Average Error: 0.4 → 0.4
Time: 5.2s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(x + \frac{2}{3} \cdot \left(\left(y - x\right) \cdot 6\right)\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(x + \frac{2}{3} \cdot \left(\left(y - x\right) \cdot 6\right)\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)
double f(double x, double y, double z) {
        double r284030 = x;
        double r284031 = y;
        double r284032 = r284031 - r284030;
        double r284033 = 6.0;
        double r284034 = r284032 * r284033;
        double r284035 = 2.0;
        double r284036 = 3.0;
        double r284037 = r284035 / r284036;
        double r284038 = z;
        double r284039 = r284037 - r284038;
        double r284040 = r284034 * r284039;
        double r284041 = r284030 + r284040;
        return r284041;
}
↓
double f(double x, double y, double z) {
        double r284042 = x;
        double r284043 = 2.0;
        double r284044 = 3.0;
        double r284045 = r284043 / r284044;
        double r284046 = y;
        double r284047 = r284046 - r284042;
        double r284048 = 6.0;
        double r284049 = r284047 * r284048;
        double r284050 = r284045 * r284049;
        double r284051 = r284042 + r284050;
        double r284052 = z;
        double r284053 = -r284052;
        double r284054 = r284049 * r284053;
        double r284055 = r284051 + r284054;
        return r284055;
}

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-lft-in0.4

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

  5. Applied associate-+r+0.4

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

  6. Simplified0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2020018 
(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))))