Average Error: 0 → 0
Time: 5.2s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(\left(\left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(20 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(1 + 0.0 i\right)\right))\]
↓
\[\Re(\left(\left(\left(1 + 0.0 i\right) + \left(\left(-1 + 1 i\right) \cdot \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) + \left(6 + 0.0 i\right)\right)\right)\right) + \left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(\left(\left(-1 + 1 i\right) \cdot \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) + \left(20 + 0.0 i\right)\right)\right) + \left(\left(-1 + 1 i\right) \cdot \left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(\left(-1 + 1 i\right) + \left(6 + 0.0 i\right)\right)\right)\right)\right)\right)\right))\]
\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(1 + 0.0 i\right) + \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)\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 r79749 = -1.0;
        double r79750 = 1.0;
        double r79751 = /* ERROR: no complex support in C */;
        double r79752 = r79751 * r79751;
        double r79753 = r79752 * r79751;
        double r79754 = r79753 * r79751;
        double r79755 = r79754 * r79751;
        double r79756 = r79755 * r79751;
        double r79757 = 6.0;
        double r79758 = 0.0;
        double r79759 = /* ERROR: no complex support in C */;
        double r79760 = r79759 * r79751;
        double r79761 = r79760 * r79751;
        double r79762 = r79761 * r79751;
        double r79763 = r79762 * r79751;
        double r79764 = r79763 * r79751;
        double r79765 = r79756 + r79764;
        double r79766 = 15.0;
        double r79767 = /* ERROR: no complex support in C */;
        double r79768 = r79767 * r79751;
        double r79769 = r79768 * r79751;
        double r79770 = r79769 * r79751;
        double r79771 = r79770 * r79751;
        double r79772 = r79765 + r79771;
        double r79773 = 20.0;
        double r79774 = /* ERROR: no complex support in C */;
        double r79775 = r79774 * r79751;
        double r79776 = r79775 * r79751;
        double r79777 = r79776 * r79751;
        double r79778 = r79772 + r79777;
        double r79779 = r79778 + r79769;
        double r79780 = r79779 + r79760;
        double r79781 = /* ERROR: no complex support in C */;
        double r79782 = r79780 + r79781;
        double r79783 = /* ERROR: no complex support in C */;
        return r79783;
}
↓
double f() {
        double r79784 = 1.0;
        double r79785 = 0.0;
        double r79786 = /* ERROR: no complex support in C */;
        double r79787 = -1.0;
        double r79788 = /* ERROR: no complex support in C */;
        double r79789 = 15.0;
        double r79790 = /* ERROR: no complex support in C */;
        double r79791 = r79790 * r79788;
        double r79792 = 6.0;
        double r79793 = /* ERROR: no complex support in C */;
        double r79794 = r79791 + r79793;
        double r79795 = r79788 * r79794;
        double r79796 = r79786 + r79795;
        double r79797 = r79788 * r79788;
        double r79798 = 20.0;
        double r79799 = /* ERROR: no complex support in C */;
        double r79800 = r79791 + r79799;
        double r79801 = r79788 * r79800;
        double r79802 = r79788 + r79793;
        double r79803 = r79797 * r79802;
        double r79804 = r79788 * r79803;
        double r79805 = r79801 + r79804;
        double r79806 = r79797 * r79805;
        double r79807 = r79796 + r79806;
        double r79808 = /* ERROR: no complex support in C */;
        return r79808;
}

Error

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. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore ()
  :name "3.9.1 real part (p56)"
  :precision binary64
  (re (+ (+ (+ (+ (+ (+ (* (* (* (* (* (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))))