Average Error: 0.0 → 0.0
Time: 886.0ms
Precision: 64
\[2 \cdot \left(x \cdot x + x \cdot y\right)\]
↓
\[\mathsf{fma}\left(x, x, x \cdot y\right) \cdot 2\]
2 \cdot \left(x \cdot x + x \cdot y\right)
↓
\mathsf{fma}\left(x, x, x \cdot y\right) \cdot 2
double f(double x, double y) {
        double r601317 = 2.0;
        double r601318 = x;
        double r601319 = r601318 * r601318;
        double r601320 = y;
        double r601321 = r601318 * r601320;
        double r601322 = r601319 + r601321;
        double r601323 = r601317 * r601322;
        return r601323;
}
↓
double f(double x, double y) {
        double r601324 = x;
        double r601325 = y;
        double r601326 = r601324 * r601325;
        double r601327 = fma(r601324, r601324, r601326);
        double r601328 = 2.0;
        double r601329 = r601327 * r601328;
        return r601329;
}

Error

Bits error versus x

Bits error versus y

Target

Original0.0
Target0.0
Herbie0.0
\[\left(x \cdot 2\right) \cdot \left(x + y\right)\]

Derivation

  1. Initial program 0.0

    \[2 \cdot \left(x \cdot x + x \cdot y\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, x \cdot y\right) \cdot 2}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, x, x \cdot y\right) \cdot 2\]

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (* (* x 2) (+ x y))

  (* 2 (+ (* x x) (* x y))))