Average Error: 0.3 → 0.2
Time: 2.6s
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 r833767 = x;
        double r833768 = y;
        double r833769 = r833768 - r833767;
        double r833770 = 6.0;
        double r833771 = r833769 * r833770;
        double r833772 = z;
        double r833773 = r833771 * r833772;
        double r833774 = r833767 + r833773;
        return r833774;
}
↓
double f(double x, double y, double z) {
        double r833775 = y;
        double r833776 = x;
        double r833777 = r833775 - r833776;
        double r833778 = 6.0;
        double r833779 = z;
        double r833780 = r833778 * r833779;
        double r833781 = fma(r833777, r833780, r833776);
        return r833781;
}

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 2020047 +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)))