double it_pol_neville_s3(double *f, double alpha) {
  double d_01 = (alpha * f[1] - (alpha - 1) * f[0]);
  double d_11 = ((alpha - 1) * f[2] - (alpha - 2) * f[1]);
  return (alpha * d_11 - (alpha - 2) * d_01) / 2;
}


x86 assembly (clang, -O0):
<it_pol_neville_s3>:
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  0xee0(%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,-0x18(%rbp)
movsd  -0x10(%rbp),%xmm0
movsd  0xea3(%rip),%xmm1
subsd  %xmm1,%xmm0
mov    -0x8(%rbp),%rax
movsd  0x10(%rax),%xmm2
movsd  -0x10(%rbp),%xmm1
movsd  0xe81(%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,-0x20(%rbp)
movsd  -0x10(%rbp),%xmm0
movsd  -0x20(%rbp),%xmm2
movsd  -0x10(%rbp),%xmm1
movsd  0xe39(%rip),%xmm3
subsd  %xmm3,%xmm1
mulsd  -0x18(%rbp),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
movsd  0xe09(%rip),%xmm1
divsd  %xmm1,%xmm0
pop    %rbp
ret

x86 assembly (clang, -O2):
<it_pol_neville_s3>:
movsd  0x8(%rdi),%xmm1
movsd  0xef3(%rip),%xmm2
addsd  %xmm0,%xmm2
movsd  (%rdi),%xmm3
mulsd  %xmm2,%xmm3
movapd %xmm0,%xmm4
mulsd  %xmm1,%xmm4
subsd  %xmm3,%xmm4
movsd  0xedb(%rip),%xmm3
addsd  %xmm0,%xmm3
mulsd  %xmm3,%xmm1
mulsd  0x10(%rdi),%xmm2
subsd  %xmm1,%xmm2
mulsd  %xmm4,%xmm3
mulsd  %xmm2,%xmm0
subsd  %xmm3,%xmm0
mulsd  0xebe(%rip),%xmm0
ret

LLVM IR (-O0):
define double @it_pol_neville_s3(double* %0, double %1) {
%3 = alloca double*
%4 = alloca double
%5 = alloca double
%6 = alloca double
store double* %0, double** %3
store double %1, double* %4
%7 = load double, double* %4
%8 = load double*, double** %3
%9 = getelementptr inbounds double, double* %8, i64 1
%10 = load double, double* %9
%11 = load double, double* %4
%12 = fsub double %11, 1.000000e+00
%13 = load double*, double** %3
%14 = getelementptr inbounds double, double* %13, i64 0
%15 = load double, double* %14
%16 = fmul double %12, %15
%17 = fneg double %16
%18 = call double @llvm.fmuladd.f64(double %7, double %10, double %17)
store double %18, double* %5
%19 = load double, double* %4
%20 = fsub double %19, 1.000000e+00
%21 = load double*, double** %3
%22 = getelementptr inbounds double, double* %21, i64 2
%23 = load double, double* %22
%24 = load double, double* %4
%25 = fsub double %24, 2.000000e+00
%26 = load double*, double** %3
%27 = getelementptr inbounds double, double* %26, i64 1
%28 = load double, double* %27
%29 = fmul double %25, %28
%30 = fneg double %29
%31 = call double @llvm.fmuladd.f64(double %20, double %23, double %30)
store double %31, double* %6
%32 = load double, double* %4
%33 = load double, double* %6
%34 = load double, double* %4
%35 = fsub double %34, 2.000000e+00
%36 = load double, double* %5
%37 = fmul double %35, %36
%38 = fneg double %37
%39 = call double @llvm.fmuladd.f64(double %32, double %33, double %38)
%40 = fdiv double %39, 2.000000e+00
ret double %40
}

LLVM IR (-O2):
define double @it_pol_neville_s3(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 = fmul double %9, %13
%17 = tail call double @llvm.fmuladd.f64(double %1, double %15, double %16)
%18 = fmul double %17, 5.000000e-01
ret double %18
}