3.9.2 real part (p56)

Average Error: 61.9 → 0

Time: 4.9s

Precision: 64

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

Math

\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]

↓

\[\Re(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\left(\frac{-1}{2} - 2\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right)\right) + \left(4 + 0.0 i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]

C

double f() {
        double r3818 = 1.0;
        double r3819 = -r3818;
        double r3820 = 2.0;
        double r3821 = r3819 / r3820;
        double r3822 = 3.0;
        double r3823 = sqrt(r3822);
        double r3824 = r3823 / r3820;
        double r3825 = /* ERROR: no complex support in C */;
        double r3826 = r3825 * r3825;
        double r3827 = r3826 * r3825;
        double r3828 = r3827 * r3825;
        double r3829 = -r3820;
        double r3830 = 0.0;
        double r3831 = /* ERROR: no complex support in C */;
        double r3832 = r3831 * r3825;
        double r3833 = r3832 * r3825;
        double r3834 = r3833 * r3825;
        double r3835 = r3828 + r3834;
        double r3836 = 5.0;
        double r3837 = /* ERROR: no complex support in C */;
        double r3838 = r3837 * r3825;
        double r3839 = r3838 * r3825;
        double r3840 = r3835 + r3839;
        double r3841 = 4.0;
        double r3842 = /* ERROR: no complex support in C */;
        double r3843 = r3842 * r3825;
        double r3844 = r3840 + r3843;
        double r3845 = 7.0;
        double r3846 = /* ERROR: no complex support in C */;
        double r3847 = r3844 + r3846;
        double r3848 = /* ERROR: no complex support in C */;
        return r3848;
}

↓

double f() {
        double r3849 = 1.0;
        double r3850 = -r3849;
        double r3851 = 2.0;
        double r3852 = r3850 / r3851;
        double r3853 = 3.0;
        double r3854 = sqrt(r3853);
        double r3855 = r3854 / r3851;
        double r3856 = /* ERROR: no complex support in C */;
        double r3857 = 5.0;
        double r3858 = 0.0;
        double r3859 = /* ERROR: no complex support in C */;
        double r3860 = r3852 - r3851;
        double r3861 = r3855 + r3858;
        double r3862 = /* ERROR: no complex support in C */;
        double r3863 = r3862 * r3856;
        double r3864 = r3859 + r3863;
        double r3865 = r3856 * r3864;
        double r3866 = 4.0;
        double r3867 = /* ERROR: no complex support in C */;
        double r3868 = r3865 + r3867;
        double r3869 = r3856 * r3868;
        double r3870 = 7.0;
        double r3871 = /* ERROR: no complex support in C */;
        double r3872 = r3869 + r3871;
        double r3873 = /* ERROR: no complex support in C */;
        return r3873;
}

Derivation

1. Initial program 61.9

   \[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]

2. Simplified 0

   \[\leadsto \color{blue}{\Re(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\left(\frac{-1}{2} - 2\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right)\right) + \left(4 + 0.0 i\right)\right)\right) + \left(7 + 0.0 i\right)\right))}\]

3. Final simplification 0

   \[\leadsto \Re(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\left(\frac{-1}{2} - 2\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right)\right) + \left(4 + 0.0 i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]

Reproduce

herbie shell --seed 2020045 
(FPCore ()
  :name "3.9.2 real part (p56)"
  :precision binary64
  (re (+ (+ (+ (+ (* (* (* (complex (/ (- 1) 2) (/ (sqrt 3) 2)) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (* (* (* (complex (- 2) 0.0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (* (* (complex 5 0.0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (* (complex 4 0.0) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (complex 7 0.0))))