Average Error: 61.9 → 0
Time: 20.7s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]
↓
\[\Re(\left(\left(7 + 0.0 i\right) + \left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(-\left(2 + \frac{1}{2}\right)\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right)\right)\right)\right) + \left(4 + 0.0 i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right))\]
\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) + 0.0 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(7 + 0.0 i\right) + \left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(-\left(2 + \frac{1}{2}\right)\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right)\right)\right)\right) + \left(4 + 0.0 i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right))
double f() {
        double r1298216 = 1.0;
        double r1298217 = -r1298216;
        double r1298218 = 2.0;
        double r1298219 = r1298217 / r1298218;
        double r1298220 = 3.0;
        double r1298221 = sqrt(r1298220);
        double r1298222 = r1298221 / r1298218;
        double r1298223 = /* ERROR: no complex support in C */;
        double r1298224 = r1298223 * r1298223;
        double r1298225 = r1298224 * r1298223;
        double r1298226 = r1298225 * r1298223;
        double r1298227 = -r1298218;
        double r1298228 = 0.0;
        double r1298229 = /* ERROR: no complex support in C */;
        double r1298230 = r1298229 * r1298223;
        double r1298231 = r1298230 * r1298223;
        double r1298232 = r1298231 * r1298223;
        double r1298233 = r1298226 + r1298232;
        double r1298234 = 5.0;
        double r1298235 = /* ERROR: no complex support in C */;
        double r1298236 = r1298235 * r1298223;
        double r1298237 = r1298236 * r1298223;
        double r1298238 = r1298233 + r1298237;
        double r1298239 = 4.0;
        double r1298240 = /* ERROR: no complex support in C */;
        double r1298241 = r1298240 * r1298223;
        double r1298242 = r1298238 + r1298241;
        double r1298243 = 7.0;
        double r1298244 = /* ERROR: no complex support in C */;
        double r1298245 = r1298242 + r1298244;
        double r1298246 = /* ERROR: no complex support in C */;
        return r1298246;
}
↓
double f() {
        double r1298247 = 7.0;
        double r1298248 = 0.0;
        double r1298249 = /* ERROR: no complex support in C */;
        double r1298250 = 1.0;
        double r1298251 = -r1298250;
        double r1298252 = 2.0;
        double r1298253 = r1298251 / r1298252;
        double r1298254 = 3.0;
        double r1298255 = sqrt(r1298254);
        double r1298256 = r1298255 / r1298252;
        double r1298257 = /* ERROR: no complex support in C */;
        double r1298258 = 5.0;
        double r1298259 = /* ERROR: no complex support in C */;
        double r1298260 = r1298250 / r1298252;
        double r1298261 = r1298252 + r1298260;
        double r1298262 = -r1298261;
        double r1298263 = r1298256 + r1298248;
        double r1298264 = /* ERROR: no complex support in C */;
        double r1298265 = r1298257 * r1298264;
        double r1298266 = r1298259 + r1298265;
        double r1298267 = r1298257 * r1298266;
        double r1298268 = 4.0;
        double r1298269 = /* ERROR: no complex support in C */;
        double r1298270 = r1298267 + r1298269;
        double r1298271 = r1298270 * r1298257;
        double r1298272 = r1298249 + r1298271;
        double r1298273 = /* ERROR: no complex support in C */;
        return r1298273;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore ()
  :name "3.9.2 real part (p56)"
  (re (+ (+ (+ (+ (* (* (* (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (* (* (* (complex (- 2.0) 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (* (* (complex 5.0 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (* (complex 4.0 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (complex 7.0 0.0))))