Average Error: 0.4 → 0.4
Time: 4.0s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(\left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \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)
double f(double x, double y, double z) {
        double r239945 = x;
        double r239946 = y;
        double r239947 = r239946 - r239945;
        double r239948 = 6.0;
        double r239949 = r239947 * r239948;
        double r239950 = 2.0;
        double r239951 = 3.0;
        double r239952 = r239950 / r239951;
        double r239953 = z;
        double r239954 = r239952 - r239953;
        double r239955 = r239949 * r239954;
        double r239956 = r239945 + r239955;
        return r239956;
}
↓
double f(double x, double y, double z) {
        double r239957 = x;
        double r239958 = y;
        double r239959 = r239958 - r239957;
        double r239960 = 6.0;
        double r239961 = r239959 * r239960;
        double r239962 = 2.0;
        double r239963 = 3.0;
        double r239964 = r239962 / r239963;
        double r239965 = r239961 * r239964;
        double r239966 = z;
        double r239967 = -r239966;
        double r239968 = r239961 * r239967;
        double r239969 = r239965 + r239968;
        double r239970 = r239957 + r239969;
        return r239970;
}

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. Final simplification0.4

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

Reproduce

herbie shell --seed 2020002 +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))))