Average Error: 0.2 → 0.2
Time: 2.5s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[y \cdot \left(3 \cdot x - 0.413793103448275856\right)\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
y \cdot \left(3 \cdot x - 0.413793103448275856\right)
double f(double x, double y) {
        double r885153 = x;
        double r885154 = 16.0;
        double r885155 = 116.0;
        double r885156 = r885154 / r885155;
        double r885157 = r885153 - r885156;
        double r885158 = 3.0;
        double r885159 = r885157 * r885158;
        double r885160 = y;
        double r885161 = r885159 * r885160;
        return r885161;
}
↓
double f(double x, double y) {
        double r885162 = y;
        double r885163 = 3.0;
        double r885164 = x;
        double r885165 = r885163 * r885164;
        double r885166 = 0.41379310344827586;
        double r885167 = r885165 - r885166;
        double r885168 = r885162 * r885167;
        return r885168;
}

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

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

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020064 +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))