double it_pol_neville_s4(double *f, double alpha) {
  static double d[4][4];
  d[0][1] = (alpha * f[1] - (alpha - 1) * f[0]);
  d[1][1] = ((alpha - 1) * f[2] - (alpha - 2) * f[1]);
  d[2][1] = ((alpha - 2) * f[3] - (alpha - 3) * f[2]);
  d[0][2] = ((alpha)*d[1][1] - (alpha - 2) * d[0][1]) / 2;
  d[1][2] = ((alpha - 1) * d[2][1] - (alpha - 3) * d[1][1]) / 2;
  return ((alpha)*d[1][2] - (alpha - 3) * d[0][2]) / 3;
}


x86 assembly (clang, -O0):
<it_pol_neville_s4>:
push   %rbp
mov    %rsp,%rbp
mov    %rdi,-0x8(%rbp)
movsd  %xmm0,-0x10(%rbp)
movsd  -0x10(%rbp),%xmm0
mov    -0x8(%rbp),%rax
movsd  0x8(%rax),%xmm2
movsd  -0x10(%rbp),%xmm1
movsd  0xee8(%rip),%xmm3
subsd  %xmm3,%xmm1
mov    -0x8(%rbp),%rax
mulsd  (%rax),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
movsd  %xmm0,0x2edd(%rip)
movsd  -0x10(%rbp),%xmm0
movsd  0xea8(%rip),%xmm1
subsd  %xmm1,%xmm0
mov    -0x8(%rbp),%rax
movsd  0x10(%rax),%xmm2
movsd  -0x10(%rbp),%xmm1
movsd  0xe86(%rip),%xmm3
subsd  %xmm3,%xmm1
mov    -0x8(%rbp),%rax
mulsd  0x8(%rax),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
movsd  %xmm0,0x2ea2(%rip)
movsd  -0x10(%rbp),%xmm0
movsd  0xe45(%rip),%xmm1
subsd  %xmm1,%xmm0
mov    -0x8(%rbp),%rax
movsd  0x18(%rax),%xmm2
movsd  -0x10(%rbp),%xmm1
movsd  0xe23(%rip),%xmm3
subsd  %xmm3,%xmm1
mov    -0x8(%rbp),%rax
mulsd  0x10(%rax),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
movsd  %xmm0,0x2e67(%rip)
movsd  -0x10(%rbp),%xmm0
movsd  0x2e3a(%rip),%xmm2
movsd  -0x10(%rbp),%xmm1
movsd  0xddd(%rip),%xmm3
subsd  %xmm3,%xmm1
mulsd  0x2e01(%rip),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
movsd  0xdaa(%rip),%xmm1
divsd  %xmm1,%xmm0
movsd  %xmm0,0x2dd6(%rip)
movsd  -0x10(%rbp),%xmm0
movsd  0xd99(%rip),%xmm1
subsd  %xmm1,%xmm0
movsd  0x2df5(%rip),%xmm2
movsd  -0x10(%rbp),%xmm1
movsd  0xd70(%rip),%xmm3
subsd  %xmm3,%xmm1
mulsd  0x2dbc(%rip),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
movsd  0xd45(%rip),%xmm1
divsd  %xmm1,%xmm0
movsd  %xmm0,0x2d91(%rip)
movsd  -0x10(%rbp),%xmm0
movsd  0x2d84(%rip),%xmm2
movsd  -0x10(%rbp),%xmm1
movsd  0xd17(%rip),%xmm3
subsd  %xmm3,%xmm1
mulsd  0x2d4b(%rip),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
movsd  0xce4(%rip),%xmm1
divsd  %xmm1,%xmm0
pop    %rbp
ret

x86 assembly (clang, -O2):
<it_pol_neville_s4>:
movsd  0xef8(%rip),%xmm1
addsd  %xmm0,%xmm1
movsd  (%rdi),%xmm2
mulsd  %xmm1,%xmm2
movsd  0x8(%rdi),%xmm3
movsd  0x10(%rdi),%xmm4
movapd %xmm0,%xmm5
mulsd  %xmm3,%xmm5
subsd  %xmm2,%xmm5
movsd  0xed6(%rip),%xmm2
addsd  %xmm0,%xmm2
mulsd  %xmm2,%xmm3
movapd %xmm1,%xmm6
mulsd  %xmm4,%xmm6
subsd  %xmm3,%xmm6
movsd  0xec2(%rip),%xmm3
addsd  %xmm0,%xmm3
mulsd  %xmm3,%xmm4
mulsd  %xmm2,%xmm5
mulsd  0x18(%rdi),%xmm2
subsd  %xmm4,%xmm2
movapd %xmm0,%xmm4
mulsd  %xmm6,%xmm4
subsd  %xmm5,%xmm4
movsd  0xea1(%rip),%xmm5
mulsd  %xmm5,%xmm4
mulsd  %xmm3,%xmm6
mulsd  %xmm1,%xmm2
subsd  %xmm6,%xmm2
mulsd  %xmm5,%xmm2
mulsd  %xmm3,%xmm4
mulsd  %xmm2,%xmm0
subsd  %xmm4,%xmm0
divsd  0xe81(%rip),%xmm0
ret

LLVM IR (-O0):
@it_pol_neville_s4.d = internal global [4 x [4 x double]] zeroinitializer
define double @it_pol_neville_s4(double* %0, double %1) {
%3 = alloca double*
%4 = alloca double
store double* %0, double** %3
store double %1, double* %4
%5 = load double, double* %4
%6 = load double*, double** %3
%7 = getelementptr inbounds double, double* %6, i64 1
%8 = load double, double* %7
%9 = load double, double* %4
%10 = fsub double %9, 1.000000e+00
%11 = load double*, double** %3
%12 = getelementptr inbounds double, double* %11, i64 0
%13 = load double, double* %12
%14 = fmul double %10, %13
%15 = fneg double %14
%16 = call double @llvm.fmuladd.f64(double %5, double %8, double %15)
store double %16, double* getelementptr inbounds ([4 x [4 x double]], [4 x [4 x double]]* @it_pol_neville_s4.d, i64 0, i64 0, i64 1)
%17 = load double, double* %4
%18 = fsub double %17, 1.000000e+00
%19 = load double*, double** %3
%20 = getelementptr inbounds double, double* %19, i64 2
%21 = load double, double* %20
%22 = load double, double* %4
%23 = fsub double %22, 2.000000e+00
%24 = load double*, double** %3
%25 = getelementptr inbounds double, double* %24, i64 1
%26 = load double, double* %25
%27 = fmul double %23, %26
%28 = fneg double %27
%29 = call double @llvm.fmuladd.f64(double %18, double %21, double %28)
store double %29, double* getelementptr inbounds ([4 x [4 x double]], [4 x [4 x double]]* @it_pol_neville_s4.d, i64 0, i64 1, i64 1)
%30 = load double, double* %4
%31 = fsub double %30, 2.000000e+00
%32 = load double*, double** %3
%33 = getelementptr inbounds double, double* %32, i64 3
%34 = load double, double* %33
%35 = load double, double* %4
%36 = fsub double %35, 3.000000e+00
%37 = load double*, double** %3
%38 = getelementptr inbounds double, double* %37, i64 2
%39 = load double, double* %38
%40 = fmul double %36, %39
%41 = fneg double %40
%42 = call double @llvm.fmuladd.f64(double %31, double %34, double %41)
store double %42, double* getelementptr inbounds ([4 x [4 x double]], [4 x [4 x double]]* @it_pol_neville_s4.d, i64 0, i64 2, i64 1)
%43 = load double, double* %4
%44 = load double, double* getelementptr inbounds ([4 x [4 x double]], [4 x [4 x double]]* @it_pol_neville_s4.d, i64 0, i64 1, i64 1)
%45 = load double, double* %4
%46 = fsub double %45, 2.000000e+00
%47 = load double, double* getelementptr inbounds ([4 x [4 x double]], [4 x [4 x double]]* @it_pol_neville_s4.d, i64 0, i64 0, i64 1)
%48 = fmul double %46, %47
%49 = fneg double %48
%50 = call double @llvm.fmuladd.f64(double %43, double %44, double %49)
%51 = fdiv double %50, 2.000000e+00
store double %51, double* getelementptr inbounds ([4 x [4 x double]], [4 x [4 x double]]* @it_pol_neville_s4.d, i64 0, i64 0, i64 2)
%52 = load double, double* %4
%53 = fsub double %52, 1.000000e+00
%54 = load double, double* getelementptr inbounds ([4 x [4 x double]], [4 x [4 x double]]* @it_pol_neville_s4.d, i64 0, i64 2, i64 1)
%55 = load double, double* %4
%56 = fsub double %55, 3.000000e+00
%57 = load double, double* getelementptr inbounds ([4 x [4 x double]], [4 x [4 x double]]* @it_pol_neville_s4.d, i64 0, i64 1, i64 1)
%58 = fmul double %56, %57
%59 = fneg double %58
%60 = call double @llvm.fmuladd.f64(double %53, double %54, double %59)
%61 = fdiv double %60, 2.000000e+00
store double %61, double* getelementptr inbounds ([4 x [4 x double]], [4 x [4 x double]]* @it_pol_neville_s4.d, i64 0, i64 1, i64 2)
%62 = load double, double* %4
%63 = load double, double* getelementptr inbounds ([4 x [4 x double]], [4 x [4 x double]]* @it_pol_neville_s4.d, i64 0, i64 1, i64 2)
%64 = load double, double* %4
%65 = fsub double %64, 3.000000e+00
%66 = load double, double* getelementptr inbounds ([4 x [4 x double]], [4 x [4 x double]]* @it_pol_neville_s4.d, i64 0, i64 0, i64 2)
%67 = fmul double %65, %66
%68 = fneg double %67
%69 = call double @llvm.fmuladd.f64(double %62, double %63, double %68)
%70 = fdiv double %69, 3.000000e+00
ret double %70
}

LLVM IR (-O2):
define double @it_pol_neville_s4(double* nocapture %0, double %1) {
%3 = getelementptr inbounds double, double* %0, i64 1
%4 = load double, double* %3
%5 = fadd double %1, -1.000000e+00
%6 = load double, double* %0
%7 = fneg double %5
%8 = fmul double %6, %7
%9 = tail call double @llvm.fmuladd.f64(double %1, double %4, double %8)
%10 = getelementptr inbounds double, double* %0, i64 2
%11 = load double, double* %10
%12 = fadd double %1, -2.000000e+00
%13 = fneg double %12
%14 = fmul double %4, %13
%15 = tail call double @llvm.fmuladd.f64(double %5, double %11, double %14)
%16 = getelementptr inbounds double, double* %0, i64 3
%17 = load double, double* %16
%18 = fadd double %1, -3.000000e+00
%19 = fneg double %18
%20 = fmul double %11, %19
%21 = tail call double @llvm.fmuladd.f64(double %12, double %17, double %20)
%22 = fmul double %9, %13
%23 = tail call double @llvm.fmuladd.f64(double %1, double %15, double %22)
%24 = fmul double %23, 5.000000e-01
%25 = fmul double %15, %19
%26 = tail call double @llvm.fmuladd.f64(double %5, double %21, double %25)
%27 = fmul double %26, 5.000000e-01
%28 = fmul double %24, %19
%29 = tail call double @llvm.fmuladd.f64(double %1, double %27, double %28)
%30 = fdiv double %29, 3.000000e+00
ret double %30
}