Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2

Average Error: 0.1 → 0.1

Time: 10.2s

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 r19028 = x;
        double r19029 = y;
        double r19030 = z;
        double r19031 = r19029 * r19030;
        double r19032 = r19031 * r19030;
        double r19033 = r19028 + r19032;
        return r19033;
}

↓

double f(double x, double y, double z) {
        double r19034 = y;
        double r19035 = z;
        double r19036 = r19034 * r19035;
        double r19037 = x;
        double r19038 = fma(r19036, r19035, r19037);
        return r19038;
}

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)))