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 r820398 = x;
        double r820399 = 16.0;
        double r820400 = 116.0;
        double r820401 = r820399 / r820400;
        double r820402 = r820398 - r820401;
        double r820403 = 3.0;
        double r820404 = r820402 * r820403;
        double r820405 = y;
        double r820406 = r820404 * r820405;
        return r820406;
}
↓
double f(double x, double y) {
        double r820407 = x;
        double r820408 = 16.0;
        double r820409 = 116.0;
        double r820410 = r820408 / r820409;
        double r820411 = r820407 - r820410;
        double r820412 = 3.0;
        double r820413 = y;
        double r820414 = r820412 * r820413;
        double r820415 = r820411 * r820414;
        return r820415;
}

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 +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))