Error

Derivation

1. Initial program 61.9

   \[\Re(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) + \left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))\]
2. Using strategy rm

3. Applied complex-mul-def61.9

   \[\leadsto \Re(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) + \left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \color{blue}{\left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) + \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) i\right)} \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))\]

4. Applied complex-mul-def61.9

   \[\leadsto \Re(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) + \left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \color{blue}{\left(\left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) i\right)}\right) + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))\]

5. Applied complex-mul-def61.9

   \[\leadsto \Re(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) + \left(\color{blue}{\left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) + \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) i\right)} \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) i\right)\right) + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))\]

6. Applied complex-mul-def61.9

   \[\leadsto \Re(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) + \color{blue}{\left(\left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) i\right)} \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) i\right)\right) + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))\]

7. Applied complex-mul-def61.9

   \[\leadsto \Re(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) + \color{blue}{\left(\left(\left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(\left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) i\right)}\right) + \left(\left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) i\right)\right) + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))\]

8. Applied complex-mul-def61.9

   \[\leadsto \Re(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\frac{-1}{2} \cdot \frac{-1}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(\frac{-1}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \cdot \frac{-1}{2}\right) i\right)} \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) + \left(\left(\left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(\left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) i\right)\right) + \left(\left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) i\right)\right) + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))\]

9. Applied complex-mul-def61.9

   \[\leadsto \Re(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\frac{-1}{2} \cdot \frac{-1}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\frac{-1}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(\left(\frac{-1}{2} \cdot \frac{-1}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\frac{-1}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) i\right)} \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) + \left(\left(\left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(\left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) i\right)\right) + \left(\left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) i\right)\right) + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))\]

10. Applied complex-mul-def61.9

    \[\leadsto \Re(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\frac{-1}{2} \cdot \frac{-1}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\frac{-1}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(\frac{-1}{2} \cdot \frac{-1}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\frac{-1}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(\left(\left(\frac{-1}{2} \cdot \frac{-1}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\frac{-1}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(\frac{-1}{2} \cdot \frac{-1}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\frac{-1}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) i\right)} + \left(\left(\left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(\left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) i\right)\right) + \left(\left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) i\right)\right) + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))\]

11. Applied complex-add-def61.9

    \[\leadsto \Re(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(\frac{-1}{2} \cdot \frac{-1}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\frac{-1}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(\frac{-1}{2} \cdot \frac{-1}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\frac{-1}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(\left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right)\right) + \left(\left(\left(\left(\frac{-1}{2} \cdot \frac{-1}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\frac{-1}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(\frac{-1}{2} \cdot \frac{-1}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\frac{-1}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) + \left(\left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right)\right) i\right)} + \left(\left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) i\right)\right) + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))\]

12. Applied complex-add-def61.9

    \[\leadsto \Re(\left(\left(\color{blue}{\left(\left(\left(\left(\left(\left(\frac{-1}{2} \cdot \frac{-1}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\frac{-1}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(\frac{-1}{2} \cdot \frac{-1}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\frac{-1}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(\left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right)\right) + \left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right)\right) + \left(\left(\left(\left(\left(\frac{-1}{2} \cdot \frac{-1}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\frac{-1}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(\frac{-1}{2} \cdot \frac{-1}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\frac{-1}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) + \left(\left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right)\right) + \left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right)\right) i\right)} + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))\]

13. Applied simplify0

    \[\leadsto \Re(\left(\left(\left(\color{blue}{\left(\left(\left(\frac{-1}{2} - \frac{3}{8}\right) - \left(\frac{1}{2} \cdot \sqrt{3}\right) \cdot \left(\left(\frac{1}{4} - \frac{3}{4}\right) \cdot \left(\frac{1}{2} \cdot \sqrt{3}\right)\right)\right) + \left(\left(\left(\left(\frac{-3}{4} + \frac{-3}{4}\right) + \left(\frac{1}{4} - \frac{3}{4}\right)\right) + \frac{5}{4}\right) - \left(\frac{5}{2} \cdot \sqrt{3}\right) \cdot \left(\frac{1}{2} \cdot \sqrt{3}\right)\right)\right)} + \left(\left(\left(\left(\left(\frac{-1}{2} \cdot \frac{-1}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\frac{-1}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(\frac{-1}{2} \cdot \frac{-1}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\frac{-1}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) + \left(\left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{-1}{2} - \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(\left(-2\right) \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(\left(-2\right) \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right)\right) + \left(\left(5 \cdot \frac{-1}{2} - 0 \cdot \frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2} + \left(5 \cdot \frac{\sqrt{3}}{2} + 0 \cdot \frac{-1}{2}\right) \cdot \frac{-1}{2}\right)\right) i\right) + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))\]

14. Applied simplify0

    \[\leadsto \Re(\left(\left(\left(\left(\left(\left(\frac{-1}{2} - \frac{3}{8}\right) - \left(\frac{1}{2} \cdot \sqrt{3}\right) \cdot \left(\left(\frac{1}{4} - \frac{3}{4}\right) \cdot \left(\frac{1}{2} \cdot \sqrt{3}\right)\right)\right) + \left(\left(\left(\left(\frac{-3}{4} + \frac{-3}{4}\right) + \left(\frac{1}{4} - \frac{3}{4}\right)\right) + \frac{5}{4}\right) - \left(\frac{5}{2} \cdot \sqrt{3}\right) \cdot \left(\frac{1}{2} \cdot \sqrt{3}\right)\right)\right) + \color{blue}{\left(\left(\left(\frac{\sqrt{3}}{-2} + \frac{\sqrt{3}}{-4}\right) + \left(\left(\frac{1}{2} \cdot \sqrt{3}\right) \cdot \sqrt{3}\right) \cdot \left(\frac{1}{2} \cdot \sqrt{3}\right)\right) + \left(\left(\frac{\frac{\sqrt{3}}{-4}}{2} + \frac{1}{4} \cdot \left(\frac{1}{2} \cdot \sqrt{3}\right)\right) + \left(\frac{-5}{4} \cdot \sqrt{3} + \left(\frac{-5}{4} \cdot \sqrt{3} + \frac{1}{2} \cdot \sqrt{3}\right)\right)\right)\right)} i\right) + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))\]

Runtime

Time bar (total: 54.0s)Debug logProfile

herbie shell --seed '#(1070991898 1055468627 4280279443 640792587 928206309 3646738750)' 
(FPCore ()
  :name "3.9.2 real part (p56)"
  (re (+ (+ (+ (+ (* (* (* (complex (/ (- 1) 2) (/ (sqrt 3) 2)) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (* (* (* (complex (- 2) 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (* (* (complex 5 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (* (complex 4 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (complex 7 0))))