3.9.2 imaginary part (p56)

Average Error: 0 → 0

Time: 20.0s

Precision: 64

Math

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

↓

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

C

double f() {
        double r670855 = 1.0;
        double r670856 = -r670855;
        double r670857 = 2.0;
        double r670858 = r670856 / r670857;
        double r670859 = 3.0;
        double r670860 = sqrt(r670859);
        double r670861 = r670860 / r670857;
        double r670862 = /* ERROR: no complex support in C */;
        double r670863 = r670862 * r670862;
        double r670864 = r670863 * r670862;
        double r670865 = r670864 * r670862;
        double r670866 = -r670857;
        double r670867 = 0.0;
        double r670868 = /* ERROR: no complex support in C */;
        double r670869 = r670868 * r670862;
        double r670870 = r670869 * r670862;
        double r670871 = r670870 * r670862;
        double r670872 = r670865 + r670871;
        double r670873 = 5.0;
        double r670874 = /* ERROR: no complex support in C */;
        double r670875 = r670874 * r670862;
        double r670876 = r670875 * r670862;
        double r670877 = r670872 + r670876;
        double r670878 = 4.0;
        double r670879 = /* ERROR: no complex support in C */;
        double r670880 = r670879 * r670862;
        double r670881 = r670877 + r670880;
        double r670882 = 7.0;
        double r670883 = /* ERROR: no complex support in C */;
        double r670884 = r670881 + r670883;
        double r670885 = /* ERROR: no complex support in C */;
        return r670885;
}

↓

double f() {
        double r670886 = 5.0;
        double r670887 = 3.0;
        double r670888 = sqrt(r670887);
        double r670889 = 2.0;
        double r670890 = r670888 / r670889;
        double r670891 = 4.0;
        double r670892 = r670890 * r670891;
        double r670893 = /* ERROR: no complex support in C */;
        double r670894 = r670890 * r670890;
        double r670895 = -r670894;
        double r670896 = 0.25;
        double r670897 = r670895 + r670896;
        double r670898 = -r670888;
        double r670899 = r670898 / r670889;
        double r670900 = /* ERROR: no complex support in C */;
        double r670901 = 6.0;
        double r670902 = -1.0;
        double r670903 = r670888 / r670902;
        double r670904 = /* ERROR: no complex support in C */;
        double r670905 = r670900 + r670904;
        double r670906 = r670905 * r670900;
        double r670907 = r670893 + r670906;
        double r670908 = /* ERROR: no complex support in C */;
        return r670908;
}

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

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019153 
(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))))