Average Error: 0.4 → 0.2
Time: 27.2s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(\left(\frac{2}{3} - z\right) \cdot 6\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(y - x\right) \cdot \left(\left(\frac{2}{3} - z\right) \cdot 6\right)
double f(double x, double y, double z) {
        double r214067 = x;
        double r214068 = y;
        double r214069 = r214068 - r214067;
        double r214070 = 6.0;
        double r214071 = r214069 * r214070;
        double r214072 = 2.0;
        double r214073 = 3.0;
        double r214074 = r214072 / r214073;
        double r214075 = z;
        double r214076 = r214074 - r214075;
        double r214077 = r214071 * r214076;
        double r214078 = r214067 + r214077;
        return r214078;
}
↓
double f(double x, double y, double z) {
        double r214079 = x;
        double r214080 = y;
        double r214081 = r214080 - r214079;
        double r214082 = 2.0;
        double r214083 = 3.0;
        double r214084 = r214082 / r214083;
        double r214085 = z;
        double r214086 = r214084 - r214085;
        double r214087 = 6.0;
        double r214088 = r214086 * r214087;
        double r214089 = r214081 * r214088;
        double r214090 = r214079 + r214089;
        return r214090;
}

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

Derivation

  1. Initial program 0.4

    \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.2

    \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\]

  4. Simplified0.2

    \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(\left(\frac{2}{3} - z\right) \cdot 6\right)}\]

  5. Final simplification0.2

    \[\leadsto x + \left(y - x\right) \cdot \left(\left(\frac{2}{3} - z\right) \cdot 6\right)\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6) (- (/ 2 3) z))))