Average Error: 0.0 → 0.0
Time: 6.9s
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 r479188 = 1.0;
        double r479189 = x;
        double r479190 = r479188 - r479189;
        double r479191 = y;
        double r479192 = r479190 * r479191;
        double r479193 = z;
        double r479194 = r479189 * r479193;
        double r479195 = r479192 + r479194;
        return r479195;
}
↓
double f(double x, double y, double z) {
        double r479196 = 1.0;
        double r479197 = x;
        double r479198 = r479196 - r479197;
        double r479199 = y;
        double r479200 = z;
        double r479201 = r479197 * r479200;
        double r479202 = fma(r479198, r479199, r479201);
        return r479202;
}

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 2019304 +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)))