double Parabolic_Minimum(double x[], double y[], double cut_off_scale_factor) {
  double d1 = (x[2] - x[1]) * (y[1] - y[0]);
  double d2 = (x[1] - x[0]) * (y[2] - y[1]);
  double denominator = 2.0 * (d1 - d2);
  double numerator = (x[2] + x[1]) * d1 - (x[1] + x[0]) * d2;
  double x_lb = x[0] - cut_off_scale_factor * (x[1] - x[0]);
  double x_ub = x[2] + cut_off_scale_factor * (x[2] - x[1]);
  double ymax = (y[2] - y[0]) * (x[1] - x[0]) / (x[2] - x[0]) + y[0];
  double xmin;
  if (y[1] >= ymax)
    xmin = (y[0] < y[2]) ? x_lb : x_ub;
  else {
    if (x_lb * denominator <= numerator)
      xmin = x_lb;
    else if (x_ub * denominator >= numerator)
      xmin = x_ub;
    else
      xmin = numerator / denominator;
  }
  return xmin;
}


x86 assembly (clang, -O0):
<Parabolic_Minimum>:
push   %rbp
mov    %rsp,%rbp
mov    %rdi,-0x8(%rbp)
mov    %rsi,-0x10(%rbp)
movsd  %xmm0,-0x18(%rbp)
mov    -0x8(%rbp),%rax
movsd  0x10(%rax),%xmm0
mov    -0x8(%rbp),%rax
subsd  0x8(%rax),%xmm0
mov    -0x10(%rbp),%rax
movsd  0x8(%rax),%xmm1
mov    -0x10(%rbp),%rax
subsd  (%rax),%xmm1
mulsd  %xmm1,%xmm0
movsd  %xmm0,-0x20(%rbp)
mov    -0x8(%rbp),%rax
movsd  0x8(%rax),%xmm0
mov    -0x8(%rbp),%rax
subsd  (%rax),%xmm0
mov    -0x10(%rbp),%rax
movsd  0x10(%rax),%xmm1
mov    -0x10(%rbp),%rax
subsd  0x8(%rax),%xmm1
mulsd  %xmm1,%xmm0
movsd  %xmm0,-0x28(%rbp)
movsd  -0x20(%rbp),%xmm1
subsd  -0x28(%rbp),%xmm1
movsd  0xe85(%rip),%xmm0
mulsd  %xmm1,%xmm0
movsd  %xmm0,-0x30(%rbp)
mov    -0x8(%rbp),%rax
movsd  0x10(%rax),%xmm0
mov    -0x8(%rbp),%rax
addsd  0x8(%rax),%xmm0
movsd  -0x20(%rbp),%xmm2
mov    -0x8(%rbp),%rax
movsd  0x8(%rax),%xmm1
mov    -0x8(%rbp),%rax
addsd  (%rax),%xmm1
mulsd  -0x28(%rbp),%xmm1
movq   %xmm1,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm1
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
movsd  %xmm0,-0x38(%rbp)
mov    -0x8(%rbp),%rax
movsd  (%rax),%xmm1
movsd  -0x18(%rbp),%xmm0
mov    -0x8(%rbp),%rax
movsd  0x8(%rax),%xmm2
mov    -0x8(%rbp),%rax
subsd  (%rax),%xmm2
movq   %xmm0,%rax
movabs $0x8000000000000000,%rcx
xor    %rcx,%rax
movq   %rax,%xmm0
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
movsd  %xmm0,-0x40(%rbp)
mov    -0x8(%rbp),%rax
movsd  0x10(%rax),%xmm1
movsd  -0x18(%rbp),%xmm0
mov    -0x8(%rbp),%rax
movsd  0x10(%rax),%xmm2
mov    -0x8(%rbp),%rax
subsd  0x8(%rax),%xmm2
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
movsd  %xmm0,-0x48(%rbp)
mov    -0x10(%rbp),%rax
movsd  0x10(%rax),%xmm0
mov    -0x10(%rbp),%rax
subsd  (%rax),%xmm0
mov    -0x8(%rbp),%rax
movsd  0x8(%rax),%xmm1
mov    -0x8(%rbp),%rax
subsd  (%rax),%xmm1
mulsd  %xmm1,%xmm0
mov    -0x8(%rbp),%rax
movsd  0x10(%rax),%xmm1
mov    -0x8(%rbp),%rax
subsd  (%rax),%xmm1
divsd  %xmm1,%xmm0
mov    -0x10(%rbp),%rax
addsd  (%rax),%xmm0
movsd  %xmm0,-0x50(%rbp)
mov    -0x10(%rbp),%rax
movsd  0x8(%rax),%xmm0
ucomisd -0x50(%rbp),%xmm0
jb     12e3 <Parabolic_Minimum+0x1e3>
mov    -0x10(%rbp),%rax
movsd  (%rax),%xmm1
mov    -0x10(%rbp),%rax
movsd  0x10(%rax),%xmm0
ucomisd %xmm1,%xmm0
jbe    12ca <Parabolic_Minimum+0x1ca>
movsd  -0x40(%rbp),%xmm0
movsd  %xmm0,-0x60(%rbp)
jmp    12d4 <Parabolic_Minimum+0x1d4>
movsd  -0x48(%rbp),%xmm0
movsd  %xmm0,-0x60(%rbp)
movsd  -0x60(%rbp),%xmm0
movsd  %xmm0,-0x58(%rbp)
jmp    1348 <Parabolic_Minimum+0x248>
movsd  -0x40(%rbp),%xmm1
mulsd  -0x30(%rbp),%xmm1
movsd  -0x38(%rbp),%xmm0
ucomisd %xmm1,%xmm0
jb     130b <Parabolic_Minimum+0x20b>
movsd  -0x40(%rbp),%xmm0
movsd  %xmm0,-0x58(%rbp)
jmp    1343 <Parabolic_Minimum+0x243>
movsd  -0x48(%rbp),%xmm0
mulsd  -0x30(%rbp),%xmm0
ucomisd -0x38(%rbp),%xmm0
jb     132f <Parabolic_Minimum+0x22f>
movsd  -0x48(%rbp),%xmm0
movsd  %xmm0,-0x58(%rbp)
jmp    133e <Parabolic_Minimum+0x23e>
movsd  -0x38(%rbp),%xmm0
divsd  -0x30(%rbp),%xmm0
movsd  %xmm0,-0x58(%rbp)
jmp    1343 <Parabolic_Minimum+0x243>
jmp    1348 <Parabolic_Minimum+0x248>
movsd  -0x58(%rbp),%xmm0
pop    %rbp
ret

x86 assembly (clang, -O2):
<Parabolic_Minimum>:
movsd  0x10(%rdi),%xmm4
movsd  (%rdi),%xmm3
movsd  0x8(%rdi),%xmm8
movapd %xmm4,%xmm1
subsd  %xmm8,%xmm1
movsd  (%rsi),%xmm7
movsd  0x8(%rsi),%xmm10
movapd %xmm8,%xmm6
subsd  %xmm3,%xmm6
movsd  0x10(%rsi),%xmm9
movapd %xmm0,%xmm5
mulsd  %xmm6,%xmm5
movapd %xmm3,%xmm11
subsd  %xmm5,%xmm11
mulsd  %xmm1,%xmm0
addsd  %xmm4,%xmm0
movapd %xmm9,%xmm5
subsd  %xmm7,%xmm5
mulsd  %xmm6,%xmm5
movapd %xmm4,%xmm2
subsd  %xmm3,%xmm2
divsd  %xmm2,%xmm5
addsd  %xmm7,%xmm5
ucomisd %xmm5,%xmm10
jae    11d6 <Parabolic_Minimum+0xd6>
subsd  %xmm10,%xmm9
subsd  %xmm7,%xmm10
mulsd  %xmm10,%xmm1
mulsd  %xmm9,%xmm6
movapd %xmm1,%xmm5
subsd  %xmm6,%xmm5
addsd  %xmm5,%xmm5
addsd  %xmm8,%xmm4
addsd  %xmm8,%xmm3
mulsd  %xmm6,%xmm3
mulsd  %xmm1,%xmm4
subsd  %xmm3,%xmm4
movapd %xmm11,%xmm1
mulsd  %xmm5,%xmm1
ucomisd %xmm1,%xmm4
jae    11d0 <Parabolic_Minimum+0xd0>
movapd %xmm0,%xmm1
mulsd  %xmm5,%xmm1
ucomisd %xmm4,%xmm1
movapd %xmm0,%xmm11
jae    11d0 <Parabolic_Minimum+0xd0>
divsd  %xmm5,%xmm4
movapd %xmm4,%xmm11
movapd %xmm11,%xmm0
ret
cmpltsd %xmm9,%xmm7
andpd  %xmm7,%xmm11
andnpd %xmm0,%xmm7
orpd   %xmm7,%xmm11
movapd %xmm11,%xmm0
ret

LLVM IR (-O0):
define double @Parabolic_Minimum(double* %0, double* %1, double %2) {
%4 = alloca double*
%5 = alloca double*
%6 = alloca double
%7 = alloca double
%8 = alloca double
%9 = alloca double
%10 = alloca double
%11 = alloca double
%12 = alloca double
%13 = alloca double
%14 = alloca double
store double* %0, double** %4
store double* %1, double** %5
store double %2, double* %6
%15 = load double*, double** %4
%16 = getelementptr inbounds double, double* %15, i64 2
%17 = load double, double* %16
%18 = load double*, double** %4
%19 = getelementptr inbounds double, double* %18, i64 1
%20 = load double, double* %19
%21 = fsub double %17, %20
%22 = load double*, double** %5
%23 = getelementptr inbounds double, double* %22, i64 1
%24 = load double, double* %23
%25 = load double*, double** %5
%26 = getelementptr inbounds double, double* %25, i64 0
%27 = load double, double* %26
%28 = fsub double %24, %27
%29 = fmul double %21, %28
store double %29, double* %7
%30 = load double*, double** %4
%31 = getelementptr inbounds double, double* %30, i64 1
%32 = load double, double* %31
%33 = load double*, double** %4
%34 = getelementptr inbounds double, double* %33, i64 0
%35 = load double, double* %34
%36 = fsub double %32, %35
%37 = load double*, double** %5
%38 = getelementptr inbounds double, double* %37, i64 2
%39 = load double, double* %38
%40 = load double*, double** %5
%41 = getelementptr inbounds double, double* %40, i64 1
%42 = load double, double* %41
%43 = fsub double %39, %42
%44 = fmul double %36, %43
store double %44, double* %8
%45 = load double, double* %7
%46 = load double, double* %8
%47 = fsub double %45, %46
%48 = fmul double 2.000000e+00, %47
store double %48, double* %9
%49 = load double*, double** %4
%50 = getelementptr inbounds double, double* %49, i64 2
%51 = load double, double* %50
%52 = load double*, double** %4
%53 = getelementptr inbounds double, double* %52, i64 1
%54 = load double, double* %53
%55 = fadd double %51, %54
%56 = load double, double* %7
%57 = load double*, double** %4
%58 = getelementptr inbounds double, double* %57, i64 1
%59 = load double, double* %58
%60 = load double*, double** %4
%61 = getelementptr inbounds double, double* %60, i64 0
%62 = load double, double* %61
%63 = fadd double %59, %62
%64 = load double, double* %8
%65 = fmul double %63, %64
%66 = fneg double %65
%67 = call double @llvm.fmuladd.f64(double %55, double %56, double %66)
store double %67, double* %10
%68 = load double*, double** %4
%69 = getelementptr inbounds double, double* %68, i64 0
%70 = load double, double* %69
%71 = load double, double* %6
%72 = load double*, double** %4
%73 = getelementptr inbounds double, double* %72, i64 1
%74 = load double, double* %73
%75 = load double*, double** %4
%76 = getelementptr inbounds double, double* %75, i64 0
%77 = load double, double* %76
%78 = fsub double %74, %77
%79 = fneg double %71
%80 = call double @llvm.fmuladd.f64(double %79, double %78, double %70)
store double %80, double* %11
%81 = load double*, double** %4
%82 = getelementptr inbounds double, double* %81, i64 2
%83 = load double, double* %82
%84 = load double, double* %6
%85 = load double*, double** %4
%86 = getelementptr inbounds double, double* %85, i64 2
%87 = load double, double* %86
%88 = load double*, double** %4
%89 = getelementptr inbounds double, double* %88, i64 1
%90 = load double, double* %89
%91 = fsub double %87, %90
%92 = call double @llvm.fmuladd.f64(double %84, double %91, double %83)
store double %92, double* %12
%93 = load double*, double** %5
%94 = getelementptr inbounds double, double* %93, i64 2
%95 = load double, double* %94
%96 = load double*, double** %5
%97 = getelementptr inbounds double, double* %96, i64 0
%98 = load double, double* %97
%99 = fsub double %95, %98
%100 = load double*, double** %4
%101 = getelementptr inbounds double, double* %100, i64 1
%102 = load double, double* %101
%103 = load double*, double** %4
%104 = getelementptr inbounds double, double* %103, i64 0
%105 = load double, double* %104
%106 = fsub double %102, %105
%107 = fmul double %99, %106
%108 = load double*, double** %4
%109 = getelementptr inbounds double, double* %108, i64 2
%110 = load double, double* %109
%111 = load double*, double** %4
%112 = getelementptr inbounds double, double* %111, i64 0
%113 = load double, double* %112
%114 = fsub double %110, %113
%115 = fdiv double %107, %114
%116 = load double*, double** %5
%117 = getelementptr inbounds double, double* %116, i64 0
%118 = load double, double* %117
%119 = fadd double %115, %118
store double %119, double* %13
%120 = load double*, double** %5
%121 = getelementptr inbounds double, double* %120, i64 1
%122 = load double, double* %121
%123 = load double, double* %13
%124 = fcmp oge double %122, %123
br i1 %124, label %125, label %139
125: ; preds = %3
%126 = load double*, double** %5
%127 = getelementptr inbounds double, double* %126, i64 0
%128 = load double, double* %127
%129 = load double*, double** %5
%130 = getelementptr inbounds double, double* %129, i64 2
%131 = load double, double* %130
%132 = fcmp olt double %128, %131
br i1 %132, label %133, label %135
133: ; preds = %125
%134 = load double, double* %11
br label %137
135: ; preds = %125
%136 = load double, double* %12
br label %137
137: ; preds = %135, %133
%138 = phi double [ %134, %133 ], [ %136, %135 ]
store double %138, double* %14
br label %161
139: ; preds = %3
%140 = load double, double* %11
%141 = load double, double* %9
%142 = fmul double %140, %141
%143 = load double, double* %10
%144 = fcmp ole double %142, %143
br i1 %144, label %145, label %147
145: ; preds = %139
%146 = load double, double* %11
store double %146, double* %14
br label %160
147: ; preds = %139
%148 = load double, double* %12
%149 = load double, double* %9
%150 = fmul double %148, %149
%151 = load double, double* %10
%152 = fcmp oge double %150, %151
br i1 %152, label %153, label %155
153: ; preds = %147
%154 = load double, double* %12
store double %154, double* %14
br label %159
155: ; preds = %147
%156 = load double, double* %10
%157 = load double, double* %9
%158 = fdiv double %156, %157
store double %158, double* %14
br label %159
159: ; preds = %155, %153
br label %160
160: ; preds = %159, %145
br label %161
161: ; preds = %160, %137
%162 = load double, double* %14
ret double %162
}

LLVM IR (-O2):
define double @Parabolic_Minimum(double* nocapture %0, double* nocapture %1, double %2) {
%4 = getelementptr inbounds double, double* %0, i64 2
%5 = load double, double* %4
%6 = getelementptr inbounds double, double* %0, i64 1
%7 = load double, double* %6
%8 = fsub double %5, %7
%9 = getelementptr inbounds double, double* %1, i64 1
%10 = load double, double* %9
%11 = load double, double* %1
%12 = fsub double %10, %11
%13 = fmul double %8, %12
%14 = load double, double* %0
%15 = fsub double %7, %14
%16 = getelementptr inbounds double, double* %1, i64 2
%17 = load double, double* %16
%18 = fsub double %17, %10
%19 = fmul double %15, %18
%20 = fsub double %13, %19
%21 = fmul double %20, 2.000000e+00
%22 = fadd double %5, %7
%23 = fadd double %7, %14
%24 = fneg double %23
%25 = fmul double %19, %24
%26 = tail call double @llvm.fmuladd.f64(double %22, double %13, double %25)
%27 = fneg double %2
%28 = tail call double @llvm.fmuladd.f64(double %27, double %15, double %14)
%29 = tail call double @llvm.fmuladd.f64(double %2, double %8, double %5)
%30 = fsub double %17, %11
%31 = fmul double %15, %30
%32 = fsub double %5, %14
%33 = fdiv double %31, %32
%34 = fadd double %11, %33
%35 = fcmp ult double %10, %34
br i1 %35, label %39, label %36
36: ; preds = %3
%37 = fcmp olt double %11, %17
%38 = select i1 %37, double %28, double %29
br label %47
39: ; preds = %3
%40 = fmul double %28, %21
%41 = fcmp ugt double %40, %26
br i1 %41, label %42, label %47
42: ; preds = %39
%43 = fmul double %29, %21
%44 = fcmp ult double %43, %26
br i1 %44, label %45, label %47
45: ; preds = %42
%46 = fdiv double %26, %21
br label %47
47: ; preds = %42, %39, %45, %36
%48 = phi double [ %38, %36 ], [ %46, %45 ], [ %28, %39 ], [ %29, %42 ]
ret double %48
}