3.9.2 real part (p56)

Average Error: 61.9 → 0

Time: 32.7s

Precision: 64

Math

\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]

↓

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

C

double f() {
        double r477355 = 1.0;
        double r477356 = -r477355;
        double r477357 = 2.0;
        double r477358 = r477356 / r477357;
        double r477359 = 3.0;
        double r477360 = sqrt(r477359);
        double r477361 = r477360 / r477357;
        double r477362 = /* ERROR: no complex support in C */;
        double r477363 = r477362 * r477362;
        double r477364 = r477363 * r477362;
        double r477365 = r477364 * r477362;
        double r477366 = -r477357;
        double r477367 = 0.0;
        double r477368 = /* ERROR: no complex support in C */;
        double r477369 = r477368 * r477362;
        double r477370 = r477369 * r477362;
        double r477371 = r477370 * r477362;
        double r477372 = r477365 + r477371;
        double r477373 = 5.0;
        double r477374 = /* ERROR: no complex support in C */;
        double r477375 = r477374 * r477362;
        double r477376 = r477375 * r477362;
        double r477377 = r477372 + r477376;
        double r477378 = 4.0;
        double r477379 = /* ERROR: no complex support in C */;
        double r477380 = r477379 * r477362;
        double r477381 = r477377 + r477380;
        double r477382 = 7.0;
        double r477383 = /* ERROR: no complex support in C */;
        double r477384 = r477381 + r477383;
        double r477385 = /* ERROR: no complex support in C */;
        return r477385;
}

↓

double f() {
        double r477386 = 5.0;
        double r477387 = 3.0;
        double r477388 = sqrt(r477387);
        double r477389 = 2.0;
        double r477390 = r477388 / r477389;
        double r477391 = 4.0;
        double r477392 = r477390 * r477391;
        double r477393 = /* ERROR: no complex support in C */;
        double r477394 = 0.25;
        double r477395 = r477390 * r477390;
        double r477396 = r477394 - r477395;
        double r477397 = -r477388;
        double r477398 = r477397 / r477389;
        double r477399 = /* ERROR: no complex support in C */;
        double r477400 = 6.0;
        double r477401 = -2.0;
        double r477402 = r477401 * r477388;
        double r477403 = r477402 / r477389;
        double r477404 = /* ERROR: no complex support in C */;
        double r477405 = r477404 + r477399;
        double r477406 = r477399 * r477405;
        double r477407 = r477393 + r477406;
        double r477408 = /* ERROR: no complex support in C */;
        return r477408;
}

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. Simplified 0

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019124 +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))))