Average Error: 0.0 → 0.0
Time: 2.7s
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 r907319 = 1.0;
        double r907320 = x;
        double r907321 = r907319 - r907320;
        double r907322 = y;
        double r907323 = r907321 * r907322;
        double r907324 = z;
        double r907325 = r907320 * r907324;
        double r907326 = r907323 + r907325;
        return r907326;
}
↓
double f(double x, double y, double z) {
        double r907327 = 1.0;
        double r907328 = x;
        double r907329 = r907327 - r907328;
        double r907330 = y;
        double r907331 = z;
        double r907332 = r907328 * r907331;
        double r907333 = fma(r907329, r907330, r907332);
        return r907333;
}

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 2020057 +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)))