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 r654423 = x;
        double r654424 = y;
        double r654425 = z;
        double r654426 = r654424 + r654425;
        double r654427 = r654423 * r654426;
        double r654428 = 5.0;
        double r654429 = r654425 * r654428;
        double r654430 = r654427 + r654429;
        return r654430;
}
↓
double f(double x, double y, double z) {
        double r654431 = x;
        double r654432 = y;
        double r654433 = z;
        double r654434 = r654432 + r654433;
        double r654435 = 5.0;
        double r654436 = r654433 * r654435;
        double r654437 = fma(r654431, r654434, r654436);
        return r654437;
}

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)))