Average Error: 0.3 → 0.2
Time: 4.1s
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 r842160 = x;
        double r842161 = y;
        double r842162 = r842161 - r842160;
        double r842163 = 6.0;
        double r842164 = r842162 * r842163;
        double r842165 = z;
        double r842166 = r842164 * r842165;
        double r842167 = r842160 + r842166;
        return r842167;
}
↓
double f(double x, double y, double z) {
        double r842168 = y;
        double r842169 = x;
        double r842170 = r842168 - r842169;
        double r842171 = 6.0;
        double r842172 = z;
        double r842173 = r842171 * r842172;
        double r842174 = fma(r842170, r842173, r842169);
        return r842174;
}

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 2020056 +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)))