Average Error: 0.2 → 0.2
Time: 7.4s
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 r956264 = x;
        double r956265 = 16.0;
        double r956266 = 116.0;
        double r956267 = r956265 / r956266;
        double r956268 = r956264 - r956267;
        double r956269 = 3.0;
        double r956270 = r956268 * r956269;
        double r956271 = y;
        double r956272 = r956270 * r956271;
        return r956272;
}
↓
double f(double x, double y) {
        double r956273 = x;
        double r956274 = 16.0;
        double r956275 = 116.0;
        double r956276 = r956274 / r956275;
        double r956277 = r956273 - r956276;
        double r956278 = 3.0;
        double r956279 = r956277 * r956278;
        double r956280 = y;
        double r956281 = r956279 * r956280;
        return r956281;
}

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 2020042 +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))