Average Error: 0.0 → 0.0
Time: 1.1s
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 r793893 = 1.0;
        double r793894 = x;
        double r793895 = r793893 - r793894;
        double r793896 = y;
        double r793897 = r793895 * r793896;
        double r793898 = z;
        double r793899 = r793894 * r793898;
        double r793900 = r793897 + r793899;
        return r793900;
}
↓
double f(double x, double y, double z) {
        double r793901 = 1.0;
        double r793902 = x;
        double r793903 = r793901 - r793902;
        double r793904 = y;
        double r793905 = z;
        double r793906 = r793902 * r793905;
        double r793907 = fma(r793903, r793904, r793906);
        return r793907;
}

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 2020035 +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)))