Average Error: 61.9 → 0
Time: 24.9s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(\frac{11}{2} + \left(\frac{\sqrt{3}}{-2} + \frac{\sqrt{3}}{-1}\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{-2} i\right) + \left(5 + \sqrt{3} \cdot 2 i\right)\right))\]
\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{11}{2} + \left(\frac{\sqrt{3}}{-2} + \frac{\sqrt{3}}{-1}\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 r1001798 = 1.0;
        double r1001799 = -r1001798;
        double r1001800 = 2.0;
        double r1001801 = r1001799 / r1001800;
        double r1001802 = 3.0;
        double r1001803 = sqrt(r1001802);
        double r1001804 = r1001803 / r1001800;
        double r1001805 = /* ERROR: no complex support in C */;
        double r1001806 = r1001805 * r1001805;
        double r1001807 = r1001806 * r1001805;
        double r1001808 = r1001807 * r1001805;
        double r1001809 = -r1001800;
        double r1001810 = 0.0;
        double r1001811 = /* ERROR: no complex support in C */;
        double r1001812 = r1001811 * r1001805;
        double r1001813 = r1001812 * r1001805;
        double r1001814 = r1001813 * r1001805;
        double r1001815 = r1001808 + r1001814;
        double r1001816 = 5.0;
        double r1001817 = /* ERROR: no complex support in C */;
        double r1001818 = r1001817 * r1001805;
        double r1001819 = r1001818 * r1001805;
        double r1001820 = r1001815 + r1001819;
        double r1001821 = 4.0;
        double r1001822 = /* ERROR: no complex support in C */;
        double r1001823 = r1001822 * r1001805;
        double r1001824 = r1001820 + r1001823;
        double r1001825 = 7.0;
        double r1001826 = /* ERROR: no complex support in C */;
        double r1001827 = r1001824 + r1001826;
        double r1001828 = /* ERROR: no complex support in C */;
        return r1001828;
}
↓
double f() {
        double r1001829 = 5.5;
        double r1001830 = 3.0;
        double r1001831 = sqrt(r1001830);
        double r1001832 = -2.0;
        double r1001833 = r1001831 / r1001832;
        double r1001834 = -1.0;
        double r1001835 = r1001831 / r1001834;
        double r1001836 = r1001833 + r1001835;
        double r1001837 = /* ERROR: no complex support in C */;
        double r1001838 = -0.5;
        double r1001839 = /* ERROR: no complex support in C */;
        double r1001840 = r1001837 * r1001839;
        double r1001841 = 5.0;
        double r1001842 = 2.0;
        double r1001843 = r1001831 * r1001842;
        double r1001844 = /* ERROR: no complex support in C */;
        double r1001845 = r1001840 + r1001844;
        double r1001846 = /* ERROR: no complex support in C */;
        return r1001846;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019139 +o rules:numerics
(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))))