void mat33_lower_tri_inv(const double *A, double *R) {
  R[0] = 1 / A[0];
  R[3] = -A[3] * R[0] / A[4];
  R[4] = 1 / A[4];
  R[6] = (-A[6] * R[0] - A[7] * R[3]) / A[8];
  R[7] = -A[7] * R[4] / A[8];
  R[8] = 1 / A[8];
}


x86 assembly (clang, -O0):
<mat33_lower_tri_inv>:
push   %rbp
mov    %rsp,%rbp
mov    %rdi,-0x8(%rbp)
mov    %rsi,-0x10(%rbp)
mov    -0x8(%rbp),%rax
movsd  0xee8(%rip),%xmm0
divsd  (%rax),%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,(%rax)
mov    -0x8(%rbp),%rax
movsd  0x18(%rax),%xmm0
movq   %xmm0,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm0
mov    -0x10(%rbp),%rax
mulsd  (%rax),%xmm0
mov    -0x8(%rbp),%rax
divsd  0x20(%rax),%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,0x18(%rax)
mov    -0x8(%rbp),%rax
movsd  0xe96(%rip),%xmm0
divsd  0x20(%rax),%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,0x20(%rax)
mov    -0x8(%rbp),%rax
movsd  0x30(%rax),%xmm0
movq   %xmm0,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm0
mov    -0x10(%rbp),%rax
movsd  (%rax),%xmm2
mov    -0x8(%rbp),%rax
movsd  0x38(%rax),%xmm1
mov    -0x10(%rbp),%rax
mulsd  0x18(%rax),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
mov    -0x8(%rbp),%rax
divsd  0x40(%rax),%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,0x30(%rax)
mov    -0x8(%rbp),%rax
movsd  0x38(%rax),%xmm0
movq   %xmm0,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm0
mov    -0x10(%rbp),%rax
mulsd  0x20(%rax),%xmm0
mov    -0x8(%rbp),%rax
divsd  0x40(%rax),%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,0x38(%rax)
mov    -0x8(%rbp),%rax
movsd  0xdd6(%rip),%xmm0
divsd  0x40(%rax),%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,0x40(%rax)
pop    %rbp
ret

x86 assembly (clang, -O2):
<mat33_lower_tri_inv>:
movsd  0xef8(%rip),%xmm0
movapd %xmm0,%xmm1
divsd  (%rdi),%xmm1
movsd  %xmm1,(%rsi)
movsd  0x18(%rdi),%xmm2
movapd 0xeef(%rip),%xmm3
xorpd  %xmm3,%xmm2
mulsd  %xmm1,%xmm2
divsd  0x20(%rdi),%xmm2
movsd  %xmm2,0x18(%rsi)
movapd %xmm0,%xmm4
divsd  0x20(%rdi),%xmm4
movsd  %xmm4,0x20(%rsi)
movsd  0x30(%rdi),%xmm5
xorpd  %xmm3,%xmm5
mulsd  0x38(%rdi),%xmm2
mulsd  %xmm1,%xmm5
subsd  %xmm2,%xmm5
divsd  0x40(%rdi),%xmm5
movsd  %xmm5,0x30(%rsi)
movsd  0x38(%rdi),%xmm1
xorpd  %xmm3,%xmm1
mulsd  %xmm4,%xmm1
divsd  0x40(%rdi),%xmm1
movsd  %xmm1,0x38(%rsi)
divsd  0x40(%rdi),%xmm0
movsd  %xmm0,0x40(%rsi)
ret

LLVM IR (-O0):
define void @mat33_lower_tri_inv(double* %0, double* %1) {
%3 = alloca double*
%4 = alloca double*
store double* %0, double** %3
store double* %1, double** %4
%5 = load double*, double** %3
%6 = getelementptr inbounds double, double* %5, i64 0
%7 = load double, double* %6
%8 = fdiv double 1.000000e+00, %7
%9 = load double*, double** %4
%10 = getelementptr inbounds double, double* %9, i64 0
store double %8, double* %10
%11 = load double*, double** %3
%12 = getelementptr inbounds double, double* %11, i64 3
%13 = load double, double* %12
%14 = fneg double %13
%15 = load double*, double** %4
%16 = getelementptr inbounds double, double* %15, i64 0
%17 = load double, double* %16
%18 = fmul double %14, %17
%19 = load double*, double** %3
%20 = getelementptr inbounds double, double* %19, i64 4
%21 = load double, double* %20
%22 = fdiv double %18, %21
%23 = load double*, double** %4
%24 = getelementptr inbounds double, double* %23, i64 3
store double %22, double* %24
%25 = load double*, double** %3
%26 = getelementptr inbounds double, double* %25, i64 4
%27 = load double, double* %26
%28 = fdiv double 1.000000e+00, %27
%29 = load double*, double** %4
%30 = getelementptr inbounds double, double* %29, i64 4
store double %28, double* %30
%31 = load double*, double** %3
%32 = getelementptr inbounds double, double* %31, i64 6
%33 = load double, double* %32
%34 = fneg double %33
%35 = load double*, double** %4
%36 = getelementptr inbounds double, double* %35, i64 0
%37 = load double, double* %36
%38 = load double*, double** %3
%39 = getelementptr inbounds double, double* %38, i64 7
%40 = load double, double* %39
%41 = load double*, double** %4
%42 = getelementptr inbounds double, double* %41, i64 3
%43 = load double, double* %42
%44 = fmul double %40, %43
%45 = fneg double %44
%46 = call double @llvm.fmuladd.f64(double %34, double %37, double %45)
%47 = load double*, double** %3
%48 = getelementptr inbounds double, double* %47, i64 8
%49 = load double, double* %48
%50 = fdiv double %46, %49
%51 = load double*, double** %4
%52 = getelementptr inbounds double, double* %51, i64 6
store double %50, double* %52
%53 = load double*, double** %3
%54 = getelementptr inbounds double, double* %53, i64 7
%55 = load double, double* %54
%56 = fneg double %55
%57 = load double*, double** %4
%58 = getelementptr inbounds double, double* %57, i64 4
%59 = load double, double* %58
%60 = fmul double %56, %59
%61 = load double*, double** %3
%62 = getelementptr inbounds double, double* %61, i64 8
%63 = load double, double* %62
%64 = fdiv double %60, %63
%65 = load double*, double** %4
%66 = getelementptr inbounds double, double* %65, i64 7
store double %64, double* %66
%67 = load double*, double** %3
%68 = getelementptr inbounds double, double* %67, i64 8
%69 = load double, double* %68
%70 = fdiv double 1.000000e+00, %69
%71 = load double*, double** %4
%72 = getelementptr inbounds double, double* %71, i64 8
store double %70, double* %72
ret void
}

LLVM IR (-O2):
define void @mat33_lower_tri_inv(double* nocapture %0, double* nocapture %1) {
%3 = load double, double* %0
%4 = fdiv double 1.000000e+00, %3
store double %4, double* %1
%5 = getelementptr inbounds double, double* %0, i64 3
%6 = load double, double* %5
%7 = fneg double %6
%8 = fmul double %4, %7
%9 = getelementptr inbounds double, double* %0, i64 4
%10 = load double, double* %9
%11 = fdiv double %8, %10
%12 = getelementptr inbounds double, double* %1, i64 3
store double %11, double* %12
%13 = load double, double* %9
%14 = fdiv double 1.000000e+00, %13
%15 = getelementptr inbounds double, double* %1, i64 4
store double %14, double* %15
%16 = getelementptr inbounds double, double* %0, i64 6
%17 = load double, double* %16
%18 = fneg double %17
%19 = getelementptr inbounds double, double* %0, i64 7
%20 = load double, double* %19
%21 = fneg double %20
%22 = fmul double %11, %21
%23 = tail call double @llvm.fmuladd.f64(double %18, double %4, double %22)
%24 = getelementptr inbounds double, double* %0, i64 8
%25 = load double, double* %24
%26 = fdiv double %23, %25
%27 = getelementptr inbounds double, double* %1, i64 6
store double %26, double* %27
%28 = load double, double* %19
%29 = fneg double %28
%30 = fmul double %14, %29
%31 = load double, double* %24
%32 = fdiv double %30, %31
%33 = getelementptr inbounds double, double* %1, i64 7
store double %32, double* %33
%34 = load double, double* %24
%35 = fdiv double 1.000000e+00, %34
%36 = getelementptr inbounds double, double* %1, i64 8
store double %35, double* %36
ret void
}