Average Error: 0.2 → 0.2
Time: 3.0s
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 r871697 = x;
        double r871698 = y;
        double r871699 = r871698 - r871697;
        double r871700 = 6.0;
        double r871701 = r871699 * r871700;
        double r871702 = z;
        double r871703 = r871701 * r871702;
        double r871704 = r871697 + r871703;
        return r871704;
}
↓
double f(double x, double y, double z) {
        double r871705 = y;
        double r871706 = x;
        double r871707 = r871705 - r871706;
        double r871708 = 6.0;
        double r871709 = z;
        double r871710 = r871708 * r871709;
        double r871711 = fma(r871707, r871710, r871706);
        return r871711;
}

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 2020060 +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)))