void invert_special44d44d(double *orig, double *inv) {
  inv[0] = orig[0];
  inv[1] = orig[4];
  inv[2] = orig[8];
  inv[4] = orig[1];
  inv[5] = orig[5];
  inv[6] = orig[9];
  inv[8] = orig[2];
  inv[9] = orig[6];
  inv[10] = orig[10];
  inv[3] = -(orig[3] * orig[0] + orig[7] * orig[4] + orig[11] * orig[8]);
  inv[7] = -(orig[3] * orig[1] + orig[7] * orig[5] + orig[11] * orig[9]);
  inv[11] = -(orig[3] * orig[2] + orig[7] * orig[6] + orig[11] * orig[10]);
  inv[12] = 0.0;
  inv[13] = 0.0;
  inv[14] = 0.0;
  inv[15] = 1.0;
}


x86 assembly (clang, -O0):
<invert_special44d44d>:
push   %rbp
mov    %rsp,%rbp
mov    %rdi,-0x8(%rbp)
mov    %rsi,-0x10(%rbp)
mov    -0x8(%rbp),%rax
movsd  (%rax),%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,(%rax)
mov    -0x8(%rbp),%rax
movsd  0x20(%rax),%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,0x8(%rax)
mov    -0x8(%rbp),%rax
movsd  0x40(%rax),%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,0x10(%rax)
mov    -0x8(%rbp),%rax
movsd  0x8(%rax),%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,0x20(%rax)
mov    -0x8(%rbp),%rax
movsd  0x28(%rax),%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,0x28(%rax)
mov    -0x8(%rbp),%rax
movsd  0x48(%rax),%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,0x30(%rax)
mov    -0x8(%rbp),%rax
movsd  0x10(%rax),%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,0x40(%rax)
mov    -0x8(%rbp),%rax
movsd  0x30(%rax),%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,0x48(%rax)
mov    -0x8(%rbp),%rax
movsd  0x50(%rax),%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,0x50(%rax)
mov    -0x8(%rbp),%rax
movsd  0x18(%rax),%xmm1
mov    -0x8(%rbp),%rax
movsd  (%rax),%xmm2
mov    -0x8(%rbp),%rax
movsd  0x38(%rax),%xmm0
mov    -0x8(%rbp),%rax
mulsd  0x20(%rax),%xmm0
mulsd  %xmm2,%xmm1
addsd  %xmm0,%xmm1
mov    -0x8(%rbp),%rax
movsd  0x58(%rax),%xmm0
mov    -0x8(%rbp),%rax
movsd  0x40(%rax),%xmm2
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
movq   %xmm0,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,0x18(%rax)
mov    -0x8(%rbp),%rax
movsd  0x18(%rax),%xmm1
mov    -0x8(%rbp),%rax
movsd  0x8(%rax),%xmm2
mov    -0x8(%rbp),%rax
movsd  0x38(%rax),%xmm0
mov    -0x8(%rbp),%rax
mulsd  0x28(%rax),%xmm0
mulsd  %xmm2,%xmm1
addsd  %xmm0,%xmm1
mov    -0x8(%rbp),%rax
movsd  0x58(%rax),%xmm0
mov    -0x8(%rbp),%rax
movsd  0x48(%rax),%xmm2
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
movq   %xmm0,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,0x38(%rax)
mov    -0x8(%rbp),%rax
movsd  0x18(%rax),%xmm1
mov    -0x8(%rbp),%rax
movsd  0x10(%rax),%xmm2
mov    -0x8(%rbp),%rax
movsd  0x38(%rax),%xmm0
mov    -0x8(%rbp),%rax
mulsd  0x30(%rax),%xmm0
mulsd  %xmm2,%xmm1
addsd  %xmm0,%xmm1
mov    -0x8(%rbp),%rax
movsd  0x58(%rax),%xmm0
mov    -0x8(%rbp),%rax
movsd  0x50(%rax),%xmm2
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
movq   %xmm0,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,0x58(%rax)
mov    -0x10(%rbp),%rax
xorps  %xmm0,%xmm0
movsd  %xmm0,0x60(%rax)
mov    -0x10(%rbp),%rax
xorps  %xmm0,%xmm0
movsd  %xmm0,0x68(%rax)
mov    -0x10(%rbp),%rax
xorps  %xmm0,%xmm0
movsd  %xmm0,0x70(%rax)
mov    -0x10(%rbp),%rax
movsd  0xcf3(%rip),%xmm0
movsd  %xmm0,0x78(%rax)
pop    %rbp
ret

x86 assembly (clang, -O2):
<invert_special44d44d>:
movsd  (%rdi),%xmm0
movsd  %xmm0,(%rsi)
movsd  0x20(%rdi),%xmm0
movsd  %xmm0,0x8(%rsi)
movsd  0x40(%rdi),%xmm0
movsd  %xmm0,0x10(%rsi)
movsd  0x8(%rdi),%xmm0
movsd  %xmm0,0x20(%rsi)
movsd  0x28(%rdi),%xmm0
movsd  %xmm0,0x28(%rsi)
movsd  0x48(%rdi),%xmm0
movsd  %xmm0,0x30(%rsi)
movsd  0x10(%rdi),%xmm0
movsd  %xmm0,0x40(%rsi)
movsd  0x30(%rdi),%xmm0
movsd  %xmm0,0x48(%rsi)
movsd  0x50(%rdi),%xmm0
movsd  %xmm0,0x50(%rsi)
movsd  0x18(%rdi),%xmm0
movsd  0x38(%rdi),%xmm1
mulsd  0x20(%rdi),%xmm1
mulsd  (%rdi),%xmm0
movsd  0x58(%rdi),%xmm2
mulsd  0x40(%rdi),%xmm2
addsd  %xmm1,%xmm0
addsd  %xmm0,%xmm2
movapd 0xe7b(%rip),%xmm0
xorpd  %xmm0,%xmm2
movlpd %xmm2,0x18(%rsi)
movsd  0x38(%rdi),%xmm1
mulsd  0x28(%rdi),%xmm1
movsd  0x18(%rdi),%xmm2
mulsd  0x8(%rdi),%xmm2
addsd  %xmm1,%xmm2
movsd  0x58(%rdi),%xmm1
mulsd  0x48(%rdi),%xmm1
addsd  %xmm2,%xmm1
xorpd  %xmm0,%xmm1
movlpd %xmm1,0x38(%rsi)
movsd  0x18(%rdi),%xmm1
movsd  0x38(%rdi),%xmm2
mulsd  0x30(%rdi),%xmm2
mulsd  0x10(%rdi),%xmm1
addsd  %xmm2,%xmm1
movsd  0x58(%rdi),%xmm2
mulsd  0x50(%rdi),%xmm2
addsd  %xmm1,%xmm2
xorpd  %xmm0,%xmm2
movlpd %xmm2,0x58(%rsi)
xorpd  %xmm0,%xmm0
movupd %xmm0,0x60(%rsi)
movq   $0x0,0x70(%rsi)
movabs $0x3ff0000000000000,%rax
mov    %rax,0x78(%rsi)
ret

LLVM IR (-O0):
define void @invert_special44d44d(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 = load double*, double** %4
%9 = getelementptr inbounds double, double* %8, i64 0
store double %7, double* %9
%10 = load double*, double** %3
%11 = getelementptr inbounds double, double* %10, i64 4
%12 = load double, double* %11
%13 = load double*, double** %4
%14 = getelementptr inbounds double, double* %13, i64 1
store double %12, double* %14
%15 = load double*, double** %3
%16 = getelementptr inbounds double, double* %15, i64 8
%17 = load double, double* %16
%18 = load double*, double** %4
%19 = getelementptr inbounds double, double* %18, i64 2
store double %17, double* %19
%20 = load double*, double** %3
%21 = getelementptr inbounds double, double* %20, i64 1
%22 = load double, double* %21
%23 = load double*, double** %4
%24 = getelementptr inbounds double, double* %23, i64 4
store double %22, double* %24
%25 = load double*, double** %3
%26 = getelementptr inbounds double, double* %25, i64 5
%27 = load double, double* %26
%28 = load double*, double** %4
%29 = getelementptr inbounds double, double* %28, i64 5
store double %27, double* %29
%30 = load double*, double** %3
%31 = getelementptr inbounds double, double* %30, i64 9
%32 = load double, double* %31
%33 = load double*, double** %4
%34 = getelementptr inbounds double, double* %33, i64 6
store double %32, double* %34
%35 = load double*, double** %3
%36 = getelementptr inbounds double, double* %35, i64 2
%37 = load double, double* %36
%38 = load double*, double** %4
%39 = getelementptr inbounds double, double* %38, i64 8
store double %37, double* %39
%40 = load double*, double** %3
%41 = getelementptr inbounds double, double* %40, i64 6
%42 = load double, double* %41
%43 = load double*, double** %4
%44 = getelementptr inbounds double, double* %43, i64 9
store double %42, double* %44
%45 = load double*, double** %3
%46 = getelementptr inbounds double, double* %45, i64 10
%47 = load double, double* %46
%48 = load double*, double** %4
%49 = getelementptr inbounds double, double* %48, i64 10
store double %47, double* %49
%50 = load double*, double** %3
%51 = getelementptr inbounds double, double* %50, i64 3
%52 = load double, double* %51
%53 = load double*, double** %3
%54 = getelementptr inbounds double, double* %53, i64 0
%55 = load double, double* %54
%56 = load double*, double** %3
%57 = getelementptr inbounds double, double* %56, i64 7
%58 = load double, double* %57
%59 = load double*, double** %3
%60 = getelementptr inbounds double, double* %59, i64 4
%61 = load double, double* %60
%62 = fmul double %58, %61
%63 = call double @llvm.fmuladd.f64(double %52, double %55, double %62)
%64 = load double*, double** %3
%65 = getelementptr inbounds double, double* %64, i64 11
%66 = load double, double* %65
%67 = load double*, double** %3
%68 = getelementptr inbounds double, double* %67, i64 8
%69 = load double, double* %68
%70 = call double @llvm.fmuladd.f64(double %66, double %69, double %63)
%71 = fneg double %70
%72 = load double*, double** %4
%73 = getelementptr inbounds double, double* %72, i64 3
store double %71, double* %73
%74 = load double*, double** %3
%75 = getelementptr inbounds double, double* %74, i64 3
%76 = load double, double* %75
%77 = load double*, double** %3
%78 = getelementptr inbounds double, double* %77, i64 1
%79 = load double, double* %78
%80 = load double*, double** %3
%81 = getelementptr inbounds double, double* %80, i64 7
%82 = load double, double* %81
%83 = load double*, double** %3
%84 = getelementptr inbounds double, double* %83, i64 5
%85 = load double, double* %84
%86 = fmul double %82, %85
%87 = call double @llvm.fmuladd.f64(double %76, double %79, double %86)
%88 = load double*, double** %3
%89 = getelementptr inbounds double, double* %88, i64 11
%90 = load double, double* %89
%91 = load double*, double** %3
%92 = getelementptr inbounds double, double* %91, i64 9
%93 = load double, double* %92
%94 = call double @llvm.fmuladd.f64(double %90, double %93, double %87)
%95 = fneg double %94
%96 = load double*, double** %4
%97 = getelementptr inbounds double, double* %96, i64 7
store double %95, double* %97
%98 = load double*, double** %3
%99 = getelementptr inbounds double, double* %98, i64 3
%100 = load double, double* %99
%101 = load double*, double** %3
%102 = getelementptr inbounds double, double* %101, i64 2
%103 = load double, double* %102
%104 = load double*, double** %3
%105 = getelementptr inbounds double, double* %104, i64 7
%106 = load double, double* %105
%107 = load double*, double** %3
%108 = getelementptr inbounds double, double* %107, i64 6
%109 = load double, double* %108
%110 = fmul double %106, %109
%111 = call double @llvm.fmuladd.f64(double %100, double %103, double %110)
%112 = load double*, double** %3
%113 = getelementptr inbounds double, double* %112, i64 11
%114 = load double, double* %113
%115 = load double*, double** %3
%116 = getelementptr inbounds double, double* %115, i64 10
%117 = load double, double* %116
%118 = call double @llvm.fmuladd.f64(double %114, double %117, double %111)
%119 = fneg double %118
%120 = load double*, double** %4
%121 = getelementptr inbounds double, double* %120, i64 11
store double %119, double* %121
%122 = load double*, double** %4
%123 = getelementptr inbounds double, double* %122, i64 12
store double 0.000000e+00, double* %123
%124 = load double*, double** %4
%125 = getelementptr inbounds double, double* %124, i64 13
store double 0.000000e+00, double* %125
%126 = load double*, double** %4
%127 = getelementptr inbounds double, double* %126, i64 14
store double 0.000000e+00, double* %127
%128 = load double*, double** %4
%129 = getelementptr inbounds double, double* %128, i64 15
store double 1.000000e+00, double* %129
ret void
}

LLVM IR (-O2):
define void @invert_special44d44d(double* nocapture %0, double* nocapture writeonly %1) {
%3 = load double, double* %0
store double %3, double* %1
%4 = getelementptr inbounds double, double* %0, i64 4
%5 = load double, double* %4
%6 = getelementptr inbounds double, double* %1, i64 1
store double %5, double* %6
%7 = getelementptr inbounds double, double* %0, i64 8
%8 = load double, double* %7
%9 = getelementptr inbounds double, double* %1, i64 2
store double %8, double* %9
%10 = getelementptr inbounds double, double* %0, i64 1
%11 = load double, double* %10
%12 = getelementptr inbounds double, double* %1, i64 4
store double %11, double* %12
%13 = getelementptr inbounds double, double* %0, i64 5
%14 = load double, double* %13
%15 = getelementptr inbounds double, double* %1, i64 5
store double %14, double* %15
%16 = getelementptr inbounds double, double* %0, i64 9
%17 = load double, double* %16
%18 = getelementptr inbounds double, double* %1, i64 6
store double %17, double* %18
%19 = getelementptr inbounds double, double* %0, i64 2
%20 = load double, double* %19
%21 = getelementptr inbounds double, double* %1, i64 8
store double %20, double* %21
%22 = getelementptr inbounds double, double* %0, i64 6
%23 = load double, double* %22
%24 = getelementptr inbounds double, double* %1, i64 9
store double %23, double* %24
%25 = getelementptr inbounds double, double* %0, i64 10
%26 = load double, double* %25
%27 = getelementptr inbounds double, double* %1, i64 10
store double %26, double* %27
%28 = getelementptr inbounds double, double* %0, i64 3
%29 = load double, double* %28
%30 = load double, double* %0
%31 = getelementptr inbounds double, double* %0, i64 7
%32 = load double, double* %31
%33 = load double, double* %4
%34 = fmul double %32, %33
%35 = tail call double @llvm.fmuladd.f64(double %29, double %30, double %34)
%36 = getelementptr inbounds double, double* %0, i64 11
%37 = load double, double* %36
%38 = load double, double* %7
%39 = tail call double @llvm.fmuladd.f64(double %37, double %38, double %35)
%40 = fneg double %39
%41 = getelementptr inbounds double, double* %1, i64 3
store double %40, double* %41
%42 = load double, double* %28
%43 = load double, double* %10
%44 = load double, double* %31
%45 = load double, double* %13
%46 = fmul double %44, %45
%47 = tail call double @llvm.fmuladd.f64(double %42, double %43, double %46)
%48 = load double, double* %36
%49 = load double, double* %16
%50 = tail call double @llvm.fmuladd.f64(double %48, double %49, double %47)
%51 = fneg double %50
%52 = getelementptr inbounds double, double* %1, i64 7
store double %51, double* %52
%53 = load double, double* %28
%54 = load double, double* %19
%55 = load double, double* %31
%56 = load double, double* %22
%57 = fmul double %55, %56
%58 = tail call double @llvm.fmuladd.f64(double %53, double %54, double %57)
%59 = load double, double* %36
%60 = load double, double* %25
%61 = tail call double @llvm.fmuladd.f64(double %59, double %60, double %58)
%62 = fneg double %61
%63 = getelementptr inbounds double, double* %1, i64 11
store double %62, double* %63
%64 = getelementptr inbounds double, double* %1, i64 12
%65 = getelementptr inbounds double, double* %1, i64 15
%66 = bitcast double* %64 to i8*
store double 1.000000e+00, double* %65
ret void
}