Average Error: 0.0 → 0.0
Time: 4.0s
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 r784998 = 1.0;
        double r784999 = x;
        double r785000 = r784998 - r784999;
        double r785001 = y;
        double r785002 = r785000 * r785001;
        double r785003 = z;
        double r785004 = r784999 * r785003;
        double r785005 = r785002 + r785004;
        return r785005;
}
↓
double f(double x, double y, double z) {
        double r785006 = 1.0;
        double r785007 = x;
        double r785008 = r785006 - r785007;
        double r785009 = y;
        double r785010 = z;
        double r785011 = r785007 * r785010;
        double r785012 = fma(r785008, r785009, r785011);
        return r785012;
}

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 2020036 +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)))