Average Error: 0.3 → 0.2
Time: 37.8s
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 r709077 = x;
        double r709078 = y;
        double r709079 = r709078 - r709077;
        double r709080 = 6.0;
        double r709081 = r709079 * r709080;
        double r709082 = z;
        double r709083 = r709081 * r709082;
        double r709084 = r709077 + r709083;
        return r709084;
}
↓
double f(double x, double y, double z) {
        double r709085 = y;
        double r709086 = x;
        double r709087 = r709085 - r709086;
        double r709088 = 6.0;
        double r709089 = z;
        double r709090 = r709088 * r709089;
        double r709091 = fma(r709087, r709090, r709086);
        return r709091;
}

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)))