Average Error: 0.1 → 0.1
Time: 7.5s
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 r664641 = x;
        double r664642 = y;
        double r664643 = z;
        double r664644 = r664642 + r664643;
        double r664645 = r664641 * r664644;
        double r664646 = 5.0;
        double r664647 = r664643 * r664646;
        double r664648 = r664645 + r664647;
        return r664648;
}
↓
double f(double x, double y, double z) {
        double r664649 = x;
        double r664650 = y;
        double r664651 = z;
        double r664652 = r664650 + r664651;
        double r664653 = 5.0;
        double r664654 = r664651 * r664653;
        double r664655 = fma(r664649, r664652, r664654);
        return r664655;
}

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 2020047 +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)))