Write a custom CUDA kernel to optimize `Isigmoid` using `float64` (double) precision.

Formula: f(x) = sigmoid(x) + alpha * (x*sigmoid(beta*x) - (-x)*sigmoid(-beta*x))

Problem Analysis:
1. Precision Issues with float32: The combination of three separate sigmoid calculations (each involving `exp`) leads to significant accumulation of rounding errors. Using `double` precision is necessary for accuracy alignment.
2. Memory Bottleneck: The operation is memory-bound, now with 8 bytes per element.

Optimization Strategy: Fused Element-wise Kernel with Double Precision

1. Data Type: All computations are performed in `double`.

2. Vectorized Loads (double2): Use `double2` to load 128 bits (2 double elements) per memory transaction.

3. Fused In-Register Math:
   - Use standard `double` precision math functions (`exp`).

4. One-Pass: Fuse all logic into a single read-compute-write kernel.
  
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

BATCH_SIZE = 4096
HIDDEN_DIM = 4096
SHAPE = (BATCH_SIZE, HIDDEN_DIM)

ALPHA_VAL = 0.1
BETA_VAL = 1.0

DTYPE = torch.float64

class Isigmoid(nn.Module):
    '''
    "The optimized deep belief networks with improved logistic sigmoid units and their application in fault diagnosis for planetary gearboxes of wind turbines" (IEEE Transactions on Industrial Electronics, 2019)

    Formula: f(x) = sigmoid(x) + alpha * (x*sigmoid(beta*x) - (-x)*sigmoid(-beta*x))
    '''
    def __init__(self, alpha=0.1, beta=1.0):
        super(Isigmoid, self).__init__()
        self.alpha = alpha
        self.beta = beta

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        sig_x = torch.sigmoid(x)
        term1 = x * torch.sigmoid(self.beta * x)
        term2 = -x * torch.sigmoid(-self.beta * x)
        leaky_part = self.alpha * (term1 - term2)
        return sig_x + leaky_part

class Model(nn.Module):
    def __init__(self, alpha=0.1, beta=1.0):
        super(Model, self).__init__()
        self.act = Isigmoid(alpha, beta)
    
    def forward(self, x):
        return self.act(x)

def get_inputs():
    input_tensor = torch.randn(SHAPE, dtype=DTYPE) * 5.0
    return [input_tensor.contiguous()]

def get_init_inputs():
    return [ALPHA_VAL, BETA_VAL]