Average Error: 0.0 → 0.0
Time: 16.2s
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 r569386 = 1.0;
        double r569387 = x;
        double r569388 = r569386 - r569387;
        double r569389 = y;
        double r569390 = r569388 * r569389;
        double r569391 = z;
        double r569392 = r569387 * r569391;
        double r569393 = r569390 + r569392;
        return r569393;
}
↓
double f(double x, double y, double z) {
        double r569394 = 1.0;
        double r569395 = x;
        double r569396 = r569394 - r569395;
        double r569397 = y;
        double r569398 = z;
        double r569399 = r569395 * r569398;
        double r569400 = fma(r569396, r569397, r569399);
        return r569400;
}

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 2019209 +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)))