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

↓

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

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 r800121 = 1.0;
        double r800122 = x;
        double r800123 = r800121 - r800122;
        double r800124 = y;
        double r800125 = r800123 * r800124;
        double r800126 = r800124 + r800121;
        double r800127 = r800125 / r800126;
        double r800128 = r800121 - r800127;
        return r800128;
}

↓

double f(double x, double y) {
        double r800129 = y;
        double r800130 = -127752568.37720934;
        bool r800131 = r800129 <= r800130;
        double r800132 = 152679725.13905564;
        bool r800133 = r800129 <= r800132;
        double r800134 = !r800133;
        bool r800135 = r800131 || r800134;
        double r800136 = x;
        double r800137 = 1.0;
        double r800138 = r800137 / r800129;
        double r800139 = r800136 + r800138;
        double r800140 = r800136 / r800129;
        double r800141 = r800137 * r800140;
        double r800142 = r800139 - r800141;
        double r800143 = r800137 - r800136;
        double r800144 = r800129 + r800137;
        double r800145 = r800129 / r800144;
        double r800146 = r800143 * r800145;
        double r800147 = r800137 - r800146;
        double r800148 = r800135 ? r800142 : r800147;
        return r800148;
}

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

In
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