Average Error: 61.9 → 0
Time: 22.3s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(\left(\left(\frac{\sqrt{3}}{2} \cdot \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) + \frac{1}{4}\right) + \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) i\right) + \left(6 + -2 \cdot \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\left(\frac{\sqrt{3}}{2} \cdot \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) + \frac{1}{4}\right) + \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) i\right) + \left(5 + \frac{\sqrt{3} \cdot 4}{2} i\right)\right))\]
\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(\left(\left(\frac{\sqrt{3}}{2} \cdot \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) + \frac{1}{4}\right) + \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) i\right) + \left(6 + -2 \cdot \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\left(\frac{\sqrt{3}}{2} \cdot \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) + \frac{1}{4}\right) + \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) i\right) + \left(5 + \frac{\sqrt{3} \cdot 4}{2} i\right)\right))
double f() {
        double r812898 = 1.0;
        double r812899 = -r812898;
        double r812900 = 2.0;
        double r812901 = r812899 / r812900;
        double r812902 = 3.0;
        double r812903 = sqrt(r812902);
        double r812904 = r812903 / r812900;
        double r812905 = /* ERROR: no complex support in C */;
        double r812906 = r812905 * r812905;
        double r812907 = r812906 * r812905;
        double r812908 = r812907 * r812905;
        double r812909 = -r812900;
        double r812910 = 0.0;
        double r812911 = /* ERROR: no complex support in C */;
        double r812912 = r812911 * r812905;
        double r812913 = r812912 * r812905;
        double r812914 = r812913 * r812905;
        double r812915 = r812908 + r812914;
        double r812916 = 5.0;
        double r812917 = /* ERROR: no complex support in C */;
        double r812918 = r812917 * r812905;
        double r812919 = r812918 * r812905;
        double r812920 = r812915 + r812919;
        double r812921 = 4.0;
        double r812922 = /* ERROR: no complex support in C */;
        double r812923 = r812922 * r812905;
        double r812924 = r812920 + r812923;
        double r812925 = 7.0;
        double r812926 = /* ERROR: no complex support in C */;
        double r812927 = r812924 + r812926;
        double r812928 = /* ERROR: no complex support in C */;
        return r812928;
}
↓
double f() {
        double r812929 = 3.0;
        double r812930 = sqrt(r812929);
        double r812931 = 2.0;
        double r812932 = r812930 / r812931;
        double r812933 = -4.0;
        double r812934 = r812930 / r812933;
        double r812935 = r812934 + r812934;
        double r812936 = r812932 * r812935;
        double r812937 = 0.25;
        double r812938 = r812936 + r812937;
        double r812939 = /* ERROR: no complex support in C */;
        double r812940 = 6.0;
        double r812941 = -2.0;
        double r812942 = r812941 * r812932;
        double r812943 = /* ERROR: no complex support in C */;
        double r812944 = r812939 + r812943;
        double r812945 = r812944 * r812939;
        double r812946 = 5.0;
        double r812947 = 4.0;
        double r812948 = r812930 * r812947;
        double r812949 = r812948 / r812931;
        double r812950 = /* ERROR: no complex support in C */;
        double r812951 = r812945 + r812950;
        double r812952 = /* ERROR: no complex support in C */;
        return r812952;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019151 +o rules:numerics
(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))))