Average Error: 61.9 → 0
Time: 23.7s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]
↓
\[\Re(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\left(2 + \frac{1}{2}\right) \cdot \frac{1}{2} - \frac{\sqrt{3}}{2} \cdot \left(\frac{\sqrt{3}}{2} + 0.0\right)\right) + \left(-\left(\left(2 + \frac{1}{2}\right) \cdot \frac{\sqrt{3}}{2} + \frac{1}{2} \cdot \left(\frac{\sqrt{3}}{2} + 0.0\right)\right)\right) i\right)\right)\right) + \left(4 + 0.0 i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0.0 i\right)\right))\]
\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(2 + \frac{1}{2}\right) \cdot \frac{1}{2} - \frac{\sqrt{3}}{2} \cdot \left(\frac{\sqrt{3}}{2} + 0.0\right)\right) + \left(-\left(\left(2 + \frac{1}{2}\right) \cdot \frac{\sqrt{3}}{2} + \frac{1}{2} \cdot \left(\frac{\sqrt{3}}{2} + 0.0\right)\right)\right) i\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 r1998244 = 1.0;
        double r1998245 = -r1998244;
        double r1998246 = 2.0;
        double r1998247 = r1998245 / r1998246;
        double r1998248 = 3.0;
        double r1998249 = sqrt(r1998248);
        double r1998250 = r1998249 / r1998246;
        double r1998251 = /* ERROR: no complex support in C */;
        double r1998252 = r1998251 * r1998251;
        double r1998253 = r1998252 * r1998251;
        double r1998254 = r1998253 * r1998251;
        double r1998255 = -r1998246;
        double r1998256 = 0.0;
        double r1998257 = /* ERROR: no complex support in C */;
        double r1998258 = r1998257 * r1998251;
        double r1998259 = r1998258 * r1998251;
        double r1998260 = r1998259 * r1998251;
        double r1998261 = r1998254 + r1998260;
        double r1998262 = 5.0;
        double r1998263 = /* ERROR: no complex support in C */;
        double r1998264 = r1998263 * r1998251;
        double r1998265 = r1998264 * r1998251;
        double r1998266 = r1998261 + r1998265;
        double r1998267 = 4.0;
        double r1998268 = /* ERROR: no complex support in C */;
        double r1998269 = r1998268 * r1998251;
        double r1998270 = r1998266 + r1998269;
        double r1998271 = 7.0;
        double r1998272 = /* ERROR: no complex support in C */;
        double r1998273 = r1998270 + r1998272;
        double r1998274 = /* ERROR: no complex support in C */;
        return r1998274;
}
↓
double f() {
        double r1998275 = 1.0;
        double r1998276 = -r1998275;
        double r1998277 = 2.0;
        double r1998278 = r1998276 / r1998277;
        double r1998279 = 3.0;
        double r1998280 = sqrt(r1998279);
        double r1998281 = r1998280 / r1998277;
        double r1998282 = /* ERROR: no complex support in C */;
        double r1998283 = 5.0;
        double r1998284 = 0.0;
        double r1998285 = /* ERROR: no complex support in C */;
        double r1998286 = r1998275 / r1998277;
        double r1998287 = r1998277 + r1998286;
        double r1998288 = r1998287 * r1998286;
        double r1998289 = r1998281 + r1998284;
        double r1998290 = r1998281 * r1998289;
        double r1998291 = r1998288 - r1998290;
        double r1998292 = r1998287 * r1998281;
        double r1998293 = r1998286 * r1998289;
        double r1998294 = r1998292 + r1998293;
        double r1998295 = -r1998294;
        double r1998296 = /* ERROR: no complex support in C */;
        double r1998297 = r1998285 + r1998296;
        double r1998298 = r1998282 * r1998297;
        double r1998299 = 4.0;
        double r1998300 = /* ERROR: no complex support in C */;
        double r1998301 = r1998298 + r1998300;
        double r1998302 = r1998301 * r1998282;
        double r1998303 = 7.0;
        double r1998304 = /* ERROR: no complex support in C */;
        double r1998305 = r1998302 + r1998304;
        double r1998306 = /* ERROR: no complex support in C */;
        return r1998306;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019172 
(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))))