Average Error: 0.2 → 0.2
Time: 26.7s
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 r433425 = x;
        double r433426 = y;
        double r433427 = r433426 - r433425;
        double r433428 = 6.0;
        double r433429 = r433427 * r433428;
        double r433430 = z;
        double r433431 = r433429 * r433430;
        double r433432 = r433425 + r433431;
        return r433432;
}
↓
double f(double x, double y, double z) {
        double r433433 = y;
        double r433434 = x;
        double r433435 = r433433 - r433434;
        double r433436 = 6.0;
        double r433437 = z;
        double r433438 = r433436 * r433437;
        double r433439 = fma(r433435, r433438, r433434);
        return r433439;
}

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 2019323 +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)))