Average Error: 0.2 → 0.3
Time: 4.3s
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 r742734 = x;
        double r742735 = 16.0;
        double r742736 = 116.0;
        double r742737 = r742735 / r742736;
        double r742738 = r742734 - r742737;
        double r742739 = 3.0;
        double r742740 = r742738 * r742739;
        double r742741 = y;
        double r742742 = r742740 * r742741;
        return r742742;
}
↓
double f(double x, double y) {
        double r742743 = x;
        double r742744 = 16.0;
        double r742745 = 116.0;
        double r742746 = r742744 / r742745;
        double r742747 = r742743 - r742746;
        double r742748 = 3.0;
        double r742749 = y;
        double r742750 = r742748 * r742749;
        double r742751 = r742747 * r742750;
        return r742751;
}

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

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 1978988140 
(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))