Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2

Average Error: 0.1 → 0.1

Time: 9.6s

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 r20682 = x;
        double r20683 = y;
        double r20684 = z;
        double r20685 = r20683 * r20684;
        double r20686 = r20685 * r20684;
        double r20687 = r20682 + r20686;
        return r20687;
}

↓

double f(double x, double y, double z) {
        double r20688 = y;
        double r20689 = z;
        double r20690 = r20688 * r20689;
        double r20691 = x;
        double r20692 = fma(r20690, r20689, r20691);
        return r20692;
}

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 2020045 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2"
  :precision binary64
  (+ x (* (* y z) z)))