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

↓

\[\begin{array}{l} \mathbf{if}\;y \le -11894198345334408230327762615508217626620:\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \mathbf{elif}\;y \le 3.827108002628365811088571233801504531292 \cdot 10^{68}:\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]

\frac{\left(x \cdot 2\right) \cdot y}{x - y}

↓

\begin{array}{l}
\mathbf{if}\;y \le -11894198345334408230327762615508217626620:\\
\;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\

\mathbf{elif}\;y \le 3.827108002628365811088571233801504531292 \cdot 10^{68}:\\
\;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\

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

\end{array}

double f(double x, double y) {
        double r479387 = x;
        double r479388 = 2.0;
        double r479389 = r479387 * r479388;
        double r479390 = y;
        double r479391 = r479389 * r479390;
        double r479392 = r479387 - r479390;
        double r479393 = r479391 / r479392;
        return r479393;
}

↓

double f(double x, double y) {
        double r479394 = y;
        double r479395 = -1.1894198345334408e+40;
        bool r479396 = r479394 <= r479395;
        double r479397 = x;
        double r479398 = 2.0;
        double r479399 = r479397 * r479398;
        double r479400 = r479397 - r479394;
        double r479401 = r479394 / r479400;
        double r479402 = r479399 * r479401;
        double r479403 = 3.827108002628366e+68;
        bool r479404 = r479394 <= r479403;
        double r479405 = r479399 / r479400;
        double r479406 = r479405 * r479394;
        double r479407 = r479400 / r479394;
        double r479408 = r479399 / r479407;
        double r479409 = r479404 ? r479406 : r479408;
        double r479410 = r479396 ? r479402 : r479409;
        return r479410;
}

Original	14.9
Target	0.4
Herbie	0.2

Derivation

Split input into 3 regimes
if y < -1.1894198345334408e+40
1. Initial program 18.3
  \[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
2. Using strategy rm
3. Applied *-un-lft-identity18.3
  \[\leadsto \frac{\left(x \cdot 2\right) \cdot y}{\color{blue}{1 \cdot \left(x - y\right)}}\]
4. Applied times-frac0.2
  \[\leadsto \color{blue}{\frac{x \cdot 2}{1} \cdot \frac{y}{x - y}}\]
5. Simplified0.2
  \[\leadsto \color{blue}{\left(x \cdot 2\right)} \cdot \frac{y}{x - y}\]
if -1.1894198345334408e+40 < y < 3.827108002628366e+68
1. Initial program 11.9
  \[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
2. Using strategy rm
3. Applied associate-/l*12.7
  \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}}\]
4. Using strategy rm
5. Applied associate-/r/0.3
  \[\leadsto \color{blue}{\frac{x \cdot 2}{x - y} \cdot y}\]
if 3.827108002628366e+68 < y
1. Initial program 20.2
  \[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
2. Using strategy rm
3. Applied associate-/l*0.1
  \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}}\]
Recombined 3 regimes into one program.
Final simplification0.2
\[\leadsto \begin{array}{l} \mathbf{if}\;y \le -11894198345334408230327762615508217626620:\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \mathbf{elif}\;y \le 3.827108002628365811088571233801504531292 \cdot 10^{68}:\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 +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)))

Error

Try it out

Target

Derivation

`if y < -1.1894198345334408e+40`

`if -1.1894198345334408e+40 < y < 3.827108002628366e+68`

`if 3.827108002628366e+68 < y`

Reproduce

In
Out