3.9.1 real part (p56)

Average Error: 0 → 0

Time: 24.8s

Precision: 64

Math

\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(\left(\left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(20 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(1 + 0.0 i\right)\right))\]

↓

\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(1 + -1\right) \cdot 15\right) \cdot \left(-1 - 1\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot 0.0\right) + \left(-1 \cdot 6 - 1 \cdot 0.0\right)\right) + \left(\left(-1 \cdot 6 - 1 \cdot 0.0\right) \cdot \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) - \left(0.0 \cdot -1 + 1 \cdot 6\right) \cdot \left(\left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) + \left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right)\right)\right)\right) + \left(\left(\left(-1 \cdot 6 - 1 \cdot 0.0\right) \cdot \left(\left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) + \left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right)\right) + \left(0.0 \cdot -1 + 1 \cdot 6\right) \cdot \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right)\right) + \left(\left(0.0 \cdot -1 + 1 \cdot 6\right) + \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot 0.0 + \left(\left(-1 + -1\right) \cdot 1\right) \cdot 15\right)\right)\right) i\right) + \left(\left(\left(\left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) + \left(\left(20 \cdot -1 - 1 \cdot 0.0\right) + \left(\left(\left(1 + -1\right) \cdot 15\right) \cdot \left(-1 - 1\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot 0.0\right)\right)\right) + \left(\left(\left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) + \left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right)\right) + \left(\left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot 0.0 + \left(\left(-1 + -1\right) \cdot 1\right) \cdot 15\right) + \left(20 \cdot 1 + 0.0 \cdot -1\right)\right)\right) i\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right) + \left(-1 + -1\right) \cdot 1 i\right)\right)\right) + \left(1 + 0.0 i\right)\right))\]

C

double f() {
        double r1111865 = -1.0;
        double r1111866 = 1.0;
        double r1111867 = /* ERROR: no complex support in C */;
        double r1111868 = r1111867 * r1111867;
        double r1111869 = r1111868 * r1111867;
        double r1111870 = r1111869 * r1111867;
        double r1111871 = r1111870 * r1111867;
        double r1111872 = r1111871 * r1111867;
        double r1111873 = 6.0;
        double r1111874 = 0.0;
        double r1111875 = /* ERROR: no complex support in C */;
        double r1111876 = r1111875 * r1111867;
        double r1111877 = r1111876 * r1111867;
        double r1111878 = r1111877 * r1111867;
        double r1111879 = r1111878 * r1111867;
        double r1111880 = r1111879 * r1111867;
        double r1111881 = r1111872 + r1111880;
        double r1111882 = 15.0;
        double r1111883 = /* ERROR: no complex support in C */;
        double r1111884 = r1111883 * r1111867;
        double r1111885 = r1111884 * r1111867;
        double r1111886 = r1111885 * r1111867;
        double r1111887 = r1111886 * r1111867;
        double r1111888 = r1111881 + r1111887;
        double r1111889 = 20.0;
        double r1111890 = /* ERROR: no complex support in C */;
        double r1111891 = r1111890 * r1111867;
        double r1111892 = r1111891 * r1111867;
        double r1111893 = r1111892 * r1111867;
        double r1111894 = r1111888 + r1111893;
        double r1111895 = r1111894 + r1111885;
        double r1111896 = r1111895 + r1111876;
        double r1111897 = /* ERROR: no complex support in C */;
        double r1111898 = r1111896 + r1111897;
        double r1111899 = /* ERROR: no complex support in C */;
        return r1111899;
}

↓

double f() {
        double r1111900 = 1.0;
        double r1111901 = -1.0;
        double r1111902 = r1111900 + r1111901;
        double r1111903 = 15.0;
        double r1111904 = r1111902 * r1111903;
        double r1111905 = r1111901 - r1111900;
        double r1111906 = r1111904 * r1111905;
        double r1111907 = r1111901 + r1111901;
        double r1111908 = r1111907 * r1111900;
        double r1111909 = 0.0;
        double r1111910 = r1111908 * r1111909;
        double r1111911 = r1111906 - r1111910;
        double r1111912 = 6.0;
        double r1111913 = r1111901 * r1111912;
        double r1111914 = r1111900 * r1111909;
        double r1111915 = r1111913 - r1111914;
        double r1111916 = r1111911 + r1111915;
        double r1111917 = r1111902 * r1111905;
        double r1111918 = r1111917 * r1111917;
        double r1111919 = r1111908 * r1111908;
        double r1111920 = r1111918 - r1111919;
        double r1111921 = r1111915 * r1111920;
        double r1111922 = r1111909 * r1111901;
        double r1111923 = r1111900 * r1111912;
        double r1111924 = r1111922 + r1111923;
        double r1111925 = r1111902 * r1111908;
        double r1111926 = r1111905 * r1111925;
        double r1111927 = r1111926 + r1111926;
        double r1111928 = r1111924 * r1111927;
        double r1111929 = r1111921 - r1111928;
        double r1111930 = r1111916 + r1111929;
        double r1111931 = r1111915 * r1111927;
        double r1111932 = r1111924 * r1111920;
        double r1111933 = r1111931 + r1111932;
        double r1111934 = r1111917 * r1111909;
        double r1111935 = r1111908 * r1111903;
        double r1111936 = r1111934 + r1111935;
        double r1111937 = r1111924 + r1111936;
        double r1111938 = r1111933 + r1111937;
        double r1111939 = /* ERROR: no complex support in C */;
        double r1111940 = 20.0;
        double r1111941 = r1111940 * r1111901;
        double r1111942 = r1111941 - r1111914;
        double r1111943 = r1111942 + r1111911;
        double r1111944 = r1111920 + r1111943;
        double r1111945 = r1111940 * r1111900;
        double r1111946 = r1111945 + r1111922;
        double r1111947 = r1111936 + r1111946;
        double r1111948 = r1111927 + r1111947;
        double r1111949 = /* ERROR: no complex support in C */;
        double r1111950 = /* ERROR: no complex support in C */;
        double r1111951 = r1111949 * r1111950;
        double r1111952 = r1111939 + r1111951;
        double r1111953 = /* ERROR: no complex support in C */;
        double r1111954 = r1111952 + r1111953;
        double r1111955 = /* ERROR: no complex support in C */;
        return r1111955;
}

Derivation

1. Initial program 0

   \[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(\left(\left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(20 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(1 + 0.0 i\right)\right))\]

2. Simplified 0

   \[\leadsto \color{blue}{\Re(\left(\left(\left(\left(\left(\left(\left(15 \cdot \left(1 + -1\right)\right) \cdot \left(-1 - 1\right) - 0.0 \cdot \left(1 \cdot \left(-1 + -1\right)\right)\right) + \left(-1 \cdot 6 - 1 \cdot 0.0\right)\right) + \left(\left(-1 \cdot 6 - 1 \cdot 0.0\right) \cdot \left(\left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) \cdot \left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) - \left(1 \cdot \left(-1 + -1\right)\right) \cdot \left(1 \cdot \left(-1 + -1\right)\right)\right) - \left(6 \cdot 1 + 0.0 \cdot -1\right) \cdot \left(\left(\left(1 \cdot \left(-1 + -1\right)\right) \cdot \left(1 + -1\right)\right) \cdot \left(-1 - 1\right) + \left(\left(1 \cdot \left(-1 + -1\right)\right) \cdot \left(1 + -1\right)\right) \cdot \left(-1 - 1\right)\right)\right)\right) + \left(\left(\left(\left(1 \cdot \left(-1 + -1\right)\right) \cdot 15 + \left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) \cdot 0.0\right) + \left(6 \cdot 1 + 0.0 \cdot -1\right)\right) + \left(\left(-1 \cdot 6 - 1 \cdot 0.0\right) \cdot \left(\left(\left(1 \cdot \left(-1 + -1\right)\right) \cdot \left(1 + -1\right)\right) \cdot \left(-1 - 1\right) + \left(\left(1 \cdot \left(-1 + -1\right)\right) \cdot \left(1 + -1\right)\right) \cdot \left(-1 - 1\right)\right) + \left(6 \cdot 1 + 0.0 \cdot -1\right) \cdot \left(\left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) \cdot \left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) - \left(1 \cdot \left(-1 + -1\right)\right) \cdot \left(1 \cdot \left(-1 + -1\right)\right)\right)\right)\right) i\right) + \left(\left(\left(-1 - 1\right) \cdot \left(1 + -1\right) + 1 \cdot \left(-1 + -1\right) i\right) \cdot \left(\left(\left(\left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) \cdot \left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) - \left(1 \cdot \left(-1 + -1\right)\right) \cdot \left(1 \cdot \left(-1 + -1\right)\right)\right) + \left(\left(\left(15 \cdot \left(1 + -1\right)\right) \cdot \left(-1 - 1\right) - 0.0 \cdot \left(1 \cdot \left(-1 + -1\right)\right)\right) + \left(-1 \cdot 20 - 1 \cdot 0.0\right)\right)\right) + \left(\left(\left(\left(1 \cdot \left(-1 + -1\right)\right) \cdot \left(1 + -1\right)\right) \cdot \left(-1 - 1\right) + \left(\left(1 \cdot \left(-1 + -1\right)\right) \cdot \left(1 + -1\right)\right) \cdot \left(-1 - 1\right)\right) + \left(\left(\left(1 \cdot \left(-1 + -1\right)\right) \cdot 15 + \left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) \cdot 0.0\right) + \left(1 \cdot 20 + 0.0 \cdot -1\right)\right)\right) i\right)\right)\right) + \left(1 + 0.0 i\right)\right))}\]

3. Final simplification 0

   \[\leadsto \Re(\left(\left(\left(\left(\left(\left(\left(\left(1 + -1\right) \cdot 15\right) \cdot \left(-1 - 1\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot 0.0\right) + \left(-1 \cdot 6 - 1 \cdot 0.0\right)\right) + \left(\left(-1 \cdot 6 - 1 \cdot 0.0\right) \cdot \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) - \left(0.0 \cdot -1 + 1 \cdot 6\right) \cdot \left(\left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) + \left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right)\right)\right)\right) + \left(\left(\left(-1 \cdot 6 - 1 \cdot 0.0\right) \cdot \left(\left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) + \left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right)\right) + \left(0.0 \cdot -1 + 1 \cdot 6\right) \cdot \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right)\right) + \left(\left(0.0 \cdot -1 + 1 \cdot 6\right) + \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot 0.0 + \left(\left(-1 + -1\right) \cdot 1\right) \cdot 15\right)\right)\right) i\right) + \left(\left(\left(\left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) + \left(\left(20 \cdot -1 - 1 \cdot 0.0\right) + \left(\left(\left(1 + -1\right) \cdot 15\right) \cdot \left(-1 - 1\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot 0.0\right)\right)\right) + \left(\left(\left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) + \left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right)\right) + \left(\left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot 0.0 + \left(\left(-1 + -1\right) \cdot 1\right) \cdot 15\right) + \left(20 \cdot 1 + 0.0 \cdot -1\right)\right)\right) i\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right) + \left(-1 + -1\right) \cdot 1 i\right)\right)\right) + \left(1 + 0.0 i\right)\right))\]

Reproduce

herbie shell --seed 2019172 
(FPCore ()
  :name "3.9.1 real part (p56)"
  (re (+ (+ (+ (+ (+ (+ (* (* (* (* (* (complex -1.0 1.0) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (* (* (* (* (* (complex 6.0 0.0) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0))) (* (* (* (* (complex 15.0 0.0) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0))) (* (* (* (complex 20.0 0.0) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0))) (* (* (complex 15.0 0.0) (complex -1.0 1.0)) (complex -1.0 1.0))) (* (complex 6.0 0.0) (complex -1.0 1.0))) (complex 1.0 0.0))))