Average Error: 0 → 0
Time: 23.6s
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 r1397629 = -1.0;
        double r1397630 = 1.0;
        double r1397631 = /* ERROR: no complex support in C */;
        double r1397632 = r1397631 * r1397631;
        double r1397633 = r1397632 * r1397631;
        double r1397634 = r1397633 * r1397631;
        double r1397635 = r1397634 * r1397631;
        double r1397636 = r1397635 * r1397631;
        double r1397637 = 6.0;
        double r1397638 = 0.0;
        double r1397639 = /* ERROR: no complex support in C */;
        double r1397640 = r1397639 * r1397631;
        double r1397641 = r1397640 * r1397631;
        double r1397642 = r1397641 * r1397631;
        double r1397643 = r1397642 * r1397631;
        double r1397644 = r1397643 * r1397631;
        double r1397645 = r1397636 + r1397644;
        double r1397646 = 15.0;
        double r1397647 = /* ERROR: no complex support in C */;
        double r1397648 = r1397647 * r1397631;
        double r1397649 = r1397648 * r1397631;
        double r1397650 = r1397649 * r1397631;
        double r1397651 = r1397650 * r1397631;
        double r1397652 = r1397645 + r1397651;
        double r1397653 = 20.0;
        double r1397654 = /* ERROR: no complex support in C */;
        double r1397655 = r1397654 * r1397631;
        double r1397656 = r1397655 * r1397631;
        double r1397657 = r1397656 * r1397631;
        double r1397658 = r1397652 + r1397657;
        double r1397659 = r1397658 + r1397649;
        double r1397660 = r1397659 + r1397640;
        double r1397661 = /* ERROR: no complex support in C */;
        double r1397662 = r1397660 + r1397661;
        double r1397663 = /* ERROR: no complex support in C */;
        return r1397663;
}
↓
double f() {
        double r1397664 = -5.0;
        double r1397665 = -24.0;
        double r1397666 = /* ERROR: no complex support in C */;
        double r1397667 = 24.0;
        double r1397668 = /* ERROR: no complex support in C */;
        double r1397669 = 0.0;
        double r1397670 = 8.0;
        double r1397671 = /* ERROR: no complex support in C */;
        double r1397672 = r1397668 + r1397671;
        double r1397673 = 40.0;
        double r1397674 = /* ERROR: no complex support in C */;
        double r1397675 = -60.0;
        double r1397676 = /* ERROR: no complex support in C */;
        double r1397677 = r1397674 + r1397676;
        double r1397678 = r1397672 + r1397677;
        double r1397679 = r1397666 + r1397678;
        double r1397680 = /* ERROR: no complex support in C */;
        return r1397680;
}


\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 2019101 
(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))))