Average Error: 61.9 → 0
Time: 26.8s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]
↓
\[\Re(\left(\left(7 + 0.0 i\right) + \left(\left(\left(4 + 0.0 i\right) + \left(\left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\left(\frac{1}{2} + 2\right) \cdot \frac{1}{2} - \frac{\sqrt{3}}{2} \cdot \left(0.0 + \frac{\sqrt{3}}{2}\right)\right) + \left(\left(-\frac{\sqrt{3}}{2}\right) \cdot \left(\frac{1}{2} + 2\right) + \left(0.0 + \frac{\sqrt{3}}{2}\right) \cdot \left(-\frac{1}{2}\right)\right) i\right)\right)\right)\right) \cdot \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right)\right)\right))\]
\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(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\left(\frac{1}{2} + 2\right) \cdot \frac{1}{2} - \frac{\sqrt{3}}{2} \cdot \left(0.0 + \frac{\sqrt{3}}{2}\right)\right) + \left(\left(-\frac{\sqrt{3}}{2}\right) \cdot \left(\frac{1}{2} + 2\right) + \left(0.0 + \frac{\sqrt{3}}{2}\right) \cdot \left(-\frac{1}{2}\right)\right) i\right)\right)\right)\right) \cdot \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right)\right)\right))
double f() {
        double r2402539 = 1.0;
        double r2402540 = -r2402539;
        double r2402541 = 2.0;
        double r2402542 = r2402540 / r2402541;
        double r2402543 = 3.0;
        double r2402544 = sqrt(r2402543);
        double r2402545 = r2402544 / r2402541;
        double r2402546 = /* ERROR: no complex support in C */;
        double r2402547 = r2402546 * r2402546;
        double r2402548 = r2402547 * r2402546;
        double r2402549 = r2402548 * r2402546;
        double r2402550 = -r2402541;
        double r2402551 = 0.0;
        double r2402552 = /* ERROR: no complex support in C */;
        double r2402553 = r2402552 * r2402546;
        double r2402554 = r2402553 * r2402546;
        double r2402555 = r2402554 * r2402546;
        double r2402556 = r2402549 + r2402555;
        double r2402557 = 5.0;
        double r2402558 = /* ERROR: no complex support in C */;
        double r2402559 = r2402558 * r2402546;
        double r2402560 = r2402559 * r2402546;
        double r2402561 = r2402556 + r2402560;
        double r2402562 = 4.0;
        double r2402563 = /* ERROR: no complex support in C */;
        double r2402564 = r2402563 * r2402546;
        double r2402565 = r2402561 + r2402564;
        double r2402566 = 7.0;
        double r2402567 = /* ERROR: no complex support in C */;
        double r2402568 = r2402565 + r2402567;
        double r2402569 = /* ERROR: no complex support in C */;
        return r2402569;
}
↓
double f() {
        double r2402570 = 7.0;
        double r2402571 = 0.0;
        double r2402572 = /* ERROR: no complex support in C */;
        double r2402573 = 4.0;
        double r2402574 = /* ERROR: no complex support in C */;
        double r2402575 = 1.0;
        double r2402576 = 2.0;
        double r2402577 = r2402575 / r2402576;
        double r2402578 = -r2402577;
        double r2402579 = 3.0;
        double r2402580 = sqrt(r2402579);
        double r2402581 = r2402580 / r2402576;
        double r2402582 = /* ERROR: no complex support in C */;
        double r2402583 = 5.0;
        double r2402584 = /* ERROR: no complex support in C */;
        double r2402585 = r2402577 + r2402576;
        double r2402586 = r2402585 * r2402577;
        double r2402587 = r2402571 + r2402581;
        double r2402588 = r2402581 * r2402587;
        double r2402589 = r2402586 - r2402588;
        double r2402590 = -r2402581;
        double r2402591 = r2402590 * r2402585;
        double r2402592 = r2402587 * r2402578;
        double r2402593 = r2402591 + r2402592;
        double r2402594 = /* ERROR: no complex support in C */;
        double r2402595 = r2402584 + r2402594;
        double r2402596 = r2402582 * r2402595;
        double r2402597 = r2402574 + r2402596;
        double r2402598 = r2402597 * r2402582;
        double r2402599 = r2402572 + r2402598;
        double r2402600 = /* ERROR: no complex support in C */;
        return r2402600;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019168 
(FPCore ()
  :name "3.9.2 real part (p56)"
  (re (+.c (+.c (+.c (+.c (*.c (*.c (*.c (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))) (*.c (*.c (*.c (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)))) (*.c (*.c (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)))) (*.c (complex 4.0 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (complex 7.0 0.0))))