3.9.1 imaginary part (p56)

Average Error: 0 → 0

Time: 1.9m

Precision: 64

Math

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

↓

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

C

double f() {
        double r1827919 = -1.0;
        double r1827920 = 1.0;
        double r1827921 = /* ERROR: no complex support in C */;
        double r1827922 = r1827921 * r1827921;
        double r1827923 = r1827922 * r1827921;
        double r1827924 = r1827923 * r1827921;
        double r1827925 = r1827924 * r1827921;
        double r1827926 = r1827925 * r1827921;
        double r1827927 = 6.0;
        double r1827928 = 0.0;
        double r1827929 = /* ERROR: no complex support in C */;
        double r1827930 = r1827929 * r1827921;
        double r1827931 = r1827930 * r1827921;
        double r1827932 = r1827931 * r1827921;
        double r1827933 = r1827932 * r1827921;
        double r1827934 = r1827933 * r1827921;
        double r1827935 = r1827926 + r1827934;
        double r1827936 = 15.0;
        double r1827937 = /* ERROR: no complex support in C */;
        double r1827938 = r1827937 * r1827921;
        double r1827939 = r1827938 * r1827921;
        double r1827940 = r1827939 * r1827921;
        double r1827941 = r1827940 * r1827921;
        double r1827942 = r1827935 + r1827941;
        double r1827943 = 20.0;
        double r1827944 = /* ERROR: no complex support in C */;
        double r1827945 = r1827944 * r1827921;
        double r1827946 = r1827945 * r1827921;
        double r1827947 = r1827946 * r1827921;
        double r1827948 = r1827942 + r1827947;
        double r1827949 = r1827948 + r1827939;
        double r1827950 = r1827949 + r1827930;
        double r1827951 = /* ERROR: no complex support in C */;
        double r1827952 = r1827950 + r1827951;
        double r1827953 = /* ERROR: no complex support in C */;
        return r1827953;
}

↓

double f() {
        double r1827954 = 1.0;
        double r1827955 = 6.0;
        double r1827956 = -1.0;
        double r1827957 = r1827955 * r1827956;
        double r1827958 = 0.0;
        double r1827959 = r1827958 * r1827954;
        double r1827960 = r1827957 - r1827959;
        double r1827961 = r1827954 + r1827960;
        double r1827962 = r1827954 * r1827955;
        double r1827963 = r1827958 + r1827962;
        double r1827964 = r1827958 * r1827956;
        double r1827965 = r1827963 + r1827964;
        double r1827966 = /* ERROR: no complex support in C */;
        double r1827967 = r1827956 - r1827954;
        double r1827968 = r1827954 + r1827956;
        double r1827969 = r1827967 * r1827968;
        double r1827970 = r1827954 + r1827954;
        double r1827971 = r1827970 * r1827956;
        double r1827972 = /* ERROR: no complex support in C */;
        double r1827973 = 15.0;
        double r1827974 = r1827973 + r1827960;
        double r1827975 = /* ERROR: no complex support in C */;
        double r1827976 = r1827972 * r1827975;
        double r1827977 = 20.0;
        double r1827978 = r1827977 * r1827956;
        double r1827979 = r1827978 - r1827959;
        double r1827980 = r1827977 * r1827954;
        double r1827981 = r1827980 + r1827964;
        double r1827982 = /* ERROR: no complex support in C */;
        double r1827983 = /* ERROR: no complex support in C */;
        double r1827984 = r1827982 + r1827983;
        double r1827985 = r1827976 + r1827984;
        double r1827986 = r1827985 * r1827972;
        double r1827987 = r1827969 * r1827956;
        double r1827988 = r1827954 * r1827971;
        double r1827989 = r1827987 - r1827988;
        double r1827990 = r1827989 * r1827989;
        double r1827991 = r1827969 * r1827954;
        double r1827992 = r1827956 * r1827971;
        double r1827993 = r1827991 + r1827992;
        double r1827994 = r1827993 * r1827993;
        double r1827995 = r1827990 - r1827994;
        double r1827996 = r1827989 * r1827993;
        double r1827997 = r1827996 + r1827996;
        double r1827998 = /* ERROR: no complex support in C */;
        double r1827999 = r1827986 + r1827998;
        double r1828000 = r1827966 + r1827999;
        double r1828001 = /* ERROR: no complex support in C */;
        return r1828001;
}

Derivation

1. Initial program 0

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

2. Simplified 0

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019200 
(FPCore ()
  :name "3.9.1 imaginary part (p56)"
  (im (+ (+ (+ (+ (+ (+ (* (* (* (* (* (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))))