Average Error: 0.4 → 0.2
Time: 3.3s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(\left(y - x\right) \cdot \left(\frac{2}{3} \cdot 6\right) + \left(y - x\right) \cdot \left(\left(-z\right) \cdot 6\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(\left(y - x\right) \cdot \left(\frac{2}{3} \cdot 6\right) + \left(y - x\right) \cdot \left(\left(-z\right) \cdot 6\right)\right)
double f(double x, double y, double z) {
        double r209329 = x;
        double r209330 = y;
        double r209331 = r209330 - r209329;
        double r209332 = 6.0;
        double r209333 = r209331 * r209332;
        double r209334 = 2.0;
        double r209335 = 3.0;
        double r209336 = r209334 / r209335;
        double r209337 = z;
        double r209338 = r209336 - r209337;
        double r209339 = r209333 * r209338;
        double r209340 = r209329 + r209339;
        return r209340;
}
↓
double f(double x, double y, double z) {
        double r209341 = x;
        double r209342 = y;
        double r209343 = r209342 - r209341;
        double r209344 = 2.0;
        double r209345 = 3.0;
        double r209346 = r209344 / r209345;
        double r209347 = 6.0;
        double r209348 = r209346 * r209347;
        double r209349 = r209343 * r209348;
        double r209350 = z;
        double r209351 = -r209350;
        double r209352 = r209351 * r209347;
        double r209353 = r209343 * r209352;
        double r209354 = r209349 + r209353;
        double r209355 = r209341 + r209354;
        return r209355;
}

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. Using strategy rm

  5. Applied sub-neg0.2

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

  6. Applied distribute-lft-in0.2

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

  7. Applied distribute-lft-in0.2

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

  8. Simplified0.2

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020002 
(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))))