Average Error: 61.9 → 0
Time: 26.2s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(\frac{-9}{2} + \left(6 \cdot \frac{\sqrt{3}}{-2} + \frac{\sqrt{3}}{2}\right) i\right) + \left(\frac{9}{2} + \left(\left(-\frac{\sqrt{3}}{-2}\right) + \sqrt{3} \cdot 2\right) i\right)\right))\]
\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(\frac{-9}{2} + \left(6 \cdot \frac{\sqrt{3}}{-2} + \frac{\sqrt{3}}{2}\right) i\right) + \left(\frac{9}{2} + \left(\left(-\frac{\sqrt{3}}{-2}\right) + \sqrt{3} \cdot 2\right) i\right)\right))
double f() {
        double r1081054 = 1.0;
        double r1081055 = -r1081054;
        double r1081056 = 2.0;
        double r1081057 = r1081055 / r1081056;
        double r1081058 = 3.0;
        double r1081059 = sqrt(r1081058);
        double r1081060 = r1081059 / r1081056;
        double r1081061 = /* ERROR: no complex support in C */;
        double r1081062 = r1081061 * r1081061;
        double r1081063 = r1081062 * r1081061;
        double r1081064 = r1081063 * r1081061;
        double r1081065 = -r1081056;
        double r1081066 = 0.0;
        double r1081067 = /* ERROR: no complex support in C */;
        double r1081068 = r1081067 * r1081061;
        double r1081069 = r1081068 * r1081061;
        double r1081070 = r1081069 * r1081061;
        double r1081071 = r1081064 + r1081070;
        double r1081072 = 5.0;
        double r1081073 = /* ERROR: no complex support in C */;
        double r1081074 = r1081073 * r1081061;
        double r1081075 = r1081074 * r1081061;
        double r1081076 = r1081071 + r1081075;
        double r1081077 = 4.0;
        double r1081078 = /* ERROR: no complex support in C */;
        double r1081079 = r1081078 * r1081061;
        double r1081080 = r1081076 + r1081079;
        double r1081081 = 7.0;
        double r1081082 = /* ERROR: no complex support in C */;
        double r1081083 = r1081080 + r1081082;
        double r1081084 = /* ERROR: no complex support in C */;
        return r1081084;
}
↓
double f() {
        double r1081085 = -4.5;
        double r1081086 = 6.0;
        double r1081087 = 3.0;
        double r1081088 = sqrt(r1081087);
        double r1081089 = -2.0;
        double r1081090 = r1081088 / r1081089;
        double r1081091 = r1081086 * r1081090;
        double r1081092 = 2.0;
        double r1081093 = r1081088 / r1081092;
        double r1081094 = r1081091 + r1081093;
        double r1081095 = /* ERROR: no complex support in C */;
        double r1081096 = 4.5;
        double r1081097 = -r1081090;
        double r1081098 = r1081088 * r1081092;
        double r1081099 = r1081097 + r1081098;
        double r1081100 = /* ERROR: no complex support in C */;
        double r1081101 = r1081095 + r1081100;
        double r1081102 = /* ERROR: no complex support in C */;
        return r1081102;
}

Error

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. Simplified0

    \[\leadsto \color{blue}{\Re(\left(\left(\left(-3 - \frac{3}{2}\right) + \left(\frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{-2} \cdot 6\right) i\right) + \left(\frac{9}{2} + \left(\frac{\sqrt{3}}{-2} \cdot -1 + 2 \cdot \sqrt{3}\right) i\right)\right))}\]

  3. Final simplification0

    \[\leadsto \Re(\left(\left(\frac{-9}{2} + \left(6 \cdot \frac{\sqrt{3}}{-2} + \frac{\sqrt{3}}{2}\right) i\right) + \left(\frac{9}{2} + \left(\left(-\frac{\sqrt{3}}{-2}\right) + \sqrt{3} \cdot 2\right) i\right)\right))\]

Reproduce

herbie shell --seed 2019141 
(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))))