Average Error: 61.9 → 0
Time: 5.4s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]
↓
\[\Re(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\left(\frac{-1}{2} - 2\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right)\right) + \left(4 + 0.0 i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]
\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(\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(\left(\frac{-1}{2} - 2\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right)\right) + \left(4 + 0.0 i\right)\right)\right) + \left(7 + 0.0 i\right)\right))
double f() {
        double r32436 = 1.0;
        double r32437 = -r32436;
        double r32438 = 2.0;
        double r32439 = r32437 / r32438;
        double r32440 = 3.0;
        double r32441 = sqrt(r32440);
        double r32442 = r32441 / r32438;
        double r32443 = /* ERROR: no complex support in C */;
        double r32444 = r32443 * r32443;
        double r32445 = r32444 * r32443;
        double r32446 = r32445 * r32443;
        double r32447 = -r32438;
        double r32448 = 0.0;
        double r32449 = /* ERROR: no complex support in C */;
        double r32450 = r32449 * r32443;
        double r32451 = r32450 * r32443;
        double r32452 = r32451 * r32443;
        double r32453 = r32446 + r32452;
        double r32454 = 5.0;
        double r32455 = /* ERROR: no complex support in C */;
        double r32456 = r32455 * r32443;
        double r32457 = r32456 * r32443;
        double r32458 = r32453 + r32457;
        double r32459 = 4.0;
        double r32460 = /* ERROR: no complex support in C */;
        double r32461 = r32460 * r32443;
        double r32462 = r32458 + r32461;
        double r32463 = 7.0;
        double r32464 = /* ERROR: no complex support in C */;
        double r32465 = r32462 + r32464;
        double r32466 = /* ERROR: no complex support in C */;
        return r32466;
}
↓
double f() {
        double r32467 = 1.0;
        double r32468 = -r32467;
        double r32469 = 2.0;
        double r32470 = r32468 / r32469;
        double r32471 = 3.0;
        double r32472 = sqrt(r32471);
        double r32473 = r32472 / r32469;
        double r32474 = /* ERROR: no complex support in C */;
        double r32475 = 5.0;
        double r32476 = 0.0;
        double r32477 = /* ERROR: no complex support in C */;
        double r32478 = r32470 - r32469;
        double r32479 = r32473 + r32476;
        double r32480 = /* ERROR: no complex support in C */;
        double r32481 = r32480 * r32474;
        double r32482 = r32477 + r32481;
        double r32483 = r32474 * r32482;
        double r32484 = 4.0;
        double r32485 = /* ERROR: no complex support in C */;
        double r32486 = r32483 + r32485;
        double r32487 = r32474 * r32486;
        double r32488 = 7.0;
        double r32489 = /* ERROR: no complex support in C */;
        double r32490 = r32487 + r32489;
        double r32491 = /* ERROR: no complex support in C */;
        return r32491;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2020045 
(FPCore ()
  :name "3.9.2 real part (p56)"
  :precision binary64
  (re (+ (+ (+ (+ (* (* (* (complex (/ (- 1) 2) (/ (sqrt 3) 2)) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (* (* (* (complex (- 2) 0.0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (* (* (complex 5 0.0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (* (complex 4 0.0) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (complex 7 0.0))))