3.9.2 real part (p56)

Average Error: 61.9 → 0

Time: 41.6s

Precision: 64

Math

\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]

↓

\[\Re(\left(\left(5 + \frac{4}{\frac{2}{\sqrt{3}}} i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(-\frac{\sqrt{3}}{2}\right) i\right) \cdot \left(\left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(-\frac{\sqrt{3}}{2}\right) i\right) + \left(6 + \frac{\sqrt{3}}{2} \cdot -2 i\right)\right)\right))\]

C

double f() {
        double r2559043 = 1.0;
        double r2559044 = -r2559043;
        double r2559045 = 2.0;
        double r2559046 = r2559044 / r2559045;
        double r2559047 = 3.0;
        double r2559048 = sqrt(r2559047);
        double r2559049 = r2559048 / r2559045;
        double r2559050 = /* ERROR: no complex support in C */;
        double r2559051 = r2559050 * r2559050;
        double r2559052 = r2559051 * r2559050;
        double r2559053 = r2559052 * r2559050;
        double r2559054 = -r2559045;
        double r2559055 = 0.0;
        double r2559056 = /* ERROR: no complex support in C */;
        double r2559057 = r2559056 * r2559050;
        double r2559058 = r2559057 * r2559050;
        double r2559059 = r2559058 * r2559050;
        double r2559060 = r2559053 + r2559059;
        double r2559061 = 5.0;
        double r2559062 = /* ERROR: no complex support in C */;
        double r2559063 = r2559062 * r2559050;
        double r2559064 = r2559063 * r2559050;
        double r2559065 = r2559060 + r2559064;
        double r2559066 = 4.0;
        double r2559067 = /* ERROR: no complex support in C */;
        double r2559068 = r2559067 * r2559050;
        double r2559069 = r2559065 + r2559068;
        double r2559070 = 7.0;
        double r2559071 = /* ERROR: no complex support in C */;
        double r2559072 = r2559069 + r2559071;
        double r2559073 = /* ERROR: no complex support in C */;
        return r2559073;
}

↓

double f() {
        double r2559074 = 5.0;
        double r2559075 = 4.0;
        double r2559076 = 2.0;
        double r2559077 = 3.0;
        double r2559078 = sqrt(r2559077);
        double r2559079 = r2559076 / r2559078;
        double r2559080 = r2559075 / r2559079;
        double r2559081 = /* ERROR: no complex support in C */;
        double r2559082 = 0.25;
        double r2559083 = r2559078 / r2559076;
        double r2559084 = r2559083 * r2559083;
        double r2559085 = r2559082 - r2559084;
        double r2559086 = -r2559083;
        double r2559087 = /* ERROR: no complex support in C */;
        double r2559088 = 6.0;
        double r2559089 = -2.0;
        double r2559090 = r2559083 * r2559089;
        double r2559091 = /* ERROR: no complex support in C */;
        double r2559092 = r2559087 + r2559091;
        double r2559093 = r2559087 * r2559092;
        double r2559094 = r2559081 + r2559093;
        double r2559095 = /* ERROR: no complex support in C */;
        return r2559095;
}

Derivation

1. Initial program 61.9

   \[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]

2. Simplified 0

   \[\leadsto \color{blue}{\Re(\left(\left(5 + \frac{4}{\frac{2}{\sqrt{3}}} i\right) + \left(\left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{\sqrt{3}}{2} \cdot -1 i\right) \cdot \left(\left(6 + \frac{\sqrt{3}}{2} \cdot -2 i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{\sqrt{3}}{2} \cdot -1 i\right)\right)\right)\right))}\]

3. Final simplification 0

   \[\leadsto \Re(\left(\left(5 + \frac{4}{\frac{2}{\sqrt{3}}} i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(-\frac{\sqrt{3}}{2}\right) i\right) \cdot \left(\left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(-\frac{\sqrt{3}}{2}\right) i\right) + \left(6 + \frac{\sqrt{3}}{2} \cdot -2 i\right)\right)\right))\]

Reproduce

herbie shell --seed 2019120 
(FPCore ()
  :name "3.9.2 real part (p56)"
  (re (+.c (+.c (+.c (+.c (*.c (*.c (*.c (complex (/ (- 1) 2) (/ (sqrt 3) 2)) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (*.c (*.c (*.c (complex (- 2) 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (*.c (*.c (complex 5 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (*.c (complex 4 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (complex 7 0))))