Average Error: 0.4 → 0.2
Time: 8.9s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(x + \left(\frac{2}{3} \cdot 6\right) \cdot \left(y - x\right)\right) + 6 \cdot \left(z \cdot \left(x - y\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(x + \left(\frac{2}{3} \cdot 6\right) \cdot \left(y - x\right)\right) + 6 \cdot \left(z \cdot \left(x - y\right)\right)
double f(double x, double y, double z) {
        double r276962 = x;
        double r276963 = y;
        double r276964 = r276963 - r276962;
        double r276965 = 6.0;
        double r276966 = r276964 * r276965;
        double r276967 = 2.0;
        double r276968 = 3.0;
        double r276969 = r276967 / r276968;
        double r276970 = z;
        double r276971 = r276969 - r276970;
        double r276972 = r276966 * r276971;
        double r276973 = r276962 + r276972;
        return r276973;
}
↓
double f(double x, double y, double z) {
        double r276974 = x;
        double r276975 = 2.0;
        double r276976 = 3.0;
        double r276977 = r276975 / r276976;
        double r276978 = 6.0;
        double r276979 = r276977 * r276978;
        double r276980 = y;
        double r276981 = r276980 - r276974;
        double r276982 = r276979 * r276981;
        double r276983 = r276974 + r276982;
        double r276984 = z;
        double r276985 = r276974 - r276980;
        double r276986 = r276984 * r276985;
        double r276987 = r276978 * r276986;
        double r276988 = r276983 + r276987;
        return r276988;
}

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. Applied associate-+r+0.2

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

  9. Simplified0.2

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

  10. Taylor expanded around inf 0.2

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

  11. Simplified0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2020045 
(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))))