Average Error: 0.2 → 0.2
Time: 12.6s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(3 \cdot x - 0.4137931034482758563264326312491903081536\right) \cdot y\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(3 \cdot x - 0.4137931034482758563264326312491903081536\right) \cdot y
double f(double x, double y) {
        double r585209 = x;
        double r585210 = 16.0;
        double r585211 = 116.0;
        double r585212 = r585210 / r585211;
        double r585213 = r585209 - r585212;
        double r585214 = 3.0;
        double r585215 = r585213 * r585214;
        double r585216 = y;
        double r585217 = r585215 * r585216;
        return r585217;
}
↓
double f(double x, double y) {
        double r585218 = 3.0;
        double r585219 = x;
        double r585220 = r585218 * r585219;
        double r585221 = 0.41379310344827586;
        double r585222 = r585220 - r585221;
        double r585223 = y;
        double r585224 = r585222 * r585223;
        return r585224;
}

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
\[y \cdot \left(x \cdot 3 - 0.4137931034482758563264326312491903081536\right)\]

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

    \[\leadsto \color{blue}{\left(3 \cdot x - 0.4137931034482758563264326312491903081536\right)} \cdot y\]

  3. Final simplification0.2

    \[\leadsto \left(3 \cdot x - 0.4137931034482758563264326312491903081536\right) \cdot y\]

Reproduce

herbie shell --seed 2019212 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.413793103448275856))

  (* (* (- x (/ 16 116)) 3) y))