Average Error: 0.0 → 0.0
Time: 2.5s
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 r604640 = 1.0;
        double r604641 = x;
        double r604642 = r604640 - r604641;
        double r604643 = y;
        double r604644 = r604642 * r604643;
        double r604645 = z;
        double r604646 = r604641 * r604645;
        double r604647 = r604644 + r604646;
        return r604647;
}
↓
double f(double x, double y, double z) {
        double r604648 = 1.0;
        double r604649 = x;
        double r604650 = r604648 - r604649;
        double r604651 = y;
        double r604652 = z;
        double r604653 = r604649 * r604652;
        double r604654 = fma(r604650, r604651, r604653);
        return r604654;
}

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 2019323 +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)))