Diagrams.TwoD.Path.Metafont.Internal:hobbyF from diagrams-contrib-1.3.0.5

Average Error: 0.5 → 0.5

Time: 36.2s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]

↓

\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{\left(3 \cdot \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y - \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)\right) + \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)\right)\right) \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{2 \cdot \left(\left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \frac{3 \cdot 3 - 5}{3 + \sqrt{5}}\right) \cdot {\left(\cos y\right)}^{2} - 2 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)\right)\right)}{{2}^{3}}\right)\]

C

double f(double x, double y) {
        double r428030 = 2.0;
        double r428031 = sqrt(r428030);
        double r428032 = x;
        double r428033 = sin(r428032);
        double r428034 = y;
        double r428035 = sin(r428034);
        double r428036 = 16.0;
        double r428037 = r428035 / r428036;
        double r428038 = r428033 - r428037;
        double r428039 = r428031 * r428038;
        double r428040 = r428033 / r428036;
        double r428041 = r428035 - r428040;
        double r428042 = r428039 * r428041;
        double r428043 = cos(r428032);
        double r428044 = cos(r428034);
        double r428045 = r428043 - r428044;
        double r428046 = r428042 * r428045;
        double r428047 = r428030 + r428046;
        double r428048 = 3.0;
        double r428049 = 1.0;
        double r428050 = 5.0;
        double r428051 = sqrt(r428050);
        double r428052 = r428051 - r428049;
        double r428053 = r428052 / r428030;
        double r428054 = r428053 * r428043;
        double r428055 = r428049 + r428054;
        double r428056 = r428048 - r428051;
        double r428057 = r428056 / r428030;
        double r428058 = r428057 * r428044;
        double r428059 = r428055 + r428058;
        double r428060 = r428048 * r428059;
        double r428061 = r428047 / r428060;
        return r428061;
}

↓

double f(double x, double y) {
        double r428062 = 2.0;
        double r428063 = sqrt(r428062);
        double r428064 = x;
        double r428065 = sin(r428064);
        double r428066 = y;
        double r428067 = sin(r428066);
        double r428068 = 16.0;
        double r428069 = r428067 / r428068;
        double r428070 = r428065 - r428069;
        double r428071 = r428063 * r428070;
        double r428072 = r428065 / r428068;
        double r428073 = r428067 - r428072;
        double r428074 = r428071 * r428073;
        double r428075 = cos(r428064);
        double r428076 = cos(r428066);
        double r428077 = r428075 - r428076;
        double r428078 = r428074 * r428077;
        double r428079 = r428062 + r428078;
        double r428080 = 3.0;
        double r428081 = r428080 * r428080;
        double r428082 = 5.0;
        double r428083 = r428081 - r428082;
        double r428084 = sqrt(r428082);
        double r428085 = r428080 + r428084;
        double r428086 = r428083 / r428085;
        double r428087 = r428086 / r428062;
        double r428088 = r428087 * r428076;
        double r428089 = 1.0;
        double r428090 = r428084 - r428089;
        double r428091 = r428090 / r428062;
        double r428092 = r428091 * r428075;
        double r428093 = r428089 + r428092;
        double r428094 = r428088 - r428093;
        double r428095 = r428088 * r428094;
        double r428096 = r428093 * r428093;
        double r428097 = r428095 + r428096;
        double r428098 = r428080 * r428097;
        double r428099 = r428093 + r428088;
        double r428100 = r428098 * r428099;
        double r428101 = r428079 / r428100;
        double r428102 = r428086 * r428086;
        double r428103 = 2.0;
        double r428104 = pow(r428076, r428103);
        double r428105 = r428102 * r428104;
        double r428106 = r428086 * r428076;
        double r428107 = r428093 * r428106;
        double r428108 = r428062 * r428107;
        double r428109 = r428105 - r428108;
        double r428110 = r428062 * r428109;
        double r428111 = 3.0;
        double r428112 = pow(r428062, r428111);
        double r428113 = r428110 / r428112;
        double r428114 = r428096 + r428113;
        double r428115 = r428101 * r428114;
        return r428115;
}

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 0.5

   \[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
2. Using strategy rm

3. Applied flip-- 0.5

   \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\color{blue}{\frac{3 \cdot 3 - \sqrt{5} \cdot \sqrt{5}}{3 + \sqrt{5}}}}{2} \cdot \cos y\right)}\]

4. Simplified 0.5

   \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{\color{blue}{3 \cdot 3 - 5}}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\]
5. Using strategy rm

6. Applied flip3-+ 0.6

   \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \color{blue}{\frac{{\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}}{\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) - \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)\right)}}}\]

7. Applied associate-*r/ 0.6

   \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{\color{blue}{\frac{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)}{\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) - \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)\right)}}}\]

8. Applied associate-/r/ 0.6

   \[\leadsto \color{blue}{\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) - \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)\right)\right)}\]
9. Using strategy rm

10. Applied associate-*l/ 0.6

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) - \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \color{blue}{\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y}{2}}\right)\right)\]

11. Applied associate-*r/ 0.6

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) - \color{blue}{\frac{\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)}{2}}\right)\right)\]

12. Applied associate-*l/ 0.6

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \color{blue}{\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y}{2}} - \frac{\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)}{2}\right)\right)\]

13. Applied associate-*l/ 0.6

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\color{blue}{\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y}{2}} \cdot \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y}{2} - \frac{\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)}{2}\right)\right)\]

14. Applied frac-times 0.6

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\color{blue}{\frac{\left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)}{2 \cdot 2}} - \frac{\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)}{2}\right)\right)\]

15. Applied frac-sub 0.6

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \color{blue}{\frac{\left(\left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)\right) \cdot 2 - \left(2 \cdot 2\right) \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)\right)}{\left(2 \cdot 2\right) \cdot 2}}\right)\]

16. Simplified 0.6

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\color{blue}{2 \cdot \left(\left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \frac{3 \cdot 3 - 5}{3 + \sqrt{5}}\right) \cdot {\left(\cos y\right)}^{2} - 2 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)\right)\right)}}{\left(2 \cdot 2\right) \cdot 2}\right)\]

17. Simplified 0.6

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{2 \cdot \left(\left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \frac{3 \cdot 3 - 5}{3 + \sqrt{5}}\right) \cdot {\left(\cos y\right)}^{2} - 2 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)\right)\right)}{\color{blue}{{2}^{3}}}\right)\]
18. Using strategy rm

19. Applied sum-cubes 0.5

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \color{blue}{\left(\left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) - \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)\right)\right) \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)\right)}} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{2 \cdot \left(\left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \frac{3 \cdot 3 - 5}{3 + \sqrt{5}}\right) \cdot {\left(\cos y\right)}^{2} - 2 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)\right)\right)}{{2}^{3}}\right)\]

20. Applied associate-*r* 0.5

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{\color{blue}{\left(3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) - \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)\right)\right)\right) \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{2 \cdot \left(\left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \frac{3 \cdot 3 - 5}{3 + \sqrt{5}}\right) \cdot {\left(\cos y\right)}^{2} - 2 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)\right)\right)}{{2}^{3}}\right)\]

21. Simplified 0.5

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{\color{blue}{\left(3 \cdot \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y - \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)\right) + \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)\right)\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{2 \cdot \left(\left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \frac{3 \cdot 3 - 5}{3 + \sqrt{5}}\right) \cdot {\left(\cos y\right)}^{2} - 2 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)\right)\right)}{{2}^{3}}\right)\]

22. Final simplification 0.5

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{\left(3 \cdot \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y - \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)\right) + \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)\right)\right) \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{2 \cdot \left(\left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \frac{3 \cdot 3 - 5}{3 + \sqrt{5}}\right) \cdot {\left(\cos y\right)}^{2} - 2 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)\right)\right)}{{2}^{3}}\right)\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x y)
  :name "Diagrams.TwoD.Path.Metafont.Internal:hobbyF from diagrams-contrib-1.3.0.5"
  :precision binary64
  (/ (+ 2 (* (* (* (sqrt 2) (- (sin x) (/ (sin y) 16))) (- (sin y) (/ (sin x) 16))) (- (cos x) (cos y)))) (* 3 (+ (+ 1 (* (/ (- (sqrt 5) 1) 2) (cos x))) (* (/ (- 3 (sqrt 5)) 2) (cos y))))))