Average Error: 0.2 → 0.3
Time: 2.3s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(x - \frac{16}{116}\right) \cdot \left(3 \cdot y\right)\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(x - \frac{16}{116}\right) \cdot \left(3 \cdot y\right)
double f(double x, double y) {
        double r822093 = x;
        double r822094 = 16.0;
        double r822095 = 116.0;
        double r822096 = r822094 / r822095;
        double r822097 = r822093 - r822096;
        double r822098 = 3.0;
        double r822099 = r822097 * r822098;
        double r822100 = y;
        double r822101 = r822099 * r822100;
        return r822101;
}
↓
double f(double x, double y) {
        double r822102 = x;
        double r822103 = 16.0;
        double r822104 = 116.0;
        double r822105 = r822103 / r822104;
        double r822106 = r822102 - r822105;
        double r822107 = 3.0;
        double r822108 = y;
        double r822109 = r822107 * r822108;
        double r822110 = r822106 * r822109;
        return r822110;
}

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
Herbie0.3
\[y \cdot \left(x \cdot 3 - 0.413793103448275856\right)\]

Derivation

  1. Initial program 0.2

    \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
  2. Using strategy rm

  3. Applied associate-*l*0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2020024 
(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))