3.9.2 imaginary part (p56)

Average Error: 0 → 0

Time: 29.8s

Precision: 64

Math

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

↓

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

C

double f() {
        double r1022781 = 1.0;
        double r1022782 = -r1022781;
        double r1022783 = 2.0;
        double r1022784 = r1022782 / r1022783;
        double r1022785 = 3.0;
        double r1022786 = sqrt(r1022785);
        double r1022787 = r1022786 / r1022783;
        double r1022788 = /* ERROR: no complex support in C */;
        double r1022789 = r1022788 * r1022788;
        double r1022790 = r1022789 * r1022788;
        double r1022791 = r1022790 * r1022788;
        double r1022792 = -r1022783;
        double r1022793 = 0.0;
        double r1022794 = /* ERROR: no complex support in C */;
        double r1022795 = r1022794 * r1022788;
        double r1022796 = r1022795 * r1022788;
        double r1022797 = r1022796 * r1022788;
        double r1022798 = r1022791 + r1022797;
        double r1022799 = 5.0;
        double r1022800 = /* ERROR: no complex support in C */;
        double r1022801 = r1022800 * r1022788;
        double r1022802 = r1022801 * r1022788;
        double r1022803 = r1022798 + r1022802;
        double r1022804 = 4.0;
        double r1022805 = /* ERROR: no complex support in C */;
        double r1022806 = r1022805 * r1022788;
        double r1022807 = r1022803 + r1022806;
        double r1022808 = 7.0;
        double r1022809 = /* ERROR: no complex support in C */;
        double r1022810 = r1022807 + r1022809;
        double r1022811 = /* ERROR: no complex support in C */;
        return r1022811;
}

↓

double f() {
        double r1022812 = -5.0;
        double r1022813 = 3.0;
        double r1022814 = sqrt(r1022813);
        double r1022815 = -r1022814;
        double r1022816 = -4.0;
        double r1022817 = r1022815 / r1022816;
        double r1022818 = r1022817 + r1022817;
        double r1022819 = r1022814 / r1022816;
        double r1022820 = r1022819 + r1022819;
        double r1022821 = 10.0;
        double r1022822 = r1022821 * r1022819;
        double r1022823 = 2.0;
        double r1022824 = r1022814 / r1022823;
        double r1022825 = r1022822 + r1022824;
        double r1022826 = r1022820 + r1022825;
        double r1022827 = r1022818 + r1022826;
        double r1022828 = /* ERROR: no complex support in C */;
        double r1022829 = 5.0;
        double r1022830 = r1022814 * r1022823;
        double r1022831 = /* ERROR: no complex support in C */;
        double r1022832 = r1022828 + r1022831;
        double r1022833 = /* ERROR: no complex support in C */;
        return r1022833;
}

Derivation

1. Initial program 0

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

2. Simplified 0

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019133 
(FPCore ()
  :name "3.9.2 imaginary part (p56)"
  (im (+.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))))