Average Error: 15.1 → 0.1
Time: 28.4s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -6.30586821746719046822219898487595819847 \cdot 10^{45}:\\ \;\;\;\;\frac{y}{x - y} \cdot \left(2 \cdot x\right)\\ \mathbf{elif}\;y \le 5.377814118926896018584556610780517528545 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(2 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x - y} \cdot \left(2 \cdot x\right)\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -6.30586821746719046822219898487595819847 \cdot 10^{45}:\\
\;\;\;\;\frac{y}{x - y} \cdot \left(2 \cdot x\right)\\

\mathbf{elif}\;y \le 5.377814118926896018584556610780517528545 \cdot 10^{-32}:\\
\;\;\;\;\frac{x}{x - y} \cdot \left(2 \cdot y\right)\\

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

\end{array}
double f(double x, double y) {
        double r19917438 = x;
        double r19917439 = 2.0;
        double r19917440 = r19917438 * r19917439;
        double r19917441 = y;
        double r19917442 = r19917440 * r19917441;
        double r19917443 = r19917438 - r19917441;
        double r19917444 = r19917442 / r19917443;
        return r19917444;
}
↓
double f(double x, double y) {
        double r19917445 = y;
        double r19917446 = -6.30586821746719e+45;
        bool r19917447 = r19917445 <= r19917446;
        double r19917448 = x;
        double r19917449 = r19917448 - r19917445;
        double r19917450 = r19917445 / r19917449;
        double r19917451 = 2.0;
        double r19917452 = r19917451 * r19917448;
        double r19917453 = r19917450 * r19917452;
        double r19917454 = 5.377814118926896e-32;
        bool r19917455 = r19917445 <= r19917454;
        double r19917456 = r19917448 / r19917449;
        double r19917457 = r19917451 * r19917445;
        double r19917458 = r19917456 * r19917457;
        double r19917459 = r19917455 ? r19917458 : r19917453;
        double r19917460 = r19917447 ? r19917453 : r19917459;
        return r19917460;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.1
Target0.4
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;x \lt -1.721044263414944729490876394165887012892 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -6.30586821746719e+45 or 5.377814118926896e-32 < y

    1. Initial program 16.7

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

    3. Applied *-un-lft-identity16.7

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

    if -6.30586821746719e+45 < y < 5.377814118926896e-32

    1. Initial program 13.6

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

    3. Applied associate-/l*14.8

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

    5. Applied div-inv14.9

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

    6. Applied times-frac0.3

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

    7. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -6.30586821746719046822219898487595819847 \cdot 10^{45}:\\ \;\;\;\;\frac{y}{x - y} \cdot \left(2 \cdot x\right)\\ \mathbf{elif}\;y \le 5.377814118926896018584556610780517528545 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(2 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x - y} \cdot \left(2 \cdot x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 +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)))