Average Error: 0.0 → 0.0
Time: 1.9s
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 r325459 = 1.0;
        double r325460 = x;
        double r325461 = r325459 - r325460;
        double r325462 = y;
        double r325463 = r325461 * r325462;
        double r325464 = z;
        double r325465 = r325460 * r325464;
        double r325466 = r325463 + r325465;
        return r325466;
}
↓
double f(double x, double y, double z) {
        double r325467 = 1.0;
        double r325468 = x;
        double r325469 = r325467 - r325468;
        double r325470 = y;
        double r325471 = z;
        double r325472 = r325468 * r325471;
        double r325473 = fma(r325469, r325470, r325472);
        return r325473;
}

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 2019362 +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)))