Average Error: 0.2 → 0.2
Time: 10.9s
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 r660773 = x;
        double r660774 = 16.0;
        double r660775 = 116.0;
        double r660776 = r660774 / r660775;
        double r660777 = r660773 - r660776;
        double r660778 = 3.0;
        double r660779 = r660777 * r660778;
        double r660780 = y;
        double r660781 = r660779 * r660780;
        return r660781;
}
↓
double f(double x, double y) {
        double r660782 = x;
        double r660783 = 16.0;
        double r660784 = 116.0;
        double r660785 = r660783 / r660784;
        double r660786 = r660782 - r660785;
        double r660787 = 3.0;
        double r660788 = r660786 * r660787;
        double r660789 = y;
        double r660790 = r660788 * r660789;
        return r660790;
}

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
\[y \cdot \left(x \cdot 3 - 0.4137931034482758563264326312491903081536\right)\]

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 2019209 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.413793103448275856))

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