Average Error: 61.9 → 0
Time: 21.9s
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 r2148732 = 1.0;
        double r2148733 = -r2148732;
        double r2148734 = 2.0;
        double r2148735 = r2148733 / r2148734;
        double r2148736 = 3.0;
        double r2148737 = sqrt(r2148736);
        double r2148738 = r2148737 / r2148734;
        double r2148739 = /* ERROR: no complex support in C */;
        double r2148740 = r2148739 * r2148739;
        double r2148741 = r2148740 * r2148739;
        double r2148742 = r2148741 * r2148739;
        double r2148743 = -r2148734;
        double r2148744 = 0.0;
        double r2148745 = /* ERROR: no complex support in C */;
        double r2148746 = r2148745 * r2148739;
        double r2148747 = r2148746 * r2148739;
        double r2148748 = r2148747 * r2148739;
        double r2148749 = r2148742 + r2148748;
        double r2148750 = 5.0;
        double r2148751 = /* ERROR: no complex support in C */;
        double r2148752 = r2148751 * r2148739;
        double r2148753 = r2148752 * r2148739;
        double r2148754 = r2148749 + r2148753;
        double r2148755 = 4.0;
        double r2148756 = /* ERROR: no complex support in C */;
        double r2148757 = r2148756 * r2148739;
        double r2148758 = r2148754 + r2148757;
        double r2148759 = 7.0;
        double r2148760 = /* ERROR: no complex support in C */;
        double r2148761 = r2148758 + r2148760;
        double r2148762 = /* ERROR: no complex support in C */;
        return r2148762;
}
↓
double f() {
        double r2148763 = 7.0;
        double r2148764 = 0.0;
        double r2148765 = /* ERROR: no complex support in C */;
        double r2148766 = 4.0;
        double r2148767 = /* ERROR: no complex support in C */;
        double r2148768 = 1.0;
        double r2148769 = 2.0;
        double r2148770 = r2148768 / r2148769;
        double r2148771 = -r2148770;
        double r2148772 = 3.0;
        double r2148773 = sqrt(r2148772);
        double r2148774 = r2148773 / r2148769;
        double r2148775 = /* ERROR: no complex support in C */;
        double r2148776 = 5.0;
        double r2148777 = /* ERROR: no complex support in C */;
        double r2148778 = r2148770 + r2148769;
        double r2148779 = r2148778 * r2148770;
        double r2148780 = r2148764 + r2148774;
        double r2148781 = r2148774 * r2148780;
        double r2148782 = r2148779 - r2148781;
        double r2148783 = -r2148774;
        double r2148784 = r2148783 * r2148778;
        double r2148785 = r2148780 * r2148771;
        double r2148786 = r2148784 + r2148785;
        double r2148787 = /* ERROR: no complex support in C */;
        double r2148788 = r2148777 + r2148787;
        double r2148789 = r2148775 * r2148788;
        double r2148790 = r2148767 + r2148789;
        double r2148791 = r2148790 * r2148775;
        double r2148792 = r2148765 + r2148791;
        double r2148793 = /* ERROR: no complex support in C */;
        return r2148793;
}

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 2019172 
(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))))