Average Error: 0.0 → 0.0
Time: 3.2s
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 r861501 = 1.0;
        double r861502 = x;
        double r861503 = r861501 - r861502;
        double r861504 = y;
        double r861505 = r861503 * r861504;
        double r861506 = z;
        double r861507 = r861502 * r861506;
        double r861508 = r861505 + r861507;
        return r861508;
}
↓
double f(double x, double y, double z) {
        double r861509 = 1.0;
        double r861510 = x;
        double r861511 = r861509 - r861510;
        double r861512 = y;
        double r861513 = z;
        double r861514 = r861510 * r861513;
        double r861515 = fma(r861511, r861512, r861514);
        return r861515;
}

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 2020018 +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)))