Average Error: 0.0 → 0.0
Time: 836.0ms
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 r848435 = 1.0;
        double r848436 = x;
        double r848437 = r848435 - r848436;
        double r848438 = y;
        double r848439 = r848437 * r848438;
        double r848440 = z;
        double r848441 = r848436 * r848440;
        double r848442 = r848439 + r848441;
        return r848442;
}
↓
double f(double x, double y, double z) {
        double r848443 = 1.0;
        double r848444 = x;
        double r848445 = r848443 - r848444;
        double r848446 = y;
        double r848447 = z;
        double r848448 = r848444 * r848447;
        double r848449 = fma(r848445, r848446, r848448);
        return r848449;
}

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 2019354 +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)))