Average Error: 0.4 → 0.2
Time: 4.8s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)
double f(double x, double y, double z) {
        double r262112 = x;
        double r262113 = y;
        double r262114 = r262113 - r262112;
        double r262115 = 6.0;
        double r262116 = r262114 * r262115;
        double r262117 = 2.0;
        double r262118 = 3.0;
        double r262119 = r262117 / r262118;
        double r262120 = z;
        double r262121 = r262119 - r262120;
        double r262122 = r262116 * r262121;
        double r262123 = r262112 + r262122;
        return r262123;
}
↓
double f(double x, double y, double z) {
        double r262124 = x;
        double r262125 = y;
        double r262126 = r262125 - r262124;
        double r262127 = 6.0;
        double r262128 = 2.0;
        double r262129 = 3.0;
        double r262130 = r262128 / r262129;
        double r262131 = z;
        double r262132 = r262130 - r262131;
        double r262133 = r262127 * r262132;
        double r262134 = r262126 * r262133;
        double r262135 = r262124 + r262134;
        return r262135;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019322 
(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))))