Average Error: 0.0 → 0.0
Time: 2.3s
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 r1322515 = 1.0;
        double r1322516 = x;
        double r1322517 = r1322515 - r1322516;
        double r1322518 = y;
        double r1322519 = r1322517 * r1322518;
        double r1322520 = z;
        double r1322521 = r1322516 * r1322520;
        double r1322522 = r1322519 + r1322521;
        return r1322522;
}
↓
double f(double x, double y, double z) {
        double r1322523 = 1.0;
        double r1322524 = x;
        double r1322525 = r1322523 - r1322524;
        double r1322526 = y;
        double r1322527 = z;
        double r1322528 = r1322524 * r1322527;
        double r1322529 = fma(r1322525, r1322526, r1322528);
        return r1322529;
}

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 2020025 +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)))