Average Error: 0.1 → 0.0
Time: 13.9s
Precision: 64
\[x \cdot \left(y + z\right) + z \cdot 5.0\]
↓
\[\mathsf{fma}\left(z, 5.0 + x, y \cdot x\right)\]
x \cdot \left(y + z\right) + z \cdot 5.0
↓
\mathsf{fma}\left(z, 5.0 + x, y \cdot x\right)
double f(double x, double y, double z) {
        double r24186221 = x;
        double r24186222 = y;
        double r24186223 = z;
        double r24186224 = r24186222 + r24186223;
        double r24186225 = r24186221 * r24186224;
        double r24186226 = 5.0;
        double r24186227 = r24186223 * r24186226;
        double r24186228 = r24186225 + r24186227;
        return r24186228;
}
↓
double f(double x, double y, double z) {
        double r24186229 = z;
        double r24186230 = 5.0;
        double r24186231 = x;
        double r24186232 = r24186230 + r24186231;
        double r24186233 = y;
        double r24186234 = r24186233 * r24186231;
        double r24186235 = fma(r24186229, r24186232, r24186234);
        return r24186235;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Target0.1
Herbie0.0
\[\left(x + 5.0\right) \cdot z + x \cdot y\]

Derivation

  1. Initial program 0.1

    \[x \cdot \left(y + z\right) + z \cdot 5.0\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(z, 5.0 + x, x \cdot y\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(z, 5.0 + x, y \cdot x\right)\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"

  :herbie-target
  (+ (* (+ x 5.0) z) (* x y))

  (+ (* x (+ y z)) (* z 5.0)))