Average Error: 0.1 → 0.0
Time: 12.3s
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 r25789049 = x;
        double r25789050 = y;
        double r25789051 = z;
        double r25789052 = r25789050 + r25789051;
        double r25789053 = r25789049 * r25789052;
        double r25789054 = 5.0;
        double r25789055 = r25789051 * r25789054;
        double r25789056 = r25789053 + r25789055;
        return r25789056;
}
↓
double f(double x, double y, double z) {
        double r25789057 = z;
        double r25789058 = 5.0;
        double r25789059 = x;
        double r25789060 = r25789058 + r25789059;
        double r25789061 = y;
        double r25789062 = r25789061 * r25789059;
        double r25789063 = fma(r25789057, r25789060, r25789062);
        return r25789063;
}

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 2019158 +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)))