Average Error: 0.1 → 0.1
Time: 13.7s
Precision: 64
\[x \cdot \left(y + z\right) + z \cdot 5\]
↓
\[\mathsf{fma}\left(x, y + z, z \cdot 5\right)\]
x \cdot \left(y + z\right) + z \cdot 5
↓
\mathsf{fma}\left(x, y + z, z \cdot 5\right)
double f(double x, double y, double z) {
        double r338536 = x;
        double r338537 = y;
        double r338538 = z;
        double r338539 = r338537 + r338538;
        double r338540 = r338536 * r338539;
        double r338541 = 5.0;
        double r338542 = r338538 * r338541;
        double r338543 = r338540 + r338542;
        return r338543;
}
↓
double f(double x, double y, double z) {
        double r338544 = x;
        double r338545 = y;
        double r338546 = z;
        double r338547 = r338545 + r338546;
        double r338548 = 5.0;
        double r338549 = r338546 * r338548;
        double r338550 = fma(r338544, r338547, r338549);
        return r338550;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Target0.1
Herbie0.1
\[\left(x + 5\right) \cdot z + x \cdot y\]

Derivation

  1. Initial program 0.1

    \[x \cdot \left(y + z\right) + z \cdot 5\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y + z, z \cdot 5\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(x, y + z, z \cdot 5\right)\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

  :herbie-target
  (+ (* (+ x 5) z) (* x y))

  (+ (* x (+ y z)) (* z 5)))