Average Error: 14.7 → 1.5
Time: 2.0s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -5.57636306111153486 \cdot 10^{137} \lor \neg \left(y \le 2.19553327371823438 \cdot 10^{93}\right):\\ \;\;\;\;\frac{x \cdot 2}{\sqrt[3]{{\left(\frac{x}{y} - 1\right)}^{3}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -5.57636306111153486 \cdot 10^{137} \lor \neg \left(y \le 2.19553327371823438 \cdot 10^{93}\right):\\
\;\;\;\;\frac{x \cdot 2}{\sqrt[3]{{\left(\frac{x}{y} - 1\right)}^{3}}}\\

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

\end{array}
double f(double x, double y) {
        double r406031 = x;
        double r406032 = 2.0;
        double r406033 = r406031 * r406032;
        double r406034 = y;
        double r406035 = r406033 * r406034;
        double r406036 = r406031 - r406034;
        double r406037 = r406035 / r406036;
        return r406037;
}
↓
double f(double x, double y) {
        double r406038 = y;
        double r406039 = -5.576363061111535e+137;
        bool r406040 = r406038 <= r406039;
        double r406041 = 2.1955332737182344e+93;
        bool r406042 = r406038 <= r406041;
        double r406043 = !r406042;
        bool r406044 = r406040 || r406043;
        double r406045 = x;
        double r406046 = 2.0;
        double r406047 = r406045 * r406046;
        double r406048 = r406045 / r406038;
        double r406049 = 1.0;
        double r406050 = r406048 - r406049;
        double r406051 = 3.0;
        double r406052 = pow(r406050, r406051);
        double r406053 = cbrt(r406052);
        double r406054 = r406047 / r406053;
        double r406055 = r406045 - r406038;
        double r406056 = r406047 / r406055;
        double r406057 = r406056 * r406038;
        double r406058 = r406044 ? r406054 : r406057;
        return r406058;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.7
Target0.3
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;x \lt -1.7210442634149447 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -5.576363061111535e+137 or 2.1955332737182344e+93 < y

    1. Initial program 20.8

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

    3. Applied associate-/l*0.0

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

    5. Applied add-cbrt-cube62.5

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

    6. Applied add-cbrt-cube63.1

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

    7. Applied cbrt-undiv63.1

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

    8. Simplified2.1

      \[\leadsto \frac{x \cdot 2}{\sqrt[3]{\color{blue}{{\left(\frac{x}{y} - 1\right)}^{3}}}}\]

    if -5.576363061111535e+137 < y < 2.1955332737182344e+93

    1. Initial program 12.0

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

    3. Applied associate-/l*11.0

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

    5. Applied associate-/r/1.3

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5.57636306111153486 \cdot 10^{137} \lor \neg \left(y \le 2.19553327371823438 \cdot 10^{93}\right):\\ \;\;\;\;\frac{x \cdot 2}{\sqrt[3]{{\left(\frac{x}{y} - 1\right)}^{3}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 +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)))