Average Error: 0.0 → 0.0
Time: 5.2s
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 r967033 = x;
        double r967034 = y;
        double r967035 = r967033 - r967034;
        double r967036 = 2.0;
        double r967037 = r967033 + r967034;
        double r967038 = r967036 - r967037;
        double r967039 = r967035 / r967038;
        return r967039;
}
↓
double f(double x, double y) {
        double r967040 = x;
        double r967041 = -1.8286949592281574;
        bool r967042 = r967040 <= r967041;
        double r967043 = 8.480069669833023e-105;
        bool r967044 = r967040 <= r967043;
        double r967045 = !r967044;
        bool r967046 = r967042 || r967045;
        double r967047 = 2.0;
        double r967048 = y;
        double r967049 = r967040 + r967048;
        double r967050 = r967047 - r967049;
        double r967051 = r967040 / r967050;
        double r967052 = r967051 * r967051;
        double r967053 = r967048 / r967050;
        double r967054 = r967053 * r967053;
        double r967055 = r967052 - r967054;
        double r967056 = r967051 + r967053;
        double r967057 = r967055 / r967056;
        double r967058 = r967047 * r967047;
        double r967059 = r967049 * r967049;
        double r967060 = r967058 - r967059;
        double r967061 = r967040 / r967060;
        double r967062 = r967047 + r967049;
        double r967063 = r967061 * r967062;
        double r967064 = r967063 - r967053;
        double r967065 = r967046 ? r967057 : r967064;
        return r967065;
}

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 +o rules:numerics
(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))))