3.9.1 real part (p56)

Average Error: 0 → 0

Time: 5.4s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f() {
        double r33697 = -1.0;
        double r33698 = 1.0;
        double r33699 = /* ERROR: no complex support in C */;
        double r33700 = r33699 * r33699;
        double r33701 = r33700 * r33699;
        double r33702 = r33701 * r33699;
        double r33703 = r33702 * r33699;
        double r33704 = r33703 * r33699;
        double r33705 = 6.0;
        double r33706 = 0.0;
        double r33707 = /* ERROR: no complex support in C */;
        double r33708 = r33707 * r33699;
        double r33709 = r33708 * r33699;
        double r33710 = r33709 * r33699;
        double r33711 = r33710 * r33699;
        double r33712 = r33711 * r33699;
        double r33713 = r33704 + r33712;
        double r33714 = 15.0;
        double r33715 = /* ERROR: no complex support in C */;
        double r33716 = r33715 * r33699;
        double r33717 = r33716 * r33699;
        double r33718 = r33717 * r33699;
        double r33719 = r33718 * r33699;
        double r33720 = r33713 + r33719;
        double r33721 = 20.0;
        double r33722 = /* ERROR: no complex support in C */;
        double r33723 = r33722 * r33699;
        double r33724 = r33723 * r33699;
        double r33725 = r33724 * r33699;
        double r33726 = r33720 + r33725;
        double r33727 = r33726 + r33717;
        double r33728 = r33727 + r33708;
        double r33729 = /* ERROR: no complex support in C */;
        double r33730 = r33728 + r33729;
        double r33731 = /* ERROR: no complex support in C */;
        return r33731;
}

↓

double f() {
        double r33732 = 1.0;
        double r33733 = 0.0;
        double r33734 = /* ERROR: no complex support in C */;
        double r33735 = -1.0;
        double r33736 = /* ERROR: no complex support in C */;
        double r33737 = 15.0;
        double r33738 = /* ERROR: no complex support in C */;
        double r33739 = r33738 * r33736;
        double r33740 = 6.0;
        double r33741 = /* ERROR: no complex support in C */;
        double r33742 = r33739 + r33741;
        double r33743 = r33736 * r33742;
        double r33744 = r33734 + r33743;
        double r33745 = r33736 * r33736;
        double r33746 = 20.0;
        double r33747 = /* ERROR: no complex support in C */;
        double r33748 = r33739 + r33747;
        double r33749 = r33736 * r33748;
        double r33750 = r33736 + r33741;
        double r33751 = r33745 * r33750;
        double r33752 = r33736 * r33751;
        double r33753 = r33749 + r33752;
        double r33754 = r33745 * r33753;
        double r33755 = r33744 + r33754;
        double r33756 = /* ERROR: no complex support in C */;
        return r33756;
}

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. Simplified 0

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2020045 +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))))