Average Error: 0.0 → 0.0
Time: 779.0ms
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 r708899 = 1.0;
        double r708900 = x;
        double r708901 = r708899 - r708900;
        double r708902 = y;
        double r708903 = r708901 * r708902;
        double r708904 = z;
        double r708905 = r708900 * r708904;
        double r708906 = r708903 + r708905;
        return r708906;
}
↓
double f(double x, double y, double z) {
        double r708907 = 1.0;
        double r708908 = x;
        double r708909 = r708907 - r708908;
        double r708910 = y;
        double r708911 = z;
        double r708912 = r708908 * r708911;
        double r708913 = fma(r708909, r708910, r708912);
        return r708913;
}

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 2020001 +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)))