3.9.2 real part (p56)

Average Error: 61.9 → 0

Time: 20.4s

Precision: 64

Math

\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]

↓

\[\Re(\left(\left(5 + \frac{4}{\frac{2}{\sqrt{3}}} i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(-\frac{\sqrt{3}}{2}\right) i\right) \cdot \left(\left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(-\frac{\sqrt{3}}{2}\right) i\right) + \left(6 + \frac{\sqrt{3}}{2} \cdot -2 i\right)\right)\right))\]

C

double f() {
        double r637730 = 1.0;
        double r637731 = -r637730;
        double r637732 = 2.0;
        double r637733 = r637731 / r637732;
        double r637734 = 3.0;
        double r637735 = sqrt(r637734);
        double r637736 = r637735 / r637732;
        double r637737 = /* ERROR: no complex support in C */;
        double r637738 = r637737 * r637737;
        double r637739 = r637738 * r637737;
        double r637740 = r637739 * r637737;
        double r637741 = -r637732;
        double r637742 = 0.0;
        double r637743 = /* ERROR: no complex support in C */;
        double r637744 = r637743 * r637737;
        double r637745 = r637744 * r637737;
        double r637746 = r637745 * r637737;
        double r637747 = r637740 + r637746;
        double r637748 = 5.0;
        double r637749 = /* ERROR: no complex support in C */;
        double r637750 = r637749 * r637737;
        double r637751 = r637750 * r637737;
        double r637752 = r637747 + r637751;
        double r637753 = 4.0;
        double r637754 = /* ERROR: no complex support in C */;
        double r637755 = r637754 * r637737;
        double r637756 = r637752 + r637755;
        double r637757 = 7.0;
        double r637758 = /* ERROR: no complex support in C */;
        double r637759 = r637756 + r637758;
        double r637760 = /* ERROR: no complex support in C */;
        return r637760;
}

↓

double f() {
        double r637761 = 5.0;
        double r637762 = 4.0;
        double r637763 = 2.0;
        double r637764 = 3.0;
        double r637765 = sqrt(r637764);
        double r637766 = r637763 / r637765;
        double r637767 = r637762 / r637766;
        double r637768 = /* ERROR: no complex support in C */;
        double r637769 = 0.25;
        double r637770 = r637765 / r637763;
        double r637771 = r637770 * r637770;
        double r637772 = r637769 - r637771;
        double r637773 = -r637770;
        double r637774 = /* ERROR: no complex support in C */;
        double r637775 = 6.0;
        double r637776 = -2.0;
        double r637777 = r637770 * r637776;
        double r637778 = /* ERROR: no complex support in C */;
        double r637779 = r637774 + r637778;
        double r637780 = r637774 * r637779;
        double r637781 = r637768 + r637780;
        double r637782 = /* ERROR: no complex support in C */;
        return r637782;
}

Derivation

1. Initial program 61.9

   \[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]

2. Simplified 0

   \[\leadsto \color{blue}{\Re(\left(\left(5 + \frac{4}{\frac{2}{\sqrt{3}}} i\right) + \left(\left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{\sqrt{3}}{2} \cdot -1 i\right) \cdot \left(\left(6 + \frac{\sqrt{3}}{2} \cdot -2 i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{\sqrt{3}}{2} \cdot -1 i\right)\right)\right)\right))}\]

3. Final simplification 0

   \[\leadsto \Re(\left(\left(5 + \frac{4}{\frac{2}{\sqrt{3}}} i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(-\frac{\sqrt{3}}{2}\right) i\right) \cdot \left(\left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(-\frac{\sqrt{3}}{2}\right) i\right) + \left(6 + \frac{\sqrt{3}}{2} \cdot -2 i\right)\right)\right))\]

Reproduce

herbie shell --seed 2019128 
(FPCore ()
  :name "3.9.2 real part (p56)"
  (re (+.c (+.c (+.c (+.c (*.c (*.c (*.c (complex (/ (- 1) 2) (/ (sqrt 3) 2)) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (*.c (*.c (*.c (complex (- 2) 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (*.c (*.c (complex 5 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (*.c (complex 4 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (complex 7 0))))