Implement the **tanh activation function** for a layer output, which squashes real-valued inputs into the range $(-1, 1)$. This is a common deep-learning basic used to add non-linearity to neural networks.

The activation is defined as:
$$
\tanh(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}}
$$

## Requirements

Implement the function
```python
def tanh_activation(x):
    \"""
    Applies the tanh activation element-wise.

    Args:
        x (np.ndarray): A 1D array of real-valued pre-activation outputs.

    Returns:
        np.ndarray: A 1D array where each element is tanh(x_i).
    \"""
    # Your solution below
```

**Rules:**
- Compute $\tanh(x_i)$ for every element in the input array `x`.
- Return a NumPy array of the same shape as `x`.
- Do not use any prebuilt tanh activation helpers (e.g., `np.tanh`, `torch.tanh`, `jax.numpy.tanh`).
- Use vectorized NumPy operations (e.g. `np.exp`) for efficiency.
- Keep the implementation numerically reasonable (e.g., avoid obvious overflow patterns when possible).

## Example

```python
x = np.array([-1.0, 0.0, 1.0])
tanh_activation(x)
```

Output:
```python
[-0.7616, 0.0, 0.7616]
```

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Activation function tanh

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730. Activation function tanh

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