Average Error: 0.2 → 0.3
Time: 11.6s
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 r950464 = x;
        double r950465 = 16.0;
        double r950466 = 116.0;
        double r950467 = r950465 / r950466;
        double r950468 = r950464 - r950467;
        double r950469 = 3.0;
        double r950470 = r950468 * r950469;
        double r950471 = y;
        double r950472 = r950470 * r950471;
        return r950472;
}
↓
double f(double x, double y) {
        double r950473 = x;
        double r950474 = 16.0;
        double r950475 = 116.0;
        double r950476 = r950474 / r950475;
        double r950477 = r950473 - r950476;
        double r950478 = 3.0;
        double r950479 = y;
        double r950480 = r950478 * r950479;
        double r950481 = r950477 * r950480;
        return r950481;
}

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))