Average Error: 0.2 → 0.2
Time: 12.5s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]
↓
\[\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot z
↓
\mathsf{fma}\left(z, \left(y - x\right) \cdot 6, x\right)
double f(double x, double y, double z) {
        double r630790 = x;
        double r630791 = y;
        double r630792 = r630791 - r630790;
        double r630793 = 6.0;
        double r630794 = r630792 * r630793;
        double r630795 = z;
        double r630796 = r630794 * r630795;
        double r630797 = r630790 + r630796;
        return r630797;
}
↓
double f(double x, double y, double z) {
        double r630798 = z;
        double r630799 = y;
        double r630800 = x;
        double r630801 = r630799 - r630800;
        double r630802 = 6.0;
        double r630803 = r630801 * r630802;
        double r630804 = fma(r630798, r630803, r630800);
        return r630804;
}

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

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

  (+ x (* (* (- y x) 6.0) z)))