Average Error: 0.4 → 0.4
Time: 2.3m
Precision: 64
\[\frac{2.0 + \left(\left(\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{3.0 - \sqrt{5.0}}{2.0} \cdot \cos y\right)}\]
↓
\[\frac{\sqrt{\sqrt{2.0}} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\sqrt[3]{\left(\left(\left(\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \sqrt{\sqrt{2.0}}\right) \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)} \cdot \sqrt[3]{\sqrt{2.0} \cdot \left(\sin y - \frac{\sin x}{16.0}\right)}\right)\right) + 2.0}{\left(\cos y \cdot \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} + \left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right)\right) \cdot 3.0}\]
\frac{2.0 + \left(\left(\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{3.0 - \sqrt{5.0}}{2.0} \cdot \cos y\right)}
↓
\frac{\sqrt{\sqrt{2.0}} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\sqrt[3]{\left(\left(\left(\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \sqrt{\sqrt{2.0}}\right) \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)} \cdot \sqrt[3]{\sqrt{2.0} \cdot \left(\sin y - \frac{\sin x}{16.0}\right)}\right)\right) + 2.0}{\left(\cos y \cdot \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} + \left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right)\right) \cdot 3.0}
double f(double x, double y) {
        double r11661960 = 2.0;
        double r11661961 = sqrt(r11661960);
        double r11661962 = x;
        double r11661963 = sin(r11661962);
        double r11661964 = y;
        double r11661965 = sin(r11661964);
        double r11661966 = 16.0;
        double r11661967 = r11661965 / r11661966;
        double r11661968 = r11661963 - r11661967;
        double r11661969 = r11661961 * r11661968;
        double r11661970 = r11661963 / r11661966;
        double r11661971 = r11661965 - r11661970;
        double r11661972 = r11661969 * r11661971;
        double r11661973 = cos(r11661962);
        double r11661974 = cos(r11661964);
        double r11661975 = r11661973 - r11661974;
        double r11661976 = r11661972 * r11661975;
        double r11661977 = r11661960 + r11661976;
        double r11661978 = 3.0;
        double r11661979 = 1.0;
        double r11661980 = 5.0;
        double r11661981 = sqrt(r11661980);
        double r11661982 = r11661981 - r11661979;
        double r11661983 = r11661982 / r11661960;
        double r11661984 = r11661983 * r11661973;
        double r11661985 = r11661979 + r11661984;
        double r11661986 = r11661978 - r11661981;
        double r11661987 = r11661986 / r11661960;
        double r11661988 = r11661987 * r11661974;
        double r11661989 = r11661985 + r11661988;
        double r11661990 = r11661978 * r11661989;
        double r11661991 = r11661977 / r11661990;
        return r11661991;
}
↓
double f(double x, double y) {
        double r11661992 = 2.0;
        double r11661993 = sqrt(r11661992);
        double r11661994 = sqrt(r11661993);
        double r11661995 = x;
        double r11661996 = cos(r11661995);
        double r11661997 = y;
        double r11661998 = cos(r11661997);
        double r11661999 = r11661996 - r11661998;
        double r11662000 = sin(r11661995);
        double r11662001 = sin(r11661997);
        double r11662002 = 16.0;
        double r11662003 = r11662001 / r11662002;
        double r11662004 = r11662000 - r11662003;
        double r11662005 = r11662004 * r11662004;
        double r11662006 = r11662000 / r11662002;
        double r11662007 = r11662001 - r11662006;
        double r11662008 = r11662005 * r11662007;
        double r11662009 = r11662008 * r11661994;
        double r11662010 = r11662007 * r11662004;
        double r11662011 = r11662009 * r11662010;
        double r11662012 = cbrt(r11662011);
        double r11662013 = r11661993 * r11662007;
        double r11662014 = cbrt(r11662013);
        double r11662015 = r11662012 * r11662014;
        double r11662016 = r11661999 * r11662015;
        double r11662017 = r11661994 * r11662016;
        double r11662018 = r11662017 + r11661992;
        double r11662019 = 3.0;
        double r11662020 = r11662019 * r11662019;
        double r11662021 = 5.0;
        double r11662022 = r11662020 - r11662021;
        double r11662023 = sqrt(r11662021);
        double r11662024 = r11662019 + r11662023;
        double r11662025 = r11662022 / r11662024;
        double r11662026 = r11662025 / r11661992;
        double r11662027 = r11661998 * r11662026;
        double r11662028 = 1.0;
        double r11662029 = r11662023 - r11662028;
        double r11662030 = r11662029 / r11661992;
        double r11662031 = r11662030 * r11661996;
        double r11662032 = r11662028 + r11662031;
        double r11662033 = r11662027 + r11662032;
        double r11662034 = r11662033 * r11662019;
        double r11662035 = r11662018 / r11662034;
        return r11662035;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

    \[\frac{2.0 + \left(\left(\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{3.0 - \sqrt{5.0}}{2.0} \cdot \cos y\right)}\]
  2. Using strategy rm

  3. Applied flip--0.5

    \[\leadsto \frac{2.0 + \left(\left(\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\color{blue}{\frac{3.0 \cdot 3.0 - \sqrt{5.0} \cdot \sqrt{5.0}}{3.0 + \sqrt{5.0}}}}{2.0} \cdot \cos y\right)}\]

  4. Simplified0.4

    \[\leadsto \frac{2.0 + \left(\left(\sqrt{2.0} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{\color{blue}{3.0 \cdot 3.0 - 5.0}}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]
  5. Using strategy rm

  6. Applied add-sqr-sqrt0.4

    \[\leadsto \frac{2.0 + \left(\left(\sqrt{\color{blue}{\sqrt{2.0} \cdot \sqrt{2.0}}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  7. Applied sqrt-prod0.4

    \[\leadsto \frac{2.0 + \left(\left(\color{blue}{\left(\sqrt{\sqrt{2.0}} \cdot \sqrt{\sqrt{2.0}}\right)} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  8. Applied associate-*l*0.4

    \[\leadsto \frac{2.0 + \left(\color{blue}{\left(\sqrt{\sqrt{2.0}} \cdot \left(\sqrt{\sqrt{2.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)\right)} \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  9. Applied associate-*l*0.4

    \[\leadsto \frac{2.0 + \color{blue}{\left(\sqrt{\sqrt{2.0}} \cdot \left(\left(\sqrt{\sqrt{2.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right)\right)} \cdot \left(\cos x - \cos y\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  10. Applied associate-*l*0.4

    \[\leadsto \frac{2.0 + \color{blue}{\sqrt{\sqrt{2.0}} \cdot \left(\left(\left(\sqrt{\sqrt{2.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\cos x - \cos y\right)\right)}}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]
  11. Using strategy rm

  12. Applied add-cbrt-cube0.4

    \[\leadsto \frac{2.0 + \sqrt{\sqrt{2.0}} \cdot \left(\left(\left(\sqrt{\sqrt{2.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \color{blue}{\sqrt[3]{\left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)}}\right) \cdot \left(\cos x - \cos y\right)\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  13. Applied add-cbrt-cube0.4

    \[\leadsto \frac{2.0 + \sqrt{\sqrt{2.0}} \cdot \left(\left(\left(\sqrt{\sqrt{2.0}} \cdot \color{blue}{\sqrt[3]{\left(\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)}}\right) \cdot \sqrt[3]{\left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)}\right) \cdot \left(\cos x - \cos y\right)\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  14. Applied add-cbrt-cube0.5

    \[\leadsto \frac{2.0 + \sqrt{\sqrt{2.0}} \cdot \left(\left(\left(\color{blue}{\sqrt[3]{\left(\sqrt{\sqrt{2.0}} \cdot \sqrt{\sqrt{2.0}}\right) \cdot \sqrt{\sqrt{2.0}}}} \cdot \sqrt[3]{\left(\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)}\right) \cdot \sqrt[3]{\left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)}\right) \cdot \left(\cos x - \cos y\right)\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  15. Applied cbrt-unprod0.4

    \[\leadsto \frac{2.0 + \sqrt{\sqrt{2.0}} \cdot \left(\left(\color{blue}{\sqrt[3]{\left(\left(\sqrt{\sqrt{2.0}} \cdot \sqrt{\sqrt{2.0}}\right) \cdot \sqrt{\sqrt{2.0}}\right) \cdot \left(\left(\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)}} \cdot \sqrt[3]{\left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)}\right) \cdot \left(\cos x - \cos y\right)\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  16. Applied cbrt-unprod0.4

    \[\leadsto \frac{2.0 + \sqrt{\sqrt{2.0}} \cdot \left(\color{blue}{\sqrt[3]{\left(\left(\left(\sqrt{\sqrt{2.0}} \cdot \sqrt{\sqrt{2.0}}\right) \cdot \sqrt{\sqrt{2.0}}\right) \cdot \left(\left(\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)\right) \cdot \left(\left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right)}} \cdot \left(\cos x - \cos y\right)\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  17. Simplified0.4

    \[\leadsto \frac{2.0 + \sqrt{\sqrt{2.0}} \cdot \left(\sqrt[3]{\color{blue}{\left(\left(\sqrt{2.0} \cdot \left(\left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)\right)\right) \cdot \sqrt{\sqrt{2.0}}\right) \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)}} \cdot \left(\cos x - \cos y\right)\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]
  18. Using strategy rm

  19. Applied add-sqr-sqrt31.7

    \[\leadsto \frac{2.0 + \sqrt{\sqrt{2.0}} \cdot \left(\sqrt[3]{\left(\left(\sqrt{2.0} \cdot \left(\left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\color{blue}{\left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \sqrt{\sin y - \frac{\sin x}{16.0}}\right)} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)\right)\right) \cdot \sqrt{\sqrt{2.0}}\right) \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)} \cdot \left(\cos x - \cos y\right)\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  20. Applied associate-*l*31.7

    \[\leadsto \frac{2.0 + \sqrt{\sqrt{2.0}} \cdot \left(\sqrt[3]{\left(\left(\sqrt{2.0} \cdot \left(\left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \color{blue}{\left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)\right)}\right)\right) \cdot \sqrt{\sqrt{2.0}}\right) \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)} \cdot \left(\cos x - \cos y\right)\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  21. Applied add-sqr-sqrt31.7

    \[\leadsto \frac{2.0 + \sqrt{\sqrt{2.0}} \cdot \left(\sqrt[3]{\left(\left(\sqrt{2.0} \cdot \left(\left(\color{blue}{\left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \sqrt{\sin y - \frac{\sin x}{16.0}}\right)} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)\right)\right)\right) \cdot \sqrt{\sqrt{2.0}}\right) \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)} \cdot \left(\cos x - \cos y\right)\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  22. Applied associate-*l*31.7

    \[\leadsto \frac{2.0 + \sqrt{\sqrt{2.0}} \cdot \left(\sqrt[3]{\left(\left(\sqrt{2.0} \cdot \left(\color{blue}{\left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)\right)} \cdot \left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)\right)\right)\right) \cdot \sqrt{\sqrt{2.0}}\right) \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)} \cdot \left(\cos x - \cos y\right)\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  23. Applied swap-sqr31.7

    \[\leadsto \frac{2.0 + \sqrt{\sqrt{2.0}} \cdot \left(\sqrt[3]{\left(\left(\sqrt{2.0} \cdot \color{blue}{\left(\left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \sqrt{\sin y - \frac{\sin x}{16.0}}\right) \cdot \left(\left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)\right)\right)}\right) \cdot \sqrt{\sqrt{2.0}}\right) \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)} \cdot \left(\cos x - \cos y\right)\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  24. Applied associate-*r*31.7

    \[\leadsto \frac{2.0 + \sqrt{\sqrt{2.0}} \cdot \left(\sqrt[3]{\left(\color{blue}{\left(\left(\sqrt{2.0} \cdot \left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \sqrt{\sin y - \frac{\sin x}{16.0}}\right)\right) \cdot \left(\left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)\right)\right)} \cdot \sqrt{\sqrt{2.0}}\right) \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)} \cdot \left(\cos x - \cos y\right)\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  25. Applied associate-*l*31.7

    \[\leadsto \frac{2.0 + \sqrt{\sqrt{2.0}} \cdot \left(\sqrt[3]{\color{blue}{\left(\left(\sqrt{2.0} \cdot \left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \sqrt{\sin y - \frac{\sin x}{16.0}}\right)\right) \cdot \left(\left(\left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)\right) \cdot \sqrt{\sqrt{2.0}}\right)\right)} \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)} \cdot \left(\cos x - \cos y\right)\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  26. Applied associate-*l*31.7

    \[\leadsto \frac{2.0 + \sqrt{\sqrt{2.0}} \cdot \left(\sqrt[3]{\color{blue}{\left(\sqrt{2.0} \cdot \left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \sqrt{\sin y - \frac{\sin x}{16.0}}\right)\right) \cdot \left(\left(\left(\left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)\right) \cdot \sqrt{\sqrt{2.0}}\right) \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)\right)}} \cdot \left(\cos x - \cos y\right)\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  27. Applied cbrt-prod31.7

    \[\leadsto \frac{2.0 + \sqrt{\sqrt{2.0}} \cdot \left(\color{blue}{\left(\sqrt[3]{\sqrt{2.0} \cdot \left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \sqrt{\sin y - \frac{\sin x}{16.0}}\right)} \cdot \sqrt[3]{\left(\left(\left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)\right) \cdot \sqrt{\sqrt{2.0}}\right) \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)}\right)} \cdot \left(\cos x - \cos y\right)\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  28. Simplified31.7

    \[\leadsto \frac{2.0 + \sqrt{\sqrt{2.0}} \cdot \left(\left(\color{blue}{\sqrt[3]{\sqrt{2.0} \cdot \left(\sin y - \frac{\sin x}{16.0}\right)}} \cdot \sqrt[3]{\left(\left(\left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sqrt{\sin y - \frac{\sin x}{16.0}} \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)\right) \cdot \sqrt{\sqrt{2.0}}\right) \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)}\right) \cdot \left(\cos x - \cos y\right)\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  29. Simplified0.4

    \[\leadsto \frac{2.0 + \sqrt{\sqrt{2.0}} \cdot \left(\left(\sqrt[3]{\sqrt{2.0} \cdot \left(\sin y - \frac{\sin x}{16.0}\right)} \cdot \color{blue}{\sqrt[3]{\left(\left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)\right) \cdot \sqrt{\sqrt{2.0}}\right) \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)}}\right) \cdot \left(\cos x - \cos y\right)\right)}{3.0 \cdot \left(\left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right) + \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} \cdot \cos y\right)}\]

  30. Final simplification0.4

    \[\leadsto \frac{\sqrt{\sqrt{2.0}} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\sqrt[3]{\left(\left(\left(\left(\sin x - \frac{\sin y}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16.0}\right)\right) \cdot \sqrt{\sqrt{2.0}}\right) \cdot \left(\left(\sin y - \frac{\sin x}{16.0}\right) \cdot \left(\sin x - \frac{\sin y}{16.0}\right)\right)} \cdot \sqrt[3]{\sqrt{2.0} \cdot \left(\sin y - \frac{\sin x}{16.0}\right)}\right)\right) + 2.0}{\left(\cos y \cdot \frac{\frac{3.0 \cdot 3.0 - 5.0}{3.0 + \sqrt{5.0}}}{2.0} + \left(1.0 + \frac{\sqrt{5.0} - 1.0}{2.0} \cdot \cos x\right)\right) \cdot 3.0}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y)
  :name "Diagrams.TwoD.Path.Metafont.Internal:hobbyF from diagrams-contrib-1.3.0.5"
  (/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y))))))