Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2

Average Error: 0.1 → 0.1

Time: 13.7s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[x + \left(y \cdot z\right) \cdot z\]

↓

\[\mathsf{fma}\left(y \cdot z, z, x\right)\]

C

double f(double x, double y, double z) {
        double r22931 = x;
        double r22932 = y;
        double r22933 = z;
        double r22934 = r22932 * r22933;
        double r22935 = r22934 * r22933;
        double r22936 = r22931 + r22935;
        return r22936;
}

↓

double f(double x, double y, double z) {
        double r22937 = y;
        double r22938 = z;
        double r22939 = r22937 * r22938;
        double r22940 = x;
        double r22941 = fma(r22939, r22938, r22940);
        return r22941;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Initial program 0.1

   \[x + \left(y \cdot z\right) \cdot z\]

2. Simplified 0.1

   \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot z, z, x\right)}\]

3. Final simplification 0.1

   \[\leadsto \mathsf{fma}\left(y \cdot z, z, x\right)\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2"
  :precision binary64
  (+ x (* (* y z) z)))