Average Error: 0.0 → 0.0
Time: 2.1s
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 r882280 = 1.0;
        double r882281 = x;
        double r882282 = r882280 - r882281;
        double r882283 = y;
        double r882284 = r882282 * r882283;
        double r882285 = z;
        double r882286 = r882281 * r882285;
        double r882287 = r882284 + r882286;
        return r882287;
}
↓
double f(double x, double y, double z) {
        double r882288 = 1.0;
        double r882289 = x;
        double r882290 = r882288 - r882289;
        double r882291 = y;
        double r882292 = z;
        double r882293 = r882289 * r882292;
        double r882294 = fma(r882290, r882291, r882293);
        return r882294;
}

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 2020060 +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)))