Average Error: 0.0 → 0.0
Time: 1.1s
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 r627841 = 1.0;
        double r627842 = x;
        double r627843 = r627841 - r627842;
        double r627844 = y;
        double r627845 = r627843 * r627844;
        double r627846 = z;
        double r627847 = r627842 * r627846;
        double r627848 = r627845 + r627847;
        return r627848;
}
↓
double f(double x, double y, double z) {
        double r627849 = 1.0;
        double r627850 = x;
        double r627851 = r627849 - r627850;
        double r627852 = y;
        double r627853 = z;
        double r627854 = r627850 * r627853;
        double r627855 = fma(r627851, r627852, r627854);
        return r627855;
}

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 2020034 +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)))