Average Error: 0.2 → 0.3
Time: 9.3s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(x - \frac{16}{116}\right) \cdot \left(3 \cdot y\right)\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(x - \frac{16}{116}\right) \cdot \left(3 \cdot y\right)
double f(double x, double y) {
        double r839947 = x;
        double r839948 = 16.0;
        double r839949 = 116.0;
        double r839950 = r839948 / r839949;
        double r839951 = r839947 - r839950;
        double r839952 = 3.0;
        double r839953 = r839951 * r839952;
        double r839954 = y;
        double r839955 = r839953 * r839954;
        return r839955;
}
↓
double f(double x, double y) {
        double r839956 = x;
        double r839957 = 16.0;
        double r839958 = 116.0;
        double r839959 = r839957 / r839958;
        double r839960 = r839956 - r839959;
        double r839961 = 3.0;
        double r839962 = y;
        double r839963 = r839961 * r839962;
        double r839964 = r839960 * r839963;
        return r839964;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.3
\[y \cdot \left(x \cdot 3 - 0.413793103448275856\right)\]

Derivation

  1. Initial program 0.2

    \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
  2. Using strategy rm

  3. Applied associate-*l*0.3

    \[\leadsto \color{blue}{\left(x - \frac{16}{116}\right) \cdot \left(3 \cdot y\right)}\]

  4. Final simplification0.3

    \[\leadsto \left(x - \frac{16}{116}\right) \cdot \left(3 \cdot y\right)\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.41379310344827586))

  (* (* (- x (/ 16 116)) 3) y))