Average Error: 0.3 → 0.3
Time: 4.1s
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 r1173331 = x;
        double r1173332 = 16.0;
        double r1173333 = 116.0;
        double r1173334 = r1173332 / r1173333;
        double r1173335 = r1173331 - r1173334;
        double r1173336 = 3.0;
        double r1173337 = r1173335 * r1173336;
        double r1173338 = y;
        double r1173339 = r1173337 * r1173338;
        return r1173339;
}
↓
double f(double x, double y) {
        double r1173340 = x;
        double r1173341 = 16.0;
        double r1173342 = 116.0;
        double r1173343 = r1173341 / r1173342;
        double r1173344 = r1173340 - r1173343;
        double r1173345 = 3.0;
        double r1173346 = y;
        double r1173347 = r1173345 * r1173346;
        double r1173348 = r1173344 * r1173347;
        return r1173348;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.2
Herbie0.3
\[y \cdot \left(x \cdot 3 - 0.413793103448275856\right)\]

Derivation

  1. Initial program 0.3

    \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
  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 2020034 +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))