Average Error: 61.9 → 0
Time: 16.3s
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 r1483709 = 1.0;
        double r1483710 = -r1483709;
        double r1483711 = 2.0;
        double r1483712 = r1483710 / r1483711;
        double r1483713 = 3.0;
        double r1483714 = sqrt(r1483713);
        double r1483715 = r1483714 / r1483711;
        double r1483716 = /* ERROR: no complex support in C */;
        double r1483717 = r1483716 * r1483716;
        double r1483718 = r1483717 * r1483716;
        double r1483719 = r1483718 * r1483716;
        double r1483720 = -r1483711;
        double r1483721 = 0.0;
        double r1483722 = /* ERROR: no complex support in C */;
        double r1483723 = r1483722 * r1483716;
        double r1483724 = r1483723 * r1483716;
        double r1483725 = r1483724 * r1483716;
        double r1483726 = r1483719 + r1483725;
        double r1483727 = 5.0;
        double r1483728 = /* ERROR: no complex support in C */;
        double r1483729 = r1483728 * r1483716;
        double r1483730 = r1483729 * r1483716;
        double r1483731 = r1483726 + r1483730;
        double r1483732 = 4.0;
        double r1483733 = /* ERROR: no complex support in C */;
        double r1483734 = r1483733 * r1483716;
        double r1483735 = r1483731 + r1483734;
        double r1483736 = 7.0;
        double r1483737 = /* ERROR: no complex support in C */;
        double r1483738 = r1483735 + r1483737;
        double r1483739 = /* ERROR: no complex support in C */;
        return r1483739;
}
↓
double f() {
        double r1483740 = -0.5;
        double r1483741 = 3.0;
        double r1483742 = sqrt(r1483741);
        double r1483743 = -r1483742;
        double r1483744 = 2.0;
        double r1483745 = r1483743 / r1483744;
        double r1483746 = /* ERROR: no complex support in C */;
        double r1483747 = 6.0;
        double r1483748 = -1.0;
        double r1483749 = r1483742 / r1483748;
        double r1483750 = /* ERROR: no complex support in C */;
        double r1483751 = r1483746 + r1483750;
        double r1483752 = r1483746 * r1483751;
        double r1483753 = 5.0;
        double r1483754 = 0.5;
        double r1483755 = r1483742 / r1483754;
        double r1483756 = /* ERROR: no complex support in C */;
        double r1483757 = r1483752 + r1483756;
        double r1483758 = /* ERROR: no complex support in C */;
        return r1483758;
}

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 2019163 +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))))