> For the complete documentation index, see [llms.txt](https://docs.zama.org/concrete/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.zama.org/concrete/2.7-1/execution-analysis/simulation.md).

# Simulation

During development, the speed of homomorphic execution can be a blocker for fast prototyping. You could call the function you're trying to compile directly, of course, but it won't be exactly the same as FHE execution, which has a certain probability of error (see [Exactness](/concrete/2.7-1/core-features/table_lookups.md#table-lookup-exactness)).

To overcome this issue, simulation is introduced:

```python
from concrete import fhe
import numpy as np

@fhe.compiler({"x": "encrypted"})
def f(x):
    return (x + 1) ** 2

inputset = [np.random.randint(0, 10, size=(10,)) for _ in range(10)]
circuit = f.compile(inputset, p_error=0.1, fhe_simulation=True)

sample = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

actual = f(sample)
simulation = circuit.simulate(sample)

print(actual.tolist())
print(simulation.tolist())
```

After the simulation runs, it prints the following:

```
[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
[1, 4, 9, 16, 16, 36, 49, 64, 81, 100]
```

{% hint style="warning" %}
There are some operations which are not supported in simulation yet. They will result in compilation failures. You can revert to simulation using graph execution using `circuit.graph(...)` instead of `circuit.simulate(...)`, which won't simulate FHE, but it will evaluate the computation graph, which is like simulating the operations without any errors due to FHE.
{% endhint %}

## Overflow Detection in Simulation

Overflow can happen during an FHE computation, leading to unexpected behaviors. Using simulation can help you detect these events by printing a warning whenever an overflow happens. This feature is disabled by default, but you can enable it by setting `detect_overflow_in_simulation=True` during compilation.

To demonstrate, we will compile the previous circuit with overflow detection enabled and trigger an overflow:

```python
# compile with overflow detection enabled
circuit = f.compile(inputset, p_error=0.1, fhe_simulation=True, detect_overflow_in_simulation=True)
# cause an overflow
circuit.simulate([0,1,2,3,4,5,6,7,8,15])
```

You will see the following warning after the simulation call:

```bash
WARNING at loc("script.py":3:0): overflow happened during addition in simulation
```

If you look at the MLIR (`circuit.mlir`), you will see that the input type is supposed to be `eint4` represented in 4 bits with a maximum value of 15. Since there's an addition of the input, we used the maximum value (15) here to trigger an overflow (15 + 1 = 16 which needs 5 bits). The warning specifies the operation that caused the overflow and its location. Similar warnings will be displayed for all basic FHE operations such as add, mul, and lookup tables.


---

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