3.9.1 imaginary part (p56)

Average Error: 0 → 0

Time: 20.1s

Precision: 64

Math

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

↓

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

C

double f() {
        double r23933 = -1.0;
        double r23934 = 1.0;
        double r23935 = /* ERROR: no complex support in C */;
        double r23936 = r23935 * r23935;
        double r23937 = r23936 * r23935;
        double r23938 = r23937 * r23935;
        double r23939 = r23938 * r23935;
        double r23940 = r23939 * r23935;
        double r23941 = 6.0;
        double r23942 = 0.0;
        double r23943 = /* ERROR: no complex support in C */;
        double r23944 = r23943 * r23935;
        double r23945 = r23944 * r23935;
        double r23946 = r23945 * r23935;
        double r23947 = r23946 * r23935;
        double r23948 = r23947 * r23935;
        double r23949 = r23940 + r23948;
        double r23950 = 15.0;
        double r23951 = /* ERROR: no complex support in C */;
        double r23952 = r23951 * r23935;
        double r23953 = r23952 * r23935;
        double r23954 = r23953 * r23935;
        double r23955 = r23954 * r23935;
        double r23956 = r23949 + r23955;
        double r23957 = 20.0;
        double r23958 = /* ERROR: no complex support in C */;
        double r23959 = r23958 * r23935;
        double r23960 = r23959 * r23935;
        double r23961 = r23960 * r23935;
        double r23962 = r23956 + r23961;
        double r23963 = r23962 + r23953;
        double r23964 = r23963 + r23944;
        double r23965 = /* ERROR: no complex support in C */;
        double r23966 = r23964 + r23965;
        double r23967 = /* ERROR: no complex support in C */;
        return r23967;
}

↓

double f() {
        double r23968 = 6.0;
        double r23969 = 0.0;
        double r23970 = /* ERROR: no complex support in C */;
        double r23971 = -1.0;
        double r23972 = 1.0;
        double r23973 = /* ERROR: no complex support in C */;
        double r23974 = r23970 * r23973;
        double r23975 = 15.0;
        double r23976 = /* ERROR: no complex support in C */;
        double r23977 = r23973 * r23976;
        double r23978 = r23973 * r23977;
        double r23979 = 20.0;
        double r23980 = /* ERROR: no complex support in C */;
        double r23981 = r23980 * r23973;
        double r23982 = r23973 * r23981;
        double r23983 = r23982 * r23973;
        double r23984 = r23973 * r23974;
        double r23985 = r23984 * r23973;
        double r23986 = r23973 * r23985;
        double r23987 = r23986 * r23973;
        double r23988 = r23973 * r23973;
        double r23989 = r23988 * r23973;
        double r23990 = r23973 * r23989;
        double r23991 = r23973 * r23990;
        double r23992 = r23991 * r23973;
        double r23993 = r23987 + r23992;
        double r23994 = r23973 * r23978;
        double r23995 = r23973 * r23994;
        double r23996 = r23993 + r23995;
        double r23997 = r23983 + r23996;
        double r23998 = r23978 + r23997;
        double r23999 = r23974 + r23998;
        double r24000 = /* ERROR: no complex support in C */;
        double r24001 = r23999 + r24000;
        double r24002 = /* ERROR: no complex support in C */;
        return r24002;
}

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. Final simplification 0

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

Reproduce

herbie shell --seed 2019195 +o rules:numerics
(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))))