Average Error: 0 → 0
Time: 20.9s
Precision: 64
\[\Im(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Im(\left(\left(5 + \frac{\sqrt{3}}{2} \cdot 4 i\right) + \left(\left(\left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right) + \left(6 + \frac{-1}{2} \cdot \frac{\sqrt{3}}{\frac{1}{2}} i\right)\right) \cdot \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right)\right)\right))\]
\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))
↓
\Im(\left(\left(5 + \frac{\sqrt{3}}{2} \cdot 4 i\right) + \left(\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)\right))
double f() {
        double r1937682 = 1.0;
        double r1937683 = -r1937682;
        double r1937684 = 2.0;
        double r1937685 = r1937683 / r1937684;
        double r1937686 = 3.0;
        double r1937687 = sqrt(r1937686);
        double r1937688 = r1937687 / r1937684;
        double r1937689 = /* ERROR: no complex support in C */;
        double r1937690 = r1937689 * r1937689;
        double r1937691 = r1937690 * r1937689;
        double r1937692 = r1937691 * r1937689;
        double r1937693 = -r1937684;
        double r1937694 = 0.0;
        double r1937695 = /* ERROR: no complex support in C */;
        double r1937696 = r1937695 * r1937689;
        double r1937697 = r1937696 * r1937689;
        double r1937698 = r1937697 * r1937689;
        double r1937699 = r1937692 + r1937698;
        double r1937700 = 5.0;
        double r1937701 = /* ERROR: no complex support in C */;
        double r1937702 = r1937701 * r1937689;
        double r1937703 = r1937702 * r1937689;
        double r1937704 = r1937699 + r1937703;
        double r1937705 = 4.0;
        double r1937706 = /* ERROR: no complex support in C */;
        double r1937707 = r1937706 * r1937689;
        double r1937708 = r1937704 + r1937707;
        double r1937709 = 7.0;
        double r1937710 = /* ERROR: no complex support in C */;
        double r1937711 = r1937708 + r1937710;
        double r1937712 = /* ERROR: no complex support in C */;
        return r1937712;
}
↓
double f() {
        double r1937713 = 5.0;
        double r1937714 = 3.0;
        double r1937715 = sqrt(r1937714);
        double r1937716 = 2.0;
        double r1937717 = r1937715 / r1937716;
        double r1937718 = 4.0;
        double r1937719 = r1937717 * r1937718;
        double r1937720 = /* ERROR: no complex support in C */;
        double r1937721 = 0.25;
        double r1937722 = r1937717 * r1937717;
        double r1937723 = r1937721 - r1937722;
        double r1937724 = -r1937715;
        double r1937725 = r1937724 / r1937716;
        double r1937726 = /* ERROR: no complex support in C */;
        double r1937727 = 6.0;
        double r1937728 = -0.5;
        double r1937729 = 0.5;
        double r1937730 = r1937715 / r1937729;
        double r1937731 = r1937728 * r1937730;
        double r1937732 = /* ERROR: no complex support in C */;
        double r1937733 = r1937726 + r1937732;
        double r1937734 = r1937733 * r1937726;
        double r1937735 = r1937720 + r1937734;
        double r1937736 = /* ERROR: no complex support in C */;
        return r1937736;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019168 
(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))))