Average Error: 0.2 → 0.2
Time: 3.8s
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 r824723 = x;
        double r824724 = 16.0;
        double r824725 = 116.0;
        double r824726 = r824724 / r824725;
        double r824727 = r824723 - r824726;
        double r824728 = 3.0;
        double r824729 = r824727 * r824728;
        double r824730 = y;
        double r824731 = r824729 * r824730;
        return r824731;
}
↓
double f(double x, double y) {
        double r824732 = x;
        double r824733 = 16.0;
        double r824734 = 116.0;
        double r824735 = r824733 / r824734;
        double r824736 = r824732 - r824735;
        double r824737 = 3.0;
        double r824738 = r824736 * r824737;
        double r824739 = y;
        double r824740 = r824738 * r824739;
        return r824740;
}

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 2020083 +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))