3.9.2 real part (p56)

Average Error: 61.9 → 0

Time: 30.0s

Precision: 64

Math

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

↓

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

C

double f() {
        double r425717 = 1.0;
        double r425718 = -r425717;
        double r425719 = 2.0;
        double r425720 = r425718 / r425719;
        double r425721 = 3.0;
        double r425722 = sqrt(r425721);
        double r425723 = r425722 / r425719;
        double r425724 = /* ERROR: no complex support in C */;
        double r425725 = r425724 * r425724;
        double r425726 = r425725 * r425724;
        double r425727 = r425726 * r425724;
        double r425728 = -r425719;
        double r425729 = 0.0;
        double r425730 = /* ERROR: no complex support in C */;
        double r425731 = r425730 * r425724;
        double r425732 = r425731 * r425724;
        double r425733 = r425732 * r425724;
        double r425734 = r425727 + r425733;
        double r425735 = 5.0;
        double r425736 = /* ERROR: no complex support in C */;
        double r425737 = r425736 * r425724;
        double r425738 = r425737 * r425724;
        double r425739 = r425734 + r425738;
        double r425740 = 4.0;
        double r425741 = /* ERROR: no complex support in C */;
        double r425742 = r425741 * r425724;
        double r425743 = r425739 + r425742;
        double r425744 = 7.0;
        double r425745 = /* ERROR: no complex support in C */;
        double r425746 = r425743 + r425745;
        double r425747 = /* ERROR: no complex support in C */;
        return r425747;
}

↓

double f() {
        double r425748 = 5.0;
        double r425749 = 3.0;
        double r425750 = sqrt(r425749);
        double r425751 = 2.0;
        double r425752 = r425750 / r425751;
        double r425753 = 4.0;
        double r425754 = r425752 * r425753;
        double r425755 = /* ERROR: no complex support in C */;
        double r425756 = 0.25;
        double r425757 = r425752 * r425752;
        double r425758 = r425756 - r425757;
        double r425759 = -r425750;
        double r425760 = r425759 / r425751;
        double r425761 = /* ERROR: no complex support in C */;
        double r425762 = 6.0;
        double r425763 = -2.0;
        double r425764 = r425763 * r425750;
        double r425765 = r425764 / r425751;
        double r425766 = /* ERROR: no complex support in C */;
        double r425767 = r425766 + r425761;
        double r425768 = r425761 * r425767;
        double r425769 = r425755 + r425768;
        double r425770 = /* ERROR: no complex support in C */;
        return r425770;
}

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. Simplified 0

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019119 +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))))