3.9.1 real part (p56)

Average Error: 0 → 0

Time: 24.6s

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 r1931886 = -1.0;
        double r1931887 = 1.0;
        double r1931888 = /* ERROR: no complex support in C */;
        double r1931889 = r1931888 * r1931888;
        double r1931890 = r1931889 * r1931888;
        double r1931891 = r1931890 * r1931888;
        double r1931892 = r1931891 * r1931888;
        double r1931893 = r1931892 * r1931888;
        double r1931894 = 6.0;
        double r1931895 = 0.0;
        double r1931896 = /* ERROR: no complex support in C */;
        double r1931897 = r1931896 * r1931888;
        double r1931898 = r1931897 * r1931888;
        double r1931899 = r1931898 * r1931888;
        double r1931900 = r1931899 * r1931888;
        double r1931901 = r1931900 * r1931888;
        double r1931902 = r1931893 + r1931901;
        double r1931903 = 15.0;
        double r1931904 = /* ERROR: no complex support in C */;
        double r1931905 = r1931904 * r1931888;
        double r1931906 = r1931905 * r1931888;
        double r1931907 = r1931906 * r1931888;
        double r1931908 = r1931907 * r1931888;
        double r1931909 = r1931902 + r1931908;
        double r1931910 = 20.0;
        double r1931911 = /* ERROR: no complex support in C */;
        double r1931912 = r1931911 * r1931888;
        double r1931913 = r1931912 * r1931888;
        double r1931914 = r1931913 * r1931888;
        double r1931915 = r1931909 + r1931914;
        double r1931916 = r1931915 + r1931906;
        double r1931917 = r1931916 + r1931897;
        double r1931918 = /* ERROR: no complex support in C */;
        double r1931919 = r1931917 + r1931918;
        double r1931920 = /* ERROR: no complex support in C */;
        return r1931920;
}

↓

double f() {
        double r1931921 = 1.0;
        double r1931922 = -1.0;
        double r1931923 = r1931921 + r1931922;
        double r1931924 = 15.0;
        double r1931925 = r1931923 * r1931924;
        double r1931926 = r1931922 - r1931921;
        double r1931927 = r1931925 * r1931926;
        double r1931928 = r1931922 + r1931922;
        double r1931929 = r1931928 * r1931921;
        double r1931930 = 0.0;
        double r1931931 = r1931929 * r1931930;
        double r1931932 = r1931927 - r1931931;
        double r1931933 = 6.0;
        double r1931934 = r1931922 * r1931933;
        double r1931935 = r1931921 * r1931930;
        double r1931936 = r1931934 - r1931935;
        double r1931937 = r1931932 + r1931936;
        double r1931938 = r1931923 * r1931926;
        double r1931939 = r1931938 * r1931938;
        double r1931940 = r1931929 * r1931929;
        double r1931941 = r1931939 - r1931940;
        double r1931942 = r1931936 * r1931941;
        double r1931943 = r1931930 * r1931922;
        double r1931944 = r1931921 * r1931933;
        double r1931945 = r1931943 + r1931944;
        double r1931946 = r1931923 * r1931929;
        double r1931947 = r1931926 * r1931946;
        double r1931948 = r1931947 + r1931947;
        double r1931949 = r1931945 * r1931948;
        double r1931950 = r1931942 - r1931949;
        double r1931951 = r1931937 + r1931950;
        double r1931952 = r1931936 * r1931948;
        double r1931953 = r1931945 * r1931941;
        double r1931954 = r1931952 + r1931953;
        double r1931955 = r1931938 * r1931930;
        double r1931956 = r1931929 * r1931924;
        double r1931957 = r1931955 + r1931956;
        double r1931958 = r1931945 + r1931957;
        double r1931959 = r1931954 + r1931958;
        double r1931960 = /* ERROR: no complex support in C */;
        double r1931961 = 20.0;
        double r1931962 = r1931961 * r1931922;
        double r1931963 = r1931962 - r1931935;
        double r1931964 = r1931963 + r1931932;
        double r1931965 = r1931941 + r1931964;
        double r1931966 = r1931961 * r1931921;
        double r1931967 = r1931966 + r1931943;
        double r1931968 = r1931957 + r1931967;
        double r1931969 = r1931948 + r1931968;
        double r1931970 = /* ERROR: no complex support in C */;
        double r1931971 = /* ERROR: no complex support in C */;
        double r1931972 = r1931970 * r1931971;
        double r1931973 = r1931960 + r1931972;
        double r1931974 = /* ERROR: no complex support in C */;
        double r1931975 = r1931973 + r1931974;
        double r1931976 = /* ERROR: no complex support in C */;
        return r1931976;
}

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 2019171 
(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))))