Average Error: 0.2 → 0.3
Time: 15.8s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(x - \frac{16}{116}\right) \cdot \left(y \cdot 3\right)\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(x - \frac{16}{116}\right) \cdot \left(y \cdot 3\right)
double f(double x, double y) {
        double r578083 = x;
        double r578084 = 16.0;
        double r578085 = 116.0;
        double r578086 = r578084 / r578085;
        double r578087 = r578083 - r578086;
        double r578088 = 3.0;
        double r578089 = r578087 * r578088;
        double r578090 = y;
        double r578091 = r578089 * r578090;
        return r578091;
}
↓
double f(double x, double y) {
        double r578092 = x;
        double r578093 = 16.0;
        double r578094 = 116.0;
        double r578095 = r578093 / r578094;
        double r578096 = r578092 - r578095;
        double r578097 = y;
        double r578098 = 3.0;
        double r578099 = r578097 * r578098;
        double r578100 = r578096 * r578099;
        return r578100;
}

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
\[y \cdot \left(x \cdot 3 - 0.4137931034482758563264326312491903081536\right)\]

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. Simplified0.3

    \[\leadsto \left(x - \frac{16}{116}\right) \cdot \color{blue}{\left(y \cdot 3\right)}\]

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.413793103448275856))

  (* (* (- x (/ 16 116)) 3) y))