Average Error: 0.2 → 0.2
Time: 3.3s
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 r783735 = x;
        double r783736 = 16.0;
        double r783737 = 116.0;
        double r783738 = r783736 / r783737;
        double r783739 = r783735 - r783738;
        double r783740 = 3.0;
        double r783741 = r783739 * r783740;
        double r783742 = y;
        double r783743 = r783741 * r783742;
        return r783743;
}
↓
double f(double x, double y) {
        double r783744 = 3.0;
        double r783745 = x;
        double r783746 = r783744 * r783745;
        double r783747 = 0.41379310344827586;
        double r783748 = r783746 - r783747;
        double r783749 = y;
        double r783750 = r783748 * r783749;
        return r783750;
}

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. Using strategy rm

  3. Applied add-cube-cbrt0.2

    \[\leadsto \left(\left(x - \frac{16}{116}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}\right)}\right) \cdot y\]

  4. Applied associate-*r*0.8

    \[\leadsto \color{blue}{\left(\left(\left(x - \frac{16}{116}\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\right) \cdot \sqrt[3]{3}\right)} \cdot y\]

  5. Taylor expanded around 0 0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020081 
(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))