Average Error: 0.2 → 0.2
Time: 14.2s
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 r974560 = x;
        double r974561 = y;
        double r974562 = r974561 - r974560;
        double r974563 = 6.0;
        double r974564 = r974562 * r974563;
        double r974565 = z;
        double r974566 = r974564 * r974565;
        double r974567 = r974560 + r974566;
        return r974567;
}
↓
double f(double x, double y, double z) {
        double r974568 = y;
        double r974569 = x;
        double r974570 = r974568 - r974569;
        double r974571 = 6.0;
        double r974572 = z;
        double r974573 = r974571 * r974572;
        double r974574 = fma(r974570, r974573, r974569);
        return r974574;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.2
Target0.2
Herbie0.2
\[x - \left(6 \cdot z\right) \cdot \left(x - y\right)\]

Derivation

  1. Initial program 0.2

    \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]

  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 2019305 +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)))