Average Error: 61.9 → 0
Time: 20.4s
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 r2615360 = 1.0;
        double r2615361 = -r2615360;
        double r2615362 = 2.0;
        double r2615363 = r2615361 / r2615362;
        double r2615364 = 3.0;
        double r2615365 = sqrt(r2615364);
        double r2615366 = r2615365 / r2615362;
        double r2615367 = /* ERROR: no complex support in C */;
        double r2615368 = r2615367 * r2615367;
        double r2615369 = r2615368 * r2615367;
        double r2615370 = r2615369 * r2615367;
        double r2615371 = -r2615362;
        double r2615372 = 0.0;
        double r2615373 = /* ERROR: no complex support in C */;
        double r2615374 = r2615373 * r2615367;
        double r2615375 = r2615374 * r2615367;
        double r2615376 = r2615375 * r2615367;
        double r2615377 = r2615370 + r2615376;
        double r2615378 = 5.0;
        double r2615379 = /* ERROR: no complex support in C */;
        double r2615380 = r2615379 * r2615367;
        double r2615381 = r2615380 * r2615367;
        double r2615382 = r2615377 + r2615381;
        double r2615383 = 4.0;
        double r2615384 = /* ERROR: no complex support in C */;
        double r2615385 = r2615384 * r2615367;
        double r2615386 = r2615382 + r2615385;
        double r2615387 = 7.0;
        double r2615388 = /* ERROR: no complex support in C */;
        double r2615389 = r2615386 + r2615388;
        double r2615390 = /* ERROR: no complex support in C */;
        return r2615390;
}
↓
double f() {
        double r2615391 = 7.0;
        double r2615392 = 0.0;
        double r2615393 = /* ERROR: no complex support in C */;
        double r2615394 = 1.0;
        double r2615395 = -r2615394;
        double r2615396 = 2.0;
        double r2615397 = r2615395 / r2615396;
        double r2615398 = 3.0;
        double r2615399 = sqrt(r2615398);
        double r2615400 = r2615399 / r2615396;
        double r2615401 = /* ERROR: no complex support in C */;
        double r2615402 = 5.0;
        double r2615403 = /* ERROR: no complex support in C */;
        double r2615404 = r2615394 / r2615396;
        double r2615405 = r2615396 + r2615404;
        double r2615406 = -r2615405;
        double r2615407 = r2615400 + r2615392;
        double r2615408 = /* ERROR: no complex support in C */;
        double r2615409 = r2615401 * r2615408;
        double r2615410 = r2615403 + r2615409;
        double r2615411 = r2615401 * r2615410;
        double r2615412 = 4.0;
        double r2615413 = /* ERROR: no complex support in C */;
        double r2615414 = r2615411 + r2615413;
        double r2615415 = r2615414 * r2615401;
        double r2615416 = r2615393 + r2615415;
        double r2615417 = /* ERROR: no complex support in C */;
        return r2615417;
}

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))))