Average Error: 0.2 → 0.3
Time: 2.2s
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 r685357 = x;
        double r685358 = 16.0;
        double r685359 = 116.0;
        double r685360 = r685358 / r685359;
        double r685361 = r685357 - r685360;
        double r685362 = 3.0;
        double r685363 = r685361 * r685362;
        double r685364 = y;
        double r685365 = r685363 * r685364;
        return r685365;
}
↓
double f(double x, double y) {
        double r685366 = x;
        double r685367 = 16.0;
        double r685368 = 116.0;
        double r685369 = r685367 / r685368;
        double r685370 = r685366 - r685369;
        double r685371 = 3.0;
        double r685372 = y;
        double r685373 = r685371 * r685372;
        double r685374 = r685370 * r685373;
        return r685374;
}

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 2020089 
(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))