Average Error: 61.9 → 0
Time: 20.7s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(\frac{5}{2} + \left(\left(\frac{\sqrt{3}}{\frac{-4}{5}} + \sqrt{3} \cdot 2\right) + \frac{\sqrt{3}}{\frac{-4}{5}}\right) i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) + \left(-2 + \left(\frac{\sqrt{3}}{2} + \frac{-\sqrt{3}}{2}\right) i\right)\right)\right))\]
\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(\frac{5}{2} + \left(\left(\frac{\sqrt{3}}{\frac{-4}{5}} + \sqrt{3} \cdot 2\right) + \frac{\sqrt{3}}{\frac{-4}{5}}\right) i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) + \left(-2 + \left(\frac{\sqrt{3}}{2} + \frac{-\sqrt{3}}{2}\right) i\right)\right)\right))
double f() {
        double r824123 = 1.0;
        double r824124 = -r824123;
        double r824125 = 2.0;
        double r824126 = r824124 / r824125;
        double r824127 = 3.0;
        double r824128 = sqrt(r824127);
        double r824129 = r824128 / r824125;
        double r824130 = /* ERROR: no complex support in C */;
        double r824131 = r824130 * r824130;
        double r824132 = r824131 * r824130;
        double r824133 = r824132 * r824130;
        double r824134 = -r824125;
        double r824135 = 0.0;
        double r824136 = /* ERROR: no complex support in C */;
        double r824137 = r824136 * r824130;
        double r824138 = r824137 * r824130;
        double r824139 = r824138 * r824130;
        double r824140 = r824133 + r824139;
        double r824141 = 5.0;
        double r824142 = /* ERROR: no complex support in C */;
        double r824143 = r824142 * r824130;
        double r824144 = r824143 * r824130;
        double r824145 = r824140 + r824144;
        double r824146 = 4.0;
        double r824147 = /* ERROR: no complex support in C */;
        double r824148 = r824147 * r824130;
        double r824149 = r824145 + r824148;
        double r824150 = 7.0;
        double r824151 = /* ERROR: no complex support in C */;
        double r824152 = r824149 + r824151;
        double r824153 = /* ERROR: no complex support in C */;
        return r824153;
}
↓
double f() {
        double r824154 = 2.5;
        double r824155 = 3.0;
        double r824156 = sqrt(r824155);
        double r824157 = -0.8;
        double r824158 = r824156 / r824157;
        double r824159 = 2.0;
        double r824160 = r824156 * r824159;
        double r824161 = r824158 + r824160;
        double r824162 = r824161 + r824158;
        double r824163 = /* ERROR: no complex support in C */;
        double r824164 = -0.5;
        double r824165 = r824156 / r824159;
        double r824166 = /* ERROR: no complex support in C */;
        double r824167 = -2.0;
        double r824168 = -r824156;
        double r824169 = r824168 / r824159;
        double r824170 = r824165 + r824169;
        double r824171 = /* ERROR: no complex support in C */;
        double r824172 = r824166 + r824171;
        double r824173 = r824163 + r824172;
        double r824174 = /* ERROR: no complex support in C */;
        return r824174;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019137 
(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))))