Average Error: 0.0 → 0.0
Time: 2.8s
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 r4646 = 1.0;
        double r4647 = x;
        double r4648 = r4646 - r4647;
        double r4649 = y;
        double r4650 = r4648 * r4649;
        double r4651 = z;
        double r4652 = r4647 * r4651;
        double r4653 = r4650 + r4652;
        return r4653;
}
↓
double f(double x, double y, double z) {
        double r4654 = 1.0;
        double r4655 = x;
        double r4656 = r4654 - r4655;
        double r4657 = y;
        double r4658 = z;
        double r4659 = r4655 * r4658;
        double r4660 = fma(r4656, r4657, r4659);
        return r4660;
}

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 2020025 +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)))