3.9.2 real part (p56)

Average Error: 61.9 → 0

Time: 31.4s

Precision: 64

Math

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

↓

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

C

double f() {
        double r1507136 = 1.0;
        double r1507137 = -r1507136;
        double r1507138 = 2.0;
        double r1507139 = r1507137 / r1507138;
        double r1507140 = 3.0;
        double r1507141 = sqrt(r1507140);
        double r1507142 = r1507141 / r1507138;
        double r1507143 = /* ERROR: no complex support in C */;
        double r1507144 = r1507143 * r1507143;
        double r1507145 = r1507144 * r1507143;
        double r1507146 = r1507145 * r1507143;
        double r1507147 = -r1507138;
        double r1507148 = 0.0;
        double r1507149 = /* ERROR: no complex support in C */;
        double r1507150 = r1507149 * r1507143;
        double r1507151 = r1507150 * r1507143;
        double r1507152 = r1507151 * r1507143;
        double r1507153 = r1507146 + r1507152;
        double r1507154 = 5.0;
        double r1507155 = /* ERROR: no complex support in C */;
        double r1507156 = r1507155 * r1507143;
        double r1507157 = r1507156 * r1507143;
        double r1507158 = r1507153 + r1507157;
        double r1507159 = 4.0;
        double r1507160 = /* ERROR: no complex support in C */;
        double r1507161 = r1507160 * r1507143;
        double r1507162 = r1507158 + r1507161;
        double r1507163 = 7.0;
        double r1507164 = /* ERROR: no complex support in C */;
        double r1507165 = r1507162 + r1507164;
        double r1507166 = /* ERROR: no complex support in C */;
        return r1507166;
}

↓

double f() {
        double r1507167 = 5.0;
        double r1507168 = 3.0;
        double r1507169 = sqrt(r1507168);
        double r1507170 = 2.0;
        double r1507171 = r1507169 / r1507170;
        double r1507172 = 4.0;
        double r1507173 = r1507171 * r1507172;
        double r1507174 = /* ERROR: no complex support in C */;
        double r1507175 = 0.25;
        double r1507176 = r1507171 * r1507171;
        double r1507177 = r1507175 - r1507176;
        double r1507178 = -r1507169;
        double r1507179 = r1507178 / r1507170;
        double r1507180 = /* ERROR: no complex support in C */;
        double r1507181 = 6.0;
        double r1507182 = -2.0;
        double r1507183 = r1507182 * r1507169;
        double r1507184 = r1507183 / r1507170;
        double r1507185 = /* ERROR: no complex support in C */;
        double r1507186 = r1507185 + r1507180;
        double r1507187 = r1507180 * r1507186;
        double r1507188 = r1507174 + r1507187;
        double r1507189 = /* ERROR: no complex support in C */;
        return r1507189;
}

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

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(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))))