Average Error: 0.4 → 0.2
Time: 12.6s
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 r221312 = x;
        double r221313 = y;
        double r221314 = r221313 - r221312;
        double r221315 = 6.0;
        double r221316 = r221314 * r221315;
        double r221317 = 2.0;
        double r221318 = 3.0;
        double r221319 = r221317 / r221318;
        double r221320 = z;
        double r221321 = r221319 - r221320;
        double r221322 = r221316 * r221321;
        double r221323 = r221312 + r221322;
        return r221323;
}
↓
double f(double x, double y, double z) {
        double r221324 = x;
        double r221325 = y;
        double r221326 = r221325 - r221324;
        double r221327 = 2.0;
        double r221328 = 3.0;
        double r221329 = r221327 / r221328;
        double r221330 = z;
        double r221331 = r221329 - r221330;
        double r221332 = 6.0;
        double r221333 = r221331 * r221332;
        double r221334 = r221326 * r221333;
        double r221335 = r221324 + r221334;
        return r221335;
}

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 2019305 
(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))))