Average Error: 0.2 → 0.2
Time: 3.0s
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 r1089859 = x;
        double r1089860 = y;
        double r1089861 = r1089860 - r1089859;
        double r1089862 = 6.0;
        double r1089863 = r1089861 * r1089862;
        double r1089864 = z;
        double r1089865 = r1089863 * r1089864;
        double r1089866 = r1089859 + r1089865;
        return r1089866;
}
↓
double f(double x, double y, double z) {
        double r1089867 = y;
        double r1089868 = x;
        double r1089869 = r1089867 - r1089868;
        double r1089870 = 6.0;
        double r1089871 = z;
        double r1089872 = r1089870 * r1089871;
        double r1089873 = fma(r1089869, r1089872, r1089868);
        return r1089873;
}

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 2020060 +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)))