Average Error: 0.0 → 0.0
Time: 2.0s
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 r728740 = 1.0;
        double r728741 = x;
        double r728742 = r728740 - r728741;
        double r728743 = y;
        double r728744 = r728742 * r728743;
        double r728745 = z;
        double r728746 = r728741 * r728745;
        double r728747 = r728744 + r728746;
        return r728747;
}
↓
double f(double x, double y, double z) {
        double r728748 = 1.0;
        double r728749 = x;
        double r728750 = r728748 - r728749;
        double r728751 = y;
        double r728752 = z;
        double r728753 = r728749 * r728752;
        double r728754 = fma(r728750, r728751, r728753);
        return r728754;
}

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 2020047 +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)))