Average Error: 0.2 → 0.3
Time: 2.4s
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 r836550 = x;
        double r836551 = 16.0;
        double r836552 = 116.0;
        double r836553 = r836551 / r836552;
        double r836554 = r836550 - r836553;
        double r836555 = 3.0;
        double r836556 = r836554 * r836555;
        double r836557 = y;
        double r836558 = r836556 * r836557;
        return r836558;
}
↓
double f(double x, double y) {
        double r836559 = x;
        double r836560 = 16.0;
        double r836561 = 116.0;
        double r836562 = r836560 / r836561;
        double r836563 = r836559 - r836562;
        double r836564 = 3.0;
        double r836565 = y;
        double r836566 = r836564 * r836565;
        double r836567 = r836563 * r836566;
        return r836567;
}

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 +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))