Repository: pytorch
Issue: Broadcasting matmul is much slower than corresponding einsum
Labels: module: performance,module: cpu,triaged,has workaround

### 🐛 Describe the bug

Asymmetric broadcasting `matmul` is much slower (hundreds of times slower) than the corresponding `einsum` operation, at least on CPU (I haven't tried on GPU yet).

```python
>>> import torch
>>> A = torch.randn(3, 64, 64)
>>> B = torch.randn(4096, 3, 64, 1) 
>>> %timeit A @ B
29.8 ms ± 697 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)
>>> %timeit torch.einsum('...ij,...jk->...ik', A, B)
396 µs ± 2.84 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)
```

### Versions

```
Collecting environment information...
PyTorch version: 2.0.1
Is debug build: False
CUDA used to build PyTorch: None
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: Could not collect
Libc version: glibc-2.37

Python version: 3.9.16 | packaged by conda-forge | (main, Feb  1 2023, 21:39:03)  [GCC 11.3.0] (64-bit runtime)
Python platform: Linux-5.19.0-29-generic-x86_64-with-glibc2.37
Is CUDA available: False
CUDA runtime version: No CUDA
CUDA_MODULE_LOADING set to: N/A
GPU models and configuration: No CUDA
Nvidia driver version: No CUDA
cuDNN version: No CUDA
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):                          16
On-line CPU(s) list:             0-15
Vendor ID:                       AuthenticAMD
Model name:                      AMD Ryzen 7 PRO 6850U with Radeon Graphics
CPU family:                      25
Model:                           68
Thread(s) per core:              2
Core(s) per socket:              8
Socket(s):                       1
Stepping:                        1
Frequency boost:                 enabled
CPU(s) scaling MHz:              44%
CPU max MHz:                     4768,0000
CPU min MHz:                     400,0000
BogoMIPS:                        5390,25
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 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 hw_pstate ssbd mba ibrs ibpb stibp vmmcall fsgsbase bmi1 avx2 smep bmi2 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 cppc 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
Virtualization:                  AMD-V
L1d cache:                       256 KiB (8 instances)
L1i cache:                       256 KiB (8 instances)
L2 cache:                        4 MiB (8 instances)
L3 cache:                        16 MiB (1 instance)
NUMA node(s):                    1
NUMA node0 CPU(s):               0-15
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 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] mypy-extensions==1.0.0
[pip3] numpy==1.25.1
[pip3] torch==2.0.1
[conda] Could not collect
```

cc @msaroufim @jgong5 @mingfeima @XiaobingSuper @sanchitintel @ashokei @jingxu10