Average Error: 0.2 → 0.2
Time: 7.3s
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 r1043220 = x;
        double r1043221 = 16.0;
        double r1043222 = 116.0;
        double r1043223 = r1043221 / r1043222;
        double r1043224 = r1043220 - r1043223;
        double r1043225 = 3.0;
        double r1043226 = r1043224 * r1043225;
        double r1043227 = y;
        double r1043228 = r1043226 * r1043227;
        return r1043228;
}
↓
double f(double x, double y) {
        double r1043229 = x;
        double r1043230 = 16.0;
        double r1043231 = 116.0;
        double r1043232 = r1043230 / r1043231;
        double r1043233 = r1043229 - r1043232;
        double r1043234 = 3.0;
        double r1043235 = r1043233 * r1043234;
        double r1043236 = y;
        double r1043237 = r1043235 * r1043236;
        return r1043237;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020042 +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))