3.9.2 real part (p56)

Average Error: 61.9 → 0

Time: 26.1s

Precision: 64

Math

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

↓

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

C

double f() {
        double r2047723 = 1.0;
        double r2047724 = -r2047723;
        double r2047725 = 2.0;
        double r2047726 = r2047724 / r2047725;
        double r2047727 = 3.0;
        double r2047728 = sqrt(r2047727);
        double r2047729 = r2047728 / r2047725;
        double r2047730 = /* ERROR: no complex support in C */;
        double r2047731 = r2047730 * r2047730;
        double r2047732 = r2047731 * r2047730;
        double r2047733 = r2047732 * r2047730;
        double r2047734 = -r2047725;
        double r2047735 = 0.0;
        double r2047736 = /* ERROR: no complex support in C */;
        double r2047737 = r2047736 * r2047730;
        double r2047738 = r2047737 * r2047730;
        double r2047739 = r2047738 * r2047730;
        double r2047740 = r2047733 + r2047739;
        double r2047741 = 5.0;
        double r2047742 = /* ERROR: no complex support in C */;
        double r2047743 = r2047742 * r2047730;
        double r2047744 = r2047743 * r2047730;
        double r2047745 = r2047740 + r2047744;
        double r2047746 = 4.0;
        double r2047747 = /* ERROR: no complex support in C */;
        double r2047748 = r2047747 * r2047730;
        double r2047749 = r2047745 + r2047748;
        double r2047750 = 7.0;
        double r2047751 = /* ERROR: no complex support in C */;
        double r2047752 = r2047749 + r2047751;
        double r2047753 = /* ERROR: no complex support in C */;
        return r2047753;
}

↓

double f() {
        double r2047754 = 7.0;
        double r2047755 = 0.0;
        double r2047756 = /* ERROR: no complex support in C */;
        double r2047757 = 4.0;
        double r2047758 = /* ERROR: no complex support in C */;
        double r2047759 = 1.0;
        double r2047760 = -r2047759;
        double r2047761 = 2.0;
        double r2047762 = r2047760 / r2047761;
        double r2047763 = 3.0;
        double r2047764 = sqrt(r2047763);
        double r2047765 = r2047764 / r2047761;
        double r2047766 = /* ERROR: no complex support in C */;
        double r2047767 = r2047759 / r2047761;
        double r2047768 = r2047767 + r2047761;
        double r2047769 = r2047767 * r2047768;
        double r2047770 = r2047765 + r2047755;
        double r2047771 = r2047765 * r2047770;
        double r2047772 = r2047769 - r2047771;
        double r2047773 = r2047770 * r2047762;
        double r2047774 = -r2047768;
        double r2047775 = r2047765 * r2047774;
        double r2047776 = r2047773 + r2047775;
        double r2047777 = /* ERROR: no complex support in C */;
        double r2047778 = 5.0;
        double r2047779 = /* ERROR: no complex support in C */;
        double r2047780 = r2047777 + r2047779;
        double r2047781 = r2047766 * r2047780;
        double r2047782 = r2047758 + r2047781;
        double r2047783 = r2047782 * r2047766;
        double r2047784 = r2047756 + r2047783;
        double r2047785 = /* ERROR: no complex support in C */;
        return r2047785;
}

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

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(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))))