Average Error: 0.3 → 0.2
Time: 11.7s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]
↓
\[x + \left(z \cdot \left(y - x\right)\right) \cdot 6\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot z
↓
x + \left(z \cdot \left(y - x\right)\right) \cdot 6
double f(double x, double y, double z) {
        double r670179 = x;
        double r670180 = y;
        double r670181 = r670180 - r670179;
        double r670182 = 6.0;
        double r670183 = r670181 * r670182;
        double r670184 = z;
        double r670185 = r670183 * r670184;
        double r670186 = r670179 + r670185;
        return r670186;
}
↓
double f(double x, double y, double z) {
        double r670187 = x;
        double r670188 = z;
        double r670189 = y;
        double r670190 = r670189 - r670187;
        double r670191 = r670188 * r670190;
        double r670192 = 6.0;
        double r670193 = r670191 * r670192;
        double r670194 = r670187 + r670193;
        return r670194;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Taylor expanded around inf 0.2

    \[\leadsto x + \color{blue}{\left(6 \cdot \left(z \cdot y\right) - 6 \cdot \left(x \cdot z\right)\right)}\]

  3. Simplified0.2

    \[\leadsto x + \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6}\]

  4. Final simplification0.2

    \[\leadsto x + \left(z \cdot \left(y - x\right)\right) \cdot 6\]

Reproduce

herbie shell --seed 2019212 
(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)))