Average Error: 0.3 → 0.3
Time: 3.4s
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 r922958 = x;
        double r922959 = 16.0;
        double r922960 = 116.0;
        double r922961 = r922959 / r922960;
        double r922962 = r922958 - r922961;
        double r922963 = 3.0;
        double r922964 = r922962 * r922963;
        double r922965 = y;
        double r922966 = r922964 * r922965;
        return r922966;
}
↓
double f(double x, double y) {
        double r922967 = x;
        double r922968 = 16.0;
        double r922969 = 116.0;
        double r922970 = r922968 / r922969;
        double r922971 = r922967 - r922970;
        double r922972 = 3.0;
        double r922973 = y;
        double r922974 = r922972 * r922973;
        double r922975 = r922971 * r922974;
        return r922975;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.3

    \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
  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 2020034 
(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))