Average Error: 61.9 → 0
Time: 41.7s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) + \left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(5 + \frac{4}{\frac{2}{\sqrt{3}}} i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(-\frac{\sqrt{3}}{2}\right) i\right) \cdot \left(\left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(-\frac{\sqrt{3}}{2}\right) i\right) + \left(6 + \frac{\sqrt{3}}{2} \cdot -2 i\right)\right)\right))\]
double f() {
        double r1675128 = 1.0;
        double r1675129 = -r1675128;
        double r1675130 = 2.0;
        double r1675131 = r1675129 / r1675130;
        double r1675132 = 3.0;
        double r1675133 = sqrt(r1675132);
        double r1675134 = r1675133 / r1675130;
        double r1675135 = /* ERROR: no complex support in C */;
        double r1675136 = r1675135 * r1675135;
        double r1675137 = r1675136 * r1675135;
        double r1675138 = r1675137 * r1675135;
        double r1675139 = -r1675130;
        double r1675140 = 0.0;
        double r1675141 = /* ERROR: no complex support in C */;
        double r1675142 = r1675141 * r1675135;
        double r1675143 = r1675142 * r1675135;
        double r1675144 = r1675143 * r1675135;
        double r1675145 = r1675138 + r1675144;
        double r1675146 = 5.0;
        double r1675147 = /* ERROR: no complex support in C */;
        double r1675148 = r1675147 * r1675135;
        double r1675149 = r1675148 * r1675135;
        double r1675150 = r1675145 + r1675149;
        double r1675151 = 4.0;
        double r1675152 = /* ERROR: no complex support in C */;
        double r1675153 = r1675152 * r1675135;
        double r1675154 = r1675150 + r1675153;
        double r1675155 = 7.0;
        double r1675156 = /* ERROR: no complex support in C */;
        double r1675157 = r1675154 + r1675156;
        double r1675158 = /* ERROR: no complex support in C */;
        return r1675158;
}
↓
double f() {
        double r1675159 = 5.0;
        double r1675160 = 4.0;
        double r1675161 = 2.0;
        double r1675162 = 3.0;
        double r1675163 = sqrt(r1675162);
        double r1675164 = r1675161 / r1675163;
        double r1675165 = r1675160 / r1675164;
        double r1675166 = /* ERROR: no complex support in C */;
        double r1675167 = 0.25;
        double r1675168 = r1675163 / r1675161;
        double r1675169 = r1675168 * r1675168;
        double r1675170 = r1675167 - r1675169;
        double r1675171 = -r1675168;
        double r1675172 = /* ERROR: no complex support in C */;
        double r1675173 = 6.0;
        double r1675174 = -2.0;
        double r1675175 = r1675168 * r1675174;
        double r1675176 = /* ERROR: no complex support in C */;
        double r1675177 = r1675172 + r1675176;
        double r1675178 = r1675172 * r1675177;
        double r1675179 = r1675166 + r1675178;
        double r1675180 = /* ERROR: no complex support in C */;
        return r1675180;
}


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

Error

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. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019102 
(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))))