Average Error: 61.9 → 0
Time: 5.5s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]
↓
\[\Re(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\left(\frac{-1}{2} - 2\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right)\right) + \left(4 + 0.0 i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0.0 i\right)\right))\]
\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) + 0.0 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 + 0.0 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 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))
↓
\Re(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\left(\frac{-1}{2} - 2\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right)\right) + \left(4 + 0.0 i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0.0 i\right)\right))
double f() {
        double r27148 = 1.0;
        double r27149 = -r27148;
        double r27150 = 2.0;
        double r27151 = r27149 / r27150;
        double r27152 = 3.0;
        double r27153 = sqrt(r27152);
        double r27154 = r27153 / r27150;
        double r27155 = /* ERROR: no complex support in C */;
        double r27156 = r27155 * r27155;
        double r27157 = r27156 * r27155;
        double r27158 = r27157 * r27155;
        double r27159 = -r27150;
        double r27160 = 0.0;
        double r27161 = /* ERROR: no complex support in C */;
        double r27162 = r27161 * r27155;
        double r27163 = r27162 * r27155;
        double r27164 = r27163 * r27155;
        double r27165 = r27158 + r27164;
        double r27166 = 5.0;
        double r27167 = /* ERROR: no complex support in C */;
        double r27168 = r27167 * r27155;
        double r27169 = r27168 * r27155;
        double r27170 = r27165 + r27169;
        double r27171 = 4.0;
        double r27172 = /* ERROR: no complex support in C */;
        double r27173 = r27172 * r27155;
        double r27174 = r27170 + r27173;
        double r27175 = 7.0;
        double r27176 = /* ERROR: no complex support in C */;
        double r27177 = r27174 + r27176;
        double r27178 = /* ERROR: no complex support in C */;
        return r27178;
}
↓
double f() {
        double r27179 = 1.0;
        double r27180 = -r27179;
        double r27181 = 2.0;
        double r27182 = r27180 / r27181;
        double r27183 = 3.0;
        double r27184 = sqrt(r27183);
        double r27185 = r27184 / r27181;
        double r27186 = /* ERROR: no complex support in C */;
        double r27187 = 5.0;
        double r27188 = 0.0;
        double r27189 = /* ERROR: no complex support in C */;
        double r27190 = r27182 - r27181;
        double r27191 = r27185 + r27188;
        double r27192 = /* ERROR: no complex support in C */;
        double r27193 = r27192 * r27186;
        double r27194 = r27189 + r27193;
        double r27195 = r27186 * r27194;
        double r27196 = 4.0;
        double r27197 = /* ERROR: no complex support in C */;
        double r27198 = r27195 + r27197;
        double r27199 = r27198 * r27186;
        double r27200 = 7.0;
        double r27201 = /* ERROR: no complex support in C */;
        double r27202 = r27199 + r27201;
        double r27203 = /* ERROR: no complex support in C */;
        return r27203;
}

Error

Derivation

  1. Initial program 61.9

    \[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]

  2. Simplified0

    \[\leadsto \color{blue}{\Re(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\left(\frac{-1}{2} - 2\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right)\right) + \left(4 + 0.0 i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0.0 i\right)\right))}\]

  3. Final simplification0

    \[\leadsto \Re(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\left(\frac{-1}{2} - 2\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right)\right) + \left(4 + 0.0 i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0.0 i\right)\right))\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore ()
  :name "3.9.2 real part (p56)"
  :precision binary64
  (re (+ (+ (+ (+ (* (* (* (complex (/ (- 1) 2) (/ (sqrt 3) 2)) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (* (* (* (complex (- 2) 0.0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (* (* (complex 5 0.0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (* (complex 4 0.0) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (complex 7 0.0))))