Average Error: 0.2 → 0.3
Time: 16.4s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(3 \cdot y\right) \cdot \left(x - \frac{16}{116}\right)\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(3 \cdot y\right) \cdot \left(x - \frac{16}{116}\right)
double f(double x, double y) {
        double r35492447 = x;
        double r35492448 = 16.0;
        double r35492449 = 116.0;
        double r35492450 = r35492448 / r35492449;
        double r35492451 = r35492447 - r35492450;
        double r35492452 = 3.0;
        double r35492453 = r35492451 * r35492452;
        double r35492454 = y;
        double r35492455 = r35492453 * r35492454;
        return r35492455;
}
↓
double f(double x, double y) {
        double r35492456 = 3.0;
        double r35492457 = y;
        double r35492458 = r35492456 * r35492457;
        double r35492459 = x;
        double r35492460 = 16.0;
        double r35492461 = 116.0;
        double r35492462 = r35492460 / r35492461;
        double r35492463 = r35492459 - r35492462;
        double r35492464 = r35492458 * r35492463;
        return r35492464;
}

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
\[y \cdot \left(x \cdot 3 - 0.4137931034482758563264326312491903081536\right)\]

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

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"

  :herbie-target
  (* y (- (* x 3.0) 0.41379310344827586))

  (* (* (- x (/ 16.0 116.0)) 3.0) y))