Repository: pytorch
Issue: Numerical differences on bf16/fp32 division and fp32 torch.cumsum
Labels: triaged,oncall: pt2,module: inductor,module: pt2 accuracy

### 🐛 Describe the bug

With the following code that does a simple division, I would expect there's no numerical difference larger than the default atol and rtol between eager mode and compiled mode, but there is

```
import torch

def division(Y, y):
    return (Y / y.to(Y.dtype).unsqueeze(-1))

Y, y = torch.randn(size=(1, 6, 128, 4, 32), dtype=torch.bfloat16, device='cuda'), torch.randn(size=(1, 6, 128, 4), dtype=torch.float32, device='cuda')

print("Y.mean()", Y.mean())
print("Y.std()", Y.std())
print("y.mean()", y.mean())
print("y.std()", y.std())

out_eager = division(Y, y)
out_compiled = torch.compile(division)(Y, y)

print(torch.allclose(out_eager, out_compiled))
print("diff", (out_eager - out_compiled).abs().max())
print("torch.version", torch.__version__)
```

This gives the following output
```
Y.mean() tensor(0.0010, device='cuda:0', dtype=torch.bfloat16)
Y.std() tensor(1., device='cuda:0', dtype=torch.bfloat16)
y.mean() tensor(-0.0218, device='cuda:0')
y.std() tensor(0.9883, device='cuda:0')
False
diff tensor(8., device='cuda:0', dtype=torch.bfloat16)
torch.version 2.4.1+cu121
```

However, I would expect the output from eager mode matches that from the compiled mode. 

If I change the division to the following, 
```
def division(Y, y):
    return (Y / y.unsqueeze(-1)).to(Y.dtype)
```

eager mode output and compiled mode output matches, which suggests division in bf16 is not handled the same way between eager mode and compiled mode?


----
Similarly, I would expect the following code to not produce numerical differences larger than the default atol and rtol, but there is

```
import torch

def fn(discount):
    discount = discount.cumsum(2, dtype=torch.float32)
    return discount


discount = torch.randn(size=(1, 6, 128, 4), dtype=torch.float32, device='cuda')

print("discount.mean()", discount.mean())
print("discount.std()", discount.std())

out_eager = fn(discount)
out_compiled = torch.compile(fn)(discount)

print(torch.allclose(out_eager, out_compiled))
print("diff:", torch.max(torch.abs(out_eager - out_compiled)))
```
will print
```
discount.mean() tensor(-0.0191, device='cuda:0')
discount.std() tensor(0.9815, device='cuda:0')
False
diff: tensor(7.6294e-06, device='cuda:0')
```



### Error logs

_No response_

### Versions

```
Collecting environment information...
PyTorch version: 2.4.1+cu121
Is debug build: False
CUDA used to build PyTorch: 12.1
ROCM used to build PyTorch: N/A

OS: Ubuntu 23.04 (x86_64)
GCC version: (Ubuntu 12.3.0-1ubuntu1~23.04) 12.3.0
Clang version: Could not collect
CMake version: version 3.25.1
Libc version: glibc-2.37

Python version: 3.11.4 (main, Dec  7 2023, 15:43:41) [GCC 12.3.0] (64-bit runtime)
Python platform: Linux-6.2.0-39-generic-x86_64-with-glibc2.37
Is CUDA available: True
CUDA runtime version: 12.2.140
CUDA_MODULE_LOADING set to: LAZY
GPU models and configuration: 
GPU 0: NVIDIA RTX A6000
GPU 1: NVIDIA RTX A6000

Nvidia driver version: 535.161.07
cuDNN version: Probably one of the following:
/usr/lib/x86_64-linux-gnu/libcudnn.so.8.9.7
/usr/lib/x86_64-linux-gnu/libcudnn_adv_infer.so.8.9.7
/usr/lib/x86_64-linux-gnu/libcudnn_adv_train.so.8.9.7
/usr/lib/x86_64-linux-gnu/libcudnn_cnn_infer.so.8.9.7
/usr/lib/x86_64-linux-gnu/libcudnn_cnn_train.so.8.9.7
/usr/lib/x86_64-linux-gnu/libcudnn_ops_infer.so.8.9.7
/usr/lib/x86_64-linux-gnu/libcudnn_ops_train.so.8.9.7
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:                      48 bits physical, 48 bits virtual
Byte Order:                         Little Endian
CPU(s):                             32
On-line CPU(s) list:                0-31
Vendor ID:                          AuthenticAMD
Model name:                         AMD Ryzen Threadripper PRO 5955WX 16-Cores
CPU family:                         25
Model:                              8
Thread(s) per core:                 2
Core(s) per socket:                 16
Socket(s):                          1
Stepping:                           2
Frequency boost:                    enabled
CPU(s) scaling MHz:                 43%
CPU max MHz:                        7031.2500
CPU min MHz:                        1800.0000
BogoMIPS:                           7985.56
Flags:                              fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ht syscall nx mmxext fxsr_opt pdpe1gb rdtscp lm constant_tsc rep_good nopl nonstop_tsc cpuid extd_apicid aperfmperf rapl pni pclmulqdq monitor ssse3 fma cx16 pcid sse4_1 sse4_2 x2apic movbe popcnt aes xsave avx f16c rdrand lahf_lm cmp_legacy svm extapic cr8_legacy abm sse4a misalignsse 3dnowprefetch osvw ibs skinit wdt tce topoext perfctr_core perfctr_nb bpext perfctr_llc mwaitx cpb cat_l3 cdp_l3 invpcid_single hw_pstate ssbd mba ibrs ibpb stibp vmmcall fsgsbase bmi1 avx2 smep bmi2 erms invpcid cqm rdt_a rdseed adx smap clflushopt clwb sha_ni xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local clzero irperf xsaveerptr rdpru wbnoinvd amd_ppin brs arat npt lbrv svm_lock nrip_save tsc_scale vmcb_clean flushbyasid decodeassists pausefilter pfthreshold avic v_vmsave_vmload vgif v_spec_ctrl umip pku ospke vaes vpclmulqdq rdpid overflow_recov succor smca fsrm
Virtualization:                     AMD-V
L1d cache:                          512 KiB (16 instances)
L1i cache:                          512 KiB (16 instances)
L2 cache:                           8 MiB (16 instances)
L3 cache:                           64 MiB (2 instances)
NUMA node(s):                       1
NUMA node0 CPU(s):                  0-31
Vulnerability Gather data sampling: Not affected
Vulnerability Itlb multihit:        Not affected
Vulnerability L1tf:                 Not affected
Vulnerability Mds:                  Not affected
Vulnerability Meltdown:             Not affected
Vulnerability Mmio stale data:      Not affected
Vulnerability Retbleed:             Not affected
Vulnerability Spec rstack overflow: Mitigation; safe RET, no microcode
Vulnerability Spec store bypass:    Mitigation; Speculative Store Bypass disabled via prctl
Vulnerability Spectre v1:           Mitigation; usercopy/swapgs barriers and __user pointer sanitization
Vulnerability Spectre v2:           Mitigation; Retpolines, IBPB conditional, IBRS_FW, STIBP always-on, RSB filling, PBRSB-eIBRS Not affected
Vulnerability Srbds:                Not affected
Vulnerability Tsx async abort:      Not affected

Versions of relevant libraries:
[pip3] jax-triton==0.1.4
[pip3] jaxlib==0.4.26+cuda12.cudnn89
[pip3] numpy==1.26.4
[pip3] nvidia-cublas-cu12==12.1.3.1
[pip3] nvidia-cuda-cupti-cu12==12.1.105
[pip3] nvidia-cuda-nvrtc-cu12==12.1.105
[pip3] nvidia-cuda-runtime-cu12==12.1.105
[pip3] nvidia-cudnn-cu12==9.1.0.70
[pip3] nvidia-cufft-cu12==11.0.2.54
[pip3] nvidia-curand-cu12==10.3.2.106
[pip3] nvidia-cusolver-cu12==11.4.5.107
[pip3] nvidia-cusparse-cu12==12.1.0.106
[pip3] nvidia-nccl-cu12==2.20.5
[pip3] nvidia-nvjitlink-cu12==12.5.82
[pip3] nvidia-nvtx-cu12==12.1.105
[pip3] optree==0.11.0
[pip3] pytorch-lightning==2.3.0
[pip3] torch==2.4.1
[pip3] torchmetrics==1.4.0.post0
[pip3] triton==3.0.0
[conda] Could not collect
```

cc @chauhang @penguinwu @voznesenskym @EikanWang @jgong5 @Guobing-Chen @XiaobingSuper @zhuhaozhe @blzheng @wenzhe-nrv @jiayisunx @ipiszy @yf225 @chenyang78 @kadeng @muchulee8 @ColinPeppler @amjames @desertfire @aakhundov