Average Error: 61.9 → 0
Time: 22.2s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]
↓
\[\Re(\left(\left(7 + 0.0 i\right) + \left(\left(\left(4 + 0.0 i\right) + \left(\left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\left(\frac{1}{2} + 2\right) \cdot \frac{1}{2} - \frac{\sqrt{3}}{2} \cdot \left(0.0 + \frac{\sqrt{3}}{2}\right)\right) + \left(\left(-\frac{\sqrt{3}}{2}\right) \cdot \left(\frac{1}{2} + 2\right) + \left(0.0 + \frac{\sqrt{3}}{2}\right) \cdot \left(-\frac{1}{2}\right)\right) i\right)\right)\right)\right) \cdot \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right)\right)\right))\]
\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) + 0.0 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 + 0.0 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 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))
↓
\Re(\left(\left(7 + 0.0 i\right) + \left(\left(\left(4 + 0.0 i\right) + \left(\left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\left(\frac{1}{2} + 2\right) \cdot \frac{1}{2} - \frac{\sqrt{3}}{2} \cdot \left(0.0 + \frac{\sqrt{3}}{2}\right)\right) + \left(\left(-\frac{\sqrt{3}}{2}\right) \cdot \left(\frac{1}{2} + 2\right) + \left(0.0 + \frac{\sqrt{3}}{2}\right) \cdot \left(-\frac{1}{2}\right)\right) i\right)\right)\right)\right) \cdot \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right)\right)\right))
double f() {
        double r2522849 = 1.0;
        double r2522850 = -r2522849;
        double r2522851 = 2.0;
        double r2522852 = r2522850 / r2522851;
        double r2522853 = 3.0;
        double r2522854 = sqrt(r2522853);
        double r2522855 = r2522854 / r2522851;
        double r2522856 = /* ERROR: no complex support in C */;
        double r2522857 = r2522856 * r2522856;
        double r2522858 = r2522857 * r2522856;
        double r2522859 = r2522858 * r2522856;
        double r2522860 = -r2522851;
        double r2522861 = 0.0;
        double r2522862 = /* ERROR: no complex support in C */;
        double r2522863 = r2522862 * r2522856;
        double r2522864 = r2522863 * r2522856;
        double r2522865 = r2522864 * r2522856;
        double r2522866 = r2522859 + r2522865;
        double r2522867 = 5.0;
        double r2522868 = /* ERROR: no complex support in C */;
        double r2522869 = r2522868 * r2522856;
        double r2522870 = r2522869 * r2522856;
        double r2522871 = r2522866 + r2522870;
        double r2522872 = 4.0;
        double r2522873 = /* ERROR: no complex support in C */;
        double r2522874 = r2522873 * r2522856;
        double r2522875 = r2522871 + r2522874;
        double r2522876 = 7.0;
        double r2522877 = /* ERROR: no complex support in C */;
        double r2522878 = r2522875 + r2522877;
        double r2522879 = /* ERROR: no complex support in C */;
        return r2522879;
}
↓
double f() {
        double r2522880 = 7.0;
        double r2522881 = 0.0;
        double r2522882 = /* ERROR: no complex support in C */;
        double r2522883 = 4.0;
        double r2522884 = /* ERROR: no complex support in C */;
        double r2522885 = 1.0;
        double r2522886 = 2.0;
        double r2522887 = r2522885 / r2522886;
        double r2522888 = -r2522887;
        double r2522889 = 3.0;
        double r2522890 = sqrt(r2522889);
        double r2522891 = r2522890 / r2522886;
        double r2522892 = /* ERROR: no complex support in C */;
        double r2522893 = 5.0;
        double r2522894 = /* ERROR: no complex support in C */;
        double r2522895 = r2522887 + r2522886;
        double r2522896 = r2522895 * r2522887;
        double r2522897 = r2522881 + r2522891;
        double r2522898 = r2522891 * r2522897;
        double r2522899 = r2522896 - r2522898;
        double r2522900 = -r2522891;
        double r2522901 = r2522900 * r2522895;
        double r2522902 = r2522897 * r2522888;
        double r2522903 = r2522901 + r2522902;
        double r2522904 = /* ERROR: no complex support in C */;
        double r2522905 = r2522894 + r2522904;
        double r2522906 = r2522892 * r2522905;
        double r2522907 = r2522884 + r2522906;
        double r2522908 = r2522907 * r2522892;
        double r2522909 = r2522882 + r2522908;
        double r2522910 = /* ERROR: no complex support in C */;
        return r2522910;
}

Error

Derivation

  1. Initial program 61.9

    \[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]

  2. Simplified0

    \[\leadsto \color{blue}{\Re(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(4 + 0.0 i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\left(\frac{-1}{2} \cdot \left(-\left(\frac{1}{2} + 2\right)\right) - \frac{\sqrt{3}}{2} \cdot \left(\frac{\sqrt{3}}{2} + 0.0\right)\right) + \left(\frac{-1}{2} \cdot \left(\frac{\sqrt{3}}{2} + 0.0\right) + \frac{\sqrt{3}}{2} \cdot \left(-\left(\frac{1}{2} + 2\right)\right)\right) i\right) + \left(5 + 0.0 i\right)\right)\right)\right)\right) + \left(7 + 0.0 i\right)\right))}\]

  3. Final simplification0

    \[\leadsto \Re(\left(\left(7 + 0.0 i\right) + \left(\left(\left(4 + 0.0 i\right) + \left(\left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\left(\frac{1}{2} + 2\right) \cdot \frac{1}{2} - \frac{\sqrt{3}}{2} \cdot \left(0.0 + \frac{\sqrt{3}}{2}\right)\right) + \left(\left(-\frac{\sqrt{3}}{2}\right) \cdot \left(\frac{1}{2} + 2\right) + \left(0.0 + \frac{\sqrt{3}}{2}\right) \cdot \left(-\frac{1}{2}\right)\right) i\right)\right)\right)\right) \cdot \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right)\right)\right))\]

Reproduce

herbie shell --seed 2019172 
(FPCore ()
  :name "3.9.2 real part (p56)"
  (re (+ (+ (+ (+ (* (* (* (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (* (* (* (complex (- 2.0) 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (* (* (complex 5.0 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (* (complex 4.0 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (complex 7.0 0.0))))