void adjoint33(double madj[3][3], double m[3][3]) {
  double m00, m01, m02, m10, m11, m12, m20, m21, m22;
  m00 = m[0][0];
  m01 = m[0][1];
  m02 = m[0][2];
  m10 = m[1][0];
  m11 = m[1][1];
  m12 = m[1][2];
  m20 = m[2][0];
  m21 = m[2][1];
  m22 = m[2][2];
  madj[0][0] = m11 * m22 - m12 * m21;
  madj[0][1] = m02 * m21 - m01 * m22;
  madj[0][2] = m01 * m12 - m02 * m11;
  madj[1][0] = m12 * m20 - m10 * m22;
  madj[1][1] = m00 * m22 - m02 * m20;
  madj[1][2] = m02 * m10 - m00 * m12;
  madj[2][0] = m10 * m21 - m11 * m20;
  madj[2][1] = m01 * m20 - m00 * m21;
  madj[2][2] = m00 * m11 - m01 * m10;
}


x86 assembly (clang, -O0):
<adjoint33>:
push   %rbp
mov    %rsp,%rbp
mov    %rdi,-0x8(%rbp)
mov    %rsi,-0x10(%rbp)
mov    -0x10(%rbp),%rax
movsd  (%rax),%xmm0
movsd  %xmm0,-0x18(%rbp)
mov    -0x10(%rbp),%rax
movsd  0x8(%rax),%xmm0
movsd  %xmm0,-0x20(%rbp)
mov    -0x10(%rbp),%rax
movsd  0x10(%rax),%xmm0
movsd  %xmm0,-0x28(%rbp)
mov    -0x10(%rbp),%rax
movsd  0x18(%rax),%xmm0
movsd  %xmm0,-0x30(%rbp)
mov    -0x10(%rbp),%rax
movsd  0x20(%rax),%xmm0
movsd  %xmm0,-0x38(%rbp)
mov    -0x10(%rbp),%rax
movsd  0x28(%rax),%xmm0
movsd  %xmm0,-0x40(%rbp)
mov    -0x10(%rbp),%rax
movsd  0x30(%rax),%xmm0
movsd  %xmm0,-0x48(%rbp)
mov    -0x10(%rbp),%rax
movsd  0x38(%rax),%xmm0
movsd  %xmm0,-0x50(%rbp)
mov    -0x10(%rbp),%rax
movsd  0x40(%rax),%xmm0
movsd  %xmm0,-0x58(%rbp)
movsd  -0x38(%rbp),%xmm0
movsd  -0x58(%rbp),%xmm2
movsd  -0x40(%rbp),%xmm1
mulsd  -0x50(%rbp),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
mov    -0x8(%rbp),%rax
movsd  %xmm0,(%rax)
movsd  -0x28(%rbp),%xmm0
movsd  -0x50(%rbp),%xmm2
movsd  -0x20(%rbp),%xmm1
mulsd  -0x58(%rbp),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
mov    -0x8(%rbp),%rax
movsd  %xmm0,0x8(%rax)
movsd  -0x20(%rbp),%xmm0
movsd  -0x40(%rbp),%xmm2
movsd  -0x28(%rbp),%xmm1
mulsd  -0x38(%rbp),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
mov    -0x8(%rbp),%rax
movsd  %xmm0,0x10(%rax)
movsd  -0x40(%rbp),%xmm0
movsd  -0x48(%rbp),%xmm2
movsd  -0x30(%rbp),%xmm1
mulsd  -0x58(%rbp),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
mov    -0x8(%rbp),%rax
movsd  %xmm0,0x18(%rax)
movsd  -0x18(%rbp),%xmm0
movsd  -0x58(%rbp),%xmm2
movsd  -0x28(%rbp),%xmm1
mulsd  -0x48(%rbp),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
mov    -0x8(%rbp),%rax
movsd  %xmm0,0x20(%rax)
movsd  -0x28(%rbp),%xmm0
movsd  -0x30(%rbp),%xmm2
movsd  -0x18(%rbp),%xmm1
mulsd  -0x40(%rbp),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
mov    -0x8(%rbp),%rax
movsd  %xmm0,0x28(%rax)
movsd  -0x30(%rbp),%xmm0
movsd  -0x50(%rbp),%xmm2
movsd  -0x38(%rbp),%xmm1
mulsd  -0x48(%rbp),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
mov    -0x8(%rbp),%rax
movsd  %xmm0,0x30(%rax)
movsd  -0x20(%rbp),%xmm0
movsd  -0x48(%rbp),%xmm2
movsd  -0x18(%rbp),%xmm1
mulsd  -0x50(%rbp),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
mov    -0x8(%rbp),%rax
movsd  %xmm0,0x38(%rax)
movsd  -0x18(%rbp),%xmm0
movsd  -0x38(%rbp),%xmm2
movsd  -0x20(%rbp),%xmm1
mulsd  -0x30(%rbp),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
mov    -0x8(%rbp),%rax
movsd  %xmm0,0x40(%rax)
pop    %rbp
ret

x86 assembly (clang, -O2):
<adjoint33>:
movsd  (%rsi),%xmm0
movupd 0x10(%rsi),%xmm6
movsd  0x20(%rsi),%xmm10
movupd 0x28(%rsi),%xmm1
movupd 0x38(%rsi),%xmm13
movsd  0x8(%rsi),%xmm9
movapd %xmm1,%xmm2
unpcklpd %xmm9,%xmm2
movapd 0xecf(%rip),%xmm4
movapd %xmm13,%xmm8
mulpd  %xmm2,%xmm8
xorpd  %xmm4,%xmm2
movapd %xmm13,%xmm3
movsd  %xmm10,%xmm3
movapd %xmm10,%xmm12
unpcklpd %xmm0,%xmm12
movapd %xmm6,%xmm11
unpcklpd %xmm0,%xmm11
mulsd  %xmm10,%xmm0
unpcklpd %xmm6,%xmm10
mulpd  %xmm6,%xmm3
movapd %xmm6,%xmm5
movapd %xmm6,%xmm7
mulpd  %xmm6,%xmm2
xorpd  %xmm4,%xmm6
shufpd $0x1,%xmm9,%xmm7
unpcklpd %xmm1,%xmm9
mulpd  %xmm1,%xmm9
xorpd  %xmm12,%xmm4
shufpd $0x1,%xmm6,%xmm4
mulpd  %xmm1,%xmm4
unpckhpd %xmm13,%xmm5
movapd %xmm1,%xmm6
shufpd $0x1,%xmm13,%xmm6
movsd  %xmm13,%xmm1
shufpd $0x1,%xmm13,%xmm13
mulpd  %xmm13,%xmm10
subpd  %xmm8,%xmm10
movupd %xmm10,(%rdi)
subpd  %xmm3,%xmm9
movupd %xmm9,0x10(%rdi)
mulpd  %xmm11,%xmm5
addpd  %xmm4,%xmm5
shufpd $0x1,%xmm5,%xmm5
movupd %xmm5,0x20(%rdi)
mulpd  %xmm12,%xmm6
mulpd  %xmm7,%xmm1
subpd  %xmm6,%xmm1
movupd %xmm1,0x30(%rdi)
unpckhpd %xmm2,%xmm2
addsd  %xmm2,%xmm0
movsd  %xmm0,0x40(%rdi)
ret

LLVM IR (-O0):
define void @adjoint33([3 x double]* %0, [3 x double]* %1) {
%3 = alloca [3 x double]*
%4 = alloca [3 x double]*
%5 = alloca double
%6 = alloca double
%7 = alloca double
%8 = alloca double
%9 = alloca double
%10 = alloca double
%11 = alloca double
%12 = alloca double
%13 = alloca double
store [3 x double]* %0, [3 x double]** %3
store [3 x double]* %1, [3 x double]** %4
%14 = load [3 x double]*, [3 x double]** %4
%15 = getelementptr inbounds [3 x double], [3 x double]* %14, i64 0
%16 = getelementptr inbounds [3 x double], [3 x double]* %15, i64 0, i64 0
%17 = load double, double* %16
store double %17, double* %5
%18 = load [3 x double]*, [3 x double]** %4
%19 = getelementptr inbounds [3 x double], [3 x double]* %18, i64 0
%20 = getelementptr inbounds [3 x double], [3 x double]* %19, i64 0, i64 1
%21 = load double, double* %20
store double %21, double* %6
%22 = load [3 x double]*, [3 x double]** %4
%23 = getelementptr inbounds [3 x double], [3 x double]* %22, i64 0
%24 = getelementptr inbounds [3 x double], [3 x double]* %23, i64 0, i64 2
%25 = load double, double* %24
store double %25, double* %7
%26 = load [3 x double]*, [3 x double]** %4
%27 = getelementptr inbounds [3 x double], [3 x double]* %26, i64 1
%28 = getelementptr inbounds [3 x double], [3 x double]* %27, i64 0, i64 0
%29 = load double, double* %28
store double %29, double* %8
%30 = load [3 x double]*, [3 x double]** %4
%31 = getelementptr inbounds [3 x double], [3 x double]* %30, i64 1
%32 = getelementptr inbounds [3 x double], [3 x double]* %31, i64 0, i64 1
%33 = load double, double* %32
store double %33, double* %9
%34 = load [3 x double]*, [3 x double]** %4
%35 = getelementptr inbounds [3 x double], [3 x double]* %34, i64 1
%36 = getelementptr inbounds [3 x double], [3 x double]* %35, i64 0, i64 2
%37 = load double, double* %36
store double %37, double* %10
%38 = load [3 x double]*, [3 x double]** %4
%39 = getelementptr inbounds [3 x double], [3 x double]* %38, i64 2
%40 = getelementptr inbounds [3 x double], [3 x double]* %39, i64 0, i64 0
%41 = load double, double* %40
store double %41, double* %11
%42 = load [3 x double]*, [3 x double]** %4
%43 = getelementptr inbounds [3 x double], [3 x double]* %42, i64 2
%44 = getelementptr inbounds [3 x double], [3 x double]* %43, i64 0, i64 1
%45 = load double, double* %44
store double %45, double* %12
%46 = load [3 x double]*, [3 x double]** %4
%47 = getelementptr inbounds [3 x double], [3 x double]* %46, i64 2
%48 = getelementptr inbounds [3 x double], [3 x double]* %47, i64 0, i64 2
%49 = load double, double* %48
store double %49, double* %13
%50 = load double, double* %9
%51 = load double, double* %13
%52 = load double, double* %10
%53 = load double, double* %12
%54 = fmul double %52, %53
%55 = fneg double %54
%56 = call double @llvm.fmuladd.f64(double %50, double %51, double %55)
%57 = load [3 x double]*, [3 x double]** %3
%58 = getelementptr inbounds [3 x double], [3 x double]* %57, i64 0
%59 = getelementptr inbounds [3 x double], [3 x double]* %58, i64 0, i64 0
store double %56, double* %59
%60 = load double, double* %7
%61 = load double, double* %12
%62 = load double, double* %6
%63 = load double, double* %13
%64 = fmul double %62, %63
%65 = fneg double %64
%66 = call double @llvm.fmuladd.f64(double %60, double %61, double %65)
%67 = load [3 x double]*, [3 x double]** %3
%68 = getelementptr inbounds [3 x double], [3 x double]* %67, i64 0
%69 = getelementptr inbounds [3 x double], [3 x double]* %68, i64 0, i64 1
store double %66, double* %69
%70 = load double, double* %6
%71 = load double, double* %10
%72 = load double, double* %7
%73 = load double, double* %9
%74 = fmul double %72, %73
%75 = fneg double %74
%76 = call double @llvm.fmuladd.f64(double %70, double %71, double %75)
%77 = load [3 x double]*, [3 x double]** %3
%78 = getelementptr inbounds [3 x double], [3 x double]* %77, i64 0
%79 = getelementptr inbounds [3 x double], [3 x double]* %78, i64 0, i64 2
store double %76, double* %79
%80 = load double, double* %10
%81 = load double, double* %11
%82 = load double, double* %8
%83 = load double, double* %13
%84 = fmul double %82, %83
%85 = fneg double %84
%86 = call double @llvm.fmuladd.f64(double %80, double %81, double %85)
%87 = load [3 x double]*, [3 x double]** %3
%88 = getelementptr inbounds [3 x double], [3 x double]* %87, i64 1
%89 = getelementptr inbounds [3 x double], [3 x double]* %88, i64 0, i64 0
store double %86, double* %89
%90 = load double, double* %5
%91 = load double, double* %13
%92 = load double, double* %7
%93 = load double, double* %11
%94 = fmul double %92, %93
%95 = fneg double %94
%96 = call double @llvm.fmuladd.f64(double %90, double %91, double %95)
%97 = load [3 x double]*, [3 x double]** %3
%98 = getelementptr inbounds [3 x double], [3 x double]* %97, i64 1
%99 = getelementptr inbounds [3 x double], [3 x double]* %98, i64 0, i64 1
store double %96, double* %99
%100 = load double, double* %7
%101 = load double, double* %8
%102 = load double, double* %5
%103 = load double, double* %10
%104 = fmul double %102, %103
%105 = fneg double %104
%106 = call double @llvm.fmuladd.f64(double %100, double %101, double %105)
%107 = load [3 x double]*, [3 x double]** %3
%108 = getelementptr inbounds [3 x double], [3 x double]* %107, i64 1
%109 = getelementptr inbounds [3 x double], [3 x double]* %108, i64 0, i64 2
store double %106, double* %109
%110 = load double, double* %8
%111 = load double, double* %12
%112 = load double, double* %9
%113 = load double, double* %11
%114 = fmul double %112, %113
%115 = fneg double %114
%116 = call double @llvm.fmuladd.f64(double %110, double %111, double %115)
%117 = load [3 x double]*, [3 x double]** %3
%118 = getelementptr inbounds [3 x double], [3 x double]* %117, i64 2
%119 = getelementptr inbounds [3 x double], [3 x double]* %118, i64 0, i64 0
store double %116, double* %119
%120 = load double, double* %6
%121 = load double, double* %11
%122 = load double, double* %5
%123 = load double, double* %12
%124 = fmul double %122, %123
%125 = fneg double %124
%126 = call double @llvm.fmuladd.f64(double %120, double %121, double %125)
%127 = load [3 x double]*, [3 x double]** %3
%128 = getelementptr inbounds [3 x double], [3 x double]* %127, i64 2
%129 = getelementptr inbounds [3 x double], [3 x double]* %128, i64 0, i64 1
store double %126, double* %129
%130 = load double, double* %5
%131 = load double, double* %9
%132 = load double, double* %6
%133 = load double, double* %8
%134 = fmul double %132, %133
%135 = fneg double %134
%136 = call double @llvm.fmuladd.f64(double %130, double %131, double %135)
%137 = load [3 x double]*, [3 x double]** %3
%138 = getelementptr inbounds [3 x double], [3 x double]* %137, i64 2
%139 = getelementptr inbounds [3 x double], [3 x double]* %138, i64 0, i64 2
store double %136, double* %139
ret void
}

LLVM IR (-O2):
define void @adjoint33([3 x double]* nocapture writeonly %0, [3 x double]* nocapture %1) {
%3 = getelementptr inbounds [3 x double], [3 x double]* %1, i64 0, i64 0
%4 = load double, double* %3
%5 = getelementptr inbounds [3 x double], [3 x double]* %1, i64 0, i64 1
%6 = load double, double* %5
%7 = getelementptr inbounds [3 x double], [3 x double]* %1, i64 0, i64 2
%8 = bitcast double* %7 to <2 x double>*
%9 = load <2 x double>, <2 x double>* %8
%10 = getelementptr inbounds [3 x double], [3 x double]* %1, i64 1, i64 1
%11 = load double, double* %10
%12 = getelementptr inbounds [3 x double], [3 x double]* %1, i64 1, i64 2
%13 = bitcast double* %12 to <2 x double>*
%14 = load <2 x double>, <2 x double>* %13
%15 = getelementptr inbounds [3 x double], [3 x double]* %1, i64 2, i64 1
%16 = bitcast double* %15 to <2 x double>*
%17 = load <2 x double>, <2 x double>* %16
%18 = shufflevector <2 x double> %17, <2 x double> poison, <2 x i32> <i32 1, i32 0>
%19 = insertelement <2 x double> %14, double %6, i64 1
%20 = fneg <2 x double> %19
%21 = fmul <2 x double> %17, %20
%22 = insertelement <2 x double> poison, double %11, i64 0
%23 = shufflevector <2 x double> %22, <2 x double> %9, <2 x i32> <i32 0, i32 2>
%24 = call <2 x double> @llvm.fmuladd.v2f64(<2 x double> %23, <2 x double> %18, <2 x double> %21)
%25 = bitcast [3 x double]* %0 to <2 x double>*
store <2 x double> %24, <2 x double>* %25
%26 = getelementptr inbounds [3 x double], [3 x double]* %0, i64 0, i64 2
%27 = fneg <2 x double> %9
%28 = insertelement <2 x double> %17, double %11, i64 0
%29 = fmul <2 x double> %28, %27
%30 = insertelement <2 x double> poison, double %6, i64 0
%31 = shufflevector <2 x double> %30, <2 x double> %14, <2 x i32> <i32 0, i32 2>
%32 = call <2 x double> @llvm.fmuladd.v2f64(<2 x double> %31, <2 x double> %14, <2 x double> %29)
%33 = bitcast double* %26 to <2 x double>*
store <2 x double> %32, <2 x double>* %33
%34 = getelementptr inbounds [3 x double], [3 x double]* %0, i64 1, i64 1
%35 = insertelement <2 x double> %22, double %4, i64 1
%36 = fneg <2 x double> %35
%37 = shufflevector <2 x double> %36, <2 x double> %27, <2 x i32> <i32 1, i32 2>
%38 = fmul <2 x double> %14, %37
%39 = insertelement <2 x double> %9, double %4, i64 1
%40 = shufflevector <2 x double> %9, <2 x double> undef, <2 x i32> <i32 1, i32 undef>
%41 = shufflevector <2 x double> %40, <2 x double> %17, <2 x i32> <i32 0, i32 3>
%42 = call <2 x double> @llvm.fmuladd.v2f64(<2 x double> %39, <2 x double> %41, <2 x double> %38)
%43 = shufflevector <2 x double> %42, <2 x double> poison, <2 x i32> <i32 1, i32 0>
%44 = bitcast double* %34 to <2 x double>*
store <2 x double> %43, <2 x double>* %44
%45 = getelementptr inbounds [3 x double], [3 x double]* %0, i64 2, i64 0
%46 = shufflevector <2 x double> %14, <2 x double> %17, <2 x i32> <i32 1, i32 2>
%47 = fmul <2 x double> %46, %36
%48 = insertelement <2 x double> %40, double %6, i64 1
%49 = shufflevector <2 x double> %17, <2 x double> %14, <2 x i32> <i32 0, i32 3>
%50 = call <2 x double> @llvm.fmuladd.v2f64(<2 x double> %48, <2 x double> %49, <2 x double> %47)
%51 = bitcast double* %45 to <2 x double>*
store <2 x double> %50, <2 x double>* %51
%52 = fmul <2 x double> %9, %20
%53 = extractelement <2 x double> %52, i64 1
%54 = tail call double @llvm.fmuladd.f64(double %4, double %11, double %53)
%55 = getelementptr inbounds [3 x double], [3 x double]* %0, i64 2, i64 2
store double %54, double* %55
ret void
}