Average Error: 0.2 → 0.2
Time: 2.7s
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 r869012 = x;
        double r869013 = 16.0;
        double r869014 = 116.0;
        double r869015 = r869013 / r869014;
        double r869016 = r869012 - r869015;
        double r869017 = 3.0;
        double r869018 = r869016 * r869017;
        double r869019 = y;
        double r869020 = r869018 * r869019;
        return r869020;
}
↓
double f(double x, double y) {
        double r869021 = 3.0;
        double r869022 = x;
        double r869023 = r869021 * r869022;
        double r869024 = 0.41379310344827586;
        double r869025 = r869023 - r869024;
        double r869026 = y;
        double r869027 = r869025 * r869026;
        return r869027;
}

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 2020057 +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))