> 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/2.5/tutorials/statistics.md). # Statistics Concrete analyzes all compiled circuits and calculates some statistics. These statistics can be used to find bottlenecks and compare circuits. Statistics are calculated in terms of basic operations. There are 6 basic operations in Concrete: * **clear addition:** x + y where x is encrypted and y is clear * **encrypted addition:** x + y where both x and y are encrypted * **clear multiplication:** x \* y where x is encrypted and y is clear * **encrypted negation:** -x where x is encrypted * **key switch:** building block for table lookups * **packing key switch:** building block for table lookups * **programmable bootstrapping:** building block for table lookups You can print all statistics using the `show_statistics` configuration option: ```python from concrete import fhe @fhe.compiler({"x": "encrypted"}) def f(x): return (x**2) + (2*x) + 4 inputset = range(2**2) circuit = f.compile(inputset, show_statistics=True) ``` This code will print: ``` Statistics -------------------------------------------------------------------------------- size_of_secret_keys: 22648 size_of_bootstrap_keys: 51274176 size_of_keyswitch_keys: 64092720 size_of_inputs: 16392 size_of_outputs: 16392 p_error: 9.627450598589458e-06 global_p_error: 9.627450598589458e-06 complexity: 99198195.0 programmable_bootstrap_count: 1 programmable_bootstrap_count_per_parameter: { BootstrapKeyParam(polynomial_size=2048, glwe_dimension=1, input_lwe_dimension=781, level=1, base_log=23, variance=9.940977002694397e-32): 1 } key_switch_count: 1 key_switch_count_per_parameter: { KeyswitchKeyParam(level=5, base_log=3, variance=1.939836732335308e-11): 1 } packing_key_switch_count: 0 clear_addition_count: 1 clear_addition_count_per_parameter: { LweSecretKeyParam(dimension=2048): 1 } encrypted_addition_count: 1 encrypted_addition_count_per_parameter: { LweSecretKeyParam(dimension=2048): 1 } clear_multiplication_count: 1 clear_multiplication_count_per_parameter: { LweSecretKeyParam(dimension=2048): 1 } encrypted_negation_count: 0 -------------------------------------------------------------------------------- ``` {% hint style="info" %} Each of these properties can be directly accessed on the circuit (e.g., `circuit.programmable_bootstrap_count`). {% endhint %} ## Tags Circuit analysis also considers [tags](/concrete/2.5/tutorials/tagging.md)! Imagine you have a neural network with 10 layers, each of them tagged. You can easily see the number of additions and multiplications required for matrix multiplications per layer: ``` Statistics -------------------------------------------------------------------------------- clear_multiplication_count_per_tag: { /model/model: 53342 /model/model.0/Gemm: 14720 /model/model.0/Gemm.matmul: 14720 /model/model.2/Gemm: 11730 /model/model.2/Gemm.matmul: 11730 /model/model.4/Gemm: 9078 /model/model.4/Gemm.matmul: 9078 /model/model.6/Gemm: 6764 /model/model.6/Gemm.matmul: 6764 /model/model.8/Gemm: 4788 /model/model.8/Gemm.matmul: 4788 /model/model.10/Gemm: 3150 /model/model.10/Gemm.matmul: 3150 /model/model.12/Gemm: 1850 /model/model.12/Gemm.matmul: 1850 /model/model.14/Gemm: 888 /model/model.14/Gemm.matmul: 888 /model/model.16/Gemm: 264 /model/model.16/Gemm.matmul: 264 /model/model.18/Gemm: 110 /model/model.18/Gemm.matmul: 110 } encrypted_addition_count_per_tag: { /model/model: 53342 /model/model.0/Gemm: 14720 /model/model.0/Gemm.matmul: 14720 /model/model.2/Gemm: 11730 /model/model.2/Gemm.matmul: 11730 /model/model.4/Gemm: 9078 /model/model.4/Gemm.matmul: 9078 /model/model.6/Gemm: 6764 /model/model.6/Gemm.matmul: 6764 /model/model.8/Gemm: 4788 /model/model.8/Gemm.matmul: 4788 /model/model.10/Gemm: 3150 /model/model.10/Gemm.matmul: 3150 /model/model.12/Gemm: 1850 /model/model.12/Gemm.matmul: 1850 /model/model.14/Gemm: 888 /model/model.14/Gemm.matmul: 888 /model/model.16/Gemm: 264 /model/model.16/Gemm.matmul: 264 /model/model.18/Gemm: 110 /model/model.18/Gemm.matmul: 110 } -------------------------------------------------------------------------------- ``` --- # Agent Instructions This documentation is published with GitBook. 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