Average Error: 0.0 → 0.3
Time: 3.9s
Precision: 64
\[\frac{x - y}{2 - \left(x + y\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -26.31554417036707249621940718498080968857 \lor \neg \left(x \le 2.234979756987889017030695587777766726471 \cdot 10^{-98}\right):\\ \;\;\;\;\frac{x}{2 - \left(x + y\right)} - \log \left(e^{\frac{y}{2 - \left(x + y\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 \cdot 2 - \left(x + y\right) \cdot \left(x + y\right)} \cdot \left(2 + \left(x + y\right)\right) - \frac{y}{2 - \left(x + y\right)}\\ \end{array}\]
\frac{x - y}{2 - \left(x + y\right)}
↓
\begin{array}{l}
\mathbf{if}\;x \le -26.31554417036707249621940718498080968857 \lor \neg \left(x \le 2.234979756987889017030695587777766726471 \cdot 10^{-98}\right):\\
\;\;\;\;\frac{x}{2 - \left(x + y\right)} - \log \left(e^{\frac{y}{2 - \left(x + y\right)}}\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 r781059 = x;
        double r781060 = y;
        double r781061 = r781059 - r781060;
        double r781062 = 2.0;
        double r781063 = r781059 + r781060;
        double r781064 = r781062 - r781063;
        double r781065 = r781061 / r781064;
        return r781065;
}
↓
double f(double x, double y) {
        double r781066 = x;
        double r781067 = -26.315544170367072;
        bool r781068 = r781066 <= r781067;
        double r781069 = 2.234979756987889e-98;
        bool r781070 = r781066 <= r781069;
        double r781071 = !r781070;
        bool r781072 = r781068 || r781071;
        double r781073 = 2.0;
        double r781074 = y;
        double r781075 = r781066 + r781074;
        double r781076 = r781073 - r781075;
        double r781077 = r781066 / r781076;
        double r781078 = r781074 / r781076;
        double r781079 = exp(r781078);
        double r781080 = log(r781079);
        double r781081 = r781077 - r781080;
        double r781082 = r781073 * r781073;
        double r781083 = r781075 * r781075;
        double r781084 = r781082 - r781083;
        double r781085 = r781066 / r781084;
        double r781086 = r781073 + r781075;
        double r781087 = r781085 * r781086;
        double r781088 = r781087 - r781078;
        double r781089 = r781072 ? r781081 : r781088;
        return r781089;
}

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
Herbie0.3
\[\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -26.315544170367072 or 2.234979756987889e-98 < 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 add-log-exp0.5

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

    if -26.315544170367072 < x < 2.234979756987889e-98

    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 simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -26.31554417036707249621940718498080968857 \lor \neg \left(x \le 2.234979756987889017030695587777766726471 \cdot 10^{-98}\right):\\ \;\;\;\;\frac{x}{2 - \left(x + y\right)} - \log \left(e^{\frac{y}{2 - \left(x + y\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 \cdot 2 - \left(x + y\right) \cdot \left(x + y\right)} \cdot \left(2 + \left(x + y\right)\right) - \frac{y}{2 - \left(x + y\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 
(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))))