Average Error: 0 → 0
Time: 29.9s
Precision: 64
\[\Im(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) + \left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Im(\left(\left(5 + \frac{\sqrt{3}}{2} \cdot 4 i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right) \cdot \left(\left(6 + \frac{-2 \cdot \sqrt{3}}{2} i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right)\right)\right))\]
double f() {
        double r939618 = 1.0;
        double r939619 = -r939618;
        double r939620 = 2.0;
        double r939621 = r939619 / r939620;
        double r939622 = 3.0;
        double r939623 = sqrt(r939622);
        double r939624 = r939623 / r939620;
        double r939625 = /* ERROR: no complex support in C */;
        double r939626 = r939625 * r939625;
        double r939627 = r939626 * r939625;
        double r939628 = r939627 * r939625;
        double r939629 = -r939620;
        double r939630 = 0.0;
        double r939631 = /* ERROR: no complex support in C */;
        double r939632 = r939631 * r939625;
        double r939633 = r939632 * r939625;
        double r939634 = r939633 * r939625;
        double r939635 = r939628 + r939634;
        double r939636 = 5.0;
        double r939637 = /* ERROR: no complex support in C */;
        double r939638 = r939637 * r939625;
        double r939639 = r939638 * r939625;
        double r939640 = r939635 + r939639;
        double r939641 = 4.0;
        double r939642 = /* ERROR: no complex support in C */;
        double r939643 = r939642 * r939625;
        double r939644 = r939640 + r939643;
        double r939645 = 7.0;
        double r939646 = /* ERROR: no complex support in C */;
        double r939647 = r939644 + r939646;
        double r939648 = /* ERROR: no complex support in C */;
        return r939648;
}
↓
double f() {
        double r939649 = 5.0;
        double r939650 = 3.0;
        double r939651 = sqrt(r939650);
        double r939652 = 2.0;
        double r939653 = r939651 / r939652;
        double r939654 = 4.0;
        double r939655 = r939653 * r939654;
        double r939656 = /* ERROR: no complex support in C */;
        double r939657 = 0.25;
        double r939658 = r939653 * r939653;
        double r939659 = r939657 - r939658;
        double r939660 = -r939651;
        double r939661 = r939660 / r939652;
        double r939662 = /* ERROR: no complex support in C */;
        double r939663 = 6.0;
        double r939664 = -2.0;
        double r939665 = r939664 * r939651;
        double r939666 = r939665 / r939652;
        double r939667 = /* ERROR: no complex support in C */;
        double r939668 = r939667 + r939662;
        double r939669 = r939662 * r939668;
        double r939670 = r939656 + r939669;
        double r939671 = /* ERROR: no complex support in C */;
        return r939671;
}


\Im(\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) + \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) + \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) + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))
↓
\Im(\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))

Error

Derivation

  1. Initial program 0

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore ()
  :name "3.9.2 imaginary part (p56)"
  (im (+.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))))