Average Error: 0.2 → 0.2
Time: 4.4s
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 r1133430 = x;
        double r1133431 = y;
        double r1133432 = r1133431 - r1133430;
        double r1133433 = 6.0;
        double r1133434 = r1133432 * r1133433;
        double r1133435 = z;
        double r1133436 = r1133434 * r1133435;
        double r1133437 = r1133430 + r1133436;
        return r1133437;
}
↓
double f(double x, double y, double z) {
        double r1133438 = y;
        double r1133439 = x;
        double r1133440 = r1133438 - r1133439;
        double r1133441 = 6.0;
        double r1133442 = z;
        double r1133443 = r1133441 * r1133442;
        double r1133444 = fma(r1133440, r1133443, r1133439);
        return r1133444;
}

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 2020034 +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)))