Average Error: 61.9 → 0
Time: 15.5s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(\left(\frac{-1}{2} + \frac{-\sqrt{3}}{2} i\right) \cdot \left(\left(\frac{-1}{2} + \frac{-\sqrt{3}}{2} i\right) + \left(6 + \frac{\sqrt{3}}{-1} i\right)\right)\right) + \left(5 + \frac{\sqrt{3}}{\frac{1}{2}} i\right)\right))\]
\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(\left(\frac{-1}{2} + \frac{-\sqrt{3}}{2} i\right) \cdot \left(\left(\frac{-1}{2} + \frac{-\sqrt{3}}{2} i\right) + \left(6 + \frac{\sqrt{3}}{-1} i\right)\right)\right) + \left(5 + \frac{\sqrt{3}}{\frac{1}{2}} i\right)\right))
double f() {
        double r1343741 = 1.0;
        double r1343742 = -r1343741;
        double r1343743 = 2.0;
        double r1343744 = r1343742 / r1343743;
        double r1343745 = 3.0;
        double r1343746 = sqrt(r1343745);
        double r1343747 = r1343746 / r1343743;
        double r1343748 = /* ERROR: no complex support in C */;
        double r1343749 = r1343748 * r1343748;
        double r1343750 = r1343749 * r1343748;
        double r1343751 = r1343750 * r1343748;
        double r1343752 = -r1343743;
        double r1343753 = 0.0;
        double r1343754 = /* ERROR: no complex support in C */;
        double r1343755 = r1343754 * r1343748;
        double r1343756 = r1343755 * r1343748;
        double r1343757 = r1343756 * r1343748;
        double r1343758 = r1343751 + r1343757;
        double r1343759 = 5.0;
        double r1343760 = /* ERROR: no complex support in C */;
        double r1343761 = r1343760 * r1343748;
        double r1343762 = r1343761 * r1343748;
        double r1343763 = r1343758 + r1343762;
        double r1343764 = 4.0;
        double r1343765 = /* ERROR: no complex support in C */;
        double r1343766 = r1343765 * r1343748;
        double r1343767 = r1343763 + r1343766;
        double r1343768 = 7.0;
        double r1343769 = /* ERROR: no complex support in C */;
        double r1343770 = r1343767 + r1343769;
        double r1343771 = /* ERROR: no complex support in C */;
        return r1343771;
}
↓
double f() {
        double r1343772 = -0.5;
        double r1343773 = 3.0;
        double r1343774 = sqrt(r1343773);
        double r1343775 = -r1343774;
        double r1343776 = 2.0;
        double r1343777 = r1343775 / r1343776;
        double r1343778 = /* ERROR: no complex support in C */;
        double r1343779 = 6.0;
        double r1343780 = -1.0;
        double r1343781 = r1343774 / r1343780;
        double r1343782 = /* ERROR: no complex support in C */;
        double r1343783 = r1343778 + r1343782;
        double r1343784 = r1343778 * r1343783;
        double r1343785 = 5.0;
        double r1343786 = 0.5;
        double r1343787 = r1343774 / r1343786;
        double r1343788 = /* ERROR: no complex support in C */;
        double r1343789 = r1343784 + r1343788;
        double r1343790 = /* ERROR: no complex support in C */;
        return r1343790;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019164 +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))))