Numerical stability discrepancy in torch.compile: LayerNorm produces NaN for large inputs (~1e37) while Eager mode is stable

I found that torch.compile produces NaN when running LayerNorm with inputs near the float32 limit (~8.5e37), while the standard Eager mode remains numerically stable.

```python
import torch, os

os.environ["INDUCTOR_SHAPE_PADDING"] = "1"

def check(label, t):
clean = t.nan_to_num()
print(f"{label} -> Min: {clean.min():.4e}, Max: {clean.max():.4e}, HasNaN: {torch.isnan(t).any()}")

x = torch.load("input.pt").cuda().float().unsqueeze(0)
check("Input Data ", x)

sd = torch.load("weight.pt")
ln = torch.nn.LayerNorm(x.size(-1)).cuda().eval()
ln.load_state_dict(sd)

print("="*30 + " Repro Results " + "="*30)
with torch.no_grad():
check("Mode A (Eager) ", ln(x))
check("Mode B (Inductor)", torch.compile(ln)(x))
```
```
Input Data -> Min: 8.5071e+37, Max: 8.5071e+37, HasNaN: False
============================== Repro Results ==============================
Mode A (Eager) -> Min: -2.5888e-01, Max: 2.0193e-01, HasNaN: False
Mode B (Inductor) -> Min: 0.0000e+00, Max: 0.0000e+00, HasNaN: True
```

[repro_inductor_nan_case.zip](https://github.com/user-attachments/files/24940178/repro_inductor_nan_case.zip)

PyTorch version: 2.6.0+cu126
Is debug build: False
CUDA used to build PyTorch: 12.6
ROCM used to build PyTorch: N/A

OS: Ubuntu 24.04.3 LTS (x86_64)
GCC version: (Ubuntu 13.3.0-6ubuntu2~24.04) 13.3.0
Clang version: Could not collect
CMake version: Could not collect
Libc version: glibc-2.39

Python version: 3.9.23 (main, Jun 5 2025, 13:40:20) [GCC 11.2.0] (64-bit runtime)
Python platform: Linux-6.8.0-90-generic-x86_64-with-glibc2.39
Is CUDA available: True
CUDA runtime version: 12.6.20
CUDA_MODULE_LOADING set to: LAZY
GPU models and configuration:
GPU 0: NVIDIA GeForce RTX 3090
GPU 1: NVIDIA GeForce RTX 3090

Nvidia driver version: 560.35.03
cuDNN version: Could not collect
HIP runtime version: N/A
MIOpen runtime version: N/A
Is XNNPACK available: True

CPU:
Architecture: x86_64
CPU op-mode(s): 32-bit, 64-bit
Address sizes: 40 bits physical, 48 bits virtual
Byte Order: Little Endian
CPU(s): 48
On-line CPU(s) list: 0-47
Vendor ID: GenuineIntel
Model name: QEMU Virtual CPU version 2.5+
CPU family: 15
Model: 107
Thread(s) per core: 1
Core(s) per socket: 48
Socket(s): 1
Stepping: 1
BogoMIPS: 4190.15
Flags: fpu de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ht syscall nx lm constant_tsc nopl xtopology cpuid tsc_known_freq pni ssse3 fma cx16 sse4_1 sse4_2 x2apic movbe popcnt aes xsave avx f16c hypervisor lahf_lm abm cpuid_fault pti bmi1 avx2 bmi2 avx512f avx512dq avx512cd avx512bw avx512vl
Hypervisor vendor: KVM
Virtualization type: full

Versions of relevant libraries:
[pip3] numpy==2.0.2
[pip3] nvidia-cublas-cu12==12.6.4.1
[pip3] nvidia-cuda-cupti-cu12==12.6.80
[pip3] nvidia-cuda-nvrtc-cu12==12.6.77
[pip3] nvidia-cuda-runtime-cu12==12.6.77
[pip3] nvidia-cudnn-cu12==9.5.1.17
[pip3] nvidia-cufft-cu12==11.3.0.4
[pip3] nvidia-curand-cu12==10.3.7.77
[pip3] nvidia-cusolver-cu12==11.7.1.2
[pip3] nvidia-cusparse-cu12==12.5.4.2
[pip3] nvidia-cusparselt-cu12==0.6.3
[pip3] nvidia-nccl-cu12==2.21.5
[pip3] nvidia-nvjitlink-cu12==12.6.85
[pip3] nvidia-nvtx-cu12==12.6.77
[pip3] torch==2.6.0+cu126
[pip3] torchaudio==2.6.0+cu126
[pip3] torchvision==0.21.0+cu126
[pip3] triton==3.2.0

cc @ezyang @gchanan @kadeng @msaroufim @chauhang @penguinwu @voznesenskym @EikanWang @jgong5 @Guobing-Chen @XiaobingSuper @zhuhaozhe @blzheng @wenzhe-nrv @jiayisunx @ipiszy @muchulee8 @amjames @aakhundov @coconutruben @jataylo