3.9.2 real part (p56)

Average Error: 61.9 → 0

Time: 29.5s

Precision: 64

Math

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

↓

\[\Re(\left(\left(-5 + \left(\left(\frac{-\sqrt{3}}{-4} + \frac{-\sqrt{3}}{-4}\right) + \left(\left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) + \left(10 \cdot \frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{2}\right)\right)\right) i\right) + \left(5 + \sqrt{3} \cdot 2 i\right)\right))\]

C

double f() {
        double r1182820 = 1.0;
        double r1182821 = -r1182820;
        double r1182822 = 2.0;
        double r1182823 = r1182821 / r1182822;
        double r1182824 = 3.0;
        double r1182825 = sqrt(r1182824);
        double r1182826 = r1182825 / r1182822;
        double r1182827 = /* ERROR: no complex support in C */;
        double r1182828 = r1182827 * r1182827;
        double r1182829 = r1182828 * r1182827;
        double r1182830 = r1182829 * r1182827;
        double r1182831 = -r1182822;
        double r1182832 = 0.0;
        double r1182833 = /* ERROR: no complex support in C */;
        double r1182834 = r1182833 * r1182827;
        double r1182835 = r1182834 * r1182827;
        double r1182836 = r1182835 * r1182827;
        double r1182837 = r1182830 + r1182836;
        double r1182838 = 5.0;
        double r1182839 = /* ERROR: no complex support in C */;
        double r1182840 = r1182839 * r1182827;
        double r1182841 = r1182840 * r1182827;
        double r1182842 = r1182837 + r1182841;
        double r1182843 = 4.0;
        double r1182844 = /* ERROR: no complex support in C */;
        double r1182845 = r1182844 * r1182827;
        double r1182846 = r1182842 + r1182845;
        double r1182847 = 7.0;
        double r1182848 = /* ERROR: no complex support in C */;
        double r1182849 = r1182846 + r1182848;
        double r1182850 = /* ERROR: no complex support in C */;
        return r1182850;
}

↓

double f() {
        double r1182851 = -5.0;
        double r1182852 = 3.0;
        double r1182853 = sqrt(r1182852);
        double r1182854 = -r1182853;
        double r1182855 = -4.0;
        double r1182856 = r1182854 / r1182855;
        double r1182857 = r1182856 + r1182856;
        double r1182858 = r1182853 / r1182855;
        double r1182859 = r1182858 + r1182858;
        double r1182860 = 10.0;
        double r1182861 = r1182860 * r1182858;
        double r1182862 = 2.0;
        double r1182863 = r1182853 / r1182862;
        double r1182864 = r1182861 + r1182863;
        double r1182865 = r1182859 + r1182864;
        double r1182866 = r1182857 + r1182865;
        double r1182867 = /* ERROR: no complex support in C */;
        double r1182868 = 5.0;
        double r1182869 = r1182853 * r1182862;
        double r1182870 = /* ERROR: no complex support in C */;
        double r1182871 = r1182867 + r1182870;
        double r1182872 = /* ERROR: no complex support in C */;
        return r1182872;
}

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

   \[\leadsto \color{blue}{\Re(\left(\left(5 + 2 \cdot \sqrt{3} i\right) + \left(-5 + \left(\left(\left(-\frac{\sqrt{3}}{-4}\right) + \left(-\frac{\sqrt{3}}{-4}\right)\right) + \left(\left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) + \left(\frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{-4} \cdot 10\right)\right)\right) i\right)\right))}\]

3. Final simplification 0

   \[\leadsto \Re(\left(\left(-5 + \left(\left(\frac{-\sqrt{3}}{-4} + \frac{-\sqrt{3}}{-4}\right) + \left(\left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) + \left(10 \cdot \frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{2}\right)\right)\right) i\right) + \left(5 + \sqrt{3} \cdot 2 i\right)\right))\]

Reproduce

herbie shell --seed 2019132 
(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))))