Average Error: 15.2 → 0.2
Time: 29.7s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1950896635033006241202453604204544:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \le 1.525261129384541486350799582595845140217 \cdot 10^{75}:\\ \;\;\;\;\left(2 \cdot x\right) \cdot \frac{y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1950896635033006241202453604204544:\\
\;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\

\mathbf{elif}\;x \le 1.525261129384541486350799582595845140217 \cdot 10^{75}:\\
\;\;\;\;\left(2 \cdot x\right) \cdot \frac{y}{x - y}\\

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

\end{array}
double f(double x, double y) {
        double r21678228 = x;
        double r21678229 = 2.0;
        double r21678230 = r21678228 * r21678229;
        double r21678231 = y;
        double r21678232 = r21678230 * r21678231;
        double r21678233 = r21678228 - r21678231;
        double r21678234 = r21678232 / r21678233;
        return r21678234;
}
↓
double f(double x, double y) {
        double r21678235 = x;
        double r21678236 = -1.9508966350330062e+33;
        bool r21678237 = r21678235 <= r21678236;
        double r21678238 = 2.0;
        double r21678239 = r21678238 * r21678235;
        double r21678240 = y;
        double r21678241 = r21678235 - r21678240;
        double r21678242 = r21678239 / r21678241;
        double r21678243 = r21678242 * r21678240;
        double r21678244 = 1.5252611293845415e+75;
        bool r21678245 = r21678235 <= r21678244;
        double r21678246 = r21678240 / r21678241;
        double r21678247 = r21678239 * r21678246;
        double r21678248 = r21678245 ? r21678247 : r21678243;
        double r21678249 = r21678237 ? r21678243 : r21678248;
        return r21678249;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.2
Target0.3
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \lt -1.721044263414944729490876394165887012892 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.9508966350330062e+33 or 1.5252611293845415e+75 < x

    1. Initial program 19.0

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

    3. Applied associate-/l*17.4

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

    5. Applied associate-/r/0.1

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

    if -1.9508966350330062e+33 < x < 1.5252611293845415e+75

    1. Initial program 12.5

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

    3. Applied *-un-lft-identity12.5

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

    4. Applied times-frac0.3

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

    5. Simplified0.3

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1950896635033006241202453604204544:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \le 1.525261129384541486350799582595845140217 \cdot 10^{75}:\\ \;\;\;\;\left(2 \cdot x\right) \cdot \frac{y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 +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)))