Average Error: 0 → 0
Time: 20.9s
Precision: 64
\[\Im(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(\left(\left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(20 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(1 + 0.0 i\right)\right))\]
↓
\[\Im(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) + \left(6 + 0.0 i\right)\right)\right) + \left(1 + 0.0 i\right)\right) + \left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(\left(\left(-1 + 1 i\right) \cdot \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) + \left(20 + 0.0 i\right)\right)\right) + \left(\left(-1 + 1 i\right) \cdot \left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(\left(-1 + 1 i\right) + \left(6 + 0.0 i\right)\right)\right)\right)\right)\right)\right))\]
\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 + 0.0 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(-1 + 1 i\right) \cdot \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) + \left(6 + 0.0 i\right)\right)\right) + \left(1 + 0.0 i\right)\right) + \left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(\left(\left(-1 + 1 i\right) \cdot \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) + \left(20 + 0.0 i\right)\right)\right) + \left(\left(-1 + 1 i\right) \cdot \left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(\left(-1 + 1 i\right) + \left(6 + 0.0 i\right)\right)\right)\right)\right)\right)\right))
double f() {
        double r9917 = -1.0;
        double r9918 = 1.0;
        double r9919 = /* ERROR: no complex support in C */;
        double r9920 = r9919 * r9919;
        double r9921 = r9920 * r9919;
        double r9922 = r9921 * r9919;
        double r9923 = r9922 * r9919;
        double r9924 = r9923 * r9919;
        double r9925 = 6.0;
        double r9926 = 0.0;
        double r9927 = /* ERROR: no complex support in C */;
        double r9928 = r9927 * r9919;
        double r9929 = r9928 * r9919;
        double r9930 = r9929 * r9919;
        double r9931 = r9930 * r9919;
        double r9932 = r9931 * r9919;
        double r9933 = r9924 + r9932;
        double r9934 = 15.0;
        double r9935 = /* ERROR: no complex support in C */;
        double r9936 = r9935 * r9919;
        double r9937 = r9936 * r9919;
        double r9938 = r9937 * r9919;
        double r9939 = r9938 * r9919;
        double r9940 = r9933 + r9939;
        double r9941 = 20.0;
        double r9942 = /* ERROR: no complex support in C */;
        double r9943 = r9942 * r9919;
        double r9944 = r9943 * r9919;
        double r9945 = r9944 * r9919;
        double r9946 = r9940 + r9945;
        double r9947 = r9946 + r9937;
        double r9948 = r9947 + r9928;
        double r9949 = /* ERROR: no complex support in C */;
        double r9950 = r9948 + r9949;
        double r9951 = /* ERROR: no complex support in C */;
        return r9951;
}
↓
double f() {
        double r9952 = -1.0;
        double r9953 = 1.0;
        double r9954 = /* ERROR: no complex support in C */;
        double r9955 = 15.0;
        double r9956 = 0.0;
        double r9957 = /* ERROR: no complex support in C */;
        double r9958 = r9957 * r9954;
        double r9959 = 6.0;
        double r9960 = /* ERROR: no complex support in C */;
        double r9961 = r9958 + r9960;
        double r9962 = r9954 * r9961;
        double r9963 = /* ERROR: no complex support in C */;
        double r9964 = r9962 + r9963;
        double r9965 = r9954 * r9954;
        double r9966 = 20.0;
        double r9967 = /* ERROR: no complex support in C */;
        double r9968 = r9958 + r9967;
        double r9969 = r9954 * r9968;
        double r9970 = r9954 + r9960;
        double r9971 = r9965 * r9970;
        double r9972 = r9954 * r9971;
        double r9973 = r9969 + r9972;
        double r9974 = r9965 * r9973;
        double r9975 = r9964 + r9974;
        double r9976 = /* ERROR: no complex support in C */;
        return r9976;
}

Error

Derivation

  1. Initial program 0

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019310 
(FPCore ()
  :name "3.9.1 imaginary part (p56)"
  :precision binary64
  (im (+ (+ (+ (+ (+ (+ (* (* (* (* (* (complex -1 1) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (* (* (* (* (* (complex 6 0.0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (* (* (* (* (complex 15 0.0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (* (* (* (complex 20 0.0) (complex -1 1)) (complex -1 1)) (complex -1 1))) (* (* (complex 15 0.0) (complex -1 1)) (complex -1 1))) (* (complex 6 0.0) (complex -1 1))) (complex 1 0.0))))