Average Error: 0.0 → 0.0
Time: 789.0ms
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 r629415 = 1.0;
        double r629416 = x;
        double r629417 = r629415 - r629416;
        double r629418 = y;
        double r629419 = r629417 * r629418;
        double r629420 = z;
        double r629421 = r629416 * r629420;
        double r629422 = r629419 + r629421;
        return r629422;
}
↓
double f(double x, double y, double z) {
        double r629423 = 1.0;
        double r629424 = x;
        double r629425 = r629423 - r629424;
        double r629426 = y;
        double r629427 = z;
        double r629428 = r629424 * r629427;
        double r629429 = fma(r629425, r629426, r629428);
        return r629429;
}

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 2020001 +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)))