Average Error: 0 → 0
Time: 22.4s
Precision: 64
\[\Im(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Im(\left(\left(\frac{11}{2} + \left(\left(-\sqrt{3}\right) - \frac{\sqrt{3}}{2}\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{-2} i\right) + \left(5 + \sqrt{3} \cdot 2 i\right)\right))\]
\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 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(\frac{11}{2} + \left(\left(-\sqrt{3}\right) - \frac{\sqrt{3}}{2}\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{-2} i\right) + \left(5 + \sqrt{3} \cdot 2 i\right)\right))
double f() {
        double r337804 = 1.0;
        double r337805 = -r337804;
        double r337806 = 2.0;
        double r337807 = r337805 / r337806;
        double r337808 = 3.0;
        double r337809 = sqrt(r337808);
        double r337810 = r337809 / r337806;
        double r337811 = /* ERROR: no complex support in C */;
        double r337812 = r337811 * r337811;
        double r337813 = r337812 * r337811;
        double r337814 = r337813 * r337811;
        double r337815 = -r337806;
        double r337816 = 0.0;
        double r337817 = /* ERROR: no complex support in C */;
        double r337818 = r337817 * r337811;
        double r337819 = r337818 * r337811;
        double r337820 = r337819 * r337811;
        double r337821 = r337814 + r337820;
        double r337822 = 5.0;
        double r337823 = /* ERROR: no complex support in C */;
        double r337824 = r337823 * r337811;
        double r337825 = r337824 * r337811;
        double r337826 = r337821 + r337825;
        double r337827 = 4.0;
        double r337828 = /* ERROR: no complex support in C */;
        double r337829 = r337828 * r337811;
        double r337830 = r337826 + r337829;
        double r337831 = 7.0;
        double r337832 = /* ERROR: no complex support in C */;
        double r337833 = r337830 + r337832;
        double r337834 = /* ERROR: no complex support in C */;
        return r337834;
}
↓
double f() {
        double r337835 = 5.5;
        double r337836 = 3.0;
        double r337837 = sqrt(r337836);
        double r337838 = -r337837;
        double r337839 = 2.0;
        double r337840 = r337837 / r337839;
        double r337841 = r337838 - r337840;
        double r337842 = /* ERROR: no complex support in C */;
        double r337843 = -0.5;
        double r337844 = -2.0;
        double r337845 = r337837 / r337844;
        double r337846 = /* ERROR: no complex support in C */;
        double r337847 = r337842 * r337846;
        double r337848 = 5.0;
        double r337849 = r337837 * r337839;
        double r337850 = /* ERROR: no complex support in C */;
        double r337851 = r337847 + r337850;
        double r337852 = /* ERROR: no complex support in C */;
        return r337852;
}

Error

Derivation

  1. Initial program 0

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto \Im(\left(\left(\frac{11}{2} + \left(\left(-\sqrt{3}\right) - \frac{\sqrt{3}}{2}\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{-2} i\right) + \left(5 + \sqrt{3} \cdot 2 i\right)\right))\]

Reproduce

herbie shell --seed 2019146 
(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))))