Average Error: 61.9 → 0
Time: 20.3s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]
↓
\[\Re(\left(\left(7 + 0.0 i\right) + \left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(-\left(2 + \frac{1}{2}\right)\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right)\right)\right)\right) + \left(4 + 0.0 i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right))\]
\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 r2533487 = 1.0;
        double r2533488 = -r2533487;
        double r2533489 = 2.0;
        double r2533490 = r2533488 / r2533489;
        double r2533491 = 3.0;
        double r2533492 = sqrt(r2533491);
        double r2533493 = r2533492 / r2533489;
        double r2533494 = /* ERROR: no complex support in C */;
        double r2533495 = r2533494 * r2533494;
        double r2533496 = r2533495 * r2533494;
        double r2533497 = r2533496 * r2533494;
        double r2533498 = -r2533489;
        double r2533499 = 0.0;
        double r2533500 = /* ERROR: no complex support in C */;
        double r2533501 = r2533500 * r2533494;
        double r2533502 = r2533501 * r2533494;
        double r2533503 = r2533502 * r2533494;
        double r2533504 = r2533497 + r2533503;
        double r2533505 = 5.0;
        double r2533506 = /* ERROR: no complex support in C */;
        double r2533507 = r2533506 * r2533494;
        double r2533508 = r2533507 * r2533494;
        double r2533509 = r2533504 + r2533508;
        double r2533510 = 4.0;
        double r2533511 = /* ERROR: no complex support in C */;
        double r2533512 = r2533511 * r2533494;
        double r2533513 = r2533509 + r2533512;
        double r2533514 = 7.0;
        double r2533515 = /* ERROR: no complex support in C */;
        double r2533516 = r2533513 + r2533515;
        double r2533517 = /* ERROR: no complex support in C */;
        return r2533517;
}
↓
double f() {
        double r2533518 = 7.0;
        double r2533519 = 0.0;
        double r2533520 = /* ERROR: no complex support in C */;
        double r2533521 = 1.0;
        double r2533522 = -r2533521;
        double r2533523 = 2.0;
        double r2533524 = r2533522 / r2533523;
        double r2533525 = 3.0;
        double r2533526 = sqrt(r2533525);
        double r2533527 = r2533526 / r2533523;
        double r2533528 = /* ERROR: no complex support in C */;
        double r2533529 = 5.0;
        double r2533530 = /* ERROR: no complex support in C */;
        double r2533531 = r2533521 / r2533523;
        double r2533532 = r2533523 + r2533531;
        double r2533533 = -r2533532;
        double r2533534 = r2533527 + r2533519;
        double r2533535 = /* ERROR: no complex support in C */;
        double r2533536 = r2533528 * r2533535;
        double r2533537 = r2533530 + r2533536;
        double r2533538 = r2533528 * r2533537;
        double r2533539 = 4.0;
        double r2533540 = /* ERROR: no complex support in C */;
        double r2533541 = r2533538 + r2533540;
        double r2533542 = r2533541 * r2533528;
        double r2533543 = r2533520 + r2533542;
        double r2533544 = /* ERROR: no complex support in C */;
        return r2533544;
}

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 2019172 +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))))