Average Error: 0 → 0
Time: 21.0s
Precision: 64
\[\Im(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Im(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(-2 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right)\right) + \left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(4 + 0 i\right)\right) + \left(7 + 0 i\right)\right))\]
\Im(\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))
↓
\Im(\left(\left(\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(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(-2 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right)\right) + \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) + \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(4 + 0 i\right)\right) + \left(7 + 0 i\right)\right))
double f() {
        double r1347412 = 1.0;
        double r1347413 = -r1347412;
        double r1347414 = 2.0;
        double r1347415 = r1347413 / r1347414;
        double r1347416 = 3.0;
        double r1347417 = sqrt(r1347416);
        double r1347418 = r1347417 / r1347414;
        double r1347419 = /* ERROR: no complex support in C */;
        double r1347420 = r1347419 * r1347419;
        double r1347421 = r1347420 * r1347419;
        double r1347422 = r1347421 * r1347419;
        double r1347423 = -r1347414;
        double r1347424 = 0.0;
        double r1347425 = /* ERROR: no complex support in C */;
        double r1347426 = r1347425 * r1347419;
        double r1347427 = r1347426 * r1347419;
        double r1347428 = r1347427 * r1347419;
        double r1347429 = r1347422 + r1347428;
        double r1347430 = 5.0;
        double r1347431 = /* ERROR: no complex support in C */;
        double r1347432 = r1347431 * r1347419;
        double r1347433 = r1347432 * r1347419;
        double r1347434 = r1347429 + r1347433;
        double r1347435 = 4.0;
        double r1347436 = /* ERROR: no complex support in C */;
        double r1347437 = r1347436 * r1347419;
        double r1347438 = r1347434 + r1347437;
        double r1347439 = 7.0;
        double r1347440 = /* ERROR: no complex support in C */;
        double r1347441 = r1347438 + r1347440;
        double r1347442 = /* ERROR: no complex support in C */;
        return r1347442;
}
↓
double f() {
        double r1347443 = -0.5;
        double r1347444 = 3.0;
        double r1347445 = sqrt(r1347444);
        double r1347446 = 2.0;
        double r1347447 = r1347445 / r1347446;
        double r1347448 = /* ERROR: no complex support in C */;
        double r1347449 = r1347448 * r1347448;
        double r1347450 = r1347449 * r1347448;
        double r1347451 = r1347448 * r1347450;
        double r1347452 = -2.0;
        double r1347453 = 0.0;
        double r1347454 = /* ERROR: no complex support in C */;
        double r1347455 = r1347454 * r1347448;
        double r1347456 = r1347448 * r1347455;
        double r1347457 = r1347448 * r1347456;
        double r1347458 = r1347451 + r1347457;
        double r1347459 = 5.0;
        double r1347460 = /* ERROR: no complex support in C */;
        double r1347461 = r1347460 * r1347448;
        double r1347462 = r1347461 * r1347448;
        double r1347463 = r1347458 + r1347462;
        double r1347464 = 4.0;
        double r1347465 = /* ERROR: no complex support in C */;
        double r1347466 = r1347448 * r1347465;
        double r1347467 = r1347463 + r1347466;
        double r1347468 = 7.0;
        double r1347469 = /* ERROR: no complex support in C */;
        double r1347470 = r1347467 + r1347469;
        double r1347471 = /* ERROR: no complex support in C */;
        return r1347471;
}

Error

Derivation

  1. Initial program 0

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

  2. Final simplification0

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

Reproduce

herbie shell --seed 2019107 
(FPCore ()
  :name "3.9.2 imaginary part (p56)"
  (im (+.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))))