Average Error: 0.2 → 0.2
Time: 5.1s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
double f(double x, double y) {
        double r802276 = x;
        double r802277 = 16.0;
        double r802278 = 116.0;
        double r802279 = r802277 / r802278;
        double r802280 = r802276 - r802279;
        double r802281 = 3.0;
        double r802282 = r802280 * r802281;
        double r802283 = y;
        double r802284 = r802282 * r802283;
        return r802284;
}
↓
double f(double x, double y) {
        double r802285 = x;
        double r802286 = 16.0;
        double r802287 = 116.0;
        double r802288 = r802286 / r802287;
        double r802289 = r802285 - r802288;
        double r802290 = 3.0;
        double r802291 = r802289 * r802290;
        double r802292 = y;
        double r802293 = r802291 * r802292;
        return r802293;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020001 +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))