Average Error: 0.4 → 0.2
Time: 15.6s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(-\left(z \cdot 6\right) \cdot \left(y - x\right)\right) + \left(x + \left(6 \cdot \frac{2}{3}\right) \cdot \left(y - x\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(-\left(z \cdot 6\right) \cdot \left(y - x\right)\right) + \left(x + \left(6 \cdot \frac{2}{3}\right) \cdot \left(y - x\right)\right)
double f(double x, double y, double z) {
        double r208447 = x;
        double r208448 = y;
        double r208449 = r208448 - r208447;
        double r208450 = 6.0;
        double r208451 = r208449 * r208450;
        double r208452 = 2.0;
        double r208453 = 3.0;
        double r208454 = r208452 / r208453;
        double r208455 = z;
        double r208456 = r208454 - r208455;
        double r208457 = r208451 * r208456;
        double r208458 = r208447 + r208457;
        return r208458;
}
↓
double f(double x, double y, double z) {
        double r208459 = z;
        double r208460 = 6.0;
        double r208461 = r208459 * r208460;
        double r208462 = y;
        double r208463 = x;
        double r208464 = r208462 - r208463;
        double r208465 = r208461 * r208464;
        double r208466 = -r208465;
        double r208467 = 2.0;
        double r208468 = 3.0;
        double r208469 = r208467 / r208468;
        double r208470 = r208460 * r208469;
        double r208471 = r208470 * r208464;
        double r208472 = r208463 + r208471;
        double r208473 = r208466 + r208472;
        return r208473;
}

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 sub-neg0.4

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

  4. Applied distribute-rgt-in0.4

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

  5. Applied associate-+r+0.4

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

  6. Simplified0.2

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

  8. Applied distribute-lft-neg-out0.2

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))