Average Error: 0.3 → 0.2
Time: 24.0s
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 r521911 = x;
        double r521912 = y;
        double r521913 = r521912 - r521911;
        double r521914 = 6.0;
        double r521915 = r521913 * r521914;
        double r521916 = z;
        double r521917 = r521915 * r521916;
        double r521918 = r521911 + r521917;
        return r521918;
}
↓
double f(double x, double y, double z) {
        double r521919 = y;
        double r521920 = x;
        double r521921 = r521919 - r521920;
        double r521922 = 6.0;
        double r521923 = z;
        double r521924 = r521922 * r521923;
        double r521925 = fma(r521921, r521924, r521920);
        return r521925;
}

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 2019326 +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)))