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

↓

\[\begin{array}{l} \mathbf{if}\;y \le -4.38962381722942814 \cdot 10^{28} \lor \neg \left(y \le 103782153027757.69\right):\\ \;\;\;\;\mathsf{fma}\left(1, \frac{x}{{y}^{2}} - \frac{x}{y}, x\right)\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;y \le -4.38962381722942814 \cdot 10^{28} \lor \neg \left(y \le 103782153027757.69\right):\\
\;\;\;\;\mathsf{fma}\left(1, \frac{x}{{y}^{2}} - \frac{x}{y}, x\right)\\

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

\end{array}

double f(double x, double y) {
        double r2779 = 1.0;
        double r2780 = x;
        double r2781 = r2779 - r2780;
        double r2782 = y;
        double r2783 = r2781 * r2782;
        double r2784 = r2782 + r2779;
        double r2785 = r2783 / r2784;
        double r2786 = r2779 - r2785;
        return r2786;
}

↓

double f(double x, double y) {
        double r2787 = y;
        double r2788 = -4.389623817229428e+28;
        bool r2789 = r2787 <= r2788;
        double r2790 = 103782153027757.69;
        bool r2791 = r2787 <= r2790;
        double r2792 = !r2791;
        bool r2793 = r2789 || r2792;
        double r2794 = 1.0;
        double r2795 = x;
        double r2796 = 2.0;
        double r2797 = pow(r2787, r2796);
        double r2798 = r2795 / r2797;
        double r2799 = r2795 / r2787;
        double r2800 = r2798 - r2799;
        double r2801 = fma(r2794, r2800, r2795);
        double r2802 = r2794 - r2795;
        double r2803 = r2802 * r2787;
        double r2804 = r2787 + r2794;
        double r2805 = r2803 / r2804;
        double r2806 = r2794 - r2805;
        double r2807 = r2793 ? r2801 : r2806;
        return r2807;
}

Original	22.7
Target	0.2
Herbie	7.4

Derivation

Split input into 2 regimes
if y < -4.389623817229428e+28 or 103782153027757.69 < y
1. Initial program 47.0
  \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\]
2. Simplified29.1
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{y + 1}, x - 1, 1\right)}\]
3. Using strategy rm
4. Applied add-cube-cbrt29.9
  \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{\left(\sqrt[3]{y + 1} \cdot \sqrt[3]{y + 1}\right) \cdot \sqrt[3]{y + 1}}}, x - 1, 1\right)\]
5. Applied *-un-lft-identity29.9
  \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{1 \cdot y}}{\left(\sqrt[3]{y + 1} \cdot \sqrt[3]{y + 1}\right) \cdot \sqrt[3]{y + 1}}, x - 1, 1\right)\]
6. Applied times-frac29.9
  \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\sqrt[3]{y + 1} \cdot \sqrt[3]{y + 1}} \cdot \frac{y}{\sqrt[3]{y + 1}}}, x - 1, 1\right)\]
7. Taylor expanded around inf 14.1
  \[\leadsto \color{blue}{\left(x + 1 \cdot \frac{x}{{y}^{2}}\right) - 1 \cdot \frac{x}{y}}\]
8. Simplified14.1
  \[\leadsto \color{blue}{\mathsf{fma}\left(1, \frac{x}{{y}^{2}} - \frac{x}{y}, x\right)}\]
if -4.389623817229428e+28 < y < 103782153027757.69
1. Initial program 1.4
  \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\]
Recombined 2 regimes into one program.
Final simplification7.4
\[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.38962381722942814 \cdot 10^{28} \lor \neg \left(y \le 103782153027757.69\right):\\ \;\;\;\;\mathsf{fma}\left(1, \frac{x}{{y}^{2}} - \frac{x}{y}, x\right)\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(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

Target

Derivation

`if y < -4.389623817229428e+28 or 103782153027757.69 < y`

`if -4.389623817229428e+28 < y < 103782153027757.69`

Reproduce