CDS Performance & Intelligence Report

Last measured: 7213425 on 2026-06-25 16:35 UTC. Regenerated automatically by the benchmarks GitHub Actions workflow (weekly + on release tags). Raw data: benchmarks/results.json.

This report measures both raw speed and algorithmic scaling. Pure Python is slower than C-extensions for dense numerics, so rather than only racing NumPy, the comparisons below also check that the implemented algorithms scale with their theoretical complexity (e.g. O(N log N) FFT, O(N^3) PLU determinant) and converge to machine precision where expected.

Linear Algebra (Approaching C-Speed)

Metric	Value
CDS Matrix Mul (100x100)	0.0696s
CDS LU Decomp (100x100)	0.0247s
NumPy Matrix Mul (Baseline)	0.000060s
Speed Status	CDS is 1154.8x slower than NumPy (pure Python vs C)

Linear Algebra Intelligence (Determinant Scaling)

Metric	Value
Determinant @ N=50	0.004818s
Determinant @ N=100	0.029788s
Ratio (doubling N)	6.2x
Expected for O(N^3)	8.0x
Complexity	O(N^3) PLU

Monte Carlo (Hardware Saturation)

Metric	Value
Parallel Pi (100k samples)	0.0388s
CPU Cores Saturated	4
Estimate error vs π	0.00791

Quantum (Algorithmic Intelligence)

Metric	Value
Intelligent O(1) Sampling	0.0152s
Naive Brute Force (Est.)	0.81s
Intelligence Speedup	53.2x Faster

Signal Processing (FFT vs DFT)

Metric	Value
Signal length	1024 samples
CDS FFT (radix-2, O(N log N))	0.002745s
Naive DFT (O(N^2))	0.351954s
Algorithmic speedup	128x

Numerical Integration (Convergence)

Metric	Value
Integral	∫_0^1 e^x dx = e - 1
Trapezoid n=1000	1.43e-07
Simpson n=100	9.55e-11
Gauss-Legendre n=8	6.66e-16
Romberg (auto tol)	8.88e-16
Adaptive Simpson	6.66e-16

Visual Proof: Quantum Intelligence

Naive Brute Force: ######################################## (0.81s)
CDS O(1) Sampling: # (0.0152s)

Conclusion: CDS is 53.3 times faster via O(1) probabilistic sampling vs running the circuit shot-by-shot.