Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2

Average Error: 0.1 → 0.1

Time: 11.4s

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 r20175 = x;
        double r20176 = y;
        double r20177 = z;
        double r20178 = r20176 * r20177;
        double r20179 = r20178 * r20177;
        double r20180 = r20175 + r20179;
        return r20180;
}

↓

double f(double x, double y, double z) {
        double r20181 = y;
        double r20182 = z;
        double r20183 = r20181 * r20182;
        double r20184 = x;
        double r20185 = fma(r20183, r20182, r20184);
        return r20185;
}

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 2019351 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2"
  :precision binary64
  (+ x (* (* y z) z)))