void LdL3(double x, double *y, double *z) {
  double L[3 + 1];
  double dL[3 + 1];
  L[0] = 1.;
  L[1] = x;
  dL[0] = 0.;
  dL[1] = 1.;
  {
    for (int i = 2; i < 3 + 1; i++) {
      L[i] = 2. * (x)*L[i - 1] - L[i - 2] -
             ((x)*L[i - 1] - L[i - 2]) / ((double)i);
      dL[i] = L[i - 1] * i + dL[i - 1] * (x);
    }
  };
  *y = L[3];
  *z = dL[3];
}


x86 assembly (clang, -O0):
<LdL3>:
push   %rbp
mov    %rsp,%rbp
movsd  %xmm0,-0x8(%rbp)
mov    %rdi,-0x10(%rbp)
mov    %rsi,-0x18(%rbp)
movsd  0xee7(%rip),%xmm0
movsd  %xmm0,-0x40(%rbp)
movsd  -0x8(%rbp),%xmm0
movsd  %xmm0,-0x38(%rbp)
xorps  %xmm0,%xmm0
movsd  %xmm0,-0x60(%rbp)
movsd  0xec8(%rip),%xmm0
movsd  %xmm0,-0x58(%rbp)
movl   $0x2,-0x64(%rbp)
cmpl   $0x4,-0x64(%rbp)
jge    1233 <LdL3+0x133>
movsd  0xeb2(%rip),%xmm0
mulsd  -0x8(%rbp),%xmm0
mov    -0x64(%rbp),%eax
sub    $0x1,%eax
cltq
movsd  -0x40(%rbp,%rax,8),%xmm2
mov    -0x64(%rbp),%eax
sub    $0x2,%eax
cltq
movsd  -0x40(%rbp,%rax,8),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
movsd  -0x8(%rbp),%xmm1
mov    -0x64(%rbp),%eax
sub    $0x1,%eax
cltq
movsd  -0x40(%rbp,%rax,8),%xmm3
mov    -0x64(%rbp),%eax
sub    $0x2,%eax
cltq
movsd  -0x40(%rbp,%rax,8),%xmm2
movq   %xmm2,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm2
mulsd  %xmm3,%xmm1
addsd  %xmm2,%xmm1
cvtsi2sdl -0x64(%rbp),%xmm2
divsd  %xmm2,%xmm1
subsd  %xmm1,%xmm0
movslq -0x64(%rbp),%rax
movsd  %xmm0,-0x40(%rbp,%rax,8)
mov    -0x64(%rbp),%eax
sub    $0x1,%eax
cltq
movsd  -0x40(%rbp,%rax,8),%xmm0
cvtsi2sdl -0x64(%rbp),%xmm2
mov    -0x64(%rbp),%eax
sub    $0x1,%eax
cltq
movsd  -0x60(%rbp,%rax,8),%xmm1
mulsd  -0x8(%rbp),%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
movslq -0x64(%rbp),%rax
movsd  %xmm0,-0x60(%rbp,%rax,8)
mov    -0x64(%rbp),%eax
add    $0x1,%eax
mov    %eax,-0x64(%rbp)
jmp    1144 <LdL3+0x44>
movsd  -0x28(%rbp),%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,(%rax)
movsd  -0x48(%rbp),%xmm0
mov    -0x18(%rbp),%rax
movsd  %xmm0,(%rax)
pop    %rbp
ret

x86 assembly (clang, -O2):
<LdL3>:
movapd %xmm0,%xmm1
addsd  %xmm0,%xmm1
movapd %xmm1,%xmm2
mulsd  %xmm0,%xmm2
movsd  0xee8(%rip),%xmm3
addsd  %xmm3,%xmm2
movapd %xmm0,%xmm4
mulsd  %xmm0,%xmm4
addsd  %xmm3,%xmm4
mulsd  0xed8(%rip),%xmm4
addsd  %xmm2,%xmm4
movapd %xmm1,%xmm2
addsd  %xmm0,%xmm2
mulsd  %xmm4,%xmm1
subsd  %xmm0,%xmm1
movapd %xmm0,%xmm3
mulsd  %xmm4,%xmm3
subsd  %xmm0,%xmm3
movsd  0xeb8(%rip),%xmm5
divsd  %xmm5,%xmm3
subsd  %xmm3,%xmm1
mulsd  %xmm0,%xmm2
mulsd  %xmm5,%xmm4
addsd  %xmm2,%xmm4
movsd  %xmm1,(%rdi)
movsd  %xmm4,(%rsi)
ret

LLVM IR (-O0):
define void @LdL3(double %0, double* %1, double* %2) {
%4 = alloca double
%5 = alloca double*
%6 = alloca double*
%7 = alloca [4 x double]
%8 = alloca [4 x double]
%9 = alloca i32
store double %0, double* %4
store double* %1, double** %5
store double* %2, double** %6
%10 = getelementptr inbounds [4 x double], [4 x double]* %7, i64 0, i64 0
store double 1.000000e+00, double* %10
%11 = load double, double* %4
%12 = getelementptr inbounds [4 x double], [4 x double]* %7, i64 0, i64 1
store double %11, double* %12
%13 = getelementptr inbounds [4 x double], [4 x double]* %8, i64 0, i64 0
store double 0.000000e+00, double* %13
%14 = getelementptr inbounds [4 x double], [4 x double]* %8, i64 0, i64 1
store double 1.000000e+00, double* %14
store i32 2, i32* %9
br label %15
15: ; preds = %71, %3
%16 = load i32, i32* %9
%17 = icmp slt i32 %16, 4
br i1 %17, label %18, label %74
18: ; preds = %15
%19 = load double, double* %4
%20 = fmul double 2.000000e+00, %19
%21 = load i32, i32* %9
%22 = sub nsw i32 %21, 1
%23 = sext i32 %22 to i64
%24 = getelementptr inbounds [4 x double], [4 x double]* %7, i64 0, i64 %23
%25 = load double, double* %24
%26 = load i32, i32* %9
%27 = sub nsw i32 %26, 2
%28 = sext i32 %27 to i64
%29 = getelementptr inbounds [4 x double], [4 x double]* %7, i64 0, i64 %28
%30 = load double, double* %29
%31 = fneg double %30
%32 = call double @llvm.fmuladd.f64(double %20, double %25, double %31)
%33 = load double, double* %4
%34 = load i32, i32* %9
%35 = sub nsw i32 %34, 1
%36 = sext i32 %35 to i64
%37 = getelementptr inbounds [4 x double], [4 x double]* %7, i64 0, i64 %36
%38 = load double, double* %37
%39 = load i32, i32* %9
%40 = sub nsw i32 %39, 2
%41 = sext i32 %40 to i64
%42 = getelementptr inbounds [4 x double], [4 x double]* %7, i64 0, i64 %41
%43 = load double, double* %42
%44 = fneg double %43
%45 = call double @llvm.fmuladd.f64(double %33, double %38, double %44)
%46 = load i32, i32* %9
%47 = sitofp i32 %46 to double
%48 = fdiv double %45, %47
%49 = fsub double %32, %48
%50 = load i32, i32* %9
%51 = sext i32 %50 to i64
%52 = getelementptr inbounds [4 x double], [4 x double]* %7, i64 0, i64 %51
store double %49, double* %52
%53 = load i32, i32* %9
%54 = sub nsw i32 %53, 1
%55 = sext i32 %54 to i64
%56 = getelementptr inbounds [4 x double], [4 x double]* %7, i64 0, i64 %55
%57 = load double, double* %56
%58 = load i32, i32* %9
%59 = sitofp i32 %58 to double
%60 = load i32, i32* %9
%61 = sub nsw i32 %60, 1
%62 = sext i32 %61 to i64
%63 = getelementptr inbounds [4 x double], [4 x double]* %8, i64 0, i64 %62
%64 = load double, double* %63
%65 = load double, double* %4
%66 = fmul double %64, %65
%67 = call double @llvm.fmuladd.f64(double %57, double %59, double %66)
%68 = load i32, i32* %9
%69 = sext i32 %68 to i64
%70 = getelementptr inbounds [4 x double], [4 x double]* %8, i64 0, i64 %69
store double %67, double* %70
br label %71
71: ; preds = %18
%72 = load i32, i32* %9
%73 = add nsw i32 %72, 1
store i32 %73, i32* %9
br label %15
74: ; preds = %15
%75 = getelementptr inbounds [4 x double], [4 x double]* %7, i64 0, i64 3
%76 = load double, double* %75
%77 = load double*, double** %5
store double %76, double* %77
%78 = getelementptr inbounds [4 x double], [4 x double]* %8, i64 0, i64 3
%79 = load double, double* %78
%80 = load double*, double** %6
store double %79, double* %80
ret void
}

LLVM IR (-O2):
define void @LdL3(double %0, double* nocapture writeonly %1, double* nocapture writeonly %2) {
%4 = fmul double %0, 2.000000e+00
%5 = tail call double @llvm.fmuladd.f64(double %4, double %0, double -1.000000e+00)
%6 = tail call double @llvm.fmuladd.f64(double %0, double %0, double -1.000000e+00)
%7 = fmul double %6, 5.000000e-01
%8 = fsub double %5, %7
%9 = tail call double @llvm.fmuladd.f64(double %0, double 2.000000e+00, double %0)
%10 = fneg double %0
%11 = tail call double @llvm.fmuladd.f64(double %4, double %8, double %10)
%12 = tail call double @llvm.fmuladd.f64(double %0, double %8, double %10)
%13 = fdiv double %12, 3.000000e+00
%14 = fsub double %11, %13
%15 = fmul double %9, %0
%16 = tail call double @llvm.fmuladd.f64(double %8, double 3.000000e+00, double %15)
store double %14, double* %1
store double %16, double* %2
ret void
}