Average Error: 0.0 → 0.0
Time: 13.5s
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 r545691 = 1.0;
        double r545692 = x;
        double r545693 = r545691 - r545692;
        double r545694 = y;
        double r545695 = r545693 * r545694;
        double r545696 = z;
        double r545697 = r545692 * r545696;
        double r545698 = r545695 + r545697;
        return r545698;
}
↓
double f(double x, double y, double z) {
        double r545699 = 1.0;
        double r545700 = x;
        double r545701 = r545699 - r545700;
        double r545702 = y;
        double r545703 = z;
        double r545704 = r545700 * r545703;
        double r545705 = fma(r545701, r545702, r545704);
        return r545705;
}

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 2019199 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"

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

  (+ (* (- 1.0 x) y) (* x z)))