Average Error: 0.3 → 0.2
Time: 3.5s
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 r852097 = x;
        double r852098 = y;
        double r852099 = r852098 - r852097;
        double r852100 = 6.0;
        double r852101 = r852099 * r852100;
        double r852102 = z;
        double r852103 = r852101 * r852102;
        double r852104 = r852097 + r852103;
        return r852104;
}
↓
double f(double x, double y, double z) {
        double r852105 = y;
        double r852106 = x;
        double r852107 = r852105 - r852106;
        double r852108 = 6.0;
        double r852109 = z;
        double r852110 = r852108 * r852109;
        double r852111 = fma(r852107, r852110, r852106);
        return r852111;
}

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 2020064 +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)))