Average Error: 0.2 → 0.3
Time: 7.0s
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 r906171 = x;
        double r906172 = 16.0;
        double r906173 = 116.0;
        double r906174 = r906172 / r906173;
        double r906175 = r906171 - r906174;
        double r906176 = 3.0;
        double r906177 = r906175 * r906176;
        double r906178 = y;
        double r906179 = r906177 * r906178;
        return r906179;
}
↓
double f(double x, double y) {
        double r906180 = x;
        double r906181 = 16.0;
        double r906182 = 116.0;
        double r906183 = r906181 / r906182;
        double r906184 = r906180 - r906183;
        double r906185 = 3.0;
        double r906186 = y;
        double r906187 = r906185 * r906186;
        double r906188 = r906184 * r906187;
        return r906188;
}

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 2020045 +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))