Average Error: 0.0 → 0.0
Time: 1.9s
Precision: 64
\[\left(1 - x\right) \cdot y + x \cdot z\]
↓
\[\mathsf{fma}\left(1 - x, y, x \cdot z\right)\]
\left(1 - x\right) \cdot y + x \cdot z
↓
\mathsf{fma}\left(1 - x, y, x \cdot z\right)
double f(double x, double y, double z) {
        double r807868 = 1.0;
        double r807869 = x;
        double r807870 = r807868 - r807869;
        double r807871 = y;
        double r807872 = r807870 * r807871;
        double r807873 = z;
        double r807874 = r807869 * r807873;
        double r807875 = r807872 + r807874;
        return r807875;
}
↓
double f(double x, double y, double z) {
        double r807876 = 1.0;
        double r807877 = x;
        double r807878 = r807876 - r807877;
        double r807879 = y;
        double r807880 = z;
        double r807881 = r807877 * r807880;
        double r807882 = fma(r807878, r807879, r807881);
        return r807882;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

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

Derivation

  1. Initial program 0.0

    \[\left(1 - x\right) \cdot y + x \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(1 - x, y, x \cdot z\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(1 - x, y, x \cdot z\right)\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

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

  (+ (* (- 1 x) y) (* x z)))