\[\frac{\left(x \cdot 2.0\right) \cdot y}{x - y}\]

↓

\[\begin{array}{l} \mathbf{if}\;y \le -3.0638957814586657 \cdot 10^{-28}:\\ \;\;\;\;\frac{y}{x - y} \cdot \left(2.0 \cdot x\right)\\ \mathbf{elif}\;y \le 1.3615474866246526 \cdot 10^{+17}:\\ \;\;\;\;\frac{2.0 \cdot x}{x - y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x - y} \cdot \left(2.0 \cdot x\right)\\ \end{array}\]

\frac{\left(x \cdot 2.0\right) \cdot y}{x - y}

↓

\begin{array}{l}
\mathbf{if}\;y \le -3.0638957814586657 \cdot 10^{-28}:\\
\;\;\;\;\frac{y}{x - y} \cdot \left(2.0 \cdot x\right)\\

\mathbf{elif}\;y \le 1.3615474866246526 \cdot 10^{+17}:\\
\;\;\;\;\frac{2.0 \cdot x}{x - y} \cdot y\\

\mathbf{else}:\\
\;\;\;\;\frac{y}{x - y} \cdot \left(2.0 \cdot x\right)\\

\end{array}

double f(double x, double y) {
        double r21772311 = x;
        double r21772312 = 2.0;
        double r21772313 = r21772311 * r21772312;
        double r21772314 = y;
        double r21772315 = r21772313 * r21772314;
        double r21772316 = r21772311 - r21772314;
        double r21772317 = r21772315 / r21772316;
        return r21772317;
}

↓

double f(double x, double y) {
        double r21772318 = y;
        double r21772319 = -3.0638957814586657e-28;
        bool r21772320 = r21772318 <= r21772319;
        double r21772321 = x;
        double r21772322 = r21772321 - r21772318;
        double r21772323 = r21772318 / r21772322;
        double r21772324 = 2.0;
        double r21772325 = r21772324 * r21772321;
        double r21772326 = r21772323 * r21772325;
        double r21772327 = 1.3615474866246526e+17;
        bool r21772328 = r21772318 <= r21772327;
        double r21772329 = r21772325 / r21772322;
        double r21772330 = r21772329 * r21772318;
        double r21772331 = r21772328 ? r21772330 : r21772326;
        double r21772332 = r21772320 ? r21772326 : r21772331;
        return r21772332;
}

Original	14.4
Target	0.3
Herbie	0.1

Derivation

Split input into 2 regimes
if y < -3.0638957814586657e-28 or 1.3615474866246526e+17 < y
1. Initial program 14.9
  \[\frac{\left(x \cdot 2.0\right) \cdot y}{x - y}\]
2. Using strategy rm
3. Applied *-un-lft-identity14.9
  \[\leadsto \frac{\left(x \cdot 2.0\right) \cdot y}{\color{blue}{1 \cdot \left(x - y\right)}}\]
4. Applied times-frac0.1
  \[\leadsto \color{blue}{\frac{x \cdot 2.0}{1} \cdot \frac{y}{x - y}}\]
5. Simplified0.1
  \[\leadsto \color{blue}{\left(2.0 \cdot x\right)} \cdot \frac{y}{x - y}\]
if -3.0638957814586657e-28 < y < 1.3615474866246526e+17
1. Initial program 13.9
  \[\frac{\left(x \cdot 2.0\right) \cdot y}{x - y}\]
2. Using strategy rm
3. Applied associate-/l*15.0
  \[\leadsto \color{blue}{\frac{x \cdot 2.0}{\frac{x - y}{y}}}\]
4. Using strategy rm
5. Applied associate-/r/0.1
  \[\leadsto \color{blue}{\frac{x \cdot 2.0}{x - y} \cdot y}\]
Recombined 2 regimes into one program.
Final simplification0.1
\[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.0638957814586657 \cdot 10^{-28}:\\ \;\;\;\;\frac{y}{x - y} \cdot \left(2.0 \cdot x\right)\\ \mathbf{elif}\;y \le 1.3615474866246526 \cdot 10^{+17}:\\ \;\;\;\;\frac{2.0 \cdot x}{x - y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x - y} \cdot \left(2.0 \cdot x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(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)))

Error

Try it out

Target

Derivation

`if y < -3.0638957814586657e-28 or 1.3615474866246526e+17 < y`

`if -3.0638957814586657e-28 < y < 1.3615474866246526e+17`

Reproduce

In
Out