Average Error: 0.2 → 0.3
Time: 11.6s
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 r802353 = x;
        double r802354 = 16.0;
        double r802355 = 116.0;
        double r802356 = r802354 / r802355;
        double r802357 = r802353 - r802356;
        double r802358 = 3.0;
        double r802359 = r802357 * r802358;
        double r802360 = y;
        double r802361 = r802359 * r802360;
        return r802361;
}
↓
double f(double x, double y) {
        double r802362 = x;
        double r802363 = 16.0;
        double r802364 = 116.0;
        double r802365 = r802363 / r802364;
        double r802366 = r802362 - r802365;
        double r802367 = 3.0;
        double r802368 = y;
        double r802369 = r802367 * r802368;
        double r802370 = r802366 * r802369;
        return r802370;
}

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 2019350 +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))