Kahan's Unum-Targeted Monster

Average Error: 60.8 → 30.7

Time: 19.4s

Precision: 64

\[1 \le y \le 9999\]

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

↓

\[\begin{array}{l} \mathbf{if}\;y \le 19.7233094313761761:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \log \left(e^{\mathsf{fma}\left(y - \mathsf{hypot}\left(y, \sqrt{1}\right), \frac{-1}{\mathsf{fma}\left(y, y, -\mathsf{fma}\left(y, y, 1\right)\right)}, \left|y - \sqrt{{y}^{2} + 1}\right|\right) + \mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(y, y, -\mathsf{fma}\left(y, y, 1\right)\right)}, y - \mathsf{hypot}\left(y, \sqrt{1}\right), \frac{\left(y - \sqrt{{y}^{2} + 1}\right) \cdot 1}{\mathsf{fma}\left(y, y, -\mathsf{fma}\left(y, y, 1\right)\right)}\right)}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\\ \mathbf{elif}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \log \left(e^{\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-1, 1, e^{\mathsf{fma}\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}, \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right), {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}\right) + \mathsf{fma}\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}, \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right), {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}\right)}\right)}{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} + 1}}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

C

double f(double y) {
        double r104771 = y;
        double r104772 = r104771 * r104771;
        double r104773 = 1.0;
        double r104774 = r104772 + r104773;
        double r104775 = sqrt(r104774);
        double r104776 = r104771 - r104775;
        double r104777 = fabs(r104776);
        double r104778 = r104771 + r104775;
        double r104779 = r104773 / r104778;
        double r104780 = r104777 - r104779;
        double r104781 = r104780 * r104780;
        double r104782 = 10.0;
        double r104783 = -300.0;
        double r104784 = pow(r104782, r104783);
        double r104785 = 10000.0;
        double r104786 = r104771 + r104773;
        double r104787 = r104785 * r104786;
        double r104788 = pow(r104784, r104787);
        double r104789 = r104781 + r104788;
        double r104790 = 0.0;
        double r104791 = r104789 == r104790;
        double r104792 = exp(r104789);
        double r104793 = r104792 - r104773;
        double r104794 = r104793 / r104789;
        double r104795 = r104791 ? r104773 : r104794;
        return r104795;
}

↓

double f(double y) {
        double r104796 = y;
        double r104797 = 19.723309431376176;
        bool r104798 = r104796 <= r104797;
        double r104799 = r104796 * r104796;
        double r104800 = 1.0;
        double r104801 = r104799 + r104800;
        double r104802 = sqrt(r104801);
        double r104803 = r104796 - r104802;
        double r104804 = fabs(r104803);
        double r104805 = r104796 + r104802;
        double r104806 = r104800 / r104805;
        double r104807 = r104804 - r104806;
        double r104808 = sqrt(r104800);
        double r104809 = hypot(r104796, r104808);
        double r104810 = r104796 - r104809;
        double r104811 = -r104800;
        double r104812 = fma(r104796, r104796, r104800);
        double r104813 = -r104812;
        double r104814 = fma(r104796, r104796, r104813);
        double r104815 = r104811 / r104814;
        double r104816 = 2.0;
        double r104817 = pow(r104796, r104816);
        double r104818 = r104817 + r104800;
        double r104819 = sqrt(r104818);
        double r104820 = r104796 - r104819;
        double r104821 = fabs(r104820);
        double r104822 = fma(r104810, r104815, r104821);
        double r104823 = r104820 * r104800;
        double r104824 = r104823 / r104814;
        double r104825 = fma(r104815, r104810, r104824);
        double r104826 = r104822 + r104825;
        double r104827 = exp(r104826);
        double r104828 = log(r104827);
        double r104829 = r104807 * r104828;
        double r104830 = 10.0;
        double r104831 = -300.0;
        double r104832 = pow(r104830, r104831);
        double r104833 = 10000.0;
        double r104834 = r104796 + r104800;
        double r104835 = r104833 * r104834;
        double r104836 = pow(r104832, r104835);
        double r104837 = r104829 + r104836;
        double r104838 = 0.0;
        double r104839 = r104837 == r104838;
        double r104840 = 0.5;
        double r104841 = 1.0;
        double r104842 = r104841 / r104796;
        double r104843 = 2.0;
        double r104844 = fma(r104843, r104796, r104821);
        double r104845 = fma(r104840, r104842, r104844);
        double r104846 = r104807 * r104845;
        double r104847 = r104846 + r104836;
        double r104848 = exp(r104847);
        double r104849 = r104848 - r104800;
        double r104850 = r104845 * r104807;
        double r104851 = r104850 + r104836;
        double r104852 = r104849 / r104851;
        double r104853 = r104839 ? r104800 : r104852;
        double r104854 = exp(r104807);
        double r104855 = log(r104854);
        double r104856 = r104807 * r104855;
        double r104857 = r104856 + r104836;
        double r104858 = r104857 == r104838;
        double r104859 = fma(r104807, r104845, r104836);
        double r104860 = r104859 + r104859;
        double r104861 = exp(r104860);
        double r104862 = fma(r104811, r104800, r104861);
        double r104863 = r104848 + r104800;
        double r104864 = r104862 / r104863;
        double r104865 = r104864 / r104851;
        double r104866 = r104858 ? r104800 : r104865;
        double r104867 = r104798 ? r104853 : r104866;
        return r104867;
}

Error

Bits error versus y

Derivation

1. Split input into 2 regimes

2. if y < 19.723309431376176

   1. Initial program 58.3

      \[\begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   2. Taylor expanded around -inf 56.8

      \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(0.5 \cdot \frac{1}{y} + \left(2 \cdot y + \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   3. Simplified 56.8

      \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   4. Taylor expanded around -inf 43.6

      \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\color{blue}{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}} - 1}{\left(0.5 \cdot \frac{1}{y} + \left(2 \cdot y + \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   5. Simplified 43.6

      \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\color{blue}{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}} - 1}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]
   6. Using strategy rm

   7. Applied add-log-exp 41.3

      \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \color{blue}{\log \left(e^{\frac{1}{y + \sqrt{y \cdot y + 1}}}\right)}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   8. Applied add-log-exp 32.6

      \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\color{blue}{\log \left(e^{\left|y - \sqrt{y \cdot y + 1}\right|}\right)} - \log \left(e^{\frac{1}{y + \sqrt{y \cdot y + 1}}}\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   9. Applied diff-log 32.6

      \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \color{blue}{\log \left(\frac{e^{\left|y - \sqrt{y \cdot y + 1}\right|}}{e^{\frac{1}{y + \sqrt{y \cdot y + 1}}}}\right)} + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   10. Simplified 33.2

       \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \log \color{blue}{\left(e^{\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}}\right)} + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]
   11. Using strategy rm

   12. Applied flip-+ 22.9

       \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \log \left(e^{\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{\color{blue}{\frac{y \cdot y - \sqrt{y \cdot y + 1} \cdot \sqrt{y \cdot y + 1}}{y - \sqrt{y \cdot y + 1}}}}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   13. Applied associate-/r/ 23.0

       \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \log \left(e^{\left|y - \sqrt{y \cdot y + 1}\right| - \color{blue}{\frac{1}{y \cdot y - \sqrt{y \cdot y + 1} \cdot \sqrt{y \cdot y + 1}} \cdot \left(y - \sqrt{y \cdot y + 1}\right)}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   14. Applied add-sqr-sqrt 22.5

       \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \log \left(e^{\color{blue}{\sqrt{\left|y - \sqrt{y \cdot y + 1}\right|} \cdot \sqrt{\left|y - \sqrt{y \cdot y + 1}\right|}} - \frac{1}{y \cdot y - \sqrt{y \cdot y + 1} \cdot \sqrt{y \cdot y + 1}} \cdot \left(y - \sqrt{y \cdot y + 1}\right)}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   15. Applied prod-diff 22.7

       \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \log \left(e^{\color{blue}{\mathsf{fma}\left(\sqrt{\left|y - \sqrt{y \cdot y + 1}\right|}, \sqrt{\left|y - \sqrt{y \cdot y + 1}\right|}, -\left(y - \sqrt{y \cdot y + 1}\right) \cdot \frac{1}{y \cdot y - \sqrt{y \cdot y + 1} \cdot \sqrt{y \cdot y + 1}}\right) + \mathsf{fma}\left(-\left(y - \sqrt{y \cdot y + 1}\right), \frac{1}{y \cdot y - \sqrt{y \cdot y + 1} \cdot \sqrt{y \cdot y + 1}}, \left(y - \sqrt{y \cdot y + 1}\right) \cdot \frac{1}{y \cdot y - \sqrt{y \cdot y + 1} \cdot \sqrt{y \cdot y + 1}}\right)}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   16. Simplified 25.5

       \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \log \left(e^{\color{blue}{\mathsf{fma}\left(y - \mathsf{hypot}\left(y, \sqrt{1}\right), \frac{-1}{\mathsf{fma}\left(y, y, -\mathsf{fma}\left(y, y, 1\right)\right)}, \left|y - \sqrt{{y}^{2} + 1}\right|\right)} + \mathsf{fma}\left(-\left(y - \sqrt{y \cdot y + 1}\right), \frac{1}{y \cdot y - \sqrt{y \cdot y + 1} \cdot \sqrt{y \cdot y + 1}}, \left(y - \sqrt{y \cdot y + 1}\right) \cdot \frac{1}{y \cdot y - \sqrt{y \cdot y + 1} \cdot \sqrt{y \cdot y + 1}}\right)}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   17. Simplified 26.7

       \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \log \left(e^{\mathsf{fma}\left(y - \mathsf{hypot}\left(y, \sqrt{1}\right), \frac{-1}{\mathsf{fma}\left(y, y, -\mathsf{fma}\left(y, y, 1\right)\right)}, \left|y - \sqrt{{y}^{2} + 1}\right|\right) + \color{blue}{\mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(y, y, -\mathsf{fma}\left(y, y, 1\right)\right)}, y - \mathsf{hypot}\left(y, \sqrt{1}\right), \frac{\left(y - \sqrt{{y}^{2} + 1}\right) \cdot 1}{\mathsf{fma}\left(y, y, -\mathsf{fma}\left(y, y, 1\right)\right)}\right)}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   if 19.723309431376176 < y

   1. Initial program 62.0

      \[\begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   2. Taylor expanded around -inf 60.4

      \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(0.5 \cdot \frac{1}{y} + \left(2 \cdot y + \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   3. Simplified 60.4

      \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   4. Taylor expanded around -inf 33.9

      \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\color{blue}{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}} - 1}{\left(0.5 \cdot \frac{1}{y} + \left(2 \cdot y + \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   5. Simplified 33.9

      \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\color{blue}{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}} - 1}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]
   6. Using strategy rm

   7. Applied add-log-exp 33.9

      \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \color{blue}{\log \left(e^{\frac{1}{y + \sqrt{y \cdot y + 1}}}\right)}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   8. Applied add-log-exp 33.4

      \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \left(\color{blue}{\log \left(e^{\left|y - \sqrt{y \cdot y + 1}\right|}\right)} - \log \left(e^{\frac{1}{y + \sqrt{y \cdot y + 1}}}\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   9. Applied diff-log 33.4

      \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \color{blue}{\log \left(\frac{e^{\left|y - \sqrt{y \cdot y + 1}\right|}}{e^{\frac{1}{y + \sqrt{y \cdot y + 1}}}}\right)} + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   10. Simplified 33.5

       \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \log \color{blue}{\left(e^{\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}}\right)} + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]
   11. Using strategy rm

   12. Applied flip-- 33.5

       \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \log \left(e^{\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} \cdot e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1 \cdot 1}{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} + 1}}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

   13. Simplified 32.6

       \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \log \left(e^{\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-1, 1, e^{\mathsf{fma}\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}, \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right), {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}\right) + \mathsf{fma}\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}, \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right), {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}\right)}\right)}{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} + 1}}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]
3. Recombined 2 regimes into one program.

4. Final simplification 30.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \le 19.7233094313761761:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \log \left(e^{\mathsf{fma}\left(y - \mathsf{hypot}\left(y, \sqrt{1}\right), \frac{-1}{\mathsf{fma}\left(y, y, -\mathsf{fma}\left(y, y, 1\right)\right)}, \left|y - \sqrt{{y}^{2} + 1}\right|\right) + \mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(y, y, -\mathsf{fma}\left(y, y, 1\right)\right)}, y - \mathsf{hypot}\left(y, \sqrt{1}\right), \frac{\left(y - \sqrt{{y}^{2} + 1}\right) \cdot 1}{\mathsf{fma}\left(y, y, -\mathsf{fma}\left(y, y, 1\right)\right)}\right)}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} - 1}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\\ \mathbf{elif}\;\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \log \left(e^{\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)} = 0.0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-1, 1, e^{\mathsf{fma}\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}, \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right), {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}\right) + \mathsf{fma}\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}, \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right), {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}\right)}\right)}{e^{\left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) \cdot \mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}} + 1}}{\mathsf{fma}\left(0.5, \frac{1}{y}, \mathsf{fma}\left(2, y, \left|y - \sqrt{{y}^{2} + 1}\right|\right)\right) \cdot \left(\left|y - \sqrt{y \cdot y + 1}\right| - \frac{1}{y + \sqrt{y \cdot y + 1}}\right) + {\left({10}^{-300}\right)}^{\left(10^{4} \cdot \left(y + 1\right)\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (y)
  :name "Kahan's Unum-Targeted Monster"
  :precision binary64
  :pre (<= 1 y 9999)
  (if (== (+ (* (- (fabs (- y (sqrt (+ (* y y) 1)))) (/ 1 (+ y (sqrt (+ (* y y) 1))))) (- (fabs (- y (sqrt (+ (* y y) 1)))) (/ 1 (+ y (sqrt (+ (* y y) 1)))))) (pow (pow 10 -300) (* 10000.0 (+ y 1)))) 0.0) 1 (/ (- (exp (+ (* (- (fabs (- y (sqrt (+ (* y y) 1)))) (/ 1 (+ y (sqrt (+ (* y y) 1))))) (- (fabs (- y (sqrt (+ (* y y) 1)))) (/ 1 (+ y (sqrt (+ (* y y) 1)))))) (pow (pow 10 -300) (* 10000.0 (+ y 1))))) 1) (+ (* (- (fabs (- y (sqrt (+ (* y y) 1)))) (/ 1 (+ y (sqrt (+ (* y y) 1))))) (- (fabs (- y (sqrt (+ (* y y) 1)))) (/ 1 (+ y (sqrt (+ (* y y) 1)))))) (pow (pow 10 -300) (* 10000.0 (+ y 1)))))))