You write custom CUDA kernels to replace the pytorch operators in the given architecture to get speedups.   
  
You have complete freedom to choose the set of operators you want to replace. You may make the decision to replace some operators with custom CUDA kernels and leave others unchanged. You may replace multiple operators with custom implementations, consider operator fusion opportunities (combining multiple operators into a single kernel, for example, combining matmul+relu), or algorithmic changes (such as online softmax). You are only limited by your imagination.  
  
Here's an example to show you the syntax of inline embedding custom CUDA operators in torch: The example given architecture is:   
  
python
import torch
import torch.nn as nn
import math

class Model(nn.Module):
    def __init__(self):
        super().__init__()

    def forward(self, price: torch.Tensor, strike: torch.Tensor, t: torch.Tensor, rate: torch.Tensor, vol: torch.Tensor) -> torch.Tensor:
        
        sqrt_t = torch.sqrt(t)
        log_val = torch.log(price / strike)
        
        d1 = (log_val + (rate + 0.5 * vol * vol) * t) / (vol * sqrt_t)
        d2 = d1 - vol * sqrt_t
        norm_d1 = 0.5 * (1.0 + torch.erf(d1 * 0.70710678))
        norm_d2 = 0.5 * (1.0 + torch.erf(d2 * 0.70710678))
        exp_val = torch.exp(-rate * t)
        call_price = price * norm_d1 - strike * exp_val * norm_d2
        
        return call_price


batch_size = 1024 * 1024
shape = (batch_size, )

def get_inputs():
    price = torch.rand(shape, dtype=torch.float32) * 100.0 + 10.0 # S: 10~110
    strike = torch.rand(shape, dtype=torch.float32) * 100.0 + 10.0 # K
    t = torch.rand(shape, dtype=torch.float32) + 0.1      # T: 0.1~1.1 年
    rate = torch.rand(shape, dtype=torch.float32) * 0.05 + 0.01 # r: 1%~6%
    vol = torch.rand(shape, dtype=torch.float32) * 0.3 + 0.1    # v: 10%~40%
    return [price, strike, t, rate, vol]

def get_init_inputs():
    return []
```