Average Error: 0.0 → 0.0
Time: 6.0s
Precision: 64
\[\left(1.0 - x\right) \cdot y + x \cdot z\]
↓
\[\mathsf{fma}\left(z - y, x, y \cdot 1.0\right)\]
\left(1.0 - x\right) \cdot y + x \cdot z
↓
\mathsf{fma}\left(z - y, x, y \cdot 1.0\right)
double f(double x, double y, double z) {
        double r34965804 = 1.0;
        double r34965805 = x;
        double r34965806 = r34965804 - r34965805;
        double r34965807 = y;
        double r34965808 = r34965806 * r34965807;
        double r34965809 = z;
        double r34965810 = r34965805 * r34965809;
        double r34965811 = r34965808 + r34965810;
        return r34965811;
}
↓
double f(double x, double y, double z) {
        double r34965812 = z;
        double r34965813 = y;
        double r34965814 = r34965812 - r34965813;
        double r34965815 = x;
        double r34965816 = 1.0;
        double r34965817 = r34965813 * r34965816;
        double r34965818 = fma(r34965814, r34965815, r34965817);
        return r34965818;
}

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

    \[\left(1.0 - x\right) \cdot y + x \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(z - y, x, y \cdot 1.0\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(z - y, x, y \cdot 1.0\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"

  :herbie-target
  (- y (* x (- y z)))

  (+ (* (- 1.0 x) y) (* x z)))