double alpha1n(mu, dt, t, t0)
double mu, dt, t, t0;
{
  double m1;
  if (mu == .5)
    return (sqrt(fabs(t - t0)) - sqrt(fabs(t - t0 - dt)));
  m1 = 1 - mu;
  return (.5 * (pow(fabs(t - t0), m1) - pow(fabs(t - t0 - dt), m1)) / m1);
}


x86 assembly (clang, -O0):
<alpha1n>:
push   %rbp
mov    %rsp,%rbp
sub    $0x40,%rsp
movsd  %xmm0,-0x10(%rbp)
movsd  %xmm1,-0x18(%rbp)
movsd  %xmm2,-0x20(%rbp)
movsd  %xmm3,-0x28(%rbp)
movsd  -0x10(%rbp),%xmm0
movsd  0xeb7(%rip),%xmm1
ucomisd %xmm1,%xmm0
jne    11ad <alpha1n+0x8d>
jp     11ad <alpha1n+0x8d>
movsd  -0x20(%rbp),%xmm0
subsd  -0x28(%rbp),%xmm0
movaps 0xea6(%rip),%xmm1
pand   %xmm1,%xmm0
call   1040 <sqrt@plt>
movsd  %xmm0,-0x38(%rbp)
movsd  -0x20(%rbp),%xmm0
subsd  -0x28(%rbp),%xmm0
subsd  -0x18(%rbp),%xmm0
movaps 0xe82(%rip),%xmm1
pand   %xmm1,%xmm0
call   1040 <sqrt@plt>
movaps %xmm0,%xmm1
movsd  -0x38(%rbp),%xmm0
subsd  %xmm1,%xmm0
movsd  %xmm0,-0x8(%rbp)
jmp    1226 <alpha1n+0x106>
movsd  0xe53(%rip),%xmm0
subsd  -0x10(%rbp),%xmm0
movsd  %xmm0,-0x30(%rbp)
movsd  -0x20(%rbp),%xmm0
subsd  -0x28(%rbp),%xmm0
movaps 0xe40(%rip),%xmm1
pand   %xmm1,%xmm0
movsd  -0x30(%rbp),%xmm1
call   1030 <pow@plt>
movsd  %xmm0,-0x40(%rbp)
movsd  -0x20(%rbp),%xmm0
subsd  -0x28(%rbp),%xmm0
subsd  -0x18(%rbp),%xmm0
movaps 0xe17(%rip),%xmm1
pand   %xmm1,%xmm0
movsd  -0x30(%rbp),%xmm1
call   1030 <pow@plt>
movsd  -0x40(%rbp),%xmm1
subsd  %xmm0,%xmm1
movsd  0xde8(%rip),%xmm0
mulsd  %xmm1,%xmm0
divsd  -0x30(%rbp),%xmm0
movsd  %xmm0,-0x8(%rbp)
movsd  -0x8(%rbp),%xmm0
add    $0x40,%rsp
pop    %rbp
ret

x86 assembly (clang, -O2):
<alpha1n>:
sub    $0x38,%rsp
movapd %xmm1,%xmm4
ucomisd 0xed0(%rip),%xmm0
jne    115a <alpha1n+0x3a>
jp     115a <alpha1n+0x3a>
subsd  %xmm3,%xmm2
movapd 0xed0(%rip),%xmm0
andpd  %xmm2,%xmm0
xorpd  %xmm3,%xmm3
ucomisd %xmm3,%xmm0
jb     11cc <alpha1n+0xac>
xorps  %xmm1,%xmm1
sqrtsd %xmm0,%xmm1
jmp    11f1 <alpha1n+0xd1>
movsd  0xea6(%rip),%xmm1
subsd  %xmm0,%xmm1
movsd  %xmm1,0x18(%rsp)
subsd  %xmm3,%xmm2
movapd %xmm2,0x20(%rsp)
movapd %xmm2,%xmm0
andpd  0xe8e(%rip),%xmm0
movsd  %xmm4,0x8(%rsp)
call   1030 <pow@plt>
movsd  %xmm0,0x10(%rsp)
movapd 0x20(%rsp),%xmm0
subsd  0x8(%rsp),%xmm0
andpd  0xe69(%rip),%xmm0
movsd  0x18(%rsp),%xmm1
call   1030 <pow@plt>
movsd  0x10(%rsp),%xmm1
subsd  %xmm0,%xmm1
mulsd  0xe3c(%rip),%xmm1
divsd  0x18(%rsp),%xmm1
jmp    1225 <alpha1n+0x105>
movapd %xmm2,0x20(%rsp)
movsd  %xmm4,0x8(%rsp)
call   1040 <sqrt@plt>
xorpd  %xmm3,%xmm3
movsd  0x8(%rsp),%xmm4
movapd 0x20(%rsp),%xmm2
movapd %xmm0,%xmm1
subsd  %xmm4,%xmm2
andpd  0xe13(%rip),%xmm2
ucomisd %xmm3,%xmm2
jb     120c <alpha1n+0xec>
xorps  %xmm0,%xmm0
sqrtsd %xmm2,%xmm0
jmp    1221 <alpha1n+0x101>
movapd %xmm2,%xmm0
movsd  %xmm1,0x10(%rsp)
call   1040 <sqrt@plt>
movsd  0x10(%rsp),%xmm1
subsd  %xmm0,%xmm1
movapd %xmm1,%xmm0
add    $0x38,%rsp
ret

LLVM IR (-O0):
define double @alpha1n(double %0, double %1, double %2, double %3) {
%5 = alloca double
%6 = alloca double
%7 = alloca double
%8 = alloca double
%9 = alloca double
%10 = alloca double
store double %0, double* %6
store double %1, double* %7
store double %2, double* %8
store double %3, double* %9
%11 = load double, double* %6
%12 = fcmp oeq double %11, 5.000000e-01
br i1 %12, label %13, label %27
13: ; preds = %4
%14 = load double, double* %8
%15 = load double, double* %9
%16 = fsub double %14, %15
%17 = call double @llvm.fabs.f64(double %16)
%18 = call double @sqrt(double %17)
%19 = load double, double* %8
%20 = load double, double* %9
%21 = fsub double %19, %20
%22 = load double, double* %7
%23 = fsub double %21, %22
%24 = call double @llvm.fabs.f64(double %23)
%25 = call double @sqrt(double %24)
%26 = fsub double %18, %25
store double %26, double* %5
br label %48
27: ; preds = %4
%28 = load double, double* %6
%29 = fsub double 1.000000e+00, %28
store double %29, double* %10
%30 = load double, double* %8
%31 = load double, double* %9
%32 = fsub double %30, %31
%33 = call double @llvm.fabs.f64(double %32)
%34 = load double, double* %10
%35 = call double @pow(double %33, double %34)
%36 = load double, double* %8
%37 = load double, double* %9
%38 = fsub double %36, %37
%39 = load double, double* %7
%40 = fsub double %38, %39
%41 = call double @llvm.fabs.f64(double %40)
%42 = load double, double* %10
%43 = call double @pow(double %41, double %42)
%44 = fsub double %35, %43
%45 = fmul double 5.000000e-01, %44
%46 = load double, double* %10
%47 = fdiv double %45, %46
store double %47, double* %5
br label %48
48: ; preds = %27, %13
%49 = load double, double* %5
ret double %49
}

LLVM IR (-O2):
define double @alpha1n(double %0, double %1, double %2, double %3) {
%5 = fcmp oeq double %0, 5.000000e-01
br i1 %5, label %6, label %14
6: ; preds = %4
%7 = fsub double %2, %3
%8 = tail call double @llvm.fabs.f64(double %7)
%9 = tail call double @sqrt(double %8)
%10 = fsub double %7, %1
%11 = tail call double @llvm.fabs.f64(double %10)
%12 = tail call double @sqrt(double %11)
%13 = fsub double %9, %12
br label %25
14: ; preds = %4
%15 = fsub double 1.000000e+00, %0
%16 = fsub double %2, %3
%17 = tail call double @llvm.fabs.f64(double %16)
%18 = tail call double @pow(double %17, double %15)
%19 = fsub double %16, %1
%20 = tail call double @llvm.fabs.f64(double %19)
%21 = tail call double @pow(double %20, double %15)
%22 = fsub double %18, %21
%23 = fmul double %22, 5.000000e-01
%24 = fdiv double %23, %15
br label %25
25: ; preds = %14, %6
%26 = phi double [ %13, %6 ], [ %24, %14 ]
ret double %26
}