Average Error: 0.0 → 0.0
Time: 5.9s
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 r811352 = 1.0;
        double r811353 = x;
        double r811354 = r811352 - r811353;
        double r811355 = y;
        double r811356 = r811354 * r811355;
        double r811357 = z;
        double r811358 = r811353 * r811357;
        double r811359 = r811356 + r811358;
        return r811359;
}
↓
double f(double x, double y, double z) {
        double r811360 = 1.0;
        double r811361 = x;
        double r811362 = r811360 - r811361;
        double r811363 = y;
        double r811364 = z;
        double r811365 = r811361 * r811364;
        double r811366 = fma(r811362, r811363, r811365);
        return r811366;
}

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 2020045 +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)))