Average Error: 0.2 → 0.3
Time: 20.5s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(3 \cdot y\right) \cdot \left(x - \frac{16}{116}\right)\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(3 \cdot y\right) \cdot \left(x - \frac{16}{116}\right)
double f(double x, double y) {
        double r22671655 = x;
        double r22671656 = 16.0;
        double r22671657 = 116.0;
        double r22671658 = r22671656 / r22671657;
        double r22671659 = r22671655 - r22671658;
        double r22671660 = 3.0;
        double r22671661 = r22671659 * r22671660;
        double r22671662 = y;
        double r22671663 = r22671661 * r22671662;
        return r22671663;
}
↓
double f(double x, double y) {
        double r22671664 = 3.0;
        double r22671665 = y;
        double r22671666 = r22671664 * r22671665;
        double r22671667 = x;
        double r22671668 = 16.0;
        double r22671669 = 116.0;
        double r22671670 = r22671668 / r22671669;
        double r22671671 = r22671667 - r22671670;
        double r22671672 = r22671666 * r22671671;
        return r22671672;
}

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

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"

  :herbie-target
  (* y (- (* x 3.0) 0.41379310344827586))

  (* (* (- x (/ 16.0 116.0)) 3.0) y))