3.9.2 real part (p56)

Average Error: 61.9 → 0

Time: 1.8m

Precision: 64

Math

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

↓

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

C

double f() {
        double r2723990 = 1.0;
        double r2723991 = -r2723990;
        double r2723992 = 2.0;
        double r2723993 = r2723991 / r2723992;
        double r2723994 = 3.0;
        double r2723995 = sqrt(r2723994);
        double r2723996 = r2723995 / r2723992;
        double r2723997 = /* ERROR: no complex support in C */;
        double r2723998 = r2723997 * r2723997;
        double r2723999 = r2723998 * r2723997;
        double r2724000 = r2723999 * r2723997;
        double r2724001 = -r2723992;
        double r2724002 = 0.0;
        double r2724003 = /* ERROR: no complex support in C */;
        double r2724004 = r2724003 * r2723997;
        double r2724005 = r2724004 * r2723997;
        double r2724006 = r2724005 * r2723997;
        double r2724007 = r2724000 + r2724006;
        double r2724008 = 5.0;
        double r2724009 = /* ERROR: no complex support in C */;
        double r2724010 = r2724009 * r2723997;
        double r2724011 = r2724010 * r2723997;
        double r2724012 = r2724007 + r2724011;
        double r2724013 = 4.0;
        double r2724014 = /* ERROR: no complex support in C */;
        double r2724015 = r2724014 * r2723997;
        double r2724016 = r2724012 + r2724015;
        double r2724017 = 7.0;
        double r2724018 = /* ERROR: no complex support in C */;
        double r2724019 = r2724016 + r2724018;
        double r2724020 = /* ERROR: no complex support in C */;
        return r2724020;
}

↓

double f() {
        double r2724021 = 1.0;
        double r2724022 = 2.0;
        double r2724023 = r2724021 / r2724022;
        double r2724024 = -r2724023;
        double r2724025 = 3.0;
        double r2724026 = sqrt(r2724025);
        double r2724027 = r2724026 / r2724022;
        double r2724028 = /* ERROR: no complex support in C */;
        double r2724029 = r2724022 + r2724023;
        double r2724030 = r2724023 * r2724029;
        double r2724031 = 0.0;
        double r2724032 = r2724031 + r2724027;
        double r2724033 = r2724027 * r2724032;
        double r2724034 = r2724030 - r2724033;
        double r2724035 = r2724029 * r2724027;
        double r2724036 = r2724032 * r2724023;
        double r2724037 = r2724035 + r2724036;
        double r2724038 = -r2724037;
        double r2724039 = /* ERROR: no complex support in C */;
        double r2724040 = 5.0;
        double r2724041 = /* ERROR: no complex support in C */;
        double r2724042 = r2724039 + r2724041;
        double r2724043 = r2724042 * r2724028;
        double r2724044 = 4.0;
        double r2724045 = /* ERROR: no complex support in C */;
        double r2724046 = r2724043 + r2724045;
        double r2724047 = r2724028 * r2724046;
        double r2724048 = 7.0;
        double r2724049 = /* ERROR: no complex support in C */;
        double r2724050 = r2724047 + r2724049;
        double r2724051 = /* ERROR: no complex support in C */;
        return r2724051;
}

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

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019200 
(FPCore ()
  :name "3.9.2 real part (p56)"
  (re (+ (+ (+ (+ (* (* (* (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (* (* (* (complex (- 2.0) 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (* (* (complex 5.0 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (* (complex 4.0 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (complex 7.0 0.0))))