Average Error: 15.2 → 0.2
Time: 10.2s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1950896635033006241202453604204544:\\ \;\;\;\;\left(y \cdot 2\right) \cdot \frac{x}{x - y}\\ \mathbf{elif}\;x \le 1.525261129384541486350799582595845140217 \cdot 10^{75}:\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 2\right) \cdot \frac{x}{x - y}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1950896635033006241202453604204544:\\
\;\;\;\;\left(y \cdot 2\right) \cdot \frac{x}{x - y}\\

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

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

\end{array}
double f(double x, double y) {
        double r25786460 = x;
        double r25786461 = 2.0;
        double r25786462 = r25786460 * r25786461;
        double r25786463 = y;
        double r25786464 = r25786462 * r25786463;
        double r25786465 = r25786460 - r25786463;
        double r25786466 = r25786464 / r25786465;
        return r25786466;
}
↓
double f(double x, double y) {
        double r25786467 = x;
        double r25786468 = -1.9508966350330062e+33;
        bool r25786469 = r25786467 <= r25786468;
        double r25786470 = y;
        double r25786471 = 2.0;
        double r25786472 = r25786470 * r25786471;
        double r25786473 = r25786467 - r25786470;
        double r25786474 = r25786467 / r25786473;
        double r25786475 = r25786472 * r25786474;
        double r25786476 = 1.5252611293845415e+75;
        bool r25786477 = r25786467 <= r25786476;
        double r25786478 = r25786467 * r25786471;
        double r25786479 = r25786470 / r25786473;
        double r25786480 = r25786478 * r25786479;
        double r25786481 = r25786477 ? r25786480 : r25786475;
        double r25786482 = r25786469 ? r25786475 : r25786481;
        return r25786482;
}

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 div-inv17.5

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

    6. Applied times-frac0.3

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

    7. Simplified0.1

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

    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

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

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)))