Average Error: 0.2 → 0.2
Time: 16.1s
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 r38163411 = x;
        double r38163412 = 16.0;
        double r38163413 = 116.0;
        double r38163414 = r38163412 / r38163413;
        double r38163415 = r38163411 - r38163414;
        double r38163416 = 3.0;
        double r38163417 = r38163415 * r38163416;
        double r38163418 = y;
        double r38163419 = r38163417 * r38163418;
        return r38163419;
}
↓
double f(double x, double y) {
        double r38163420 = 3.0;
        double r38163421 = x;
        double r38163422 = r38163420 * r38163421;
        double r38163423 = 0.41379310344827586;
        double r38163424 = r38163422 - r38163423;
        double r38163425 = y;
        double r38163426 = r38163424 * r38163425;
        return r38163426;
}

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 +o rules:numerics
(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))