Average Error: 0.2 → 0.2
Time: 5.1s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
double f(double x, double y) {
        double r741122 = x;
        double r741123 = 16.0;
        double r741124 = 116.0;
        double r741125 = r741123 / r741124;
        double r741126 = r741122 - r741125;
        double r741127 = 3.0;
        double r741128 = r741126 * r741127;
        double r741129 = y;
        double r741130 = r741128 * r741129;
        return r741130;
}
↓
double f(double x, double y) {
        double r741131 = x;
        double r741132 = 16.0;
        double r741133 = 116.0;
        double r741134 = r741132 / r741133;
        double r741135 = r741131 - r741134;
        double r741136 = 3.0;
        double r741137 = r741135 * r741136;
        double r741138 = y;
        double r741139 = r741137 * r741138;
        return r741139;
}

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

Derivation

  1. Initial program 0.2

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2020001 +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))