Average Error: 0 → 0
Time: 23.8s
Precision: 64
\[\Im(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Im(\left(\left(\frac{11}{2} + \left(\frac{\sqrt{3}}{-2} + \frac{\sqrt{3}}{-1}\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{-2} i\right) + \left(5 + \sqrt{3} \cdot 2 i\right)\right))\]
\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(\frac{11}{2} + \left(\frac{\sqrt{3}}{-2} + \frac{\sqrt{3}}{-1}\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{-2} i\right) + \left(5 + \sqrt{3} \cdot 2 i\right)\right))
double f() {
        double r967035 = 1.0;
        double r967036 = -r967035;
        double r967037 = 2.0;
        double r967038 = r967036 / r967037;
        double r967039 = 3.0;
        double r967040 = sqrt(r967039);
        double r967041 = r967040 / r967037;
        double r967042 = /* ERROR: no complex support in C */;
        double r967043 = r967042 * r967042;
        double r967044 = r967043 * r967042;
        double r967045 = r967044 * r967042;
        double r967046 = -r967037;
        double r967047 = 0.0;
        double r967048 = /* ERROR: no complex support in C */;
        double r967049 = r967048 * r967042;
        double r967050 = r967049 * r967042;
        double r967051 = r967050 * r967042;
        double r967052 = r967045 + r967051;
        double r967053 = 5.0;
        double r967054 = /* ERROR: no complex support in C */;
        double r967055 = r967054 * r967042;
        double r967056 = r967055 * r967042;
        double r967057 = r967052 + r967056;
        double r967058 = 4.0;
        double r967059 = /* ERROR: no complex support in C */;
        double r967060 = r967059 * r967042;
        double r967061 = r967057 + r967060;
        double r967062 = 7.0;
        double r967063 = /* ERROR: no complex support in C */;
        double r967064 = r967061 + r967063;
        double r967065 = /* ERROR: no complex support in C */;
        return r967065;
}
↓
double f() {
        double r967066 = 5.5;
        double r967067 = 3.0;
        double r967068 = sqrt(r967067);
        double r967069 = -2.0;
        double r967070 = r967068 / r967069;
        double r967071 = -1.0;
        double r967072 = r967068 / r967071;
        double r967073 = r967070 + r967072;
        double r967074 = /* ERROR: no complex support in C */;
        double r967075 = -0.5;
        double r967076 = /* ERROR: no complex support in C */;
        double r967077 = r967074 * r967076;
        double r967078 = 5.0;
        double r967079 = 2.0;
        double r967080 = r967068 * r967079;
        double r967081 = /* ERROR: no complex support in C */;
        double r967082 = r967077 + r967081;
        double r967083 = /* ERROR: no complex support in C */;
        return r967083;
}

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

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

  3. Final simplification0

    \[\leadsto \Im(\left(\left(\frac{11}{2} + \left(\frac{\sqrt{3}}{-2} + \frac{\sqrt{3}}{-1}\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{-2} i\right) + \left(5 + \sqrt{3} \cdot 2 i\right)\right))\]

Reproduce

herbie shell --seed 2019138 +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))))