Average Error: 61.9 → 0
Time: 17.3s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(5 + \frac{\sqrt{3} \cdot 4}{2} i\right) + \left(\left(\frac{\sqrt{3} \cdot \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right)}{2} + \frac{1}{4}\right) + \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) i\right) \cdot \left(\left(6 + -2 \cdot \frac{\sqrt{3}}{2} i\right) + \left(\left(\frac{\sqrt{3} \cdot \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right)}{2} + \frac{1}{4}\right) + \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) i\right)\right)\right))\]
\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(5 + \frac{\sqrt{3} \cdot 4}{2} i\right) + \left(\left(\frac{\sqrt{3} \cdot \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right)}{2} + \frac{1}{4}\right) + \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) i\right) \cdot \left(\left(6 + -2 \cdot \frac{\sqrt{3}}{2} i\right) + \left(\left(\frac{\sqrt{3} \cdot \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right)}{2} + \frac{1}{4}\right) + \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) i\right)\right)\right))
double f() {
        double r648416 = 1.0;
        double r648417 = -r648416;
        double r648418 = 2.0;
        double r648419 = r648417 / r648418;
        double r648420 = 3.0;
        double r648421 = sqrt(r648420);
        double r648422 = r648421 / r648418;
        double r648423 = /* ERROR: no complex support in C */;
        double r648424 = r648423 * r648423;
        double r648425 = r648424 * r648423;
        double r648426 = r648425 * r648423;
        double r648427 = -r648418;
        double r648428 = 0.0;
        double r648429 = /* ERROR: no complex support in C */;
        double r648430 = r648429 * r648423;
        double r648431 = r648430 * r648423;
        double r648432 = r648431 * r648423;
        double r648433 = r648426 + r648432;
        double r648434 = 5.0;
        double r648435 = /* ERROR: no complex support in C */;
        double r648436 = r648435 * r648423;
        double r648437 = r648436 * r648423;
        double r648438 = r648433 + r648437;
        double r648439 = 4.0;
        double r648440 = /* ERROR: no complex support in C */;
        double r648441 = r648440 * r648423;
        double r648442 = r648438 + r648441;
        double r648443 = 7.0;
        double r648444 = /* ERROR: no complex support in C */;
        double r648445 = r648442 + r648444;
        double r648446 = /* ERROR: no complex support in C */;
        return r648446;
}
↓
double f() {
        double r648447 = 5.0;
        double r648448 = 3.0;
        double r648449 = sqrt(r648448);
        double r648450 = 4.0;
        double r648451 = r648449 * r648450;
        double r648452 = 2.0;
        double r648453 = r648451 / r648452;
        double r648454 = /* ERROR: no complex support in C */;
        double r648455 = -4.0;
        double r648456 = r648449 / r648455;
        double r648457 = r648456 + r648456;
        double r648458 = r648449 * r648457;
        double r648459 = r648458 / r648452;
        double r648460 = 0.25;
        double r648461 = r648459 + r648460;
        double r648462 = /* ERROR: no complex support in C */;
        double r648463 = 6.0;
        double r648464 = -2.0;
        double r648465 = r648449 / r648452;
        double r648466 = r648464 * r648465;
        double r648467 = /* ERROR: no complex support in C */;
        double r648468 = r648467 + r648462;
        double r648469 = r648462 * r648468;
        double r648470 = r648454 + r648469;
        double r648471 = /* ERROR: no complex support in C */;
        return r648471;
}

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

    \[\leadsto \color{blue}{\Re(\left(\left(5 + \frac{4 \cdot \sqrt{3}}{2} i\right) + \left(\left(\left(\frac{1}{4} + \frac{\sqrt{3} \cdot \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right)}{2}\right) + \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) i\right) \cdot \left(\left(\left(\frac{1}{4} + \frac{\sqrt{3} \cdot \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right)}{2}\right) + \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) i\right) + \left(6 + \frac{\sqrt{3}}{2} \cdot -2 i\right)\right)\right)\right))}\]

  3. Final simplification0

    \[\leadsto \Re(\left(\left(5 + \frac{\sqrt{3} \cdot 4}{2} i\right) + \left(\left(\frac{\sqrt{3} \cdot \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right)}{2} + \frac{1}{4}\right) + \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) i\right) \cdot \left(\left(6 + -2 \cdot \frac{\sqrt{3}}{2} i\right) + \left(\left(\frac{\sqrt{3} \cdot \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right)}{2} + \frac{1}{4}\right) + \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) i\right)\right)\right))\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(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))))