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Thoughts on Dynamic Patching

Need:

  1. $\operatorname{theoreticalMax}(C_{i,j})$ which is the theoretical maximum value of any element in $C_{i,j}$.
  2. $M$ which is the number of entries we use to calculate variance in the matrix $C$. Should be equal to $|\sim!\operatorname{eye}(C)|$ which I think is then equal to either $\frac{\operatorname{width}(C)\cdot(\operatorname{width}(C)+1)}{2}$ or $2\times$ that depending on whether we are just using the upper triangle or both the upper and lower triangle
  3. $v_\text{max}$ which is a calculation using the two above values.
  4. $R_\text{patch}$ which I think is the number of races that the patch adds.
  5. $S_\text{remaining}$ which is the sum of all the remaining spots we need to fill.
  6. $R_\text{min,patch}$ which is the theoretical mimumum number of races we add with our patch. Calculation using the above value.
  7. $v$ which is the variance of the matrix $C$ without the diagonal elements.
  8. $E$ which is the error. Lower for this value is better. $\lambda$ should control how much weight is given to either the length or variance.