Average Error: 0.0 → 0.0
Time: 17.8s
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 r584535 = 1.0;
        double r584536 = x;
        double r584537 = r584535 - r584536;
        double r584538 = y;
        double r584539 = r584537 * r584538;
        double r584540 = z;
        double r584541 = r584536 * r584540;
        double r584542 = r584539 + r584541;
        return r584542;
}
↓
double f(double x, double y, double z) {
        double r584543 = 1.0;
        double r584544 = x;
        double r584545 = r584543 - r584544;
        double r584546 = y;
        double r584547 = z;
        double r584548 = r584544 * r584547;
        double r584549 = fma(r584545, r584546, r584548);
        return r584549;
}

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 2019208 +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)))