Average Error: 61.9 → 0
Time: 15.8s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]
↓
\[\Re(\left(\left(\left(\left(4 + 0.0 i\right) + \left(\left(\left(5 + 0.0 i\right) + \left(\left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(-\left(\frac{1}{2} + 2\right)\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right)\right)\right) \cdot \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right)\right)\right) \cdot \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0.0 i\right)\right))\]
\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(\left(\left(4 + 0.0 i\right) + \left(\left(\left(5 + 0.0 i\right) + \left(\left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(-\left(\frac{1}{2} + 2\right)\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right)\right)\right) \cdot \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right)\right)\right) \cdot \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0.0 i\right)\right))
double f() {
        double r26700 = 1.0;
        double r26701 = -r26700;
        double r26702 = 2.0;
        double r26703 = r26701 / r26702;
        double r26704 = 3.0;
        double r26705 = sqrt(r26704);
        double r26706 = r26705 / r26702;
        double r26707 = /* ERROR: no complex support in C */;
        double r26708 = r26707 * r26707;
        double r26709 = r26708 * r26707;
        double r26710 = r26709 * r26707;
        double r26711 = -r26702;
        double r26712 = 0.0;
        double r26713 = /* ERROR: no complex support in C */;
        double r26714 = r26713 * r26707;
        double r26715 = r26714 * r26707;
        double r26716 = r26715 * r26707;
        double r26717 = r26710 + r26716;
        double r26718 = 5.0;
        double r26719 = /* ERROR: no complex support in C */;
        double r26720 = r26719 * r26707;
        double r26721 = r26720 * r26707;
        double r26722 = r26717 + r26721;
        double r26723 = 4.0;
        double r26724 = /* ERROR: no complex support in C */;
        double r26725 = r26724 * r26707;
        double r26726 = r26722 + r26725;
        double r26727 = 7.0;
        double r26728 = /* ERROR: no complex support in C */;
        double r26729 = r26726 + r26728;
        double r26730 = /* ERROR: no complex support in C */;
        return r26730;
}
↓
double f() {
        double r26731 = 4.0;
        double r26732 = 0.0;
        double r26733 = /* ERROR: no complex support in C */;
        double r26734 = 5.0;
        double r26735 = /* ERROR: no complex support in C */;
        double r26736 = 1.0;
        double r26737 = 2.0;
        double r26738 = r26736 / r26737;
        double r26739 = -r26738;
        double r26740 = 3.0;
        double r26741 = sqrt(r26740);
        double r26742 = r26741 / r26737;
        double r26743 = /* ERROR: no complex support in C */;
        double r26744 = r26738 + r26737;
        double r26745 = -r26744;
        double r26746 = r26742 + r26732;
        double r26747 = /* ERROR: no complex support in C */;
        double r26748 = r26743 * r26747;
        double r26749 = r26735 + r26748;
        double r26750 = r26749 * r26743;
        double r26751 = r26733 + r26750;
        double r26752 = r26751 * r26743;
        double r26753 = 7.0;
        double r26754 = /* ERROR: no complex support in C */;
        double r26755 = r26752 + r26754;
        double r26756 = /* ERROR: no complex support in C */;
        return r26756;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019196 
(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))))