Average Error: 0.3 → 0.2
Time: 16.3s
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 r922895 = x;
        double r922896 = y;
        double r922897 = r922896 - r922895;
        double r922898 = 6.0;
        double r922899 = r922897 * r922898;
        double r922900 = z;
        double r922901 = r922899 * r922900;
        double r922902 = r922895 + r922901;
        return r922902;
}
↓
double f(double x, double y, double z) {
        double r922903 = y;
        double r922904 = x;
        double r922905 = r922903 - r922904;
        double r922906 = 6.0;
        double r922907 = z;
        double r922908 = r922906 * r922907;
        double r922909 = fma(r922905, r922908, r922904);
        return r922909;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.3
Target0.2
Herbie0.2
\[x - \left(6 \cdot z\right) \cdot \left(x - y\right)\]

Derivation

  1. Initial program 0.3

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

  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 2020042 +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)))