Average Error: 0.4 → 0.3
Time: 11.9s
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 r213613 = x;
        double r213614 = y;
        double r213615 = r213614 - r213613;
        double r213616 = 6.0;
        double r213617 = r213615 * r213616;
        double r213618 = 2.0;
        double r213619 = 3.0;
        double r213620 = r213618 / r213619;
        double r213621 = z;
        double r213622 = r213620 - r213621;
        double r213623 = r213617 * r213622;
        double r213624 = r213613 + r213623;
        return r213624;
}
↓
double f(double x, double y, double z) {
        double r213625 = x;
        double r213626 = y;
        double r213627 = r213626 - r213625;
        double r213628 = 2.0;
        double r213629 = 3.0;
        double r213630 = r213628 / r213629;
        double r213631 = z;
        double r213632 = r213630 - r213631;
        double r213633 = 6.0;
        double r213634 = r213632 * r213633;
        double r213635 = r213627 * r213634;
        double r213636 = r213625 + r213635;
        return r213636;
}

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*0.3

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

  4. Simplified0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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))))