Average Error: 0.1 → 0.1
Time: 7.9s
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 r323483 = x;
        double r323484 = y;
        double r323485 = z;
        double r323486 = r323484 + r323485;
        double r323487 = r323483 * r323486;
        double r323488 = 5.0;
        double r323489 = r323485 * r323488;
        double r323490 = r323487 + r323489;
        return r323490;
}
↓
double f(double x, double y, double z) {
        double r323491 = x;
        double r323492 = y;
        double r323493 = z;
        double r323494 = r323492 + r323493;
        double r323495 = 5.0;
        double r323496 = r323493 * r323495;
        double r323497 = fma(r323491, r323494, r323496);
        return r323497;
}

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 2020043 +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)))