Average Error: 0.0 → 0.0
Time: 8.3s
Precision: 64
\[2 \cdot \left(x \cdot x + x \cdot y\right)\]
↓
\[2 \cdot \mathsf{fma}\left(x, x, x \cdot y\right)\]
2 \cdot \left(x \cdot x + x \cdot y\right)
↓
2 \cdot \mathsf{fma}\left(x, x, x \cdot y\right)
double f(double x, double y) {
        double r433530 = 2.0;
        double r433531 = x;
        double r433532 = r433531 * r433531;
        double r433533 = y;
        double r433534 = r433531 * r433533;
        double r433535 = r433532 + r433534;
        double r433536 = r433530 * r433535;
        return r433536;
}
↓
double f(double x, double y) {
        double r433537 = 2.0;
        double r433538 = x;
        double r433539 = y;
        double r433540 = r433538 * r433539;
        double r433541 = fma(r433538, r433538, r433540);
        double r433542 = r433537 * r433541;
        return r433542;
}

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. Using strategy rm

  3. Applied fma-def0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019209 +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))))