Average Error: 61.9 → 0
Time: 42.0s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(5 + \frac{\sqrt{3}}{2} \cdot 4 i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) i\right) \cdot \left(\left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) i\right) + \left(6 + -2 \cdot \frac{\sqrt{3}}{2} i\right)\right)\right))\]
\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 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}}{2} \cdot 4 i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) i\right) \cdot \left(\left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) i\right) + \left(6 + -2 \cdot \frac{\sqrt{3}}{2} i\right)\right)\right))
double f() {
        double r2413473 = 1.0;
        double r2413474 = -r2413473;
        double r2413475 = 2.0;
        double r2413476 = r2413474 / r2413475;
        double r2413477 = 3.0;
        double r2413478 = sqrt(r2413477);
        double r2413479 = r2413478 / r2413475;
        double r2413480 = /* ERROR: no complex support in C */;
        double r2413481 = r2413480 * r2413480;
        double r2413482 = r2413481 * r2413480;
        double r2413483 = r2413482 * r2413480;
        double r2413484 = -r2413475;
        double r2413485 = 0.0;
        double r2413486 = /* ERROR: no complex support in C */;
        double r2413487 = r2413486 * r2413480;
        double r2413488 = r2413487 * r2413480;
        double r2413489 = r2413488 * r2413480;
        double r2413490 = r2413483 + r2413489;
        double r2413491 = 5.0;
        double r2413492 = /* ERROR: no complex support in C */;
        double r2413493 = r2413492 * r2413480;
        double r2413494 = r2413493 * r2413480;
        double r2413495 = r2413490 + r2413494;
        double r2413496 = 4.0;
        double r2413497 = /* ERROR: no complex support in C */;
        double r2413498 = r2413497 * r2413480;
        double r2413499 = r2413495 + r2413498;
        double r2413500 = 7.0;
        double r2413501 = /* ERROR: no complex support in C */;
        double r2413502 = r2413499 + r2413501;
        double r2413503 = /* ERROR: no complex support in C */;
        return r2413503;
}
↓
double f() {
        double r2413504 = 5.0;
        double r2413505 = 3.0;
        double r2413506 = sqrt(r2413505);
        double r2413507 = 2.0;
        double r2413508 = r2413506 / r2413507;
        double r2413509 = 4.0;
        double r2413510 = r2413508 * r2413509;
        double r2413511 = /* ERROR: no complex support in C */;
        double r2413512 = 0.25;
        double r2413513 = r2413508 * r2413508;
        double r2413514 = r2413512 - r2413513;
        double r2413515 = -4.0;
        double r2413516 = r2413506 / r2413515;
        double r2413517 = r2413516 + r2413516;
        double r2413518 = /* ERROR: no complex support in C */;
        double r2413519 = 6.0;
        double r2413520 = -2.0;
        double r2413521 = r2413520 * r2413508;
        double r2413522 = /* ERROR: no complex support in C */;
        double r2413523 = r2413518 + r2413522;
        double r2413524 = r2413518 * r2413523;
        double r2413525 = r2413511 + r2413524;
        double r2413526 = /* ERROR: no complex support in C */;
        return r2413526;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019128 +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))))