math.log10 on complex, real part

Average Error: 30.4 → 17.9

Time: 19.1s

Precision: 64

Math

\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]

↓

\[\begin{array}{l} \mathbf{if}\;im \le -3.494473208647424 \cdot 10^{+151}:\\ \;\;\;\;\left(\frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right) \cdot \left(\left(-2 \cdot \log \left(\frac{-1}{im}\right)\right) \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right)\\ \mathbf{elif}\;im \le -1.4780679115634563 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{\log \left(im \cdot im + re \cdot re\right)}{\sqrt{\sqrt{\log 10}}} \cdot \sqrt{\frac{1}{2}}}{\frac{\sqrt{\log 10}}{\sqrt{\frac{1}{2}}} \cdot \sqrt{\sqrt{\log 10}}}\\ \mathbf{elif}\;im \le -6.847505130661582 \cdot 10^{-247}:\\ \;\;\;\;\left(\left(\log re \cdot 2\right) \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right) \cdot \left(\frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right)\\ \mathbf{elif}\;im \le 9.270740708287654 \cdot 10^{+63}:\\ \;\;\;\;\sqrt{\frac{1}{2}} \cdot \left(\frac{\sqrt{\frac{1}{2}}}{\sqrt{\log 10}} \cdot \frac{\log \left(im \cdot im + re \cdot re\right)}{\sqrt{\log 10}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \left(2 \cdot \left(\log im \cdot \sqrt{\frac{1}{\log 10}}\right)\right)\\ \end{array}\]

C

double f(double re, double im) {
        double r1172734 = re;
        double r1172735 = r1172734 * r1172734;
        double r1172736 = im;
        double r1172737 = r1172736 * r1172736;
        double r1172738 = r1172735 + r1172737;
        double r1172739 = sqrt(r1172738);
        double r1172740 = log(r1172739);
        double r1172741 = 10.0;
        double r1172742 = log(r1172741);
        double r1172743 = r1172740 / r1172742;
        return r1172743;
}

↓

double f(double re, double im) {
        double r1172744 = im;
        double r1172745 = -3.494473208647424e+151;
        bool r1172746 = r1172744 <= r1172745;
        double r1172747 = 0.5;
        double r1172748 = cbrt(r1172747);
        double r1172749 = 10.0;
        double r1172750 = log(r1172749);
        double r1172751 = cbrt(r1172750);
        double r1172752 = r1172748 / r1172751;
        double r1172753 = r1172752 * r1172752;
        double r1172754 = -2.0;
        double r1172755 = -1.0;
        double r1172756 = r1172755 / r1172744;
        double r1172757 = log(r1172756);
        double r1172758 = r1172754 * r1172757;
        double r1172759 = r1172758 * r1172752;
        double r1172760 = r1172753 * r1172759;
        double r1172761 = -1.4780679115634563e-120;
        bool r1172762 = r1172744 <= r1172761;
        double r1172763 = r1172744 * r1172744;
        double r1172764 = re;
        double r1172765 = r1172764 * r1172764;
        double r1172766 = r1172763 + r1172765;
        double r1172767 = log(r1172766);
        double r1172768 = sqrt(r1172750);
        double r1172769 = sqrt(r1172768);
        double r1172770 = r1172767 / r1172769;
        double r1172771 = sqrt(r1172747);
        double r1172772 = r1172770 * r1172771;
        double r1172773 = r1172768 / r1172771;
        double r1172774 = r1172773 * r1172769;
        double r1172775 = r1172772 / r1172774;
        double r1172776 = -6.847505130661582e-247;
        bool r1172777 = r1172744 <= r1172776;
        double r1172778 = log(r1172764);
        double r1172779 = 2.0;
        double r1172780 = r1172778 * r1172779;
        double r1172781 = r1172780 * r1172752;
        double r1172782 = r1172781 * r1172753;
        double r1172783 = 9.270740708287654e+63;
        bool r1172784 = r1172744 <= r1172783;
        double r1172785 = r1172771 / r1172768;
        double r1172786 = r1172767 / r1172768;
        double r1172787 = r1172785 * r1172786;
        double r1172788 = r1172771 * r1172787;
        double r1172789 = r1172747 / r1172768;
        double r1172790 = log(r1172744);
        double r1172791 = 1.0;
        double r1172792 = r1172791 / r1172750;
        double r1172793 = sqrt(r1172792);
        double r1172794 = r1172790 * r1172793;
        double r1172795 = r1172779 * r1172794;
        double r1172796 = r1172789 * r1172795;
        double r1172797 = r1172784 ? r1172788 : r1172796;
        double r1172798 = r1172777 ? r1172782 : r1172797;
        double r1172799 = r1172762 ? r1172775 : r1172798;
        double r1172800 = r1172746 ? r1172760 : r1172799;
        return r1172800;
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Split input into 5 regimes

2. if im < -3.494473208647424e+151

   1. Initial program 61.4

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
   2. Using strategy rm

   3. Applied pow1/2 61.4

      \[\leadsto \frac{\log \color{blue}{\left({\left(re \cdot re + im \cdot im\right)}^{\frac{1}{2}}\right)}}{\log 10}\]

   4. Applied log-pow 61.4

      \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot \log \left(re \cdot re + im \cdot im\right)}}{\log 10}\]

   5. Applied associate-/l* 61.4

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{\log 10}{\log \left(re \cdot re + im \cdot im\right)}}}\]
   6. Using strategy rm

   7. Applied pow1 61.4

      \[\leadsto \frac{\frac{1}{2}}{\frac{\log 10}{\log \color{blue}{\left({\left(re \cdot re + im \cdot im\right)}^{1}\right)}}}\]

   8. Applied log-pow 61.4

      \[\leadsto \frac{\frac{1}{2}}{\frac{\log 10}{\color{blue}{1 \cdot \log \left(re \cdot re + im \cdot im\right)}}}\]

   9. Applied add-cube-cbrt 61.4

      \[\leadsto \frac{\frac{1}{2}}{\frac{\color{blue}{\left(\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}\right) \cdot \sqrt[3]{\log 10}}}{1 \cdot \log \left(re \cdot re + im \cdot im\right)}}\]

   10. Applied times-frac 61.4

       \[\leadsto \frac{\frac{1}{2}}{\color{blue}{\frac{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}}{1} \cdot \frac{\sqrt[3]{\log 10}}{\log \left(re \cdot re + im \cdot im\right)}}}\]

   11. Applied add-cube-cbrt 61.4

       \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot \sqrt[3]{\frac{1}{2}}}}{\frac{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}}{1} \cdot \frac{\sqrt[3]{\log 10}}{\log \left(re \cdot re + im \cdot im\right)}}\]

   12. Applied times-frac 61.4

       \[\leadsto \color{blue}{\frac{\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}}{\frac{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}}{1}} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\frac{\sqrt[3]{\log 10}}{\log \left(re \cdot re + im \cdot im\right)}}}\]

   13. Simplified 61.4

       \[\leadsto \color{blue}{\left(\frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right)} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\frac{\sqrt[3]{\log 10}}{\log \left(re \cdot re + im \cdot im\right)}}\]

   14. Simplified 61.4

       \[\leadsto \left(\frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right) \cdot \color{blue}{\left(\log \left(im \cdot im + re \cdot re\right) \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right)}\]

   15. Taylor expanded around -inf 6.6

       \[\leadsto \left(\frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right) \cdot \left(\color{blue}{\left(-2 \cdot \log \left(\frac{-1}{im}\right)\right)} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right)\]

   16. Simplified 6.6

       \[\leadsto \left(\frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right) \cdot \left(\color{blue}{\left(\log \left(\frac{-1}{im}\right) \cdot -2\right)} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right)\]

   if -3.494473208647424e+151 < im < -1.4780679115634563e-120

   1. Initial program 15.7

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
   2. Using strategy rm

   3. Applied add-sqr-sqrt 15.7

      \[\leadsto \frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\color{blue}{\sqrt{\log 10} \cdot \sqrt{\log 10}}}\]

   4. Applied pow1/2 15.7

      \[\leadsto \frac{\log \color{blue}{\left({\left(re \cdot re + im \cdot im\right)}^{\frac{1}{2}}\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]

   5. Applied log-pow 15.7

      \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot \log \left(re \cdot re + im \cdot im\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]

   6. Applied times-frac 15.6

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}}\]
   7. Using strategy rm

   8. Applied add-sqr-sqrt 15.6

      \[\leadsto \frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\color{blue}{\sqrt{\log 10} \cdot \sqrt{\log 10}}}}\]

   9. Applied sqrt-prod 16.1

      \[\leadsto \frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\color{blue}{\sqrt{\sqrt{\log 10}} \cdot \sqrt{\sqrt{\log 10}}}}\]

   10. Applied associate-/r* 16.2

       \[\leadsto \frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \color{blue}{\frac{\frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\sqrt{\log 10}}}}{\sqrt{\sqrt{\log 10}}}}\]

   11. Applied add-sqr-sqrt 15.6

       \[\leadsto \frac{\color{blue}{\sqrt{\frac{1}{2}} \cdot \sqrt{\frac{1}{2}}}}{\sqrt{\log 10}} \cdot \frac{\frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\sqrt{\log 10}}}}{\sqrt{\sqrt{\log 10}}}\]

   12. Applied associate-/l* 15.6

       \[\leadsto \color{blue}{\frac{\sqrt{\frac{1}{2}}}{\frac{\sqrt{\log 10}}{\sqrt{\frac{1}{2}}}}} \cdot \frac{\frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\sqrt{\log 10}}}}{\sqrt{\sqrt{\log 10}}}\]

   13. Applied frac-times 15.6

       \[\leadsto \color{blue}{\frac{\sqrt{\frac{1}{2}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\sqrt{\log 10}}}}{\frac{\sqrt{\log 10}}{\sqrt{\frac{1}{2}}} \cdot \sqrt{\sqrt{\log 10}}}}\]

   if -1.4780679115634563e-120 < im < -6.847505130661582e-247

   1. Initial program 25.4

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
   2. Using strategy rm

   3. Applied pow1/2 25.4

      \[\leadsto \frac{\log \color{blue}{\left({\left(re \cdot re + im \cdot im\right)}^{\frac{1}{2}}\right)}}{\log 10}\]

   4. Applied log-pow 25.4

      \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot \log \left(re \cdot re + im \cdot im\right)}}{\log 10}\]

   5. Applied associate-/l* 25.4

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{\log 10}{\log \left(re \cdot re + im \cdot im\right)}}}\]
   6. Using strategy rm

   7. Applied pow1 25.4

      \[\leadsto \frac{\frac{1}{2}}{\frac{\log 10}{\log \color{blue}{\left({\left(re \cdot re + im \cdot im\right)}^{1}\right)}}}\]

   8. Applied log-pow 25.4

      \[\leadsto \frac{\frac{1}{2}}{\frac{\log 10}{\color{blue}{1 \cdot \log \left(re \cdot re + im \cdot im\right)}}}\]

   9. Applied add-cube-cbrt 25.9

      \[\leadsto \frac{\frac{1}{2}}{\frac{\color{blue}{\left(\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}\right) \cdot \sqrt[3]{\log 10}}}{1 \cdot \log \left(re \cdot re + im \cdot im\right)}}\]

   10. Applied times-frac 25.9

       \[\leadsto \frac{\frac{1}{2}}{\color{blue}{\frac{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}}{1} \cdot \frac{\sqrt[3]{\log 10}}{\log \left(re \cdot re + im \cdot im\right)}}}\]

   11. Applied add-cube-cbrt 25.3

       \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot \sqrt[3]{\frac{1}{2}}}}{\frac{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}}{1} \cdot \frac{\sqrt[3]{\log 10}}{\log \left(re \cdot re + im \cdot im\right)}}\]

   12. Applied times-frac 25.3

       \[\leadsto \color{blue}{\frac{\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}}{\frac{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}}{1}} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\frac{\sqrt[3]{\log 10}}{\log \left(re \cdot re + im \cdot im\right)}}}\]

   13. Simplified 25.3

       \[\leadsto \color{blue}{\left(\frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right)} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\frac{\sqrt[3]{\log 10}}{\log \left(re \cdot re + im \cdot im\right)}}\]

   14. Simplified 25.3

       \[\leadsto \left(\frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right) \cdot \color{blue}{\left(\log \left(im \cdot im + re \cdot re\right) \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right)}\]

   15. Taylor expanded around 0 37.5

       \[\leadsto \left(\frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right) \cdot \left(\color{blue}{\left(2 \cdot \log re\right)} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right)\]

   if -6.847505130661582e-247 < im < 9.270740708287654e+63

   1. Initial program 21.9

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
   2. Using strategy rm

   3. Applied add-sqr-sqrt 21.9

      \[\leadsto \frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\color{blue}{\sqrt{\log 10} \cdot \sqrt{\log 10}}}\]

   4. Applied pow1/2 21.9

      \[\leadsto \frac{\log \color{blue}{\left({\left(re \cdot re + im \cdot im\right)}^{\frac{1}{2}}\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]

   5. Applied log-pow 21.9

      \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot \log \left(re \cdot re + im \cdot im\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]

   6. Applied times-frac 21.9

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}}\]
   7. Using strategy rm

   8. Applied *-un-lft-identity 21.9

      \[\leadsto \frac{\frac{1}{2}}{\color{blue}{1 \cdot \sqrt{\log 10}}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}\]

   9. Applied add-sqr-sqrt 21.9

      \[\leadsto \frac{\color{blue}{\sqrt{\frac{1}{2}} \cdot \sqrt{\frac{1}{2}}}}{1 \cdot \sqrt{\log 10}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}\]

   10. Applied times-frac 21.9

       \[\leadsto \color{blue}{\left(\frac{\sqrt{\frac{1}{2}}}{1} \cdot \frac{\sqrt{\frac{1}{2}}}{\sqrt{\log 10}}\right)} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}\]

   11. Applied associate-*l* 21.8

       \[\leadsto \color{blue}{\frac{\sqrt{\frac{1}{2}}}{1} \cdot \left(\frac{\sqrt{\frac{1}{2}}}{\sqrt{\log 10}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}\right)}\]

   if 9.270740708287654e+63 < im

   1. Initial program 44.6

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
   2. Using strategy rm

   3. Applied add-sqr-sqrt 44.6

      \[\leadsto \frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\color{blue}{\sqrt{\log 10} \cdot \sqrt{\log 10}}}\]

   4. Applied pow1/2 44.6

      \[\leadsto \frac{\log \color{blue}{\left({\left(re \cdot re + im \cdot im\right)}^{\frac{1}{2}}\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]

   5. Applied log-pow 44.6

      \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot \log \left(re \cdot re + im \cdot im\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]

   6. Applied times-frac 44.6

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\log 10}}}\]

   7. Taylor expanded around 0 10.0

      \[\leadsto \frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \color{blue}{\left(2 \cdot \left(\log im \cdot \sqrt{\frac{1}{\log 10}}\right)\right)}\]
3. Recombined 5 regimes into one program.

4. Final simplification 17.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;im \le -3.494473208647424 \cdot 10^{+151}:\\ \;\;\;\;\left(\frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right) \cdot \left(\left(-2 \cdot \log \left(\frac{-1}{im}\right)\right) \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right)\\ \mathbf{elif}\;im \le -1.4780679115634563 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{\log \left(im \cdot im + re \cdot re\right)}{\sqrt{\sqrt{\log 10}}} \cdot \sqrt{\frac{1}{2}}}{\frac{\sqrt{\log 10}}{\sqrt{\frac{1}{2}}} \cdot \sqrt{\sqrt{\log 10}}}\\ \mathbf{elif}\;im \le -6.847505130661582 \cdot 10^{-247}:\\ \;\;\;\;\left(\left(\log re \cdot 2\right) \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right) \cdot \left(\frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{\log 10}}\right)\\ \mathbf{elif}\;im \le 9.270740708287654 \cdot 10^{+63}:\\ \;\;\;\;\sqrt{\frac{1}{2}} \cdot \left(\frac{\sqrt{\frac{1}{2}}}{\sqrt{\log 10}} \cdot \frac{\log \left(im \cdot im + re \cdot re\right)}{\sqrt{\log 10}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \left(2 \cdot \left(\log im \cdot \sqrt{\frac{1}{\log 10}}\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (re im)
  :name "math.log10 on complex, real part"
  (/ (log (sqrt (+ (* re re) (* im im)))) (log 10)))