Average Error: 0.3 → 0.2
Time: 3.6s
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 r812004 = x;
        double r812005 = y;
        double r812006 = r812005 - r812004;
        double r812007 = 6.0;
        double r812008 = r812006 * r812007;
        double r812009 = z;
        double r812010 = r812008 * r812009;
        double r812011 = r812004 + r812010;
        return r812011;
}
↓
double f(double x, double y, double z) {
        double r812012 = y;
        double r812013 = x;
        double r812014 = r812012 - r812013;
        double r812015 = 6.0;
        double r812016 = z;
        double r812017 = r812015 * r812016;
        double r812018 = fma(r812014, r812017, r812013);
        return r812018;
}

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 2020021 +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)))