Average Error: 0.2 → 0.2
Time: 2.6s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[y \cdot \left(3 \cdot x - 0.413793103448275856\right)\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
y \cdot \left(3 \cdot x - 0.413793103448275856\right)
double f(double x, double y) {
        double r1013509 = x;
        double r1013510 = 16.0;
        double r1013511 = 116.0;
        double r1013512 = r1013510 / r1013511;
        double r1013513 = r1013509 - r1013512;
        double r1013514 = 3.0;
        double r1013515 = r1013513 * r1013514;
        double r1013516 = y;
        double r1013517 = r1013515 * r1013516;
        return r1013517;
}
↓
double f(double x, double y) {
        double r1013518 = y;
        double r1013519 = 3.0;
        double r1013520 = x;
        double r1013521 = r1013519 * r1013520;
        double r1013522 = 0.41379310344827586;
        double r1013523 = r1013521 - r1013522;
        double r1013524 = r1013518 * r1013523;
        return r1013524;
}

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
\[y \cdot \left(x \cdot 3 - 0.413793103448275856\right)\]

Derivation

  1. Initial program 0.2

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

  2. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right) - 0.413793103448275856 \cdot y}\]

  3. Simplified0.2

    \[\leadsto \color{blue}{y \cdot \left(3 \cdot x - 0.413793103448275856\right)}\]

  4. Final simplification0.2

    \[\leadsto y \cdot \left(3 \cdot x - 0.413793103448275856\right)\]

Reproduce

herbie shell --seed 2020100 
(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))