\[1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\]

↓

\[\begin{array}{l} \mathbf{if}\;y \le -82325870.8211927711963653564453125 \lor \neg \left(y \le 156431656.8362415730953216552734375\right):\\ \;\;\;\;1 \cdot \left(\frac{1}{y} - \frac{x}{y}\right) + x\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y \cdot y - 1 \cdot 1} \cdot \left(y - 1\right)\\ \end{array}\]

1 - \frac{\left(1 - x\right) \cdot y}{y + 1}

↓

\begin{array}{l}
\mathbf{if}\;y \le -82325870.8211927711963653564453125 \lor \neg \left(y \le 156431656.8362415730953216552734375\right):\\
\;\;\;\;1 \cdot \left(\frac{1}{y} - \frac{x}{y}\right) + x\\

\mathbf{else}:\\
\;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y \cdot y - 1 \cdot 1} \cdot \left(y - 1\right)\\

\end{array}

double f(double x, double y) {
        double r762383 = 1.0;
        double r762384 = x;
        double r762385 = r762383 - r762384;
        double r762386 = y;
        double r762387 = r762385 * r762386;
        double r762388 = r762386 + r762383;
        double r762389 = r762387 / r762388;
        double r762390 = r762383 - r762389;
        return r762390;
}

↓

double f(double x, double y) {
        double r762391 = y;
        double r762392 = -82325870.82119277;
        bool r762393 = r762391 <= r762392;
        double r762394 = 156431656.83624157;
        bool r762395 = r762391 <= r762394;
        double r762396 = !r762395;
        bool r762397 = r762393 || r762396;
        double r762398 = 1.0;
        double r762399 = 1.0;
        double r762400 = r762399 / r762391;
        double r762401 = x;
        double r762402 = r762401 / r762391;
        double r762403 = r762400 - r762402;
        double r762404 = r762398 * r762403;
        double r762405 = r762404 + r762401;
        double r762406 = r762398 - r762401;
        double r762407 = r762406 * r762391;
        double r762408 = r762391 * r762391;
        double r762409 = r762398 * r762398;
        double r762410 = r762408 - r762409;
        double r762411 = r762407 / r762410;
        double r762412 = r762391 - r762398;
        double r762413 = r762411 * r762412;
        double r762414 = r762398 - r762413;
        double r762415 = r762397 ? r762405 : r762414;
        return r762415;
}

Original	22.5
Target	0.2
Herbie	0.2

Derivation

Split input into 2 regimes
if y < -82325870.82119277 or 156431656.83624157 < y
1. Initial program 46.0
  \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\]
2. Taylor expanded around inf 0.2
  \[\leadsto \color{blue}{\left(x + 1 \cdot \frac{1}{y}\right) - 1 \cdot \frac{x}{y}}\]
3. Simplified0.2
  \[\leadsto \color{blue}{1 \cdot \left(\frac{1}{y} - \frac{x}{y}\right) + x}\]
if -82325870.82119277 < y < 156431656.83624157
1. Initial program 0.1
  \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\]
2. Using strategy rm
3. Applied flip-+0.2
  \[\leadsto 1 - \frac{\left(1 - x\right) \cdot y}{\color{blue}{\frac{y \cdot y - 1 \cdot 1}{y - 1}}}\]
4. Applied associate-/r/0.2
  \[\leadsto 1 - \color{blue}{\frac{\left(1 - x\right) \cdot y}{y \cdot y - 1 \cdot 1} \cdot \left(y - 1\right)}\]
Recombined 2 regimes into one program.
Final simplification0.2
\[\leadsto \begin{array}{l} \mathbf{if}\;y \le -82325870.8211927711963653564453125 \lor \neg \left(y \le 156431656.8362415730953216552734375\right):\\ \;\;\;\;1 \cdot \left(\frac{1}{y} - \frac{x}{y}\right) + x\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y \cdot y - 1 \cdot 1} \cdot \left(y - 1\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (if (< y -3693.8482788297247) (- (/ 1 y) (- (/ x y) x)) (if (< y 6799310503.41891) (- 1 (/ (* (- 1 x) y) (+ y 1))) (- (/ 1 y) (- (/ x y) x))))

  (- 1 (/ (* (- 1 x) y) (+ y 1))))

Error

Try it out

Target

Derivation

`if y < -82325870.82119277 or 156431656.83624157 < y`

`if -82325870.82119277 < y < 156431656.83624157`

Reproduce

In
Out