Average Error: 0.0 → 0.0
Time: 9.5s
Precision: 64
\[\left(1 - x\right) \cdot y + x \cdot z\]
↓
\[\mathsf{fma}\left(z, x, \left(1 - x\right) \cdot y\right)\]
\left(1 - x\right) \cdot y + x \cdot z
↓
\mathsf{fma}\left(z, x, \left(1 - x\right) \cdot y\right)
double f(double x, double y, double z) {
        double r565876 = 1.0;
        double r565877 = x;
        double r565878 = r565876 - r565877;
        double r565879 = y;
        double r565880 = r565878 * r565879;
        double r565881 = z;
        double r565882 = r565877 * r565881;
        double r565883 = r565880 + r565882;
        return r565883;
}
↓
double f(double x, double y, double z) {
        double r565884 = z;
        double r565885 = x;
        double r565886 = 1.0;
        double r565887 = r565886 - r565885;
        double r565888 = y;
        double r565889 = r565887 * r565888;
        double r565890 = fma(r565884, r565885, r565889);
        return r565890;
}

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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(x \cdot z + 1 \cdot y\right) - x \cdot y}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(z, x, \left(1 - x\right) \cdot y\right)}\]

  5. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(z, x, \left(1 - x\right) \cdot y\right)\]

Reproduce

herbie shell --seed 2019212 +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)))