Average Error: 0.0 → 0.0
Time: 1.7s
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 r739150 = 1.0;
        double r739151 = x;
        double r739152 = r739150 - r739151;
        double r739153 = y;
        double r739154 = r739152 * r739153;
        double r739155 = z;
        double r739156 = r739151 * r739155;
        double r739157 = r739154 + r739156;
        return r739157;
}
↓
double f(double x, double y, double z) {
        double r739158 = 1.0;
        double r739159 = x;
        double r739160 = r739158 - r739159;
        double r739161 = y;
        double r739162 = z;
        double r739163 = r739159 * r739162;
        double r739164 = fma(r739160, r739161, r739163);
        return r739164;
}

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 2020021 +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)))