Average Error: 15.2 → 14.7
Time: 19.1s
Precision: 64
\[1 - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\]
↓
\[\left(\left(\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot 1\right) + 1 \cdot 1\right) \cdot \left(\left(\frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)} - 1 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) + 1 \cdot 1\right)\right) \cdot \frac{\log \left(e^{1 \cdot \left(1 \cdot 1\right) - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \left(0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)}\right)}{\left(0.5 \cdot \left(1 \cdot \left(1 \cdot 1\right) + \frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \left(\frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)\right) \cdot \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1\right) \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right) + \left(\left(\frac{1}{\mathsf{hypot}\left(1, x\right)} - 1\right) \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)} + 1 \cdot 1\right) \cdot \left(\left(1 \cdot 1\right) \cdot \left(1 \cdot 1\right) + \left(1 \cdot \left(0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)\right) \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}\]
1 - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}
↓
\left(\left(\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot 1\right) + 1 \cdot 1\right) \cdot \left(\left(\frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)} - 1 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) + 1 \cdot 1\right)\right) \cdot \frac{\log \left(e^{1 \cdot \left(1 \cdot 1\right) - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \left(0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)}\right)}{\left(0.5 \cdot \left(1 \cdot \left(1 \cdot 1\right) + \frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \left(\frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)\right) \cdot \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1\right) \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right) + \left(\left(\frac{1}{\mathsf{hypot}\left(1, x\right)} - 1\right) \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)} + 1 \cdot 1\right) \cdot \left(\left(1 \cdot 1\right) \cdot \left(1 \cdot 1\right) + \left(1 \cdot \left(0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)\right) \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}
double f(double x) {
        double r11528803 = 1.0;
        double r11528804 = 0.5;
        double r11528805 = x;
        double r11528806 = hypot(r11528803, r11528805);
        double r11528807 = r11528803 / r11528806;
        double r11528808 = r11528803 + r11528807;
        double r11528809 = r11528804 * r11528808;
        double r11528810 = sqrt(r11528809);
        double r11528811 = r11528803 - r11528810;
        return r11528811;
}
↓
double f(double x) {
        double r11528812 = 0.5;
        double r11528813 = 1.0;
        double r11528814 = x;
        double r11528815 = hypot(r11528813, r11528814);
        double r11528816 = r11528813 / r11528815;
        double r11528817 = r11528813 + r11528816;
        double r11528818 = r11528812 * r11528817;
        double r11528819 = sqrt(r11528818);
        double r11528820 = r11528819 * r11528819;
        double r11528821 = r11528819 * r11528813;
        double r11528822 = r11528820 - r11528821;
        double r11528823 = r11528813 * r11528813;
        double r11528824 = r11528822 + r11528823;
        double r11528825 = r11528816 * r11528816;
        double r11528826 = r11528813 * r11528816;
        double r11528827 = r11528825 - r11528826;
        double r11528828 = r11528827 + r11528823;
        double r11528829 = r11528824 * r11528828;
        double r11528830 = r11528813 * r11528823;
        double r11528831 = r11528819 * r11528818;
        double r11528832 = r11528830 - r11528831;
        double r11528833 = exp(r11528832);
        double r11528834 = log(r11528833);
        double r11528835 = r11528816 * r11528825;
        double r11528836 = r11528830 + r11528835;
        double r11528837 = r11528812 * r11528836;
        double r11528838 = r11528819 - r11528813;
        double r11528839 = r11528838 * r11528819;
        double r11528840 = r11528823 + r11528839;
        double r11528841 = r11528837 * r11528840;
        double r11528842 = r11528816 - r11528813;
        double r11528843 = r11528842 * r11528816;
        double r11528844 = r11528843 + r11528823;
        double r11528845 = r11528823 * r11528823;
        double r11528846 = r11528813 * r11528818;
        double r11528847 = r11528846 * r11528819;
        double r11528848 = r11528845 + r11528847;
        double r11528849 = r11528844 * r11528848;
        double r11528850 = r11528841 + r11528849;
        double r11528851 = r11528834 / r11528850;
        double r11528852 = r11528829 * r11528851;
        return r11528852;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.2

    \[1 - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\]
  2. Using strategy rm

  3. Applied flip3--15.4

    \[\leadsto \color{blue}{\frac{{1}^{3} - {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}}{1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} + 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}}\]

  4. Simplified15.1

    \[\leadsto \frac{\color{blue}{1 \cdot \left(1 \cdot 1\right) - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \left(0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)}}{1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} + 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}\]

  5. Simplified14.7

    \[\leadsto \frac{1 \cdot \left(1 \cdot 1\right) - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \left(0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)}{\color{blue}{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) + 1 \cdot \left(1 + \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}}\]
  6. Using strategy rm

  7. Applied flip3-+15.1

    \[\leadsto \frac{1 \cdot \left(1 \cdot 1\right) - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \left(0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)}{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) + 1 \cdot \color{blue}{\frac{{1}^{3} + {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}}{1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}}}\]

  8. Applied associate-*r/15.1

    \[\leadsto \frac{1 \cdot \left(1 \cdot 1\right) - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \left(0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)}{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) + \color{blue}{\frac{1 \cdot \left({1}^{3} + {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}{1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}}}\]

  9. Applied flip3-+15.1

    \[\leadsto \frac{1 \cdot \left(1 \cdot 1\right) - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \left(0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)}{0.5 \cdot \color{blue}{\frac{{1}^{3} + {\left(\frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}^{3}}{1 \cdot 1 + \left(\frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)} - 1 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}} + \frac{1 \cdot \left({1}^{3} + {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}{1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}}\]

  10. Applied associate-*r/15.1

    \[\leadsto \frac{1 \cdot \left(1 \cdot 1\right) - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \left(0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)}{\color{blue}{\frac{0.5 \cdot \left({1}^{3} + {\left(\frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}^{3}\right)}{1 \cdot 1 + \left(\frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)} - 1 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}} + \frac{1 \cdot \left({1}^{3} + {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}{1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}}\]

  11. Applied frac-add14.7

    \[\leadsto \frac{1 \cdot \left(1 \cdot 1\right) - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \left(0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)}{\color{blue}{\frac{\left(0.5 \cdot \left({1}^{3} + {\left(\frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}^{3}\right)\right) \cdot \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right) + \left(1 \cdot 1 + \left(\frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)} - 1 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right) \cdot \left(1 \cdot \left({1}^{3} + {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)\right)}{\left(1 \cdot 1 + \left(\frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)} - 1 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right) \cdot \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right)}}}\]

  12. Applied associate-/r/14.7

    \[\leadsto \color{blue}{\frac{1 \cdot \left(1 \cdot 1\right) - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \left(0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)}{\left(0.5 \cdot \left({1}^{3} + {\left(\frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}^{3}\right)\right) \cdot \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right) + \left(1 \cdot 1 + \left(\frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)} - 1 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right) \cdot \left(1 \cdot \left({1}^{3} + {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)\right)} \cdot \left(\left(1 \cdot 1 + \left(\frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)} - 1 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right) \cdot \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right)\right)}\]

  13. Simplified14.7

    \[\leadsto \color{blue}{\frac{\left(1 \cdot 1\right) \cdot 1 - \left(0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right) \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}}{\left(\frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \left(\frac{1}{\mathsf{hypot}\left(1, x\right)} - 1\right) + 1 \cdot 1\right) \cdot \left(\left(1 \cdot \left(0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)\right) \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} + \left(1 \cdot 1\right) \cdot \left(1 \cdot 1\right)\right) + \left(1 \cdot 1 + \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1\right)\right) \cdot \left(0.5 \cdot \left(\left(1 \cdot 1\right) \cdot 1 + \frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \left(\frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)\right)}} \cdot \left(\left(1 \cdot 1 + \left(\frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)} - 1 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right) \cdot \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right)\right)\]
  14. Using strategy rm

  15. Applied add-log-exp14.7

    \[\leadsto \frac{\color{blue}{\log \left(e^{\left(1 \cdot 1\right) \cdot 1 - \left(0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right) \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}}\right)}}{\left(\frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \left(\frac{1}{\mathsf{hypot}\left(1, x\right)} - 1\right) + 1 \cdot 1\right) \cdot \left(\left(1 \cdot \left(0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)\right) \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} + \left(1 \cdot 1\right) \cdot \left(1 \cdot 1\right)\right) + \left(1 \cdot 1 + \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1\right)\right) \cdot \left(0.5 \cdot \left(\left(1 \cdot 1\right) \cdot 1 + \frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \left(\frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)\right)} \cdot \left(\left(1 \cdot 1 + \left(\frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)} - 1 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right) \cdot \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right)\right)\]

  16. Final simplification14.7

    \[\leadsto \left(\left(\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot 1\right) + 1 \cdot 1\right) \cdot \left(\left(\frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)} - 1 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) + 1 \cdot 1\right)\right) \cdot \frac{\log \left(e^{1 \cdot \left(1 \cdot 1\right) - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \left(0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)}\right)}{\left(0.5 \cdot \left(1 \cdot \left(1 \cdot 1\right) + \frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \left(\frac{1}{\mathsf{hypot}\left(1, x\right)} \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)\right) \cdot \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1\right) \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right) + \left(\left(\frac{1}{\mathsf{hypot}\left(1, x\right)} - 1\right) \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)} + 1 \cdot 1\right) \cdot \left(\left(1 \cdot 1\right) \cdot \left(1 \cdot 1\right) + \left(1 \cdot \left(0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)\right)\right) \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x)
  :name "Given's Rotation SVD example, simplified"
  (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))