Average Error: 61.9 → 0
Time: 24.6s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]
↓
\[\Re(\left(\left(7 + 0.0 i\right) + \left(\left(\left(4 + 0.0 i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\left(\frac{1}{2} \cdot \left(\frac{1}{2} + 2\right) - \frac{\sqrt{3}}{2} \cdot \left(\frac{\sqrt{3}}{2} + 0.0\right)\right) + \left(\left(\frac{\sqrt{3}}{2} + 0.0\right) \cdot \frac{-1}{2} + \frac{\sqrt{3}}{2} \cdot \left(-\left(\frac{1}{2} + 2\right)\right)\right) i\right) + \left(5 + 0.0 i\right)\right)\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right))\]
\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(4 + 0.0 i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\left(\frac{1}{2} \cdot \left(\frac{1}{2} + 2\right) - \frac{\sqrt{3}}{2} \cdot \left(\frac{\sqrt{3}}{2} + 0.0\right)\right) + \left(\left(\frac{\sqrt{3}}{2} + 0.0\right) \cdot \frac{-1}{2} + \frac{\sqrt{3}}{2} \cdot \left(-\left(\frac{1}{2} + 2\right)\right)\right) i\right) + \left(5 + 0.0 i\right)\right)\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right))
double f() {
        double r1284195 = 1.0;
        double r1284196 = -r1284195;
        double r1284197 = 2.0;
        double r1284198 = r1284196 / r1284197;
        double r1284199 = 3.0;
        double r1284200 = sqrt(r1284199);
        double r1284201 = r1284200 / r1284197;
        double r1284202 = /* ERROR: no complex support in C */;
        double r1284203 = r1284202 * r1284202;
        double r1284204 = r1284203 * r1284202;
        double r1284205 = r1284204 * r1284202;
        double r1284206 = -r1284197;
        double r1284207 = 0.0;
        double r1284208 = /* ERROR: no complex support in C */;
        double r1284209 = r1284208 * r1284202;
        double r1284210 = r1284209 * r1284202;
        double r1284211 = r1284210 * r1284202;
        double r1284212 = r1284205 + r1284211;
        double r1284213 = 5.0;
        double r1284214 = /* ERROR: no complex support in C */;
        double r1284215 = r1284214 * r1284202;
        double r1284216 = r1284215 * r1284202;
        double r1284217 = r1284212 + r1284216;
        double r1284218 = 4.0;
        double r1284219 = /* ERROR: no complex support in C */;
        double r1284220 = r1284219 * r1284202;
        double r1284221 = r1284217 + r1284220;
        double r1284222 = 7.0;
        double r1284223 = /* ERROR: no complex support in C */;
        double r1284224 = r1284221 + r1284223;
        double r1284225 = /* ERROR: no complex support in C */;
        return r1284225;
}
↓
double f() {
        double r1284226 = 7.0;
        double r1284227 = 0.0;
        double r1284228 = /* ERROR: no complex support in C */;
        double r1284229 = 4.0;
        double r1284230 = /* ERROR: no complex support in C */;
        double r1284231 = 1.0;
        double r1284232 = -r1284231;
        double r1284233 = 2.0;
        double r1284234 = r1284232 / r1284233;
        double r1284235 = 3.0;
        double r1284236 = sqrt(r1284235);
        double r1284237 = r1284236 / r1284233;
        double r1284238 = /* ERROR: no complex support in C */;
        double r1284239 = r1284231 / r1284233;
        double r1284240 = r1284239 + r1284233;
        double r1284241 = r1284239 * r1284240;
        double r1284242 = r1284237 + r1284227;
        double r1284243 = r1284237 * r1284242;
        double r1284244 = r1284241 - r1284243;
        double r1284245 = r1284242 * r1284234;
        double r1284246 = -r1284240;
        double r1284247 = r1284237 * r1284246;
        double r1284248 = r1284245 + r1284247;
        double r1284249 = /* ERROR: no complex support in C */;
        double r1284250 = 5.0;
        double r1284251 = /* ERROR: no complex support in C */;
        double r1284252 = r1284249 + r1284251;
        double r1284253 = r1284238 * r1284252;
        double r1284254 = r1284230 + r1284253;
        double r1284255 = r1284254 * r1284238;
        double r1284256 = r1284228 + r1284255;
        double r1284257 = /* ERROR: no complex support in C */;
        return r1284257;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019179 +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))))