Average Error: 0.2 → 0.2
Time: 3.3s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
double f(double x, double y) {
        double r856082 = x;
        double r856083 = 16.0;
        double r856084 = 116.0;
        double r856085 = r856083 / r856084;
        double r856086 = r856082 - r856085;
        double r856087 = 3.0;
        double r856088 = r856086 * r856087;
        double r856089 = y;
        double r856090 = r856088 * r856089;
        return r856090;
}
↓
double f(double x, double y) {
        double r856091 = x;
        double r856092 = 16.0;
        double r856093 = 116.0;
        double r856094 = r856092 / r856093;
        double r856095 = r856091 - r856094;
        double r856096 = 3.0;
        double r856097 = r856095 * r856096;
        double r856098 = y;
        double r856099 = r856097 * r856098;
        return r856099;
}

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

Derivation

  1. Initial program 0.2

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(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))