3.9.2 real part (p56)

Average Error: 61.9 → 0

Time: 19.4s

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 r866412 = 1.0;
        double r866413 = -r866412;
        double r866414 = 2.0;
        double r866415 = r866413 / r866414;
        double r866416 = 3.0;
        double r866417 = sqrt(r866416);
        double r866418 = r866417 / r866414;
        double r866419 = /* ERROR: no complex support in C */;
        double r866420 = r866419 * r866419;
        double r866421 = r866420 * r866419;
        double r866422 = r866421 * r866419;
        double r866423 = -r866414;
        double r866424 = 0.0;
        double r866425 = /* ERROR: no complex support in C */;
        double r866426 = r866425 * r866419;
        double r866427 = r866426 * r866419;
        double r866428 = r866427 * r866419;
        double r866429 = r866422 + r866428;
        double r866430 = 5.0;
        double r866431 = /* ERROR: no complex support in C */;
        double r866432 = r866431 * r866419;
        double r866433 = r866432 * r866419;
        double r866434 = r866429 + r866433;
        double r866435 = 4.0;
        double r866436 = /* ERROR: no complex support in C */;
        double r866437 = r866436 * r866419;
        double r866438 = r866434 + r866437;
        double r866439 = 7.0;
        double r866440 = /* ERROR: no complex support in C */;
        double r866441 = r866438 + r866440;
        double r866442 = /* ERROR: no complex support in C */;
        return r866442;
}

↓

double f() {
        double r866443 = 5.0;
        double r866444 = 3.0;
        double r866445 = sqrt(r866444);
        double r866446 = 2.0;
        double r866447 = r866445 / r866446;
        double r866448 = 4.0;
        double r866449 = r866447 * r866448;
        double r866450 = /* ERROR: no complex support in C */;
        double r866451 = r866447 * r866447;
        double r866452 = -r866451;
        double r866453 = 0.25;
        double r866454 = r866452 + r866453;
        double r866455 = -r866445;
        double r866456 = r866455 / r866446;
        double r866457 = /* ERROR: no complex support in C */;
        double r866458 = 6.0;
        double r866459 = -1.0;
        double r866460 = r866445 / r866459;
        double r866461 = /* ERROR: no complex support in C */;
        double r866462 = r866457 + r866461;
        double r866463 = r866462 * r866457;
        double r866464 = r866450 + r866463;
        double r866465 = /* ERROR: no complex support in C */;
        return r866465;
}

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))))