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 r736791 = 1.0;
        double r736792 = x;
        double r736793 = r736791 - r736792;
        double r736794 = y;
        double r736795 = r736793 * r736794;
        double r736796 = z;
        double r736797 = r736792 * r736796;
        double r736798 = r736795 + r736797;
        return r736798;
}
↓
double f(double x, double y, double z) {
        double r736799 = 1.0;
        double r736800 = x;
        double r736801 = r736799 - r736800;
        double r736802 = y;
        double r736803 = z;
        double r736804 = r736800 * r736803;
        double r736805 = fma(r736801, r736802, r736804);
        return r736805;
}

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 2020089 +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)))