Average Error: 61.9 → 0
Time: 22.6s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(\left(7 - \frac{4}{2}\right) + 4 \cdot \frac{\sqrt{3}}{2} i\right) + \left(\left(5 + \left(1 + \left(\frac{\frac{1}{2}}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right)\right)\right) + \left(\left(-\left(\frac{\frac{\sqrt{3}}{2}}{2} + \frac{\frac{\sqrt{3}}{2}}{2}\right)\right) + \frac{\sqrt{3}}{2} \cdot \left(-2\right)\right) i\right) \cdot \left(\left(\frac{\frac{1}{2}}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(-\left(\frac{\frac{\sqrt{3}}{2}}{2} + \frac{\frac{\sqrt{3}}{2}}{2}\right)\right) i\right)\right))\]
\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(\left(7 - \frac{4}{2}\right) + 4 \cdot \frac{\sqrt{3}}{2} i\right) + \left(\left(5 + \left(1 + \left(\frac{\frac{1}{2}}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right)\right)\right) + \left(\left(-\left(\frac{\frac{\sqrt{3}}{2}}{2} + \frac{\frac{\sqrt{3}}{2}}{2}\right)\right) + \frac{\sqrt{3}}{2} \cdot \left(-2\right)\right) i\right) \cdot \left(\left(\frac{\frac{1}{2}}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(-\left(\frac{\frac{\sqrt{3}}{2}}{2} + \frac{\frac{\sqrt{3}}{2}}{2}\right)\right) i\right)\right))
double f() {
        double r1451119 = 1.0;
        double r1451120 = -r1451119;
        double r1451121 = 2.0;
        double r1451122 = r1451120 / r1451121;
        double r1451123 = 3.0;
        double r1451124 = sqrt(r1451123);
        double r1451125 = r1451124 / r1451121;
        double r1451126 = /* ERROR: no complex support in C */;
        double r1451127 = r1451126 * r1451126;
        double r1451128 = r1451127 * r1451126;
        double r1451129 = r1451128 * r1451126;
        double r1451130 = -r1451121;
        double r1451131 = 0.0;
        double r1451132 = /* ERROR: no complex support in C */;
        double r1451133 = r1451132 * r1451126;
        double r1451134 = r1451133 * r1451126;
        double r1451135 = r1451134 * r1451126;
        double r1451136 = r1451129 + r1451135;
        double r1451137 = 5.0;
        double r1451138 = /* ERROR: no complex support in C */;
        double r1451139 = r1451138 * r1451126;
        double r1451140 = r1451139 * r1451126;
        double r1451141 = r1451136 + r1451140;
        double r1451142 = 4.0;
        double r1451143 = /* ERROR: no complex support in C */;
        double r1451144 = r1451143 * r1451126;
        double r1451145 = r1451141 + r1451144;
        double r1451146 = 7.0;
        double r1451147 = /* ERROR: no complex support in C */;
        double r1451148 = r1451145 + r1451147;
        double r1451149 = /* ERROR: no complex support in C */;
        return r1451149;
}
↓
double f() {
        double r1451150 = 7.0;
        double r1451151 = 4.0;
        double r1451152 = 2.0;
        double r1451153 = r1451151 / r1451152;
        double r1451154 = r1451150 - r1451153;
        double r1451155 = 3.0;
        double r1451156 = sqrt(r1451155);
        double r1451157 = r1451156 / r1451152;
        double r1451158 = r1451151 * r1451157;
        double r1451159 = /* ERROR: no complex support in C */;
        double r1451160 = 5.0;
        double r1451161 = 1.0;
        double r1451162 = r1451161 / r1451152;
        double r1451163 = r1451162 / r1451152;
        double r1451164 = r1451157 * r1451157;
        double r1451165 = r1451163 - r1451164;
        double r1451166 = r1451161 + r1451165;
        double r1451167 = r1451160 + r1451166;
        double r1451168 = r1451157 / r1451152;
        double r1451169 = r1451168 + r1451168;
        double r1451170 = -r1451169;
        double r1451171 = -r1451152;
        double r1451172 = r1451157 * r1451171;
        double r1451173 = r1451170 + r1451172;
        double r1451174 = /* ERROR: no complex support in C */;
        double r1451175 = /* ERROR: no complex support in C */;
        double r1451176 = r1451174 * r1451175;
        double r1451177 = r1451159 + r1451176;
        double r1451178 = /* ERROR: no complex support in C */;
        return r1451178;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019134 
(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))))