3.9.1 imaginary part (p56)

Average Error: 0 → 0

Time: 21.0s

Precision: 64

Math

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

↓

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

C

double f() {
        double r33642 = -1.0;
        double r33643 = 1.0;
        double r33644 = /* ERROR: no complex support in C */;
        double r33645 = r33644 * r33644;
        double r33646 = r33645 * r33644;
        double r33647 = r33646 * r33644;
        double r33648 = r33647 * r33644;
        double r33649 = r33648 * r33644;
        double r33650 = 6.0;
        double r33651 = 0.0;
        double r33652 = /* ERROR: no complex support in C */;
        double r33653 = r33652 * r33644;
        double r33654 = r33653 * r33644;
        double r33655 = r33654 * r33644;
        double r33656 = r33655 * r33644;
        double r33657 = r33656 * r33644;
        double r33658 = r33649 + r33657;
        double r33659 = 15.0;
        double r33660 = /* ERROR: no complex support in C */;
        double r33661 = r33660 * r33644;
        double r33662 = r33661 * r33644;
        double r33663 = r33662 * r33644;
        double r33664 = r33663 * r33644;
        double r33665 = r33658 + r33664;
        double r33666 = 20.0;
        double r33667 = /* ERROR: no complex support in C */;
        double r33668 = r33667 * r33644;
        double r33669 = r33668 * r33644;
        double r33670 = r33669 * r33644;
        double r33671 = r33665 + r33670;
        double r33672 = r33671 + r33662;
        double r33673 = r33672 + r33653;
        double r33674 = /* ERROR: no complex support in C */;
        double r33675 = r33673 + r33674;
        double r33676 = /* ERROR: no complex support in C */;
        return r33676;
}

↓

double f() {
        double r33677 = 6.0;
        double r33678 = 0.0;
        double r33679 = /* ERROR: no complex support in C */;
        double r33680 = -1.0;
        double r33681 = 1.0;
        double r33682 = /* ERROR: no complex support in C */;
        double r33683 = r33679 * r33682;
        double r33684 = 15.0;
        double r33685 = /* ERROR: no complex support in C */;
        double r33686 = r33682 * r33685;
        double r33687 = r33682 * r33686;
        double r33688 = 20.0;
        double r33689 = /* ERROR: no complex support in C */;
        double r33690 = r33689 * r33682;
        double r33691 = r33682 * r33690;
        double r33692 = r33691 * r33682;
        double r33693 = r33682 * r33683;
        double r33694 = r33693 * r33682;
        double r33695 = r33682 * r33694;
        double r33696 = r33695 * r33682;
        double r33697 = r33682 * r33682;
        double r33698 = r33697 * r33682;
        double r33699 = r33682 * r33698;
        double r33700 = r33682 * r33699;
        double r33701 = r33700 * r33682;
        double r33702 = r33696 + r33701;
        double r33703 = r33682 * r33687;
        double r33704 = r33682 * r33703;
        double r33705 = r33702 + r33704;
        double r33706 = r33692 + r33705;
        double r33707 = r33687 + r33706;
        double r33708 = r33683 + r33707;
        double r33709 = /* ERROR: no complex support in C */;
        double r33710 = r33708 + r33709;
        double r33711 = /* ERROR: no complex support in C */;
        return r33711;
}

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. Final simplification 0

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

Reproduce

herbie shell --seed 2019174 
(FPCore ()
  :name "3.9.1 imaginary part (p56)"
  (im (+ (+ (+ (+ (+ (+ (* (* (* (* (* (complex -1.0 1.0) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (* (* (* (* (* (complex 6.0 0.0) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0))) (* (* (* (* (complex 15.0 0.0) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0))) (* (* (* (complex 20.0 0.0) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0))) (* (* (complex 15.0 0.0) (complex -1.0 1.0)) (complex -1.0 1.0))) (* (complex 6.0 0.0) (complex -1.0 1.0))) (complex 1.0 0.0))))