3.9.2 real part (p56)

Average Error: 61.9 → 0

Time: 19.8s

Precision: 64

Math

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

↓

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

C

double f() {
        double r683493 = 1.0;
        double r683494 = -r683493;
        double r683495 = 2.0;
        double r683496 = r683494 / r683495;
        double r683497 = 3.0;
        double r683498 = sqrt(r683497);
        double r683499 = r683498 / r683495;
        double r683500 = /* ERROR: no complex support in C */;
        double r683501 = r683500 * r683500;
        double r683502 = r683501 * r683500;
        double r683503 = r683502 * r683500;
        double r683504 = -r683495;
        double r683505 = 0.0;
        double r683506 = /* ERROR: no complex support in C */;
        double r683507 = r683506 * r683500;
        double r683508 = r683507 * r683500;
        double r683509 = r683508 * r683500;
        double r683510 = r683503 + r683509;
        double r683511 = 5.0;
        double r683512 = /* ERROR: no complex support in C */;
        double r683513 = r683512 * r683500;
        double r683514 = r683513 * r683500;
        double r683515 = r683510 + r683514;
        double r683516 = 4.0;
        double r683517 = /* ERROR: no complex support in C */;
        double r683518 = r683517 * r683500;
        double r683519 = r683515 + r683518;
        double r683520 = 7.0;
        double r683521 = /* ERROR: no complex support in C */;
        double r683522 = r683519 + r683521;
        double r683523 = /* ERROR: no complex support in C */;
        return r683523;
}

↓

double f() {
        double r683524 = 5.0;
        double r683525 = 3.0;
        double r683526 = sqrt(r683525);
        double r683527 = 2.0;
        double r683528 = r683526 / r683527;
        double r683529 = 4.0;
        double r683530 = r683528 * r683529;
        double r683531 = /* ERROR: no complex support in C */;
        double r683532 = r683528 * r683528;
        double r683533 = -r683532;
        double r683534 = 0.25;
        double r683535 = r683533 + r683534;
        double r683536 = -r683526;
        double r683537 = r683536 / r683527;
        double r683538 = /* ERROR: no complex support in C */;
        double r683539 = 6.0;
        double r683540 = -1.0;
        double r683541 = r683526 / r683540;
        double r683542 = /* ERROR: no complex support in C */;
        double r683543 = r683538 + r683542;
        double r683544 = r683543 * r683538;
        double r683545 = r683531 + r683544;
        double r683546 = /* ERROR: no complex support in C */;
        return r683546;
}

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

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019153 
(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))))