Average Error: 0.2 → 0.2
Time: 8.0s
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 r866153 = x;
        double r866154 = 16.0;
        double r866155 = 116.0;
        double r866156 = r866154 / r866155;
        double r866157 = r866153 - r866156;
        double r866158 = 3.0;
        double r866159 = r866157 * r866158;
        double r866160 = y;
        double r866161 = r866159 * r866160;
        return r866161;
}
↓
double f(double x, double y) {
        double r866162 = 3.0;
        double r866163 = x;
        double r866164 = r866162 * r866163;
        double r866165 = 0.41379310344827586;
        double r866166 = r866164 - r866165;
        double r866167 = y;
        double r866168 = r866166 * r866167;
        return r866168;
}

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 2020043 +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))