Average Error: 0 → 0
Time: 20.4s
Precision: 64
\[\Im(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Im(\left(\left(5 + \frac{\sqrt{3}}{2} \cdot 4 i\right) + \left(\left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right) + \left(6 + \frac{-1}{2} \cdot \frac{\sqrt{3}}{\frac{1}{2}} i\right)\right) \cdot \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right)\right))\]
\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(\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))
double f() {
        double r1776060 = 1.0;
        double r1776061 = -r1776060;
        double r1776062 = 2.0;
        double r1776063 = r1776061 / r1776062;
        double r1776064 = 3.0;
        double r1776065 = sqrt(r1776064);
        double r1776066 = r1776065 / r1776062;
        double r1776067 = /* ERROR: no complex support in C */;
        double r1776068 = r1776067 * r1776067;
        double r1776069 = r1776068 * r1776067;
        double r1776070 = r1776069 * r1776067;
        double r1776071 = -r1776062;
        double r1776072 = 0.0;
        double r1776073 = /* ERROR: no complex support in C */;
        double r1776074 = r1776073 * r1776067;
        double r1776075 = r1776074 * r1776067;
        double r1776076 = r1776075 * r1776067;
        double r1776077 = r1776070 + r1776076;
        double r1776078 = 5.0;
        double r1776079 = /* ERROR: no complex support in C */;
        double r1776080 = r1776079 * r1776067;
        double r1776081 = r1776080 * r1776067;
        double r1776082 = r1776077 + r1776081;
        double r1776083 = 4.0;
        double r1776084 = /* ERROR: no complex support in C */;
        double r1776085 = r1776084 * r1776067;
        double r1776086 = r1776082 + r1776085;
        double r1776087 = 7.0;
        double r1776088 = /* ERROR: no complex support in C */;
        double r1776089 = r1776086 + r1776088;
        double r1776090 = /* ERROR: no complex support in C */;
        return r1776090;
}
↓
double f() {
        double r1776091 = 5.0;
        double r1776092 = 3.0;
        double r1776093 = sqrt(r1776092);
        double r1776094 = 2.0;
        double r1776095 = r1776093 / r1776094;
        double r1776096 = 4.0;
        double r1776097 = r1776095 * r1776096;
        double r1776098 = /* ERROR: no complex support in C */;
        double r1776099 = 0.25;
        double r1776100 = r1776095 * r1776095;
        double r1776101 = r1776099 - r1776100;
        double r1776102 = -r1776093;
        double r1776103 = r1776102 / r1776094;
        double r1776104 = /* ERROR: no complex support in C */;
        double r1776105 = 6.0;
        double r1776106 = -0.5;
        double r1776107 = 0.5;
        double r1776108 = r1776093 / r1776107;
        double r1776109 = r1776106 * r1776108;
        double r1776110 = /* ERROR: no complex support in C */;
        double r1776111 = r1776104 + r1776110;
        double r1776112 = r1776111 * r1776104;
        double r1776113 = r1776098 + r1776112;
        double r1776114 = /* ERROR: no complex support in C */;
        return r1776114;
}

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

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

Reproduce

herbie shell --seed 2019163 
(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))))