Average Error: 61.9 → 0
Time: 21.1s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(5 + \frac{\sqrt{3}}{2} \cdot 4 i\right) + \left(\left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right) + \left(6 + \frac{-1}{2} \cdot \frac{\sqrt{3}}{\frac{1}{2}} i\right)\right) \cdot \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right)\right))\]
\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(5 + \frac{\sqrt{3}}{2} \cdot 4 i\right) + \left(\left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right) + \left(6 + \frac{-1}{2} \cdot \frac{\sqrt{3}}{\frac{1}{2}} i\right)\right) \cdot \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right)\right))
double f() {
        double r1814731 = 1.0;
        double r1814732 = -r1814731;
        double r1814733 = 2.0;
        double r1814734 = r1814732 / r1814733;
        double r1814735 = 3.0;
        double r1814736 = sqrt(r1814735);
        double r1814737 = r1814736 / r1814733;
        double r1814738 = /* ERROR: no complex support in C */;
        double r1814739 = r1814738 * r1814738;
        double r1814740 = r1814739 * r1814738;
        double r1814741 = r1814740 * r1814738;
        double r1814742 = -r1814733;
        double r1814743 = 0.0;
        double r1814744 = /* ERROR: no complex support in C */;
        double r1814745 = r1814744 * r1814738;
        double r1814746 = r1814745 * r1814738;
        double r1814747 = r1814746 * r1814738;
        double r1814748 = r1814741 + r1814747;
        double r1814749 = 5.0;
        double r1814750 = /* ERROR: no complex support in C */;
        double r1814751 = r1814750 * r1814738;
        double r1814752 = r1814751 * r1814738;
        double r1814753 = r1814748 + r1814752;
        double r1814754 = 4.0;
        double r1814755 = /* ERROR: no complex support in C */;
        double r1814756 = r1814755 * r1814738;
        double r1814757 = r1814753 + r1814756;
        double r1814758 = 7.0;
        double r1814759 = /* ERROR: no complex support in C */;
        double r1814760 = r1814757 + r1814759;
        double r1814761 = /* ERROR: no complex support in C */;
        return r1814761;
}
↓
double f() {
        double r1814762 = 5.0;
        double r1814763 = 3.0;
        double r1814764 = sqrt(r1814763);
        double r1814765 = 2.0;
        double r1814766 = r1814764 / r1814765;
        double r1814767 = 4.0;
        double r1814768 = r1814766 * r1814767;
        double r1814769 = /* ERROR: no complex support in C */;
        double r1814770 = 0.25;
        double r1814771 = r1814766 * r1814766;
        double r1814772 = r1814770 - r1814771;
        double r1814773 = -r1814764;
        double r1814774 = r1814773 / r1814765;
        double r1814775 = /* ERROR: no complex support in C */;
        double r1814776 = 6.0;
        double r1814777 = -0.5;
        double r1814778 = 0.5;
        double r1814779 = r1814764 / r1814778;
        double r1814780 = r1814777 * r1814779;
        double r1814781 = /* ERROR: no complex support in C */;
        double r1814782 = r1814775 + r1814781;
        double r1814783 = r1814782 * r1814775;
        double r1814784 = r1814769 + r1814783;
        double r1814785 = /* ERROR: no complex support in C */;
        return r1814785;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019163 
(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))))