Average Error: 61.9 → 0
Time: 21.2s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(\frac{5}{2} + \left(\left(\frac{\sqrt{3}}{\frac{-4}{5}} + \sqrt{3} \cdot 2\right) + \frac{\sqrt{3}}{\frac{-4}{5}}\right) i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) + \left(-2 + \left(\frac{\sqrt{3}}{2} + \frac{-\sqrt{3}}{2}\right) i\right)\right)\right))\]
\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(\frac{5}{2} + \left(\left(\frac{\sqrt{3}}{\frac{-4}{5}} + \sqrt{3} \cdot 2\right) + \frac{\sqrt{3}}{\frac{-4}{5}}\right) i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) + \left(-2 + \left(\frac{\sqrt{3}}{2} + \frac{-\sqrt{3}}{2}\right) i\right)\right)\right))
double f() {
        double r941842 = 1.0;
        double r941843 = -r941842;
        double r941844 = 2.0;
        double r941845 = r941843 / r941844;
        double r941846 = 3.0;
        double r941847 = sqrt(r941846);
        double r941848 = r941847 / r941844;
        double r941849 = /* ERROR: no complex support in C */;
        double r941850 = r941849 * r941849;
        double r941851 = r941850 * r941849;
        double r941852 = r941851 * r941849;
        double r941853 = -r941844;
        double r941854 = 0.0;
        double r941855 = /* ERROR: no complex support in C */;
        double r941856 = r941855 * r941849;
        double r941857 = r941856 * r941849;
        double r941858 = r941857 * r941849;
        double r941859 = r941852 + r941858;
        double r941860 = 5.0;
        double r941861 = /* ERROR: no complex support in C */;
        double r941862 = r941861 * r941849;
        double r941863 = r941862 * r941849;
        double r941864 = r941859 + r941863;
        double r941865 = 4.0;
        double r941866 = /* ERROR: no complex support in C */;
        double r941867 = r941866 * r941849;
        double r941868 = r941864 + r941867;
        double r941869 = 7.0;
        double r941870 = /* ERROR: no complex support in C */;
        double r941871 = r941868 + r941870;
        double r941872 = /* ERROR: no complex support in C */;
        return r941872;
}
↓
double f() {
        double r941873 = 2.5;
        double r941874 = 3.0;
        double r941875 = sqrt(r941874);
        double r941876 = -0.8;
        double r941877 = r941875 / r941876;
        double r941878 = 2.0;
        double r941879 = r941875 * r941878;
        double r941880 = r941877 + r941879;
        double r941881 = r941880 + r941877;
        double r941882 = /* ERROR: no complex support in C */;
        double r941883 = -0.5;
        double r941884 = r941875 / r941878;
        double r941885 = /* ERROR: no complex support in C */;
        double r941886 = -2.0;
        double r941887 = -r941875;
        double r941888 = r941887 / r941878;
        double r941889 = r941884 + r941888;
        double r941890 = /* ERROR: no complex support in C */;
        double r941891 = r941885 + r941890;
        double r941892 = r941882 + r941891;
        double r941893 = /* ERROR: no complex support in C */;
        return r941893;
}

Error

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. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019135 
(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))))