Average Error: 0.0 → 0.0
Time: 635.0ms
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 r773779 = 1.0;
        double r773780 = x;
        double r773781 = r773779 - r773780;
        double r773782 = y;
        double r773783 = r773781 * r773782;
        double r773784 = z;
        double r773785 = r773780 * r773784;
        double r773786 = r773783 + r773785;
        return r773786;
}
↓
double f(double x, double y, double z) {
        double r773787 = 1.0;
        double r773788 = x;
        double r773789 = r773787 - r773788;
        double r773790 = y;
        double r773791 = z;
        double r773792 = r773788 * r773791;
        double r773793 = fma(r773789, r773790, r773792);
        return r773793;
}

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 2020020 +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)))