Average Error: 0.0 → 0.0
Time: 3.5s
Precision: 64
\[\frac{x - y}{2 - \left(x + y\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.8286949592281574 \lor \neg \left(x \le 8.4800696698330235 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{\frac{x}{2 - \left(x + y\right)} \cdot \frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)} \cdot \frac{y}{2 - \left(x + y\right)}}{\frac{x}{2 - \left(x + y\right)} + \frac{y}{2 - \left(x + y\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 \cdot 2 - \left(x + y\right) \cdot \left(x + y\right)} \cdot \left(2 + \left(x + y\right)\right) - \frac{y}{2 - \left(x + y\right)}\\ \end{array}\]
\frac{x - y}{2 - \left(x + y\right)}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.8286949592281574 \lor \neg \left(x \le 8.4800696698330235 \cdot 10^{-105}\right):\\
\;\;\;\;\frac{\frac{x}{2 - \left(x + y\right)} \cdot \frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)} \cdot \frac{y}{2 - \left(x + y\right)}}{\frac{x}{2 - \left(x + y\right)} + \frac{y}{2 - \left(x + y\right)}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{2 \cdot 2 - \left(x + y\right) \cdot \left(x + y\right)} \cdot \left(2 + \left(x + y\right)\right) - \frac{y}{2 - \left(x + y\right)}\\

\end{array}
double f(double x, double y) {
        double r1346864 = x;
        double r1346865 = y;
        double r1346866 = r1346864 - r1346865;
        double r1346867 = 2.0;
        double r1346868 = r1346864 + r1346865;
        double r1346869 = r1346867 - r1346868;
        double r1346870 = r1346866 / r1346869;
        return r1346870;
}
↓
double f(double x, double y) {
        double r1346871 = x;
        double r1346872 = -1.8286949592281574;
        bool r1346873 = r1346871 <= r1346872;
        double r1346874 = 8.480069669833023e-105;
        bool r1346875 = r1346871 <= r1346874;
        double r1346876 = !r1346875;
        bool r1346877 = r1346873 || r1346876;
        double r1346878 = 2.0;
        double r1346879 = y;
        double r1346880 = r1346871 + r1346879;
        double r1346881 = r1346878 - r1346880;
        double r1346882 = r1346871 / r1346881;
        double r1346883 = r1346882 * r1346882;
        double r1346884 = r1346879 / r1346881;
        double r1346885 = r1346884 * r1346884;
        double r1346886 = r1346883 - r1346885;
        double r1346887 = r1346882 + r1346884;
        double r1346888 = r1346886 / r1346887;
        double r1346889 = r1346878 * r1346878;
        double r1346890 = r1346880 * r1346880;
        double r1346891 = r1346889 - r1346890;
        double r1346892 = r1346871 / r1346891;
        double r1346893 = r1346878 + r1346880;
        double r1346894 = r1346892 * r1346893;
        double r1346895 = r1346894 - r1346884;
        double r1346896 = r1346877 ? r1346888 : r1346895;
        return r1346896;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.8286949592281574 or 8.480069669833023e-105 < x

    1. Initial program 0.0

      \[\frac{x - y}{2 - \left(x + y\right)}\]
    2. Using strategy rm

    3. Applied div-sub0.0

      \[\leadsto \color{blue}{\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}}\]
    4. Using strategy rm

    5. Applied flip--0.0

      \[\leadsto \color{blue}{\frac{\frac{x}{2 - \left(x + y\right)} \cdot \frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)} \cdot \frac{y}{2 - \left(x + y\right)}}{\frac{x}{2 - \left(x + y\right)} + \frac{y}{2 - \left(x + y\right)}}}\]

    if -1.8286949592281574 < x < 8.480069669833023e-105

    1. Initial program 0.0

      \[\frac{x - y}{2 - \left(x + y\right)}\]
    2. Using strategy rm

    3. Applied div-sub0.0

      \[\leadsto \color{blue}{\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}}\]
    4. Using strategy rm

    5. Applied flip--0.0

      \[\leadsto \frac{x}{\color{blue}{\frac{2 \cdot 2 - \left(x + y\right) \cdot \left(x + y\right)}{2 + \left(x + y\right)}}} - \frac{y}{2 - \left(x + y\right)}\]

    6. Applied associate-/r/0.0

      \[\leadsto \color{blue}{\frac{x}{2 \cdot 2 - \left(x + y\right) \cdot \left(x + y\right)} \cdot \left(2 + \left(x + y\right)\right)} - \frac{y}{2 - \left(x + y\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.8286949592281574 \lor \neg \left(x \le 8.4800696698330235 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{\frac{x}{2 - \left(x + y\right)} \cdot \frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)} \cdot \frac{y}{2 - \left(x + y\right)}}{\frac{x}{2 - \left(x + y\right)} + \frac{y}{2 - \left(x + y\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 \cdot 2 - \left(x + y\right) \cdot \left(x + y\right)} \cdot \left(2 + \left(x + y\right)\right) - \frac{y}{2 - \left(x + y\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2 (+ x y))) (/ y (- 2 (+ x y))))

  (/ (- x y) (- 2 (+ x y))))