Average Error: 0.0 → 0.0
Time: 9.1s
Precision: 64
\[\left(1 - x\right) \cdot y + x \cdot z\]
↓
\[\mathsf{fma}\left(y, 1, \left(z - y\right) \cdot x\right)\]
\left(1 - x\right) \cdot y + x \cdot z
↓
\mathsf{fma}\left(y, 1, \left(z - y\right) \cdot x\right)
double f(double x, double y, double z) {
        double r31817073 = 1.0;
        double r31817074 = x;
        double r31817075 = r31817073 - r31817074;
        double r31817076 = y;
        double r31817077 = r31817075 * r31817076;
        double r31817078 = z;
        double r31817079 = r31817074 * r31817078;
        double r31817080 = r31817077 + r31817079;
        return r31817080;
}
↓
double f(double x, double y, double z) {
        double r31817081 = y;
        double r31817082 = 1.0;
        double r31817083 = z;
        double r31817084 = r31817083 - r31817081;
        double r31817085 = x;
        double r31817086 = r31817084 * r31817085;
        double r31817087 = fma(r31817081, r31817082, r31817086);
        return r31817087;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, 1, x \cdot \left(z - y\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, 1, \left(z - y\right) \cdot x\right)\]

Reproduce

herbie shell --seed 2019169 +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)))