Average Error: 61.9 → 0
Time: 20.0s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(5 + \frac{\sqrt{3} \cdot 4}{2} i\right) + \left(\left(\frac{1}{4} + \left(-\frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right)\right) + \left(-\frac{\sqrt{3}}{2}\right) i\right) \cdot \left(\left(\left(\frac{1}{4} + \left(-\frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right)\right) + \left(-\frac{\sqrt{3}}{2}\right) i\right) + \left(6 + \frac{\sqrt{3}}{2} \cdot -2 i\right)\right)\right))\]
\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} \cdot 4}{2} i\right) + \left(\left(\frac{1}{4} + \left(-\frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right)\right) + \left(-\frac{\sqrt{3}}{2}\right) i\right) \cdot \left(\left(\left(\frac{1}{4} + \left(-\frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right)\right) + \left(-\frac{\sqrt{3}}{2}\right) i\right) + \left(6 + \frac{\sqrt{3}}{2} \cdot -2 i\right)\right)\right))
double f() {
        double r1615124 = 1.0;
        double r1615125 = -r1615124;
        double r1615126 = 2.0;
        double r1615127 = r1615125 / r1615126;
        double r1615128 = 3.0;
        double r1615129 = sqrt(r1615128);
        double r1615130 = r1615129 / r1615126;
        double r1615131 = /* ERROR: no complex support in C */;
        double r1615132 = r1615131 * r1615131;
        double r1615133 = r1615132 * r1615131;
        double r1615134 = r1615133 * r1615131;
        double r1615135 = -r1615126;
        double r1615136 = 0.0;
        double r1615137 = /* ERROR: no complex support in C */;
        double r1615138 = r1615137 * r1615131;
        double r1615139 = r1615138 * r1615131;
        double r1615140 = r1615139 * r1615131;
        double r1615141 = r1615134 + r1615140;
        double r1615142 = 5.0;
        double r1615143 = /* ERROR: no complex support in C */;
        double r1615144 = r1615143 * r1615131;
        double r1615145 = r1615144 * r1615131;
        double r1615146 = r1615141 + r1615145;
        double r1615147 = 4.0;
        double r1615148 = /* ERROR: no complex support in C */;
        double r1615149 = r1615148 * r1615131;
        double r1615150 = r1615146 + r1615149;
        double r1615151 = 7.0;
        double r1615152 = /* ERROR: no complex support in C */;
        double r1615153 = r1615150 + r1615152;
        double r1615154 = /* ERROR: no complex support in C */;
        return r1615154;
}
↓
double f() {
        double r1615155 = 5.0;
        double r1615156 = 3.0;
        double r1615157 = sqrt(r1615156);
        double r1615158 = 4.0;
        double r1615159 = r1615157 * r1615158;
        double r1615160 = 2.0;
        double r1615161 = r1615159 / r1615160;
        double r1615162 = /* ERROR: no complex support in C */;
        double r1615163 = 0.25;
        double r1615164 = r1615157 / r1615160;
        double r1615165 = r1615164 * r1615164;
        double r1615166 = -r1615165;
        double r1615167 = r1615163 + r1615166;
        double r1615168 = -r1615164;
        double r1615169 = /* ERROR: no complex support in C */;
        double r1615170 = 6.0;
        double r1615171 = -2.0;
        double r1615172 = r1615164 * r1615171;
        double r1615173 = /* ERROR: no complex support in C */;
        double r1615174 = r1615169 + r1615173;
        double r1615175 = r1615169 * r1615174;
        double r1615176 = r1615162 + r1615175;
        double r1615177 = /* ERROR: no complex support in C */;
        return r1615177;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019163 +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))))