Average Error: 0.2 → 0.2
Time: 24.7s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]
↓
\[\mathsf{fma}\left(y - x, 6 \cdot z, x\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot z
↓
\mathsf{fma}\left(y - x, 6 \cdot z, x\right)
double f(double x, double y, double z) {
        double r519271 = x;
        double r519272 = y;
        double r519273 = r519272 - r519271;
        double r519274 = 6.0;
        double r519275 = r519273 * r519274;
        double r519276 = z;
        double r519277 = r519275 * r519276;
        double r519278 = r519271 + r519277;
        return r519278;
}
↓
double f(double x, double y, double z) {
        double r519279 = y;
        double r519280 = x;
        double r519281 = r519279 - r519280;
        double r519282 = 6.0;
        double r519283 = z;
        double r519284 = r519282 * r519283;
        double r519285 = fma(r519281, r519284, r519280);
        return r519285;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.2
Target0.2
Herbie0.2
\[x - \left(6 \cdot z\right) \cdot \left(x - y\right)\]

Derivation

  1. Initial program 0.2

    \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]

  2. Simplified0.2

    \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot z, x\right)}\]

  3. Final simplification0.2

    \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot z, x\right)\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6 z) (- x y)))

  (+ x (* (* (- y x) 6) z)))