void compute_root_from_lambda(lambda, r, omega) double lambda;
double *r;
double *omega;
{
  double xi;
  double tmp, tmp2;
  tmp = sqrt(3 + 144 * lambda);
  xi = 1 - 96 * lambda + 24 * lambda * tmp;
  *omega = atan(sqrt((144 * lambda - 1.0) / xi));
  tmp2 = sqrt(xi);
  *r = (24 * lambda - 1 - tmp2) / (24 * lambda) *
       sqrt((48 * lambda + 24 * lambda * tmp)) / tmp2;
  return;
}


x86 assembly (clang, -O0):
<compute_root_from_lambda>:
push   %rbp
mov    %rsp,%rbp
sub    $0x40,%rsp
movsd  %xmm0,-0x8(%rbp)
mov    %rdi,-0x10(%rbp)
mov    %rsi,-0x18(%rbp)
movsd  -0x8(%rbp),%xmm0
movsd  0xed6(%rip),%xmm1
mulsd  %xmm1,%xmm0
movsd  0xee2(%rip),%xmm1
addsd  %xmm1,%xmm0
call   1040 <sqrt@plt>
movsd  %xmm0,-0x28(%rbp)
movsd  -0x8(%rbp),%xmm1
movsd  0xeb7(%rip),%xmm0
mulsd  %xmm0,%xmm1
movsd  0xeb3(%rip),%xmm0
addsd  %xmm0,%xmm1
movsd  0xe87(%rip),%xmm0
mulsd  -0x8(%rbp),%xmm0
movsd  -0x28(%rbp),%xmm2
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
movsd  %xmm0,-0x20(%rbp)
movsd  -0x8(%rbp),%xmm0
movsd  0xe73(%rip),%xmm1
mulsd  %xmm1,%xmm0
movsd  0xe5f(%rip),%xmm1
addsd  %xmm1,%xmm0
divsd  -0x20(%rbp),%xmm0
call   1040 <sqrt@plt>
call   1030 <atan@plt>
mov    -0x18(%rbp),%rax
movsd  %xmm0,(%rax)
movsd  -0x20(%rbp),%xmm0
call   1040 <sqrt@plt>
movsd  %xmm0,-0x30(%rbp)
movsd  -0x8(%rbp),%xmm0
movsd  0xe20(%rip),%xmm1
mulsd  %xmm1,%xmm0
movsd  0xe1c(%rip),%xmm1
addsd  %xmm1,%xmm0
subsd  -0x30(%rbp),%xmm0
movsd  0xe03(%rip),%xmm1
mulsd  -0x8(%rbp),%xmm1
divsd  %xmm1,%xmm0
movsd  %xmm0,-0x38(%rbp)
movsd  -0x8(%rbp),%xmm0
movsd  0xde8(%rip),%xmm1
mulsd  -0x8(%rbp),%xmm1
mulsd  -0x28(%rbp),%xmm1
movsd  0xdce(%rip),%xmm2
mulsd  %xmm2,%xmm0
addsd  %xmm1,%xmm0
call   1040 <sqrt@plt>
movaps %xmm0,%xmm1
movsd  -0x38(%rbp),%xmm0
mulsd  %xmm1,%xmm0
divsd  -0x30(%rbp),%xmm0
mov    -0x10(%rbp),%rax
movsd  %xmm0,(%rax)
add    $0x40,%rsp
pop    %rbp
ret

x86 assembly (clang, -O2):
<compute_root_from_lambda>:
push   %r14
push   %rbx
sub    $0x28,%rsp
mov    %rsi,%rbx
mov    %rdi,%r14
movapd %xmm0,%xmm1
movsd  0xec7(%rip),%xmm4
mulsd  %xmm0,%xmm4
movsd  0xec3(%rip),%xmm0
addsd  %xmm4,%xmm0
xorpd  %xmm5,%xmm5
ucomisd %xmm5,%xmm0
movsd  %xmm1,0x10(%rsp)
jb     115f <compute_root_from_lambda+0x3f>
sqrtsd %xmm0,%xmm0
jmp    117a <compute_root_from_lambda+0x5a>
movsd  %xmm4,0x8(%rsp)
call   1040 <sqrt@plt>
xorpd  %xmm5,%xmm5
movsd  0x8(%rsp),%xmm4
movsd  0x10(%rsp),%xmm1
movsd  0xe8e(%rip),%xmm3
mulsd  %xmm1,%xmm3
addsd  0xe8a(%rip),%xmm3
movsd  0xe8a(%rip),%xmm2
mulsd  %xmm1,%xmm2
movsd  %xmm2,0x20(%rsp)
mulsd  %xmm2,%xmm0
addsd  0xe7c(%rip),%xmm4
movsd  %xmm0,0x8(%rsp)
addsd  %xmm0,%xmm3
movsd  %xmm3,0x18(%rsp)
divsd  %xmm3,%xmm4
ucomisd %xmm5,%xmm4
jb     11cf <compute_root_from_lambda+0xaf>
xorps  %xmm0,%xmm0
sqrtsd %xmm4,%xmm0
jmp    11d8 <compute_root_from_lambda+0xb8>
movapd %xmm4,%xmm0
call   1040 <sqrt@plt>
call   1030 <atan@plt>
movsd  %xmm0,(%rbx)
xorpd  %xmm3,%xmm3
movsd  0x18(%rsp),%xmm0
ucomisd %xmm3,%xmm0
jb     11fa <compute_root_from_lambda+0xda>
xorps  %xmm2,%xmm2
sqrtsd %xmm0,%xmm2
jmp    1207 <compute_root_from_lambda+0xe7>
call   1040 <sqrt@plt>
xorpd  %xmm3,%xmm3
movapd %xmm0,%xmm2
movsd  0x10(%rsp),%xmm0
movsd  0xe13(%rip),%xmm4
movsd  0x20(%rsp),%xmm1
addsd  %xmm1,%xmm4
subsd  %xmm2,%xmm4
mulsd  0xe05(%rip),%xmm0
divsd  %xmm1,%xmm4
addsd  0x8(%rsp),%xmm0
ucomisd %xmm3,%xmm0
jb     1241 <compute_root_from_lambda+0x121>
sqrtsd %xmm0,%xmm0
jmp    125e <compute_root_from_lambda+0x13e>
movsd  %xmm2,0x10(%rsp)
movsd  %xmm4,0x8(%rsp)
call   1040 <sqrt@plt>
movsd  0x8(%rsp),%xmm4
movsd  0x10(%rsp),%xmm2
mulsd  %xmm4,%xmm0
divsd  %xmm2,%xmm0
movsd  %xmm0,(%r14)
add    $0x28,%rsp
pop    %rbx
pop    %r14
ret

LLVM IR (-O0):
define void @compute_root_from_lambda(double %0, double* %1, double* %2) {
%4 = alloca double
%5 = alloca double*
%6 = alloca double*
%7 = alloca double
%8 = alloca double
%9 = alloca double
store double %0, double* %4
store double* %1, double** %5
store double* %2, double** %6
%10 = load double, double* %4
%11 = call double @llvm.fmuladd.f64(double 1.440000e+02, double %10, double 3.000000e+00)
%12 = call double @sqrt(double %11)
store double %12, double* %8
%13 = load double, double* %4
%14 = call double @llvm.fmuladd.f64(double -9.600000e+01, double %13, double 1.000000e+00)
%15 = load double, double* %4
%16 = fmul double 2.400000e+01, %15
%17 = load double, double* %8
%18 = call double @llvm.fmuladd.f64(double %16, double %17, double %14)
store double %18, double* %7
%19 = load double, double* %4
%20 = call double @llvm.fmuladd.f64(double 1.440000e+02, double %19, double -1.000000e+00)
%21 = load double, double* %7
%22 = fdiv double %20, %21
%23 = call double @sqrt(double %22)
%24 = call double @atan(double %23)
%25 = load double*, double** %6
store double %24, double* %25
%26 = load double, double* %7
%27 = call double @sqrt(double %26)
store double %27, double* %9
%28 = load double, double* %4
%29 = call double @llvm.fmuladd.f64(double 2.400000e+01, double %28, double -1.000000e+00)
%30 = load double, double* %9
%31 = fsub double %29, %30
%32 = load double, double* %4
%33 = fmul double 2.400000e+01, %32
%34 = fdiv double %31, %33
%35 = load double, double* %4
%36 = load double, double* %4
%37 = fmul double 2.400000e+01, %36
%38 = load double, double* %8
%39 = fmul double %37, %38
%40 = call double @llvm.fmuladd.f64(double 4.800000e+01, double %35, double %39)
%41 = call double @sqrt(double %40)
%42 = fmul double %34, %41
%43 = load double, double* %9
%44 = fdiv double %42, %43
%45 = load double*, double** %5
store double %44, double* %45
ret void
}

LLVM IR (-O2):
define void @compute_root_from_lambda(double %0, double* nocapture writeonly %1, double* nocapture writeonly %2) {
%4 = tail call double @llvm.fmuladd.f64(double %0, double 1.440000e+02, double 3.000000e+00)
%5 = tail call double @sqrt(double %4)
%6 = tail call double @llvm.fmuladd.f64(double %0, double -9.600000e+01, double 1.000000e+00)
%7 = fmul double %0, 2.400000e+01
%8 = tail call double @llvm.fmuladd.f64(double %7, double %5, double %6)
%9 = tail call double @llvm.fmuladd.f64(double %0, double 1.440000e+02, double -1.000000e+00)
%10 = fdiv double %9, %8
%11 = tail call double @sqrt(double %10)
%12 = tail call double @atan(double %11)
store double %12, double* %2
%13 = tail call double @sqrt(double %8)
%14 = tail call double @llvm.fmuladd.f64(double %0, double 2.400000e+01, double -1.000000e+00)
%15 = fsub double %14, %13
%16 = fdiv double %15, %7
%17 = fmul double %7, %5
%18 = tail call double @llvm.fmuladd.f64(double %0, double 4.800000e+01, double %17)
%19 = tail call double @sqrt(double %18)
%20 = fmul double %19, %16
%21 = fdiv double %20, %13
store double %21, double* %1
ret void
}