Average Error: 0.2 → 0.2
Time: 8.7s
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 r896604 = x;
        double r896605 = 16.0;
        double r896606 = 116.0;
        double r896607 = r896605 / r896606;
        double r896608 = r896604 - r896607;
        double r896609 = 3.0;
        double r896610 = r896608 * r896609;
        double r896611 = y;
        double r896612 = r896610 * r896611;
        return r896612;
}
↓
double f(double x, double y) {
        double r896613 = x;
        double r896614 = 16.0;
        double r896615 = 116.0;
        double r896616 = r896614 / r896615;
        double r896617 = r896613 - r896616;
        double r896618 = 3.0;
        double r896619 = r896617 * r896618;
        double r896620 = y;
        double r896621 = r896619 * r896620;
        return r896621;
}

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 2020046 +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))