Average Error: 0.2 → 0.2
Time: 2.1s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(3 \cdot x - 0.413793103448275856\right) \cdot y\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(3 \cdot x - 0.413793103448275856\right) \cdot y
double f(double x, double y) {
        double r1355259 = x;
        double r1355260 = 16.0;
        double r1355261 = 116.0;
        double r1355262 = r1355260 / r1355261;
        double r1355263 = r1355259 - r1355262;
        double r1355264 = 3.0;
        double r1355265 = r1355263 * r1355264;
        double r1355266 = y;
        double r1355267 = r1355265 * r1355266;
        return r1355267;
}
↓
double f(double x, double y) {
        double r1355268 = 3.0;
        double r1355269 = x;
        double r1355270 = r1355268 * r1355269;
        double r1355271 = 0.41379310344827586;
        double r1355272 = r1355270 - r1355271;
        double r1355273 = y;
        double r1355274 = r1355272 * r1355273;
        return r1355274;
}

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. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{\left(3 \cdot x - 0.413793103448275856\right)} \cdot y\]

  3. Final simplification0.2

    \[\leadsto \left(3 \cdot x - 0.413793103448275856\right) \cdot y\]

Reproduce

herbie shell --seed 2020065 
(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))