Average Error: 0 → 0
Time: 2.0m
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(\left(\left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(20 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(1 + 0.0 i\right)\right))\]
↓
\[\Re(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) + \left(6 + 0.0 i\right)\right)\right) + \left(1 + 0.0 i\right)\right) + \left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(\left(\left(-1 + 1 i\right) \cdot \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) + \left(20 + 0.0 i\right)\right)\right) + \left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(\left(-1 + 1 i\right) + \left(6 + 0.0 i\right)\right)\right)\right)\right)\right))\]
\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(\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(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\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))
double f() {
        double r42589 = -1.0;
        double r42590 = 1.0;
        double r42591 = /* ERROR: no complex support in C */;
        double r42592 = r42591 * r42591;
        double r42593 = r42592 * r42591;
        double r42594 = r42593 * r42591;
        double r42595 = r42594 * r42591;
        double r42596 = r42595 * r42591;
        double r42597 = 6.0;
        double r42598 = 0.0;
        double r42599 = /* ERROR: no complex support in C */;
        double r42600 = r42599 * r42591;
        double r42601 = r42600 * r42591;
        double r42602 = r42601 * r42591;
        double r42603 = r42602 * r42591;
        double r42604 = r42603 * r42591;
        double r42605 = r42596 + r42604;
        double r42606 = 15.0;
        double r42607 = /* ERROR: no complex support in C */;
        double r42608 = r42607 * r42591;
        double r42609 = r42608 * r42591;
        double r42610 = r42609 * r42591;
        double r42611 = r42610 * r42591;
        double r42612 = r42605 + r42611;
        double r42613 = 20.0;
        double r42614 = /* ERROR: no complex support in C */;
        double r42615 = r42614 * r42591;
        double r42616 = r42615 * r42591;
        double r42617 = r42616 * r42591;
        double r42618 = r42612 + r42617;
        double r42619 = r42618 + r42609;
        double r42620 = r42619 + r42600;
        double r42621 = /* ERROR: no complex support in C */;
        double r42622 = r42620 + r42621;
        double r42623 = /* ERROR: no complex support in C */;
        return r42623;
}
↓
double f() {
        double r42624 = -1.0;
        double r42625 = 1.0;
        double r42626 = /* ERROR: no complex support in C */;
        double r42627 = 15.0;
        double r42628 = 0.0;
        double r42629 = /* ERROR: no complex support in C */;
        double r42630 = r42629 * r42626;
        double r42631 = 6.0;
        double r42632 = /* ERROR: no complex support in C */;
        double r42633 = r42630 + r42632;
        double r42634 = r42626 * r42633;
        double r42635 = /* ERROR: no complex support in C */;
        double r42636 = r42634 + r42635;
        double r42637 = r42626 * r42626;
        double r42638 = 20.0;
        double r42639 = /* ERROR: no complex support in C */;
        double r42640 = r42630 + r42639;
        double r42641 = r42626 * r42640;
        double r42642 = r42637 * r42626;
        double r42643 = r42626 + r42632;
        double r42644 = r42642 * r42643;
        double r42645 = r42641 + r42644;
        double r42646 = r42637 * r42645;
        double r42647 = r42636 + r42646;
        double r42648 = /* ERROR: no complex support in C */;
        return r42648;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019202 
(FPCore ()
  :name "3.9.1 real part (p56)"
  (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))))