Average Error: 0.2 → 0.2
Time: 13.8s
Precision: 64
\[\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y\]
↓
\[\left(3.0 \cdot x - 0.41379310344827586\right) \cdot y\]
\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y
↓
\left(3.0 \cdot x - 0.41379310344827586\right) \cdot y
double f(double x, double y) {
        double r41098548 = x;
        double r41098549 = 16.0;
        double r41098550 = 116.0;
        double r41098551 = r41098549 / r41098550;
        double r41098552 = r41098548 - r41098551;
        double r41098553 = 3.0;
        double r41098554 = r41098552 * r41098553;
        double r41098555 = y;
        double r41098556 = r41098554 * r41098555;
        return r41098556;
}
↓
double f(double x, double y) {
        double r41098557 = 3.0;
        double r41098558 = x;
        double r41098559 = r41098557 * r41098558;
        double r41098560 = 0.41379310344827586;
        double r41098561 = r41098559 - r41098560;
        double r41098562 = y;
        double r41098563 = r41098561 * r41098562;
        return r41098563;
}

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
\[y \cdot \left(x \cdot 3.0 - 0.41379310344827586\right)\]

Derivation

  1. Initial program 0.2

    \[\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y\]

  2. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{\left(3.0 \cdot x - 0.41379310344827586\right)} \cdot y\]

  3. Final simplification0.2

    \[\leadsto \left(3.0 \cdot x - 0.41379310344827586\right) \cdot y\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"

  :herbie-target
  (* y (- (* x 3.0) 0.41379310344827586))

  (* (* (- x (/ 16.0 116.0)) 3.0) y))