Average Error: 14.4 → 1.3
Time: 8.6s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -8.31176856225810498717589484339856368443 \cdot 10^{108} \lor \neg \left(x \le 9.562858780549262910479627469187876635734 \cdot 10^{83}\right):\\ \;\;\;\;\left(\frac{x \cdot 2}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}} \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{x - y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -8.31176856225810498717589484339856368443 \cdot 10^{108} \lor \neg \left(x \le 9.562858780549262910479627469187876635734 \cdot 10^{83}\right):\\
\;\;\;\;\left(\frac{x \cdot 2}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}} \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{x - y}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\

\end{array}
double f(double x, double y) {
        double r608499 = x;
        double r608500 = 2.0;
        double r608501 = r608499 * r608500;
        double r608502 = y;
        double r608503 = r608501 * r608502;
        double r608504 = r608499 - r608502;
        double r608505 = r608503 / r608504;
        return r608505;
}
↓
double f(double x, double y) {
        double r608506 = x;
        double r608507 = -8.311768562258105e+108;
        bool r608508 = r608506 <= r608507;
        double r608509 = 9.562858780549263e+83;
        bool r608510 = r608506 <= r608509;
        double r608511 = !r608510;
        bool r608512 = r608508 || r608511;
        double r608513 = 2.0;
        double r608514 = r608506 * r608513;
        double r608515 = y;
        double r608516 = r608506 - r608515;
        double r608517 = cbrt(r608516);
        double r608518 = r608517 * r608517;
        double r608519 = r608514 / r608518;
        double r608520 = cbrt(r608515);
        double r608521 = r608520 * r608520;
        double r608522 = cbrt(r608518);
        double r608523 = r608521 / r608522;
        double r608524 = r608519 * r608523;
        double r608525 = cbrt(r608517);
        double r608526 = r608520 / r608525;
        double r608527 = r608524 * r608526;
        double r608528 = r608516 / r608515;
        double r608529 = r608514 / r608528;
        double r608530 = r608512 ? r608527 : r608529;
        return r608530;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.4
Target0.4
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;x \lt -1.721044263414944729490876394165887012892 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -8.311768562258105e+108 or 9.562858780549263e+83 < x

    1. Initial program 19.8

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

    3. Applied add-cube-cbrt20.6

      \[\leadsto \frac{\left(x \cdot 2\right) \cdot y}{\color{blue}{\left(\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}\right) \cdot \sqrt[3]{x - y}}}\]

    4. Applied times-frac7.4

      \[\leadsto \color{blue}{\frac{x \cdot 2}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}} \cdot \frac{y}{\sqrt[3]{x - y}}}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt7.5

      \[\leadsto \frac{x \cdot 2}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}} \cdot \frac{y}{\sqrt[3]{\color{blue}{\left(\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}\right) \cdot \sqrt[3]{x - y}}}}\]

    7. Applied cbrt-prod7.6

      \[\leadsto \frac{x \cdot 2}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}} \cdot \frac{y}{\color{blue}{\sqrt[3]{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}} \cdot \sqrt[3]{\sqrt[3]{x - y}}}}\]

    8. Applied add-cube-cbrt7.7

      \[\leadsto \frac{x \cdot 2}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}} \cdot \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\sqrt[3]{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}} \cdot \sqrt[3]{\sqrt[3]{x - y}}}\]

    9. Applied times-frac7.7

      \[\leadsto \frac{x \cdot 2}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}} \cdot \color{blue}{\left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{x - y}}}\right)}\]

    10. Applied associate-*r*1.8

      \[\leadsto \color{blue}{\left(\frac{x \cdot 2}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}} \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{x - y}}}}\]

    if -8.311768562258105e+108 < x < 9.562858780549263e+83

    1. Initial program 11.6

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

    3. Applied associate-/l*1.1

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -8.31176856225810498717589484339856368443 \cdot 10^{108} \lor \neg \left(x \le 9.562858780549262910479627469187876635734 \cdot 10^{83}\right):\\ \;\;\;\;\left(\frac{x \cdot 2}{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}} \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{x - y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (if (< x -1.7210442634149447e+81) (* (/ (* 2 x) (- x y)) y) (if (< x 83645045635564432) (/ (* x 2) (/ (- x y) y)) (* (/ (* 2 x) (- x y)) y)))

  (/ (* (* x 2) y) (- x y)))