Average Error: 0.4 → 0.2
Time: 27.0s
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 r177104 = x;
        double r177105 = y;
        double r177106 = r177105 - r177104;
        double r177107 = 6.0;
        double r177108 = r177106 * r177107;
        double r177109 = 2.0;
        double r177110 = 3.0;
        double r177111 = r177109 / r177110;
        double r177112 = z;
        double r177113 = r177111 - r177112;
        double r177114 = r177108 * r177113;
        double r177115 = r177104 + r177114;
        return r177115;
}
↓
double f(double x, double y, double z) {
        double r177116 = x;
        double r177117 = y;
        double r177118 = r177117 - r177116;
        double r177119 = 2.0;
        double r177120 = 3.0;
        double r177121 = r177119 / r177120;
        double r177122 = z;
        double r177123 = r177121 - r177122;
        double r177124 = 6.0;
        double r177125 = r177123 * r177124;
        double r177126 = r177118 * r177125;
        double r177127 = r177116 + r177126;
        return r177127;
}

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 2019325 
(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))))