\[0.0 \lt x \lt 1 \land y \lt 1\]

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

↓

\[\begin{array}{l} \mathbf{if}\;y \le -5.375278492253273374474910915175481103343 \cdot 10^{150}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \le \frac{-8857542091609865}{1.013065324433836171511818326096474890384 \cdot 10^{177}}:\\ \;\;\;\;\frac{1}{\frac{x \cdot x + y \cdot y}{\left(x - y\right) \cdot \left(x + y\right)}}\\ \mathbf{elif}\;y \le \frac{544484586544869}{1.425762693006936005825366126781341039029 \cdot 10^{191}}:\\ \;\;\;\;\log \left(e^{1}\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(e^{\frac{\left(x - y\right) \cdot x + \left(x - y\right) \cdot y}{x \cdot x + y \cdot y}}\right)\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;y \le -5.375278492253273374474910915175481103343 \cdot 10^{150}:\\
\;\;\;\;-1\\

\mathbf{elif}\;y \le \frac{-8857542091609865}{1.013065324433836171511818326096474890384 \cdot 10^{177}}:\\
\;\;\;\;\frac{1}{\frac{x \cdot x + y \cdot y}{\left(x - y\right) \cdot \left(x + y\right)}}\\

\mathbf{elif}\;y \le \frac{544484586544869}{1.425762693006936005825366126781341039029 \cdot 10^{191}}:\\
\;\;\;\;\log \left(e^{1}\right)\\

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

\end{array}

double f(double x, double y) {
        double r74858 = x;
        double r74859 = y;
        double r74860 = r74858 - r74859;
        double r74861 = r74858 + r74859;
        double r74862 = r74860 * r74861;
        double r74863 = r74858 * r74858;
        double r74864 = r74859 * r74859;
        double r74865 = r74863 + r74864;
        double r74866 = r74862 / r74865;
        return r74866;
}

↓

double f(double x, double y) {
        double r74867 = y;
        double r74868 = -5.3752784922532734e+150;
        bool r74869 = r74867 <= r74868;
        double r74870 = -1.0;
        double r74871 = -8857542091609865.0;
        double r74872 = 1.0130653244338362e+177;
        double r74873 = r74871 / r74872;
        bool r74874 = r74867 <= r74873;
        double r74875 = 1.0;
        double r74876 = x;
        double r74877 = r74876 * r74876;
        double r74878 = r74867 * r74867;
        double r74879 = r74877 + r74878;
        double r74880 = r74876 - r74867;
        double r74881 = r74876 + r74867;
        double r74882 = r74880 * r74881;
        double r74883 = r74879 / r74882;
        double r74884 = r74875 / r74883;
        double r74885 = 544484586544869.0;
        double r74886 = 1.425762693006936e+191;
        double r74887 = r74885 / r74886;
        bool r74888 = r74867 <= r74887;
        double r74889 = exp(r74875);
        double r74890 = log(r74889);
        double r74891 = r74880 * r74876;
        double r74892 = r74880 * r74867;
        double r74893 = r74891 + r74892;
        double r74894 = r74893 / r74879;
        double r74895 = exp(r74894);
        double r74896 = log(r74895);
        double r74897 = r74888 ? r74890 : r74896;
        double r74898 = r74874 ? r74884 : r74897;
        double r74899 = r74869 ? r74870 : r74898;
        return r74899;
}

Original	20.5
Target	0.0
Herbie	5.0

Derivation

Split input into 4 regimes
if y < -5.3752784922532734e+150
1. Initial program 62.7
  \[\frac{\left(x - y\right) \cdot \left(x + y\right)}{x \cdot x + y \cdot y}\]
2. Using strategy rm
3. Applied clear-num62.7
  \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + y \cdot y}{\left(x - y\right) \cdot \left(x + y\right)}}}\]
4. Taylor expanded around 0 0
  \[\leadsto \frac{1}{\color{blue}{-1}}\]
if -5.3752784922532734e+150 < y < -8.743307936790759e-162
1. Initial program 0.0
  \[\frac{\left(x - y\right) \cdot \left(x + y\right)}{x \cdot x + y \cdot y}\]
2. Using strategy rm
3. Applied clear-num0.1
  \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + y \cdot y}{\left(x - y\right) \cdot \left(x + y\right)}}}\]
if -8.743307936790759e-162 < y < 3.81890050297606e-177
1. Initial program 30.1
  \[\frac{\left(x - y\right) \cdot \left(x + y\right)}{x \cdot x + y \cdot y}\]
2. Using strategy rm
3. Applied distribute-lft-in30.1
  \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot x + \left(x - y\right) \cdot y}}{x \cdot x + y \cdot y}\]
4. Using strategy rm
5. Applied add-log-exp30.1
  \[\leadsto \color{blue}{\log \left(e^{\frac{\left(x - y\right) \cdot x + \left(x - y\right) \cdot y}{x \cdot x + y \cdot y}}\right)}\]
6. Taylor expanded around inf 14.8
  \[\leadsto \log \left(e^{\color{blue}{1}}\right)\]
if 3.81890050297606e-177 < y
1. Initial program 3.0
  \[\frac{\left(x - y\right) \cdot \left(x + y\right)}{x \cdot x + y \cdot y}\]
2. Using strategy rm
3. Applied distribute-lft-in3.0
  \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot x + \left(x - y\right) \cdot y}}{x \cdot x + y \cdot y}\]
4. Using strategy rm
5. Applied add-log-exp3.0
  \[\leadsto \color{blue}{\log \left(e^{\frac{\left(x - y\right) \cdot x + \left(x - y\right) \cdot y}{x \cdot x + y \cdot y}}\right)}\]
Recombined 4 regimes into one program.
Final simplification5.0
\[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5.375278492253273374474910915175481103343 \cdot 10^{150}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \le \frac{-8857542091609865}{1.013065324433836171511818326096474890384 \cdot 10^{177}}:\\ \;\;\;\;\frac{1}{\frac{x \cdot x + y \cdot y}{\left(x - y\right) \cdot \left(x + y\right)}}\\ \mathbf{elif}\;y \le \frac{544484586544869}{1.425762693006936005825366126781341039029 \cdot 10^{191}}:\\ \;\;\;\;\log \left(e^{1}\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(e^{\frac{\left(x - y\right) \cdot x + \left(x - y\right) \cdot y}{x \cdot x + y \cdot y}}\right)\\ \end{array}\]

Error

Try it out

Target

Derivation

`if y < -5.3752784922532734e+150`

`if -5.3752784922532734e+150 < y < -8.743307936790759e-162`

`if -8.743307936790759e-162 < y < 3.81890050297606e-177`

`if 3.81890050297606e-177 < y`

Reproduce

In
Out