Average Error: 0.3 → 0.2
Time: 14.4s
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 r597292 = x;
        double r597293 = y;
        double r597294 = r597293 - r597292;
        double r597295 = 6.0;
        double r597296 = r597294 * r597295;
        double r597297 = z;
        double r597298 = r597296 * r597297;
        double r597299 = r597292 + r597298;
        return r597299;
}
↓
double f(double x, double y, double z) {
        double r597300 = y;
        double r597301 = x;
        double r597302 = r597300 - r597301;
        double r597303 = 6.0;
        double r597304 = z;
        double r597305 = r597303 * r597304;
        double r597306 = fma(r597302, r597305, r597301);
        return r597306;
}

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 2019235 +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)))