Average Error: 0 → 0
Time: 21.2s
Precision: 64
\[\Im(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]
↓
\[\Im(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(4 + 0.0 i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]
\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) + 0.0 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))
↓
\Im(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \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)\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\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(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(4 + 0.0 i\right)\right)\right) + \left(7 + 0.0 i\right)\right))
double f() {
        double r2172842 = 1.0;
        double r2172843 = -r2172842;
        double r2172844 = 2.0;
        double r2172845 = r2172843 / r2172844;
        double r2172846 = 3.0;
        double r2172847 = sqrt(r2172846);
        double r2172848 = r2172847 / r2172844;
        double r2172849 = /* ERROR: no complex support in C */;
        double r2172850 = r2172849 * r2172849;
        double r2172851 = r2172850 * r2172849;
        double r2172852 = r2172851 * r2172849;
        double r2172853 = -r2172844;
        double r2172854 = 0.0;
        double r2172855 = /* ERROR: no complex support in C */;
        double r2172856 = r2172855 * r2172849;
        double r2172857 = r2172856 * r2172849;
        double r2172858 = r2172857 * r2172849;
        double r2172859 = r2172852 + r2172858;
        double r2172860 = 5.0;
        double r2172861 = /* ERROR: no complex support in C */;
        double r2172862 = r2172861 * r2172849;
        double r2172863 = r2172862 * r2172849;
        double r2172864 = r2172859 + r2172863;
        double r2172865 = 4.0;
        double r2172866 = /* ERROR: no complex support in C */;
        double r2172867 = r2172866 * r2172849;
        double r2172868 = r2172864 + r2172867;
        double r2172869 = 7.0;
        double r2172870 = /* ERROR: no complex support in C */;
        double r2172871 = r2172868 + r2172870;
        double r2172872 = /* ERROR: no complex support in C */;
        return r2172872;
}
↓
double f() {
        double r2172873 = 1.0;
        double r2172874 = -r2172873;
        double r2172875 = 2.0;
        double r2172876 = r2172874 / r2172875;
        double r2172877 = 3.0;
        double r2172878 = sqrt(r2172877);
        double r2172879 = r2172878 / r2172875;
        double r2172880 = /* ERROR: no complex support in C */;
        double r2172881 = r2172880 * r2172880;
        double r2172882 = r2172881 * r2172880;
        double r2172883 = r2172880 * r2172882;
        double r2172884 = -r2172875;
        double r2172885 = 0.0;
        double r2172886 = /* ERROR: no complex support in C */;
        double r2172887 = r2172886 * r2172880;
        double r2172888 = r2172880 * r2172887;
        double r2172889 = r2172880 * r2172888;
        double r2172890 = r2172883 + r2172889;
        double r2172891 = 5.0;
        double r2172892 = /* ERROR: no complex support in C */;
        double r2172893 = r2172892 * r2172880;
        double r2172894 = r2172893 * r2172880;
        double r2172895 = r2172890 + r2172894;
        double r2172896 = 4.0;
        double r2172897 = /* ERROR: no complex support in C */;
        double r2172898 = r2172880 * r2172897;
        double r2172899 = r2172895 + r2172898;
        double r2172900 = 7.0;
        double r2172901 = /* ERROR: no complex support in C */;
        double r2172902 = r2172899 + r2172901;
        double r2172903 = /* ERROR: no complex support in C */;
        return r2172903;
}

Error

Derivation

  1. Initial program 0

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

  2. Final simplification0

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore ()
  :name "3.9.2 imaginary part (p56)"
  (im (+ (+ (+ (+ (* (* (* (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))))