Distribution Explorer
Two views on the cost of probability. Left: canonical PDFs and PMFs ranked by SuperBEST node cost. Right: how the 265 catalog equations distribute across cost bins — the shape of the working cost landscape.
Canonical distributions
- Uniform PDF3n
1 / (b − a)sub + recip - Exponential PDF3n
λ · e^(−λx)exp + mul (positive) - Geometric PMF4n
(1−p)^(k−1) · ppow + mul (positive) - Cauchy PDF4n
1 / (π·(1 + x²))pow + add + recip + π - Bernoulli PMF5n
px(1−p)^(1−x)pow + sub-exponent + mul - Poisson PMF5n
λᵏ · e⁻λ / k!pow + exp + factorial lookup - Laplace PDF5n
(1/2b) · e^(−|x−μ|/b)abs adds 2n vs Gaussian - Student-t PDF6n
(1 + t²/ν)^(−(ν+1)/2)pow + div + add - Sigmoid CDF (logistic)6n
1 / (1 + e^(−(x−μ)/s))σ + substitution — composite - Binomial PMF7n
C(n,k) · p^k · (1−p)^(n−k)C lookup + two pow + mul chain - Beta PDF7n
x^(α−1) · (1−x)^(β−1) / B(α,β)two pow + mul + Beta lookup - Gaussian PDF8n
(1/√(2πσ²)) · e^(−(x−μ)²/(2σ²))pow + sub + div + exp + sqrt + mul - Log-normal PDF9n
same Gaussian on ln xGaussian + ln wrap - Gamma PDF9n
x^(k−1) · e^(−x/θ) / Γ(k) / θᵏpow + exp + div + Γ lookup - χ² PDF9n
k = 2ν Gamma special casesame as Gamma with k=ν/2, θ=2 - Weibull PDF10n
(k/λ) · (x/λ)^(k−1) · e^(−(x/λ)ᵏ)pow nested inside exp
Catalog cost histogram
177 equations- 1 – 3n2011%
- 4 – 6n3922%
- 7 – 10n5431%
- 11 – 15n3419%
- 16+n3017%
Most catalog equations cost between 4 and 10 nodes. The long tail (16+) is the expensive compound domain: coupled ODE expressions, multi-factor economics, composite thermodynamic potentials.