Average Error: 61.9 → 0
Time: 22.0s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]
↓
\[\Re(\left(\left(7 + 0.0 i\right) + \left(\left(\left(4 + 0.0 i\right) + \left(\left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\left(\frac{1}{2} + 2\right) \cdot \frac{1}{2} - \frac{\sqrt{3}}{2} \cdot \left(0.0 + \frac{\sqrt{3}}{2}\right)\right) + \left(\left(-\frac{\sqrt{3}}{2}\right) \cdot \left(\frac{1}{2} + 2\right) + \left(0.0 + \frac{\sqrt{3}}{2}\right) \cdot \left(-\frac{1}{2}\right)\right) i\right)\right)\right)\right) \cdot \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right)\right)\right))\]
\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) + 0.0 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 + 0.0 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 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))
↓
\Re(\left(\left(7 + 0.0 i\right) + \left(\left(\left(4 + 0.0 i\right) + \left(\left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\left(\frac{1}{2} + 2\right) \cdot \frac{1}{2} - \frac{\sqrt{3}}{2} \cdot \left(0.0 + \frac{\sqrt{3}}{2}\right)\right) + \left(\left(-\frac{\sqrt{3}}{2}\right) \cdot \left(\frac{1}{2} + 2\right) + \left(0.0 + \frac{\sqrt{3}}{2}\right) \cdot \left(-\frac{1}{2}\right)\right) i\right)\right)\right)\right) \cdot \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right)\right)\right))
double f() {
        double r3585776 = 1.0;
        double r3585777 = -r3585776;
        double r3585778 = 2.0;
        double r3585779 = r3585777 / r3585778;
        double r3585780 = 3.0;
        double r3585781 = sqrt(r3585780);
        double r3585782 = r3585781 / r3585778;
        double r3585783 = /* ERROR: no complex support in C */;
        double r3585784 = r3585783 * r3585783;
        double r3585785 = r3585784 * r3585783;
        double r3585786 = r3585785 * r3585783;
        double r3585787 = -r3585778;
        double r3585788 = 0.0;
        double r3585789 = /* ERROR: no complex support in C */;
        double r3585790 = r3585789 * r3585783;
        double r3585791 = r3585790 * r3585783;
        double r3585792 = r3585791 * r3585783;
        double r3585793 = r3585786 + r3585792;
        double r3585794 = 5.0;
        double r3585795 = /* ERROR: no complex support in C */;
        double r3585796 = r3585795 * r3585783;
        double r3585797 = r3585796 * r3585783;
        double r3585798 = r3585793 + r3585797;
        double r3585799 = 4.0;
        double r3585800 = /* ERROR: no complex support in C */;
        double r3585801 = r3585800 * r3585783;
        double r3585802 = r3585798 + r3585801;
        double r3585803 = 7.0;
        double r3585804 = /* ERROR: no complex support in C */;
        double r3585805 = r3585802 + r3585804;
        double r3585806 = /* ERROR: no complex support in C */;
        return r3585806;
}
↓
double f() {
        double r3585807 = 7.0;
        double r3585808 = 0.0;
        double r3585809 = /* ERROR: no complex support in C */;
        double r3585810 = 4.0;
        double r3585811 = /* ERROR: no complex support in C */;
        double r3585812 = 1.0;
        double r3585813 = 2.0;
        double r3585814 = r3585812 / r3585813;
        double r3585815 = -r3585814;
        double r3585816 = 3.0;
        double r3585817 = sqrt(r3585816);
        double r3585818 = r3585817 / r3585813;
        double r3585819 = /* ERROR: no complex support in C */;
        double r3585820 = 5.0;
        double r3585821 = /* ERROR: no complex support in C */;
        double r3585822 = r3585814 + r3585813;
        double r3585823 = r3585822 * r3585814;
        double r3585824 = r3585808 + r3585818;
        double r3585825 = r3585818 * r3585824;
        double r3585826 = r3585823 - r3585825;
        double r3585827 = -r3585818;
        double r3585828 = r3585827 * r3585822;
        double r3585829 = r3585824 * r3585815;
        double r3585830 = r3585828 + r3585829;
        double r3585831 = /* ERROR: no complex support in C */;
        double r3585832 = r3585821 + r3585831;
        double r3585833 = r3585819 * r3585832;
        double r3585834 = r3585811 + r3585833;
        double r3585835 = r3585834 * r3585819;
        double r3585836 = r3585809 + r3585835;
        double r3585837 = /* ERROR: no complex support in C */;
        return r3585837;
}

Error

Derivation

  1. Initial program 61.9

    \[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]

  2. Simplified0

    \[\leadsto \color{blue}{\Re(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(4 + 0.0 i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\left(\frac{-1}{2} \cdot \left(-\left(\frac{1}{2} + 2\right)\right) - \frac{\sqrt{3}}{2} \cdot \left(\frac{\sqrt{3}}{2} + 0.0\right)\right) + \left(\frac{-1}{2} \cdot \left(\frac{\sqrt{3}}{2} + 0.0\right) + \frac{\sqrt{3}}{2} \cdot \left(-\left(\frac{1}{2} + 2\right)\right)\right) i\right) + \left(5 + 0.0 i\right)\right)\right)\right)\right) + \left(7 + 0.0 i\right)\right))}\]

  3. Final simplification0

    \[\leadsto \Re(\left(\left(7 + 0.0 i\right) + \left(\left(\left(4 + 0.0 i\right) + \left(\left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\left(\frac{1}{2} + 2\right) \cdot \frac{1}{2} - \frac{\sqrt{3}}{2} \cdot \left(0.0 + \frac{\sqrt{3}}{2}\right)\right) + \left(\left(-\frac{\sqrt{3}}{2}\right) \cdot \left(\frac{1}{2} + 2\right) + \left(0.0 + \frac{\sqrt{3}}{2}\right) \cdot \left(-\frac{1}{2}\right)\right) i\right)\right)\right)\right) \cdot \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right)\right)\right))\]

Reproduce

herbie shell --seed 2019171 
(FPCore ()
  :name "3.9.2 real part (p56)"
  (re (+ (+ (+ (+ (* (* (* (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (* (* (* (complex (- 2.0) 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (* (* (complex 5.0 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (* (complex 4.0 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (complex 7.0 0.0))))