void vec3d_rot(double n[3], const double a[3], const double b[3]) {
  n[0] = a[1] * b[2] - a[2] * b[1];
  n[1] = a[2] * b[0] - a[0] * b[2];
  n[2] = a[0] * b[1] - a[1] * b[0];
}


x86 assembly (clang, -O0):
<vec3d_rot>:
push   %rbp
mov    %rsp,%rbp
mov    %rdi,-0x8(%rbp)
mov    %rsi,-0x10(%rbp)
mov    %rdx,-0x18(%rbp)
mov    -0x10(%rbp),%rax
movsd  0x8(%rax),%xmm0
mov    -0x18(%rbp),%rax
movsd  0x10(%rax),%xmm2
mov    -0x10(%rbp),%rax
movsd  0x10(%rax),%xmm1
mov    -0x18(%rbp),%rax
mulsd  0x8(%rax),%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)
mov    -0x10(%rbp),%rax
movsd  0x10(%rax),%xmm0
mov    -0x18(%rbp),%rax
movsd  (%rax),%xmm2
mov    -0x10(%rbp),%rax
movsd  (%rax),%xmm1
mov    -0x18(%rbp),%rax
mulsd  0x10(%rax),%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)
mov    -0x10(%rbp),%rax
movsd  (%rax),%xmm0
mov    -0x18(%rbp),%rax
movsd  0x8(%rax),%xmm2
mov    -0x10(%rbp),%rax
movsd  0x8(%rax),%xmm1
mov    -0x18(%rbp),%rax
mulsd  (%rax),%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)
pop    %rbp
ret

x86 assembly (clang, -O2):
<vec3d_rot>:
movsd  0x8(%rsi),%xmm0
movsd  0x8(%rdx),%xmm1
mulsd  0x10(%rsi),%xmm1
mulsd  0x10(%rdx),%xmm0
subsd  %xmm1,%xmm0
movsd  %xmm0,(%rdi)
movsd  0x10(%rsi),%xmm0
movsd  0x10(%rdx),%xmm1
mulsd  (%rsi),%xmm1
mulsd  (%rdx),%xmm0
subsd  %xmm1,%xmm0
movsd  %xmm0,0x8(%rdi)
movsd  (%rsi),%xmm0
movsd  (%rdx),%xmm1
mulsd  0x8(%rsi),%xmm1
mulsd  0x8(%rdx),%xmm0
subsd  %xmm1,%xmm0
movsd  %xmm0,0x10(%rdi)
ret

LLVM IR (-O0):
define void @vec3d_rot(double* %0, double* %1, double* %2) {
%4 = alloca double*
%5 = alloca double*
%6 = alloca double*
store double* %0, double** %4
store double* %1, double** %5
store double* %2, double** %6
%7 = load double*, double** %5
%8 = getelementptr inbounds double, double* %7, i64 1
%9 = load double, double* %8
%10 = load double*, double** %6
%11 = getelementptr inbounds double, double* %10, i64 2
%12 = load double, double* %11
%13 = load double*, double** %5
%14 = getelementptr inbounds double, double* %13, i64 2
%15 = load double, double* %14
%16 = load double*, double** %6
%17 = getelementptr inbounds double, double* %16, i64 1
%18 = load double, double* %17
%19 = fmul double %15, %18
%20 = fneg double %19
%21 = call double @llvm.fmuladd.f64(double %9, double %12, double %20)
%22 = load double*, double** %4
%23 = getelementptr inbounds double, double* %22, i64 0
store double %21, double* %23
%24 = load double*, double** %5
%25 = getelementptr inbounds double, double* %24, i64 2
%26 = load double, double* %25
%27 = load double*, double** %6
%28 = getelementptr inbounds double, double* %27, i64 0
%29 = load double, double* %28
%30 = load double*, double** %5
%31 = getelementptr inbounds double, double* %30, i64 0
%32 = load double, double* %31
%33 = load double*, double** %6
%34 = getelementptr inbounds double, double* %33, i64 2
%35 = load double, double* %34
%36 = fmul double %32, %35
%37 = fneg double %36
%38 = call double @llvm.fmuladd.f64(double %26, double %29, double %37)
%39 = load double*, double** %4
%40 = getelementptr inbounds double, double* %39, i64 1
store double %38, double* %40
%41 = load double*, double** %5
%42 = getelementptr inbounds double, double* %41, i64 0
%43 = load double, double* %42
%44 = load double*, double** %6
%45 = getelementptr inbounds double, double* %44, i64 1
%46 = load double, double* %45
%47 = load double*, double** %5
%48 = getelementptr inbounds double, double* %47, i64 1
%49 = load double, double* %48
%50 = load double*, double** %6
%51 = getelementptr inbounds double, double* %50, i64 0
%52 = load double, double* %51
%53 = fmul double %49, %52
%54 = fneg double %53
%55 = call double @llvm.fmuladd.f64(double %43, double %46, double %54)
%56 = load double*, double** %4
%57 = getelementptr inbounds double, double* %56, i64 2
store double %55, double* %57
ret void
}

LLVM IR (-O2):
define void @vec3d_rot(double* nocapture writeonly %0, double* nocapture %1, double* nocapture %2) {
%4 = getelementptr inbounds double, double* %1, i64 1
%5 = load double, double* %4
%6 = getelementptr inbounds double, double* %2, i64 2
%7 = load double, double* %6
%8 = getelementptr inbounds double, double* %1, i64 2
%9 = load double, double* %8
%10 = getelementptr inbounds double, double* %2, i64 1
%11 = load double, double* %10
%12 = fneg double %9
%13 = fmul double %11, %12
%14 = tail call double @llvm.fmuladd.f64(double %5, double %7, double %13)
store double %14, double* %0
%15 = load double, double* %8
%16 = load double, double* %2
%17 = load double, double* %1
%18 = load double, double* %6
%19 = fneg double %17
%20 = fmul double %18, %19
%21 = tail call double @llvm.fmuladd.f64(double %15, double %16, double %20)
%22 = getelementptr inbounds double, double* %0, i64 1
store double %21, double* %22
%23 = load double, double* %1
%24 = load double, double* %10
%25 = load double, double* %4
%26 = load double, double* %2
%27 = fneg double %25
%28 = fmul double %26, %27
%29 = tail call double @llvm.fmuladd.f64(double %23, double %24, double %28)
%30 = getelementptr inbounds double, double* %0, i64 2
store double %29, double* %30
ret void
}