Average Error: 0.0 → 0.0
Time: 539.0ms
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 r512610 = 2.0;
        double r512611 = x;
        double r512612 = r512611 * r512611;
        double r512613 = y;
        double r512614 = r512611 * r512613;
        double r512615 = r512612 + r512614;
        double r512616 = r512610 * r512615;
        return r512616;
}
↓
double f(double x, double y) {
        double r512617 = x;
        double r512618 = y;
        double r512619 = r512617 * r512618;
        double r512620 = fma(r512617, r512617, r512619);
        double r512621 = 2.0;
        double r512622 = r512620 * r512621;
        return r512622;
}

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 2020062 +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))))