x[1]^2 * x[2], sin(x[1]) + x[2]^3)

function J_flat(x::SVector{2,T}) where T
    y = ForwardDiff.jacobian(f, x)
    SVector{2,T}(y[1], y[2])
end

function nested_jacobian(x0)
    return ForwardDiff.jacobian(J_flat, x0)
end

x0 = SVector(1.0, 2.0)

@code_warntype nested_jacobian(x0) # no type instability
@btime nested_jacobian($x0) # 9.781 ns (0 allocations: 0 bytes)

```

However, for my case of Lie brackets, this doesn’t work, so this might not work outside of your MWE. I’ll share my example below.

Maybe you could add the tags `forwarddiff` and `staticarrays` (maybe even `autodiff`) to help experts find this discussion.

---

<div class="post-metadata">

**Author:** ![tremelow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tremelow/32/221943_2.png) [@tremelow](https://discourse.julialang.org/u/tremelow)\
**Post date:** [May 19, 2026, 10:50am UTC](https://discourse.julialang.org/t/allocations-with-nested-jacobians-with-staticarrays-and-forwarddiff/136789/4 "2026-05-19T10:50:11Z")

</div>

On your example, something odd is that using `@code_llvm` instead of `@code_warntype`, we can also detect that after the redefinition, the inner functions of `ForwardDiff/partials.jl` get called more often than before.

Just in case someone can parse them, here are the traces of `@code_llvm` before and after redefining `J_flat` in my code above.

```julia
; @ REPL[4]:1 within `nested_jacobian`
define nonnull {}* @julia_nested_jacobian_324([1 x [2 x double]]* nocapture noundef nonnull readonly align 8 dereferenceable(16) %0) #0 {
top:
  %1 = alloca [3 x {}*], align 8
  %gcframe10 = alloca [4 x {}*], align 16
  %gcframe10.sub = getelementptr inbounds [4 x {}*], [4 x {}*]* %gcframe10, i64 0, i64 0
  %.sub = getelementptr inbounds [3 x {}*], [3 x {}*]* %1, i64 0, i64 0
  %2 = bitcast [4 x {}*]* %gcframe10 to i8*
  call void @llvm.memset.p0i8.i64(i8* align 16 %2, i8 0, i64 32, i1 true)
  %3 = alloca [1 x [2 x { double, [1 x [2 x double]] }]], align 8
  %thread_ptr = call i8* asm "movq %fs:0, $0", "=r"() #9
  %tls_ppgcstack = getelementptr i8, i8* %thread_ptr, i64 -8
  %4 = bitcast i8* %tls_ppgcstack to {} ****
  %tls_pgcstack = load {} ***, {}**** %4, align 8
; @ REPL[4]:2 within `nested_jacobian`
; ┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/ext/ForwardDiffStaticArraysExt.jl:66 within `jacobian`
; │┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/ext/ForwardDiffStaticArraysExt.jl:91 within `vector_mode_jacobian`
    %5 = bitcast [4 x {}*]* %gcframe10 to i64*
    store i64 8, i64* %5, align 16
    %6 = getelementptr inbounds [4 x {}*], [4 x {}*]* %gcframe10, i64 0, i64 1
    %7 = bitcast {} **%6 to {}***
    %8 = load {} **, {}*** %tls_pgcstack, align 8
    store {} **%8, {}*** %7, align 8
    %9 = bitcast {} ***%tls_pgcstack to {}***
    store {} **%gcframe10.sub, {}*** %9, align 8
    call void @j_static_dual_eval_326([1 x [2 x { double, [1 x [2 x double]] }]]* noalias nocapture noundef nonnull sret([1 x [2 x { double, [1 x [2 x double]] }]]) %3, [1 x [2 x double]]* nocapture nonnull readonly %0)
    %ptls_field11 = getelementptr inbounds {} **, {}*** %tls_pgcstack, i64 2
    %10 = bitcast {} ***%ptls_field11 to i8**
    %ptls_load1213 = load i8*, i8** %10, align 8
    %box = call noalias nonnull dereferenceable(64) {}* @ijl_gc_pool_alloc(i8* %ptls_load1213, i32 896, i32 64) #6
    %11 = bitcast {}* %box to i64*
    %12 = getelementptr inbounds i64, i64* %11, i64 -1
    store atomic i64 133696916920400, i64* %12 unordered, align 8
    %13 = bitcast {}* %box to i8*
    %14 = bitcast [1 x [2 x { double, [1 x [2 x double]] }]]* %3 to i8*
    call void @llvm.memcpy.p0i8.p0i8.i64(i8* noundef align 8 dereferenceable(48) %13, i8* noundef nonnull align 8 dereferenceable(48) %14, i64 48, i1 false)
    %15 = getelementptr inbounds [4 x {}*], [4 x {}*]* %gcframe10, i64 0, i64 3
    store {}* %box, {}** %15, align 8
    %ptls_load81415 = load i8*, i8** %10, align 8
    %box3 = call noalias nonnull dereferenceable(32) {}* @ijl_gc_pool_alloc(i8* %ptls_load81415, i32 800, i32 32) #6
    %16 = bitcast {}* %box3 to i64*
    %17 = getelementptr inbounds i64, i64* %16, i64 -1
    store atomic i64 133696928609808, i64* %17 unordered, align 8
    %18 = bitcast {}* %box3 to i8*
    %19 = bitcast [1 x [2 x double]]* %0 to i8*
    call void @llvm.memcpy.p0i8.p0i8.i64(i8* noundef align 8 dereferenceable(16) %18, i8* noundef nonnull align 8 dereferenceable(16) %19, i64 16, i1 false)
    %20 = getelementptr inbounds [4 x {}*], [4 x {}*]* %gcframe10, i64 0, i64 2
    store {}* %box3, {}** %20, align 16
    store {}* inttoptr (i64 133696925208208 to {}*), {}** %.sub, align 8
    %21 = getelementptr inbounds [3 x {}*], [3 x {}*]* %1, i64 0, i64 1
    store {}* %box, {}** %21, align 8
    %22 = getelementptr inbounds [3 x {}*], [3 x {}*]* %1, i64 0, i64 2
    store {}* %box3, {}** %22, align 8
    %23 = call nonnull {}* @ijl_apply_generic({}* inttoptr (i64 133696871410736 to {}*), {}** nonnull %.sub, i32 3)
    %24 = load {}*, {}** %6, align 8
    %25 = bitcast {} ***%tls_pgcstack to {}**
    store {}* %24, {}** %25, align 8
; └└
  ret {}* %23
}

```

```julia
; @ REPL[4]:1 within `nested_jacobian`
define void @julia_nested_jacobian_343([1 x [4 x double]]* noalias nocapture noundef nonnull sret([1 x [4 x double]]) align 8 dereferenceable(32) %0, [1 x [2 x double]]* nocapture noundef nonnull readonly align 8 dereferenceable(16) %1) #0 {
top:
  %2 = alloca [2 x double], align 8
; @ REPL[4]:2 within `nested_jacobian`
; ┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/ext/ForwardDiffStaticArraysExt.jl:66 within `jacobian`
; │┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/ext/ForwardDiffStaticArraysExt.jl:91 within `vector_mode_jacobian`
; ││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/ext/ForwardDiffStaticArraysExt.jl:24 within `static_dual_eval`
; │││┌ @ REPL[8]:2 within `J_flat`
; ││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/ext/ForwardDiffStaticArraysExt.jl:66 within `jacobian`
; │││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/ext/ForwardDiffStaticArraysExt.jl:91 within `vector_mode_jacobian`
; ││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/ext/ForwardDiffStaticArraysExt.jl:24 within `static_dual_eval`
; │││││││┌ @ REPL[2]:1 within `f`
; ││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:693 within `sin`
; │││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:703 within `sincos`
; ││││││││││┌ @ tuple.jl:92 within `indexed_iterate` @ tuple.jl:92
             %3 = getelementptr inbounds [2 x double], [2 x double]* %2, i64 0, i64 0
; │││││││││││ @ tuple.jl:92 within `indexed_iterate`
             %4 = getelementptr inbounds [2 x double], [2 x double]* %2, i64 0, i64 1
; └└└└└└└└└└└
  %newstruct13.sroa.0.0..sroa_idx = getelementptr inbounds [1 x [4 x double]], [1 x [4 x double]]* %0, i64 0, i64 0, i64 0
  %newstruct13.sroa.2.0..sroa_idx14 = getelementptr inbounds [1 x [4 x double]], [1 x [4 x double]]* %0, i64 0, i64 0, i64 1
  %newstruct13.sroa.3.0..sroa_idx15 = getelementptr inbounds [1 x [4 x double]], [1 x [4 x double]]* %0, i64 0, i64 0, i64 2
; ┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/ext/ForwardDiffStaticArraysExt.jl:66 within `jacobian`
; │┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/ext/ForwardDiffStaticArraysExt.jl:91 within `vector_mode_jacobian`
; ││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/ext/ForwardDiffStaticArraysExt.jl:24 within `static_dual_eval`
; │││┌ @ REPL[8]:2 within `J_flat`
; ││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/ext/ForwardDiffStaticArraysExt.jl:66 within `jacobian`
; │││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/ext/ForwardDiffStaticArraysExt.jl:91 within `vector_mode_jacobian`
; ││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/ext/ForwardDiffStaticArraysExt.jl:24 within `static_dual_eval`
; │││││││┌ @ REPL[2]:1 within `f`
; ││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:577 within `literal_pow` @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:577 @ intfuncs.jl:332
; │││││││││┌ @ float.jl:411 within `*`
            %5 = bitcast [1 x [2 x double]]* %1 to <2 x double>*
            %6 = load <2 x double>, <2 x double>* %5, align 8
; │││││││││└
; │││││││││ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:577 within `literal_pow` @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:578
; │││││││││┌ @ promotion.jl:423 within `*` @ float.jl:411
            %7 = insertelement <2 x double> %6, double 2.000000e+00, i64 0
            %8 = fmul <2 x double> %6, %7
; │││││││││└
; │││││││││ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:577 within `literal_pow` @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:579
; │││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:83 within `*` @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:110
; ││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:199 within `scale_tuple`
; │││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; ││││││││││││┌ @ float.jl:411 within `*`
               %9 = fmul <2 x double> %8, <double 0.000000e+00, double 3.000000e+00>
; │││││││││└└└└
; │││││││││ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:579 within `literal_pow`
; │││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:83 within `*` @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:110
; ││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:199 within `scale_tuple`
; │││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; ││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:286 within `*`
; │││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:218 within `dual_definition_retval`
; ││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:118 within `_mul_partials`
; │││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:219 within `mul_tuples`
; ││││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; │││││││││││││││││┌ @ float.jl:409 within `+`
                    %10 = extractelement <2 x double> %9, i64 0
                    %11 = fadd double %10, 2.000000e+00
                    %12 = fadd double %10, 0.000000e+00
; ││││││││└└└└└└└└└└
; ││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:286 within `*`
; │││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:218 within `dual_definition_retval`
; ││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:118 within `_mul_partials`
; │││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:219 within `mul_tuples`
; ││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; │││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:286 within `*`
; ││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:218 within `dual_definition_retval`
; │││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:118 within `_mul_partials`
; ││││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:219 within `mul_tuples`
; │││││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; ││││││││││││││││││┌ @ float.jl:411 within `*`
                     %13 = extractelement <2 x double> %6, i64 1
                     %14 = fmul double %13, %11
; ││││││││││││││││││└
; ││││││││││││││││││┌ @ float.jl:409 within `+`
                     %15 = fadd double %10, %14
; ││││││││└└└└└└└└└└└
; ││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:578 within `literal_pow` @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:578
; │││││││││┌ @ promotion.jl:423 within `*` @ float.jl:411
            %16 = fmul double %13, 2.000000e+00
; │││││││││└
; │││││││││ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:577 within `literal_pow` @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:577 @ intfuncs.jl:332
; │││││││││┌ @ float.jl:411 within `*`
            %17 = insertelement <2 x double> %6, double %16, i64 1
            %18 = insertelement <2 x double> %6, double 3.000000e+00, i64 1
            %19 = fmul <2 x double> %17, %18
; ││││││││└└
; ││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:286 within `*`
; │││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:218 within `dual_definition_retval`
; ││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:118 within `_mul_partials`
; │││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:219 within `mul_tuples`
; ││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; │││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:286 within `*`
; ││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:218 within `dual_definition_retval`
; │││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:118 within `_mul_partials`
; ││││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:219 within `mul_tuples`
; │││││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; ││││││││││││││││││┌ @ float.jl:411 within `*`
                     %20 = fmul <2 x double> %19, zeroinitializer
; ││││││││││││││││││└
; ││││││││││││││││││┌ @ float.jl:409 within `+`
                     %21 = fadd <2 x double> %9, %20
                     %22 = extractelement <2 x double> %21, i64 0
; │││││││││││││└└└└└└
; │││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:487 within `+` @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:80
; ││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:207 within `add_tuples`
; │││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; ││││││││││││││││┌ @ float.jl:409 within `+`
                   %23 = fadd double %22, %15
; ││││││││└└└└└└└└└
; ││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:693 within `sin`
; │││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:703 within `sincos`
            %24 = extractelement <2 x double> %6, i64 0
            call void @j_sincos_345([2 x double]* noalias nocapture noundef nonnull sret([2 x double]) %2, double %24)
; ││││││││││ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:704 within `sincos`
; ││││││││││┌ @ float.jl:407 within `-`
             %unbox7 = load double, double* %3, align 8
; ││││││││└└└
; ││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:286 within `*`
; │││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:218 within `dual_definition_retval`
; ││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:118 within `_mul_partials`
; │││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:219 within `mul_tuples`
; ││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; │││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:286 within `*`
; ││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:218 within `dual_definition_retval`
; │││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:118 within `_mul_partials`
; ││││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:219 within `mul_tuples`
; │││││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; ││││││││││││││││││┌ @ float.jl:411 within `*`
                     %25 = insertelement <2 x double> %6, double %unbox7, i64 0
                     %26 = insertelement <2 x double> <double 0.000000e+00, double poison>, double %12, i64 1
                     %27 = fmul <2 x double> %25, %26
; ││││││││└└└└└└└└└└└
; ││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:694 within `sin`
; │││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:83 within `*` @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:110
; ││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:199 within `scale_tuple`
; │││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; ││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:286 within `*`
; │││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:218 within `dual_definition_retval`
; ││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:118 within `_mul_partials`
; │││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:219 within `mul_tuples`
; ││││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; │││││││││││││││││┌ @ float.jl:411 within `*`
                    %unbox8 = load double, double* %4, align 8
                    %28 = fmul double %unbox8, 0.000000e+00
; │││││││││││││││││└
; │││││││││││││││││┌ @ float.jl:409 within `+`
                    %29 = fsub double %28, %unbox7
; ││││││││└└└└└└└└└└
; ││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:286 within `*`
; │││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:218 within `dual_definition_retval`
; ││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:118 within `_mul_partials`
; │││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:219 within `mul_tuples`
; ││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; │││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:286 within `*`
; ││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:218 within `dual_definition_retval`
; │││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:118 within `_mul_partials`
; ││││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:219 within `mul_tuples`
; │││││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; ││││││││││││││││││┌ @ float.jl:409 within `+`
                     %30 = insertelement <2 x double> poison, double %28, i64 0
                     %31 = shufflevector <2 x double> %30, <2 x double> %8, <2 x i32> <i32 0, i32 2>
                     %32 = fadd <2 x double> %31, %27
                     %33 = fsub <2 x double> %31, %27
                     %34 = shufflevector <2 x double> %32, <2 x double> %33, <2 x i32> <i32 1, i32 2>
; ││││││││└└└└└└└└└└└
; ││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:578 within `literal_pow` @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:579
; │││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:83 within `*` @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:110
; ││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:199 within `scale_tuple`
; │││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; ││││││││││││┌ @ float.jl:411 within `*`
               %35 = fmul double %16, 0.000000e+00
; │││││││││└└└└
; │││││││││ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:578 within `literal_pow`
; │││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:296 within `*`
; ││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:215 within `dual_definition_retval`
; │││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:83 within `*` @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:110
; ││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:199 within `scale_tuple`
; │││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; ││││││││││││││┌ @ promotion.jl:423 within `*` @ float.jl:411
                 %36 = fmul double %35, 3.000000e+00
; ││││││││└└└└└└└
; ││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:286 within `*`
; │││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:218 within `dual_definition_retval`
; ││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:118 within `_mul_partials`
; │││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:219 within `mul_tuples`
; ││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; │││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:286 within `*`
; ││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:218 within `dual_definition_retval`
; │││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:118 within `_mul_partials`
; ││││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:219 within `mul_tuples`
; │││││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; ││││││││││││││││││┌ @ float.jl:411 within `*`
                     %37 = fmul <2 x double> %9, zeroinitializer
; ││││││││└└└└└└└└└└└
; ││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:579 within `literal_pow`
; │││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:83 within `*` @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:110
; ││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:199 within `scale_tuple`
; │││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; ││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:286 within `*`
; │││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:218 within `dual_definition_retval`
; ││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:118 within `_mul_partials`
; │││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:219 within `mul_tuples`
; ││││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; │││││││││││││││││┌ @ float.jl:411 within `*`
                    %38 = fmul double %36, 0.000000e+00
; │││││││││││││││││└
; │││││││││││││││││┌ @ float.jl:409 within `+`
                    %39 = extractelement <2 x double> %37, i64 1
                    %40 = fadd double %39, %38
; ││││││││└└└└└└└└└└
; ││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:286 within `*`
; │││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:218 within `dual_definition_retval`
; ││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:118 within `_mul_partials`
; │││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:219 within `mul_tuples`
; ││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; │││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:286 within `*`
; ││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:218 within `dual_definition_retval`
; │││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:118 within `_mul_partials`
; ││││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:219 within `mul_tuples`
; │││││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; ││││││││││││││││││┌ @ float.jl:409 within `+`
                     %41 = fadd <2 x double> %37, %20
; ││││││││└└└└└└└└└└└
; ││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:487 within `+` @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:80
; │││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:207 within `add_tuples`
; ││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; │││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:487 within `+` @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:80
; ││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:207 within `add_tuples`
; │││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; ││││││││││││││┌ @ float.jl:409 within `+`
                 %42 = fadd double %29, %40
; ││││││││└└└└└└└
; ││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:286 within `*`
; │││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:218 within `dual_definition_retval`
; ││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:118 within `_mul_partials`
; │││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:219 within `mul_tuples`
; ││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; │││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/dual.jl:487 within `+` @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:80
; ││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:207 within `add_tuples`
; │││││││││││││││┌ @ /home/tremelow/.julia/packages/ForwardDiff/X74OO/src/partials.jl:156 within `macro expansion`
; ││││││││││││││││┌ @ float.jl:409 within `+`
                   %43 = fadd <2 x double> %41, %34
; └└└└└└└└└└└└└└└└└
  store double %23, double* %newstruct13.sroa.0.0..sroa_idx, align 8
  store double %42, double* %newstruct13.sroa.2.0..sroa_idx14, align 8
  %44 = bitcast double* %newstruct13.sroa.3.0..sroa_idx15 to <2 x double>*
  store <2 x double> %43, <2 x double>* %44, align 8
  ret void
}

```

---

<div class="post-metadata">

**Author:** ![tremelow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tremelow/32/221943_2.png) [@tremelow](https://discourse.julialang.org/u/tremelow)\
**Post date:** [May 19, 2026, 10:58am UTC](https://discourse.julialang.org/t/allocations-with-nested-jacobians-with-staticarrays-and-forwarddiff/136789/5 "2026-05-19T10:58:57Z")

</div>

Here is my example for Lie brackets

```julia
using ForwardDiff, StaticArrays, BenchmarkTools

f(x::SVector{2,T}) where T = SVector{2,T}(x[1] * exp(x[2]), -exp(x[1]))
g(x::SVector{2,T}) where T = SVector{2,T}(exp(0.9 * x[2]), -1.2 * exp(x[1]))
x0 = @SVector [0.2, 0.5]

function fg(x::SVector{2,T}) where T
    fx, jacfx = f(x), ForwardDiff.jacobian(f, x)
    gx, jacgx = g(x), ForwardDiff.jacobian(g, x)
    return SVector{2,T}(jacgx * fx - jacfx * gx)
end

function jacfg(x::SVector{2,T}) where T
    valx = fg(x)
    jacx = ForwardDiff.jacobian(fg, x)
    return valx, jacx
end

@btime jacfg($x0) # 229.431 ns (6 allocations: 272 bytes)

function fg(x::SVector{2,T}) where T
    fx, jacfx = f(x), ForwardDiff.jacobian(f, x)
    gx, jacgx = g(x), ForwardDiff.jacobian(g, x)
    return SVector{2,T}(jacgx * fx - jacfx * gx)
end

@btime jacfg($x0) # 58.745 ns (0 allocations: 0 bytes)

```

To avoid redefining `fg`, I found an ugly _ad-hoc_ fix by adding the following lines before calling `jacfg`:

```julia
xtmp = @SVector ForwardDiff.Dual{ForwardDiff.Tag{typeof(fg), Float64}, Float64, 2}[ForwardDiff.Dual{ForwardDiff.Tag{typeof(fg), Float64}}(0.2,1.0,0.0), ForwardDiff.Dual{ForwardDiff.Tag{typeof(fg), Float64}}(0.5,0.0,1.0)]
ForwardDiff.jacobian(f, xtmp)
ForwardDiff.jacobian(g, xtmp)

```

but I wouldn’t know how to generalize this for deeper nesting…

---

<div class="post-metadata">

**Author:** ![tduretz](https://avatars.discourse-cdn.com/v4/letter/t/bcef8e/32.png) [@tduretz](https://discourse.julialang.org/u/tduretz)\
**Post date:** [May 23, 2026, 6:12am UTC](https://discourse.julialang.org/t/allocations-with-nested-jacobians-with-staticarrays-and-forwarddiff/136789/6 "2026-05-23T06:12:00Z")

</div>

For me, this MWE shows allocations: `44.746 ns (2 allocs: 96 bytes)`

> **Summary**
>
> ```julia
> using ForwardDiff, StaticArrays, Chairmarks
> 
> @inline f(x::SVector{N, T}) where {N, T} = SVector{N, T}(x[1]^2 * x[2], sin(x[1]) + x[2]^3)
> 
> @inline function J_flat(x::SVector{2,T}) where T
> y = ForwardDiff.jacobian(f, x)
> SVector{2,T}(y[1], y[2])
> end
> 
> function nested_jacobian(x0)
> return ForwardDiff.jacobian(J_flat, x0)
> end
> 
> x0 = SVector(1.0, 2.0)
> 
> @b nested_jacobian($x0) 
> 
> ```

---

<div class="post-metadata">

**Author:** ![tremelow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tremelow/32/221943_2.png) [@tremelow](https://discourse.julialang.org/u/tremelow)\
**Post date:** [May 23, 2026, 7:49am UTC](https://discourse.julialang.org/t/allocations-with-nested-jacobians-with-staticarrays-and-forwarddiff/136789/7 "2026-05-23T07:49:22Z")

</div>

Same here, that’s odd. It seems that specifying the signature of `f` has this impact, since the only difference is `f(x::SVector{N,T})` instead of `f(x)`. What’s weird as well is that `@code_warntype` raises no flags.

After checking, `f(x::SVector)` does not allocate either, and `{N,T}` can be removed from `J_flat` as well. But this does not work in the Lie bracket example.

---

<div class="post-metadata">

**Author:** ![Albert\_de\_montserrat](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/albert_de_montserrat/32/9135_2.png) [@Albert\_de\_montserrat](https://discourse.julialang.org/u/Albert_de_montserrat)\
**Post date:** [June 10, 2026, 1:35pm UTC](https://discourse.julialang.org/t/allocations-with-nested-jacobians-with-staticarrays-and-forwarddiff/136789/8 "2026-06-10T13:35:47Z")

</div>

I managed to fix this issue for most of our cases of interest with [this PR](https://github.com/JuliaDiff/ForwardDiff.jl/pull/810#pullrequestreview-4467448288).

@tremelow it would be interesting to see if it also helps your cases.

---

<div class="post-metadata">

**Author:** ![tremelow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tremelow/32/221943_2.png) [@tremelow](https://discourse.julialang.org/u/tremelow)\
**Post date:** [June 12, 2026, 10:27am UTC](https://discourse.julialang.org/t/allocations-with-nested-jacobians-with-staticarrays-and-forwarddiff/136789/9 "2026-06-12T10:27:27Z")

</div>

After updating ForwardDiff, I just tried it on the Lie bracket example, and it worked! Great work, thanks