Average Error: 0 → 0
Time: 22.3s
Precision: 64
\[\Im(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(\left(\left(\left(6 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(\left(15 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(20 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(15 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(6 + 0 i\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(1 + 0 i\right)\right))\]
↓
\[\Im(\left(\left(-5 + -24 i\right) + \left(\left(\left(24 + -24 i\right) + \left(0 + 8 i\right)\right) + \left(\left(40 + 40 i\right) + \left(-60 + 0 i\right)\right)\right)\right))\]
\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 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 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 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 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(6 + 0 i\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(1 + 0 i\right)\right))
↓
\Im(\left(\left(-5 + -24 i\right) + \left(\left(\left(24 + -24 i\right) + \left(0 + 8 i\right)\right) + \left(\left(40 + 40 i\right) + \left(-60 + 0 i\right)\right)\right)\right))
double f() {
        double r1448953 = -1.0;
        double r1448954 = 1.0;
        double r1448955 = /* ERROR: no complex support in C */;
        double r1448956 = r1448955 * r1448955;
        double r1448957 = r1448956 * r1448955;
        double r1448958 = r1448957 * r1448955;
        double r1448959 = r1448958 * r1448955;
        double r1448960 = r1448959 * r1448955;
        double r1448961 = 6.0;
        double r1448962 = 0.0;
        double r1448963 = /* ERROR: no complex support in C */;
        double r1448964 = r1448963 * r1448955;
        double r1448965 = r1448964 * r1448955;
        double r1448966 = r1448965 * r1448955;
        double r1448967 = r1448966 * r1448955;
        double r1448968 = r1448967 * r1448955;
        double r1448969 = r1448960 + r1448968;
        double r1448970 = 15.0;
        double r1448971 = /* ERROR: no complex support in C */;
        double r1448972 = r1448971 * r1448955;
        double r1448973 = r1448972 * r1448955;
        double r1448974 = r1448973 * r1448955;
        double r1448975 = r1448974 * r1448955;
        double r1448976 = r1448969 + r1448975;
        double r1448977 = 20.0;
        double r1448978 = /* ERROR: no complex support in C */;
        double r1448979 = r1448978 * r1448955;
        double r1448980 = r1448979 * r1448955;
        double r1448981 = r1448980 * r1448955;
        double r1448982 = r1448976 + r1448981;
        double r1448983 = r1448982 + r1448973;
        double r1448984 = r1448983 + r1448964;
        double r1448985 = /* ERROR: no complex support in C */;
        double r1448986 = r1448984 + r1448985;
        double r1448987 = /* ERROR: no complex support in C */;
        return r1448987;
}
↓
double f() {
        double r1448988 = -5.0;
        double r1448989 = -24.0;
        double r1448990 = /* ERROR: no complex support in C */;
        double r1448991 = 24.0;
        double r1448992 = /* ERROR: no complex support in C */;
        double r1448993 = 0.0;
        double r1448994 = 8.0;
        double r1448995 = /* ERROR: no complex support in C */;
        double r1448996 = r1448992 + r1448995;
        double r1448997 = 40.0;
        double r1448998 = /* ERROR: no complex support in C */;
        double r1448999 = -60.0;
        double r1449000 = /* ERROR: no complex support in C */;
        double r1449001 = r1448998 + r1449000;
        double r1449002 = r1448996 + r1449001;
        double r1449003 = r1448990 + r1449002;
        double r1449004 = /* ERROR: no complex support in C */;
        return r1449004;
}

Error

Derivation

  1. Initial program 0

    \[\Im(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(\left(\left(\left(6 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(\left(15 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(20 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(15 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(6 + 0 i\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(1 + 0 i\right)\right))\]

  2. Simplified0

    \[\leadsto \color{blue}{\Im(\left(\left(-5 + -24 i\right) + \left(\left(\left(40 + 40 i\right) + \left(-60 + 0 i\right)\right) + \left(\left(24 + -24 i\right) + \left(0 + 8 i\right)\right)\right)\right))}\]

  3. Final simplification0

    \[\leadsto \Im(\left(\left(-5 + -24 i\right) + \left(\left(\left(24 + -24 i\right) + \left(0 + 8 i\right)\right) + \left(\left(40 + 40 i\right) + \left(-60 + 0 i\right)\right)\right)\right))\]

Reproduce

herbie shell --seed 2019120 +o rules:numerics
(FPCore ()
  :name "3.9.1 imaginary part (p56)"
  (im (+.c (+.c (+.c (+.c (+.c (+.c (*.c (*.c (*.c (*.c (*.c (complex -1 1) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (*.c (*.c (*.c (*.c (*.c (complex 6 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (*.c (*.c (complex 15 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (*.c (complex 20 0) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (complex 15 0) (complex -1 1)) (complex -1 1))) (*.c (complex 6 0) (complex -1 1))) (complex 1 0))))