Error

Derivation

1. Initial program 61.9

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

2. Initial simplification61.9

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

4. Applied complex-mul-def61.9

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

5. Simplified0

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

6. Simplified0

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

7. Final simplification0

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

Runtime

Time bar (total: 25.6s)Debug logProfile

herbie shell --seed 2018230 +o rules:numerics
(FPCore ()
  :name "3.9.2 real part (p56)"
  (re (+.c (+.c (+.c (+.c (*.c (*.c (*.c (complex (/ (- 1) 2) (/ (sqrt 3) 2)) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (*.c (*.c (*.c (complex (- 2) 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (*.c (*.c (complex 5 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (*.c (complex 4 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (complex 7 0))))