Average Error: 14.9 → 0.5
Time: 30.1s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -5.795611421145836744402935774403637790937 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(2 \cdot y\right)\\ \mathbf{elif}\;x \le 3.247588547814785746124721995699073933232 \cdot 10^{-105}:\\ \;\;\;\;\frac{1}{\frac{\frac{x - y}{y}}{x \cdot 2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(2 \cdot y\right)\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -5.795611421145836744402935774403637790937 \cdot 10^{-17}:\\
\;\;\;\;\frac{x}{x - y} \cdot \left(2 \cdot y\right)\\

\mathbf{elif}\;x \le 3.247588547814785746124721995699073933232 \cdot 10^{-105}:\\
\;\;\;\;\frac{1}{\frac{\frac{x - y}{y}}{x \cdot 2}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{x - y} \cdot \left(2 \cdot y\right)\\

\end{array}
double f(double x, double y) {
        double r37273099 = x;
        double r37273100 = 2.0;
        double r37273101 = r37273099 * r37273100;
        double r37273102 = y;
        double r37273103 = r37273101 * r37273102;
        double r37273104 = r37273099 - r37273102;
        double r37273105 = r37273103 / r37273104;
        return r37273105;
}
↓
double f(double x, double y) {
        double r37273106 = x;
        double r37273107 = -5.795611421145837e-17;
        bool r37273108 = r37273106 <= r37273107;
        double r37273109 = y;
        double r37273110 = r37273106 - r37273109;
        double r37273111 = r37273106 / r37273110;
        double r37273112 = 2.0;
        double r37273113 = r37273112 * r37273109;
        double r37273114 = r37273111 * r37273113;
        double r37273115 = 3.2475885478147857e-105;
        bool r37273116 = r37273106 <= r37273115;
        double r37273117 = 1.0;
        double r37273118 = r37273110 / r37273109;
        double r37273119 = r37273106 * r37273112;
        double r37273120 = r37273118 / r37273119;
        double r37273121 = r37273117 / r37273120;
        double r37273122 = r37273116 ? r37273121 : r37273114;
        double r37273123 = r37273108 ? r37273114 : r37273122;
        return r37273123;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.9
Target0.4
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;x \lt -1.721044263414944729490876394165887012892 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -5.795611421145837e-17 or 3.2475885478147857e-105 < x

    1. Initial program 14.4

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

    3. Applied associate-/l*12.6

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

    5. Applied div-inv12.7

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

    6. Applied times-frac0.8

      \[\leadsto \color{blue}{\frac{x}{x - y} \cdot \frac{2}{\frac{1}{y}}}\]

    7. Simplified0.7

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

    if -5.795611421145837e-17 < x < 3.2475885478147857e-105

    1. Initial program 15.6

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
    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 clear-num0.2

      \[\leadsto \color{blue}{\frac{1}{\frac{\frac{x - y}{y}}{x \cdot 2}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -5.795611421145836744402935774403637790937 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(2 \cdot y\right)\\ \mathbf{elif}\;x \le 3.247588547814785746124721995699073933232 \cdot 10^{-105}:\\ \;\;\;\;\frac{1}{\frac{\frac{x - y}{y}}{x \cdot 2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(2 \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"

  :herbie-target
  (if (< x -1.7210442634149447e+81) (* (/ (* 2.0 x) (- x y)) y) (if (< x 8.364504563556443e+16) (/ (* x 2.0) (/ (- x y) y)) (* (/ (* 2.0 x) (- x y)) y)))

  (/ (* (* x 2.0) y) (- x y)))