Average Error: 0.1 → 0.0
Time: 12.2s
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 r14230230 = x;
        double r14230231 = y;
        double r14230232 = z;
        double r14230233 = r14230231 + r14230232;
        double r14230234 = r14230230 * r14230233;
        double r14230235 = 5.0;
        double r14230236 = r14230232 * r14230235;
        double r14230237 = r14230234 + r14230236;
        return r14230237;
}
↓
double f(double x, double y, double z) {
        double r14230238 = z;
        double r14230239 = 5.0;
        double r14230240 = x;
        double r14230241 = r14230239 + r14230240;
        double r14230242 = y;
        double r14230243 = r14230242 * r14230240;
        double r14230244 = fma(r14230238, r14230241, r14230243);
        return r14230244;
}

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 2019163 +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)))