Average Error: 0.4 → 0.4
Time: 16.1s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(-z\right) \cdot \left(\left(y - x\right) \cdot 6\right) + \left(x + \frac{2}{3} \cdot \left(\left(y - x\right) \cdot 6\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(-z\right) \cdot \left(\left(y - x\right) \cdot 6\right) + \left(x + \frac{2}{3} \cdot \left(\left(y - x\right) \cdot 6\right)\right)
double f(double x, double y, double z) {
        double r13269446 = x;
        double r13269447 = y;
        double r13269448 = r13269447 - r13269446;
        double r13269449 = 6.0;
        double r13269450 = r13269448 * r13269449;
        double r13269451 = 2.0;
        double r13269452 = 3.0;
        double r13269453 = r13269451 / r13269452;
        double r13269454 = z;
        double r13269455 = r13269453 - r13269454;
        double r13269456 = r13269450 * r13269455;
        double r13269457 = r13269446 + r13269456;
        return r13269457;
}
↓
double f(double x, double y, double z) {
        double r13269458 = z;
        double r13269459 = -r13269458;
        double r13269460 = y;
        double r13269461 = x;
        double r13269462 = r13269460 - r13269461;
        double r13269463 = 6.0;
        double r13269464 = r13269462 * r13269463;
        double r13269465 = r13269459 * r13269464;
        double r13269466 = 2.0;
        double r13269467 = 3.0;
        double r13269468 = r13269466 / r13269467;
        double r13269469 = r13269468 * r13269464;
        double r13269470 = r13269461 + r13269469;
        double r13269471 = r13269465 + r13269470;
        return r13269471;
}

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. Final simplification0.4

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

Reproduce

herbie shell --seed 2019174 
(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))))