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

↓

\[\begin{array}{l} \mathbf{if}\;y \le -127752568.37720934 \lor \neg \left(y \le 152679725.13905564\right):\\ \;\;\;\;\left(x + \frac{1}{y}\right) - 1 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;y \le -127752568.37720934 \lor \neg \left(y \le 152679725.13905564\right):\\
\;\;\;\;\left(x + \frac{1}{y}\right) - 1 \cdot \frac{x}{y}\\

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

\end{array}

double f(double x, double y) {
        double r705446 = 1.0;
        double r705447 = x;
        double r705448 = r705446 - r705447;
        double r705449 = y;
        double r705450 = r705448 * r705449;
        double r705451 = r705449 + r705446;
        double r705452 = r705450 / r705451;
        double r705453 = r705446 - r705452;
        return r705453;
}

↓

double f(double x, double y) {
        double r705454 = y;
        double r705455 = -127752568.37720934;
        bool r705456 = r705454 <= r705455;
        double r705457 = 152679725.13905564;
        bool r705458 = r705454 <= r705457;
        double r705459 = !r705458;
        bool r705460 = r705456 || r705459;
        double r705461 = x;
        double r705462 = 1.0;
        double r705463 = r705462 / r705454;
        double r705464 = r705461 + r705463;
        double r705465 = r705461 / r705454;
        double r705466 = r705462 * r705465;
        double r705467 = r705464 - r705466;
        double r705468 = r705462 - r705461;
        double r705469 = r705454 + r705462;
        double r705470 = r705454 / r705469;
        double r705471 = r705468 * r705470;
        double r705472 = r705462 - r705471;
        double r705473 = r705460 ? r705467 : r705472;
        return r705473;
}

Original	21.9
Target	0.2
Herbie	0.2

Derivation

Split input into 2 regimes
if y < -127752568.37720934 or 152679725.13905564 < y
1. Initial program 45.0
  \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\]
2. Using strategy rm
3. Applied *-un-lft-identity45.0
  \[\leadsto 1 - \frac{\left(1 - x\right) \cdot y}{\color{blue}{1 \cdot \left(y + 1\right)}}\]
4. Applied times-frac29.0
  \[\leadsto 1 - \color{blue}{\frac{1 - x}{1} \cdot \frac{y}{y + 1}}\]
5. Simplified29.0
  \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \cdot \frac{y}{y + 1}\]
6. Taylor expanded around inf 0.2
  \[\leadsto \color{blue}{\left(x + 1 \cdot \frac{1}{y}\right) - 1 \cdot \frac{x}{y}}\]
7. Simplified0.2
  \[\leadsto \color{blue}{\left(x + \frac{1}{y}\right) - 1 \cdot \frac{x}{y}}\]
if -127752568.37720934 < y < 152679725.13905564
1. Initial program 0.2
  \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\]
2. Using strategy rm
3. Applied *-un-lft-identity0.2
  \[\leadsto 1 - \frac{\left(1 - x\right) \cdot y}{\color{blue}{1 \cdot \left(y + 1\right)}}\]
4. Applied times-frac0.1
  \[\leadsto 1 - \color{blue}{\frac{1 - x}{1} \cdot \frac{y}{y + 1}}\]
5. Simplified0.1
  \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \cdot \frac{y}{y + 1}\]
Recombined 2 regimes into one program.
Final simplification0.2
\[\leadsto \begin{array}{l} \mathbf{if}\;y \le -127752568.37720934 \lor \neg \left(y \le 152679725.13905564\right):\\ \;\;\;\;\left(x + \frac{1}{y}\right) - 1 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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))))

Falling back on racket egraph because egg-herbie package not installed (more)

Error

Try it out

Target

Derivation

`if y < -127752568.37720934 or 152679725.13905564 < y`

`if -127752568.37720934 < y < 152679725.13905564`

Reproduce

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