Average Error: 0.2 → 0.2
Time: 12.2s
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 r563330 = x;
        double r563331 = 16.0;
        double r563332 = 116.0;
        double r563333 = r563331 / r563332;
        double r563334 = r563330 - r563333;
        double r563335 = 3.0;
        double r563336 = r563334 * r563335;
        double r563337 = y;
        double r563338 = r563336 * r563337;
        return r563338;
}
↓
double f(double x, double y) {
        double r563339 = x;
        double r563340 = 16.0;
        double r563341 = 116.0;
        double r563342 = r563340 / r563341;
        double r563343 = r563339 - r563342;
        double r563344 = 3.0;
        double r563345 = r563343 * r563344;
        double r563346 = y;
        double r563347 = r563345 * r563346;
        return r563347;
}

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 2019323 +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))