Average Error: 0.0 → 0.0
Time: 18.5s
Precision: 64
\[\left(1 - x\right) \cdot y + x \cdot z\]
↓
\[\mathsf{fma}\left(y, 1 - x, z \cdot x\right)\]
\left(1 - x\right) \cdot y + x \cdot z
↓
\mathsf{fma}\left(y, 1 - x, z \cdot x\right)
double f(double x, double y, double z) {
        double r35938213 = 1.0;
        double r35938214 = x;
        double r35938215 = r35938213 - r35938214;
        double r35938216 = y;
        double r35938217 = r35938215 * r35938216;
        double r35938218 = z;
        double r35938219 = r35938214 * r35938218;
        double r35938220 = r35938217 + r35938219;
        return r35938220;
}
↓
double f(double x, double y, double z) {
        double r35938221 = y;
        double r35938222 = 1.0;
        double r35938223 = x;
        double r35938224 = r35938222 - r35938223;
        double r35938225 = z;
        double r35938226 = r35938225 * r35938223;
        double r35938227 = fma(r35938221, r35938224, r35938226);
        return r35938227;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 +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)))