Average Error: 0.3 → 0.2
Time: 4.7s
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 r854767 = x;
        double r854768 = y;
        double r854769 = r854768 - r854767;
        double r854770 = 6.0;
        double r854771 = r854769 * r854770;
        double r854772 = z;
        double r854773 = r854771 * r854772;
        double r854774 = r854767 + r854773;
        return r854774;
}
↓
double f(double x, double y, double z) {
        double r854775 = y;
        double r854776 = x;
        double r854777 = r854775 - r854776;
        double r854778 = 6.0;
        double r854779 = z;
        double r854780 = r854778 * r854779;
        double r854781 = fma(r854777, r854780, r854776);
        return r854781;
}

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 2020100 +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)))