Average Error: 0.2 → 0.2
Time: 13.7s
Precision: 64
\[\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y\]
↓
\[\left(3.0 \cdot x - 0.41379310344827586\right) \cdot y\]
\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y
↓
\left(3.0 \cdot x - 0.41379310344827586\right) \cdot y
double f(double x, double y) {
        double r41349045 = x;
        double r41349046 = 16.0;
        double r41349047 = 116.0;
        double r41349048 = r41349046 / r41349047;
        double r41349049 = r41349045 - r41349048;
        double r41349050 = 3.0;
        double r41349051 = r41349049 * r41349050;
        double r41349052 = y;
        double r41349053 = r41349051 * r41349052;
        return r41349053;
}
↓
double f(double x, double y) {
        double r41349054 = 3.0;
        double r41349055 = x;
        double r41349056 = r41349054 * r41349055;
        double r41349057 = 0.41379310344827586;
        double r41349058 = r41349056 - r41349057;
        double r41349059 = y;
        double r41349060 = r41349058 * r41349059;
        return r41349060;
}

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
Herbie0.2
\[y \cdot \left(x \cdot 3.0 - 0.41379310344827586\right)\]

Derivation

  1. Initial program 0.2

    \[\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y\]

  2. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{3.0 \cdot \left(x \cdot y\right) - 0.41379310344827586 \cdot y}\]

  3. Simplified0.2

    \[\leadsto \color{blue}{y \cdot \left(x \cdot 3.0 - 0.41379310344827586\right)}\]

  4. Final simplification0.2

    \[\leadsto \left(3.0 \cdot x - 0.41379310344827586\right) \cdot y\]

Reproduce

herbie shell --seed 2019164 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"

  :herbie-target
  (* y (- (* x 3.0) 0.41379310344827586))

  (* (* (- x (/ 16.0 116.0)) 3.0) y))