Average Error: 0.4 → 0.4
Time: 46.8s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\mathsf{fma}\left(\mathsf{fma}\left(1, \sin x, -\frac{\sqrt[3]{\sin y}}{\sqrt[3]{16}} \cdot \frac{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}}{\sqrt[3]{16} \cdot \sqrt[3]{16}}\right), \sqrt{2}, \mathsf{fma}\left({\left(\frac{\sqrt[3]{\sin y}}{\sqrt[3]{16}}\right)}^{3}, \sqrt{2}, -\sqrt{2} \cdot {\left(\frac{\sqrt[3]{\sin y}}{\sqrt[3]{16}}\right)}^{3}\right)\right) \cdot \log \left(e^{\mathsf{fma}\left(1, \sin y, -\frac{\sqrt[3]{\sin x}}{\sqrt[3]{16}} \cdot \frac{\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}}{\sqrt[3]{16} \cdot \sqrt[3]{16}}\right)}\right) + \mathsf{fma}\left(\mathsf{fma}\left(1, \sin x, -\frac{\sqrt[3]{\sin y}}{\sqrt[3]{16}} \cdot \frac{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}}{\sqrt[3]{16} \cdot \sqrt[3]{16}}\right), \sqrt{2}, \mathsf{fma}\left({\left(\frac{\sqrt[3]{\sin y}}{\sqrt[3]{16}}\right)}^{3}, \sqrt{2}, -\sqrt{2} \cdot {\left(\frac{\sqrt[3]{\sin y}}{\sqrt[3]{16}}\right)}^{3}\right)\right) \cdot \log \left(e^{\mathsf{fma}\left(-\frac{\sqrt[3]{\sin x}}{\sqrt[3]{16}}, \frac{\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}}{\sqrt[3]{16} \cdot \sqrt[3]{16}}, \frac{\sqrt[3]{\sin x}}{\sqrt[3]{16}} \cdot \frac{\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}}{\sqrt[3]{16} \cdot \sqrt[3]{16}}\right)}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
\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)}{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(\mathsf{fma}\left(\mathsf{fma}\left(1, \sin x, -\frac{\sqrt[3]{\sin y}}{\sqrt[3]{16}} \cdot \frac{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}}{\sqrt[3]{16} \cdot \sqrt[3]{16}}\right), \sqrt{2}, \mathsf{fma}\left({\left(\frac{\sqrt[3]{\sin y}}{\sqrt[3]{16}}\right)}^{3}, \sqrt{2}, -\sqrt{2} \cdot {\left(\frac{\sqrt[3]{\sin y}}{\sqrt[3]{16}}\right)}^{3}\right)\right) \cdot \log \left(e^{\mathsf{fma}\left(1, \sin y, -\frac{\sqrt[3]{\sin x}}{\sqrt[3]{16}} \cdot \frac{\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}}{\sqrt[3]{16} \cdot \sqrt[3]{16}}\right)}\right) + \mathsf{fma}\left(\mathsf{fma}\left(1, \sin x, -\frac{\sqrt[3]{\sin y}}{\sqrt[3]{16}} \cdot \frac{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}}{\sqrt[3]{16} \cdot \sqrt[3]{16}}\right), \sqrt{2}, \mathsf{fma}\left({\left(\frac{\sqrt[3]{\sin y}}{\sqrt[3]{16}}\right)}^{3}, \sqrt{2}, -\sqrt{2} \cdot {\left(\frac{\sqrt[3]{\sin y}}{\sqrt[3]{16}}\right)}^{3}\right)\right) \cdot \log \left(e^{\mathsf{fma}\left(-\frac{\sqrt[3]{\sin x}}{\sqrt[3]{16}}, \frac{\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}}{\sqrt[3]{16} \cdot \sqrt[3]{16}}, \frac{\sqrt[3]{\sin x}}{\sqrt[3]{16}} \cdot \frac{\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}}{\sqrt[3]{16} \cdot \sqrt[3]{16}}\right)}\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)}
double code(double x, double y) {
	return ((double) (((double) (2.0 + ((double) (((double) (((double) (((double) sqrt(2.0)) * ((double) (((double) sin(x)) - ((double) (((double) sin(y)) / 16.0)))))) * ((double) (((double) sin(y)) - ((double) (((double) sin(x)) / 16.0)))))) * ((double) (((double) cos(x)) - ((double) cos(y)))))))) / ((double) (3.0 * ((double) (((double) (1.0 + ((double) (((double) (((double) (((double) sqrt(5.0)) - 1.0)) / 2.0)) * ((double) cos(x)))))) + ((double) (((double) (((double) (3.0 - ((double) sqrt(5.0)))) / 2.0)) * ((double) cos(y))))))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (2.0 + ((double) (((double) (((double) (((double) fma(((double) fma(1.0, ((double) sin(x)), ((double) -(((double) (((double) (((double) cbrt(((double) sin(y)))) / ((double) cbrt(16.0)))) * ((double) (((double) (((double) cbrt(((double) sin(y)))) * ((double) cbrt(((double) sin(y)))))) / ((double) (((double) cbrt(16.0)) * ((double) cbrt(16.0)))))))))))), ((double) sqrt(2.0)), ((double) fma(((double) pow(((double) (((double) cbrt(((double) sin(y)))) / ((double) cbrt(16.0)))), 3.0)), ((double) sqrt(2.0)), ((double) -(((double) (((double) sqrt(2.0)) * ((double) pow(((double) (((double) cbrt(((double) sin(y)))) / ((double) cbrt(16.0)))), 3.0)))))))))) * ((double) log(((double) exp(((double) fma(1.0, ((double) sin(y)), ((double) -(((double) (((double) (((double) cbrt(((double) sin(x)))) / ((double) cbrt(16.0)))) * ((double) (((double) (((double) cbrt(((double) sin(x)))) * ((double) cbrt(((double) sin(x)))))) / ((double) (((double) cbrt(16.0)) * ((double) cbrt(16.0)))))))))))))))))) + ((double) (((double) fma(((double) fma(1.0, ((double) sin(x)), ((double) -(((double) (((double) (((double) cbrt(((double) sin(y)))) / ((double) cbrt(16.0)))) * ((double) (((double) (((double) cbrt(((double) sin(y)))) * ((double) cbrt(((double) sin(y)))))) / ((double) (((double) cbrt(16.0)) * ((double) cbrt(16.0)))))))))))), ((double) sqrt(2.0)), ((double) fma(((double) pow(((double) (((double) cbrt(((double) sin(y)))) / ((double) cbrt(16.0)))), 3.0)), ((double) sqrt(2.0)), ((double) -(((double) (((double) sqrt(2.0)) * ((double) pow(((double) (((double) cbrt(((double) sin(y)))) / ((double) cbrt(16.0)))), 3.0)))))))))) * ((double) log(((double) exp(((double) fma(((double) -(((double) (((double) cbrt(((double) sin(x)))) / ((double) cbrt(16.0)))))), ((double) (((double) (((double) cbrt(((double) sin(x)))) * ((double) cbrt(((double) sin(x)))))) / ((double) (((double) cbrt(16.0)) * ((double) cbrt(16.0)))))), ((double) (((double) (((double) cbrt(((double) sin(x)))) / ((double) cbrt(16.0)))) * ((double) (((double) (((double) cbrt(((double) sin(x)))) * ((double) cbrt(((double) sin(x)))))) / ((double) (((double) cbrt(16.0)) * ((double) cbrt(16.0)))))))))))))))))) * ((double) (((double) cos(x)) - ((double) cos(y)))))))) / ((double) (3.0 * ((double) (((double) (1.0 + ((double) (((double) (((double) (((double) sqrt(5.0)) - 1.0)) / 2.0)) * ((double) cos(x)))))) + ((double) (((double) (((double) (3.0 - ((double) sqrt(5.0)))) / 2.0)) * ((double) cos(y))))))))));
}

Error

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Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

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

  3. Applied add-log-exp0.5

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

  5. Applied add-cube-cbrt0.4

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

  6. Applied add-cube-cbrt0.4

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

  7. Applied times-frac0.4

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

  8. Applied add-sqr-sqrt31.7

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

  9. Applied prod-diff31.7

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

  10. Applied distribute-lft-in31.7

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

  11. Simplified0.4

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

  12. Simplified0.4

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

  14. Applied add-cube-cbrt0.4

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

  15. Applied add-cube-cbrt0.4

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

  16. Applied times-frac0.4

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

  17. Applied add-sqr-sqrt32.4

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

  18. Applied prod-diff32.4

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

  19. Applied distribute-lft-in32.4

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

  20. Applied exp-sum32.4

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

  21. Applied log-prod32.4

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

  22. Simplified0.4

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

  23. Simplified0.4

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

  24. Final simplification0.4

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

Reproduce

herbie shell --seed 2020113 +o rules:numerics
(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))))))