Average Error: 0 → 0
Time: 22.5s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right) + \left(\left(\left(\left(\left(6 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(\left(15 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(20 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(15 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(6 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) + \left(1 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(-5 + -24 i\right) + \left(\left(\left(24 + -24 i\right) + \left(0 + 8 i\right)\right) + \left(\left(40 + 40 i\right) + \left(-60 + 0 i\right)\right)\right)\right))\]
double f() {
        double r1191717 = -1.0;
        double r1191718 = 1.0;
        double r1191719 = /* ERROR: no complex support in C */;
        double r1191720 = r1191719 * r1191719;
        double r1191721 = r1191720 * r1191719;
        double r1191722 = r1191721 * r1191719;
        double r1191723 = r1191722 * r1191719;
        double r1191724 = r1191723 * r1191719;
        double r1191725 = 6.0;
        double r1191726 = 0.0;
        double r1191727 = /* ERROR: no complex support in C */;
        double r1191728 = r1191727 * r1191719;
        double r1191729 = r1191728 * r1191719;
        double r1191730 = r1191729 * r1191719;
        double r1191731 = r1191730 * r1191719;
        double r1191732 = r1191731 * r1191719;
        double r1191733 = r1191724 + r1191732;
        double r1191734 = 15.0;
        double r1191735 = /* ERROR: no complex support in C */;
        double r1191736 = r1191735 * r1191719;
        double r1191737 = r1191736 * r1191719;
        double r1191738 = r1191737 * r1191719;
        double r1191739 = r1191738 * r1191719;
        double r1191740 = r1191733 + r1191739;
        double r1191741 = 20.0;
        double r1191742 = /* ERROR: no complex support in C */;
        double r1191743 = r1191742 * r1191719;
        double r1191744 = r1191743 * r1191719;
        double r1191745 = r1191744 * r1191719;
        double r1191746 = r1191740 + r1191745;
        double r1191747 = r1191746 + r1191737;
        double r1191748 = r1191747 + r1191728;
        double r1191749 = /* ERROR: no complex support in C */;
        double r1191750 = r1191748 + r1191749;
        double r1191751 = /* ERROR: no complex support in C */;
        return r1191751;
}
↓
double f() {
        double r1191752 = -5.0;
        double r1191753 = -24.0;
        double r1191754 = /* ERROR: no complex support in C */;
        double r1191755 = 24.0;
        double r1191756 = /* ERROR: no complex support in C */;
        double r1191757 = 0.0;
        double r1191758 = 8.0;
        double r1191759 = /* ERROR: no complex support in C */;
        double r1191760 = r1191756 + r1191759;
        double r1191761 = 40.0;
        double r1191762 = /* ERROR: no complex support in C */;
        double r1191763 = -60.0;
        double r1191764 = /* ERROR: no complex support in C */;
        double r1191765 = r1191762 + r1191764;
        double r1191766 = r1191760 + r1191765;
        double r1191767 = r1191754 + r1191766;
        double r1191768 = /* ERROR: no complex support in C */;
        return r1191768;
}


\Re(\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) + \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) + \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) + \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) + \left(\left(15 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(6 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) + \left(1 + 0 i\right)\right))
↓
\Re(\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))

Error

Derivation

  1. Initial program 0

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019102 
(FPCore ()
  :name "3.9.1 real part (p56)"
  (re (+.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))))