Average Error: 61.9 → 0
Time: 26.9s
Precision: 64
Internal Precision: 1088
\[\Re(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) + \left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(\left(7 + 0 i\right) + \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\left(-5\right) \cdot \frac{1}{2} + 4\right) + \frac{\sqrt{3}}{2} \cdot 5 i\right)\right) + \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\left(\left(-2\right) + 0 i\right) + \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\left(\frac{1}{2} \cdot \frac{1}{2} - \frac{\frac{3}{2}}{2}\right) + \frac{-1}{2 \cdot 2} \cdot \left(\sqrt{3} + \sqrt{3}\right) i\right)\right)\right))\]

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. Applied simplify61.9

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

  4. Applied complex-mul-def61.9

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

  5. Applied simplify0

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

  6. Applied simplify0

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

Runtime

Time bar (total: 26.9s)Debug logProfile

herbie shell --seed '#(1072840222 1305617769 1692503039 1353360431 4178980589 1488672652)' +o rules:numerics
(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))))