Average Error: 0.0 → 0.3
Time: 3.7s
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 r838487 = x;
        double r838488 = y;
        double r838489 = r838487 - r838488;
        double r838490 = 2.0;
        double r838491 = r838487 + r838488;
        double r838492 = r838490 - r838491;
        double r838493 = r838489 / r838492;
        return r838493;
}
↓
double f(double x, double y) {
        double r838494 = x;
        double r838495 = -26.315544170367072;
        bool r838496 = r838494 <= r838495;
        double r838497 = 2.234979756987889e-98;
        bool r838498 = r838494 <= r838497;
        double r838499 = !r838498;
        bool r838500 = r838496 || r838499;
        double r838501 = 2.0;
        double r838502 = y;
        double r838503 = r838494 + r838502;
        double r838504 = r838501 - r838503;
        double r838505 = r838494 / r838504;
        double r838506 = r838502 / r838504;
        double r838507 = exp(r838506);
        double r838508 = log(r838507);
        double r838509 = r838505 - r838508;
        double r838510 = r838501 * r838501;
        double r838511 = r838503 * r838503;
        double r838512 = r838510 - r838511;
        double r838513 = r838494 / r838512;
        double r838514 = r838501 + r838503;
        double r838515 = r838513 * r838514;
        double r838516 = r838515 - r838506;
        double r838517 = r838500 ? r838509 : r838516;
        return r838517;
}

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))))