Average Error: 0.3 → 0.2
Time: 25.0s
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 r583189 = x;
        double r583190 = y;
        double r583191 = r583190 - r583189;
        double r583192 = 6.0;
        double r583193 = r583191 * r583192;
        double r583194 = z;
        double r583195 = r583193 * r583194;
        double r583196 = r583189 + r583195;
        return r583196;
}
↓
double f(double x, double y, double z) {
        double r583197 = y;
        double r583198 = x;
        double r583199 = r583197 - r583198;
        double r583200 = 6.0;
        double r583201 = z;
        double r583202 = r583200 * r583201;
        double r583203 = fma(r583199, r583202, r583198);
        return r583203;
}

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)))