Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2

Average Error: 0.1 → 0.1

Time: 12.8s

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 r16328 = x;
        double r16329 = y;
        double r16330 = z;
        double r16331 = r16329 * r16330;
        double r16332 = r16331 * r16330;
        double r16333 = r16328 + r16332;
        return r16333;
}

↓

double f(double x, double y, double z) {
        double r16334 = y;
        double r16335 = z;
        double r16336 = r16334 * r16335;
        double r16337 = x;
        double r16338 = fma(r16336, r16335, r16337);
        return r16338;
}

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)))