3.9.2 real part (p56)

Average Error: 61.9 → 0

Time: 21.3s

Precision: 64

Math

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

↓

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

C

double f() {
        double r2127715 = 1.0;
        double r2127716 = -r2127715;
        double r2127717 = 2.0;
        double r2127718 = r2127716 / r2127717;
        double r2127719 = 3.0;
        double r2127720 = sqrt(r2127719);
        double r2127721 = r2127720 / r2127717;
        double r2127722 = /* ERROR: no complex support in C */;
        double r2127723 = r2127722 * r2127722;
        double r2127724 = r2127723 * r2127722;
        double r2127725 = r2127724 * r2127722;
        double r2127726 = -r2127717;
        double r2127727 = 0.0;
        double r2127728 = /* ERROR: no complex support in C */;
        double r2127729 = r2127728 * r2127722;
        double r2127730 = r2127729 * r2127722;
        double r2127731 = r2127730 * r2127722;
        double r2127732 = r2127725 + r2127731;
        double r2127733 = 5.0;
        double r2127734 = /* ERROR: no complex support in C */;
        double r2127735 = r2127734 * r2127722;
        double r2127736 = r2127735 * r2127722;
        double r2127737 = r2127732 + r2127736;
        double r2127738 = 4.0;
        double r2127739 = /* ERROR: no complex support in C */;
        double r2127740 = r2127739 * r2127722;
        double r2127741 = r2127737 + r2127740;
        double r2127742 = 7.0;
        double r2127743 = /* ERROR: no complex support in C */;
        double r2127744 = r2127741 + r2127743;
        double r2127745 = /* ERROR: no complex support in C */;
        return r2127745;
}

↓

double f() {
        double r2127746 = 7.0;
        double r2127747 = 0.0;
        double r2127748 = /* ERROR: no complex support in C */;
        double r2127749 = 4.0;
        double r2127750 = /* ERROR: no complex support in C */;
        double r2127751 = 1.0;
        double r2127752 = 2.0;
        double r2127753 = r2127751 / r2127752;
        double r2127754 = -r2127753;
        double r2127755 = 3.0;
        double r2127756 = sqrt(r2127755);
        double r2127757 = r2127756 / r2127752;
        double r2127758 = /* ERROR: no complex support in C */;
        double r2127759 = 5.0;
        double r2127760 = /* ERROR: no complex support in C */;
        double r2127761 = r2127753 + r2127752;
        double r2127762 = r2127761 * r2127753;
        double r2127763 = r2127747 + r2127757;
        double r2127764 = r2127757 * r2127763;
        double r2127765 = r2127762 - r2127764;
        double r2127766 = -r2127757;
        double r2127767 = r2127766 * r2127761;
        double r2127768 = r2127763 * r2127754;
        double r2127769 = r2127767 + r2127768;
        double r2127770 = /* ERROR: no complex support in C */;
        double r2127771 = r2127760 + r2127770;
        double r2127772 = r2127758 * r2127771;
        double r2127773 = r2127750 + r2127772;
        double r2127774 = r2127773 * r2127758;
        double r2127775 = r2127748 + r2127774;
        double r2127776 = /* ERROR: no complex support in C */;
        return r2127776;
}

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. Simplified 0

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019169 
(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))))