Average Error: 0.0 → 0.0
Time: 2.1s
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 r859692 = 1.0;
        double r859693 = x;
        double r859694 = r859692 - r859693;
        double r859695 = y;
        double r859696 = r859694 * r859695;
        double r859697 = z;
        double r859698 = r859693 * r859697;
        double r859699 = r859696 + r859698;
        return r859699;
}
↓
double f(double x, double y, double z) {
        double r859700 = 1.0;
        double r859701 = x;
        double r859702 = r859700 - r859701;
        double r859703 = y;
        double r859704 = z;
        double r859705 = r859701 * r859704;
        double r859706 = fma(r859702, r859703, r859705);
        return r859706;
}

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 2019353 +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)))