Decay Curve

The FMA staircase. Seven compound-operator patterns, applied to the 265-equation catalog in order, cumulate to 15.5% aggregate node savings. The first pattern alone (a·b + c) captures almost half the total.

0%5%10%15%target 15.5%T1T2T3T4T5T6T7PATTERN TIER
Step function: each tier folds one compound-operator pattern into a single SuperBEST block. Dashed line marks the terminal 15.5% target.
T1

FMA core (a·b + c)

+6.8%

The base case: a single multiply followed by an add fuses into a 2-node block. ~37% of catalog rows match this pattern.

cumulative6.8%
T2

Scaled FMA (α·a·b + c)

+3.3%

The constant multiplier α folds into the EPL exponent. Appears in harmonic oscillator energies, Arrhenius rate constants.

cumulative10.1%
T3

FMA-sub (a·b − c)

+1.8%

The sign flip reuses the same 2-node skeleton. Gibbs free energy, Nernst equation.

cumulative11.9%
T4

Reciprocal-FMA (a·b / c)

+1.4%

Div-by-constant folds into F15. Adds the positivity hint on c.

cumulative13.3%
T5

Quadratic-FMA (a·b² + c)

+1.0%

Square of a product unfolds via EPL. Kinetic energy, Coulomb potential.

cumulative14.3%
T6

Log-FMA (a·b + ln c)

+0.6%

The ln term routes through EXL without extra cost. Helmholtz free energy, chemical potentials.

cumulative14.9%
T7

Exp-FMA (a·b · exp(c))

+0.6%

Terminal tier: exp wrap fuses via F14. Arrhenius kernels, integrated first-order decays.

cumulative15.5%