Average Error: 0.0 → 0.0
Time: 6.3s
Precision: 64
\[\left(1 - x\right) \cdot y + x \cdot z\]
↓
\[\mathsf{fma}\left(x, z - y, 1 \cdot y\right)\]
\left(1 - x\right) \cdot y + x \cdot z
↓
\mathsf{fma}\left(x, z - y, 1 \cdot y\right)
double f(double x, double y, double z) {
        double r718339 = 1.0;
        double r718340 = x;
        double r718341 = r718339 - r718340;
        double r718342 = y;
        double r718343 = r718341 * r718342;
        double r718344 = z;
        double r718345 = r718340 * r718344;
        double r718346 = r718343 + r718345;
        return r718346;
}
↓
double f(double x, double y, double z) {
        double r718347 = x;
        double r718348 = z;
        double r718349 = y;
        double r718350 = r718348 - r718349;
        double r718351 = 1.0;
        double r718352 = r718351 * r718349;
        double r718353 = fma(r718347, r718350, r718352);
        return r718353;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, z - y, y \cdot 1\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, z - y, 1 \cdot y\right)\]

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"

  :herbie-target
  (- y (* x (- y z)))

  (+ (* (- 1.0 x) y) (* x z)))